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particle

particle Sentence Examples

  • Let x, y, z be the co-ordinates of any particle of the medium in its natural state, and, 7 7, the displacements of the same particle at the end of time t, measured in the directions of the three axes respectively.

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  • It remained a desideratum to express by equations the motion of a particle of the fluid in any assigned direction.

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  • A particle of this mass is easily visible microscopically, and a velocity of 2 mm.

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  • In starting the furnace, the bottom is prepared by ramming it with charcoal-powder that has been soaked in milk of lime and dried, so that each particle is coated with a film of lime, which serves to reduce the loss of current by conduction through the lining when the furnace becomes hot.

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  • An intelligent creature, or "demon," possessed of unlimited powers of vision, is placed in charge of each door, with instructions to open the door whenever a particle in A comes towards it with more than a certain velocity V, and to keep it closed against all particles in A moving with less than this velocity, but, on the other hand, to open the door whenever a particle in B approaches it with less than a certain velocity v, which is not greater than V, and to keep it closed against all particles in B moving with a greater velocity than this.

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  • The word "alcohol" is of Arabic origin, being derived from the particle al and the word kohl, an impalpable powder used in the East for painting the eyebrows.

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  • molecula, the diminutive of moles, a mass), in chemistry and physics, the minutest particle of matter capable of separate existence.

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  • When the fluids inside a particle were mixed together, the particle was neutral; when they were more or less completely separated, the particle became magnetized to an intensity depending upon the magnetic force applied; the whole body therefore consisted of a number of little spheres having north and south poles, each of which exerted an elementary action at a distance.

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  • On account of the smallness of the particles, the forces acting throughout the volume of any individual particle are all of the same intensity and direction, and may be considered as a whole.

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  • We may now investigate the mathematical expression for the disturbance propagated in any direction from a small particle upon which a beam of light strikes.

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  • Each bombardment will, however, change the motion of the particle, so that changes are too frequent for the separate motions to be individually visible.

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  • Two typical forms are in use; in one a liquid is prepared in which the crystal freely swims, the density of the liquid being ascertained by the pycnometer or other methods; in the other a liquid of variable density, the so-called "diffusion column," is prepared, and observation is made of the level at which the particle comes to rest.

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  • By his discovery that the attracting force in any direction of a mass upon a particle could be obtained by the direct process of differentiating a single function, Laplace laid the foundations of the mathematical sciences of heat, electricity and magnetism.

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  • Thrombosis is an accident of not dissimilar character, whereby a vessel is blocked not by a travelling particle, but by a clotting of the blood in situ, probably on the occasion of some harm to the epithelial lining of the vessel.

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  • The only circumstance which physics has to consider is the transference of movement from one particle to another, and the change of its direction.

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  • The growth of an organic being is simply a process of enlargement, as a particle of dry gelatine may be swelled up by the intussusception of water; its death is a shrinkage, such as the swelled jelly might undergo on desiccation.

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  • Within a quarter of an hour after a quantity of cinnabar has been injected into the blood of the frog nearly every particle will be found engulfed by the protoplasm of the leucocytes of the circulating blood.

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  • This, however, is not exactly accurate, if it be thereby implied that all living things have a visible organization, as there are numerous forms of living matter of which it cannot properly be said that they possess either a definite structure or permanently specialized organs: though, doubtless, the simplest particle of living matter must possess a highly complex molecular structure, which is far beyond the reach of vision.

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  • The strongest direct evidence seems to be that the nuclear substances are the only parts of the cells which are always equivalent in quantity, and that in the higher plants and animals the male organ or spermatozoid is composed almost entirely of the nucleus, and that the male nucleus is carried into the female cell without a particle of cytoplasm.i Since, however, the nucleus of the female cell is always accompanied by a larger or smaller quantity of cytoplasm, and that in a large majority of the power plants and animals the male cell also contains cytoplasm, it cannot yet be definitely stated that the cytoplasm does not play some part in the process.

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  • The Dynamics of a Particle was written on the occasion of the contest between Gladstone and Mr Gathorne Hardy (afterwards earl of Cranbrook); and The New Belfry in ridicule of the erection put up at Christ Church for the bells that were removed from the Cathedral tower.

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  • 2 = o, (8) so that a liquid particle remains always on a similar ellipsoid.

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  • (5) (8) (I) The components of acceleration of a particle of fluid are consequently Du dudu du du dt = dt +u dx +v dy + wdz' Dr dv dv dv dv dt -dt+udx+vdy+wdz' dt v = dtJ+udx+vdy +w dx' leading to the equations of motion above.

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  • - Nervous System of the Pond knob - like particle Snail, Limnaeus stagnalis, as a type of the (Neritina and Palu- short-looped euthyneurous condition.

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  • Other writers have derived the word from the Arabic particle al (the definite article), and geber, meaning " man."

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  • The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.

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  • Of the former, the first, published in 1896, was on the dynamics of a particle; and afterwards there followed a number of concise treatises on thermodynamics, heat, light, properties of matter and dynamics, together with an admirably lucid volume of popular lectures on Recent Advances in Physical Science.

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  • Finally, in a celebrated memoir, Theorie des attractions des spheroides et de la figure des planetes, published in 1785 among the Paris Memoirs for the year 1782, although written after the treatise of 1784, Laplace treated exhaustively the general problem of the attraction of any spheroid upon a particle situated outside or upon its surface.

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  • The method of using these liquids is in all cases the same; a particle is dropped in; if it floats a diluent is added and the mixture well stirred.

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  • Archimedes maintained that each particle of a fluid mass, when in equilibrium, is equally pressed in every direction; and he inquired into the conditions according to which a solid body floating in a fluid should assume and preserve a position of equilibrium.

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  • In the Eulerian method the attention is fixed on a particular point of space, and the change is observed there of pressure, density and velocity, which takes place during the motion; but in the Lagrangian method we follow up a particle of fluid and observe how it changes.

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  • d - K dK dK _ dK dK dK ?dx n dyd °, udx dz - ° and K=fdp/o+V+2q 2 =H (3) is constant along a vortex line, and a stream line, the path of a fluid particle, so that the fluid is traversed by a series of H surfaces, each covered by a network of stream lines and vortex lines; and if the motion is irrotational H is a constant throughout the fluid.

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  • Along the path of a particle, defined by the of (3), _ c) sine 2e, - x 2 + y2 = y a 2 ' (Io) sin B' de' _ 2y-c dy 2 ds ds' on the radius of curvature is 4a 2 /(ylc), which shows that the curve is an Elastica or Lintearia.

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  • with A' =0 over the surface of the paraboloid; and then' = ZU[y 2 - pJ (x2 + y2) + px ]; (9) =-2U p [1/ (x2 + y2)-x]; (io) 4, = - ZUp log [J(x2+y2)+x] (II) The relative path of a liquid particle is along a stream line 1,L'= 2Uc 2, a constant, (12) = /,2 3, 2 _ (y 2 _ C 2) 2 2 2 2' - C2 2 x 2p(y2 - c2) /' J(x2 +y 2)= py ` 2p(y2_c2)) (13) a C4; while the absolute path of a particle in space will be given by dy_ r - x _ y 2 - c2 dx_ - y - 2py y 2 - c 2 = a 2 e -x 1 46.

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  • As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.

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  • A magnetizable substance was supposed to consist of an indefinite number of spherical particles, each containing equivalent quantities of the two fluids, which could move freely within a particle, but could never pass from one particle to another.

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  • The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity.

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  • Under such conditions each particle of soil is surrounded by a thin film of water and in the pore-space air can freely circulate.

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  • When the wind rises above the snow-capped Andes, the last particle of moisture is wrung from it that a very low temperature can extract.

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  • well-known theorem in attractions that if a shell is made of gravitative matter whose inner and outer surfaces are similar ellipsoids, it exercises no attraction on a particle of matter in its interior.

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  • The Arhab district, through which these two great wadis run, was formerly the centre of the Himyar kingdom; cultivation is now only to be found in the lower parts on the borders of the watercourses, all above being naked rock from which every particle of soil has been denuded.

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  • If the particle enveloped by the protoplasm be of an organic nature, such as a bacterium, it undergoes digestion, and ultimately becomes destroyed, and accordingly the term " phagocyte " is now in common use to indicate cells having the above properties.

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  • (16) Along the path of a liquid particle 4)' is constant, and putting it equal to 2Uc2, (r 2 - a 3 /r) sin 2 0 = c 2, sin 2 0 = c2r/(r3 - a3), (17) the polar equation; or y 2 = c2r3/(r3 - a 3), r3 = a3y2 /(y2._ c2), (18) a curve of the 10th degree (C10).

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  • But it can be shown that from the aggregation of these separate short motions the particle ought to have a resultant motion, described with an average velocity which, although much smaller than 2 mm.

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  • Finally the word (confused not unnaturally with the particle usually attached to it) was borrowed by the West, and is the origin of the English "admiral."

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  • ii.) gave the first direct demonstration that no function of the distance except the inverse square can satisfy the condition that a uniform spherical shell exerts no force on a particle within it.

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  • We must remember that the ocean is a continuous sheet of water of a certain depth, and the conditions of continuity which hold good for all fluids require that there should be no vacant space within it; hence if a single water particle is set in motion, the whole ocean must respond, as Varenius pointed out in 1650.

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  • This deflecting force is directly proportional to the velocity and the mass of the particle and also to the sine of the latitude; hence it is zero at the equator and comes to a maximum at the poles.

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  • - If particles of matter attract one another according to the law of the inverse square the attraction of all sections of a cone for a particle at the vertex is the same.

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  • " Atom " has mainly a chemical import, being defined as the smallest particle of matter which can take part in a chemical reaction; a " molecule " is composed of atoms, generally two or more.

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  • The above relates to a single particle.

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  • (27) Now u/U = - dy/dx, (28) for the particle at A moves over dy backwards, while the disturbance moves over U.

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  • General motion of a particle.

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  • However, two differences between an orb and a dust particle are that dust has a defined nucleus while an orb is translucent, and dust tends to float while orbs "fly".

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  • If the velocity of a particle at A relative to the undisturbed parts is u from left to right, the velocity of the matter moving out at A is U - u, and the momentum carried out by the moving matter is p(U - u) 2.

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  • io) represents the displacement curve of a train of waves, will represent the pressure excess and particle velocity, and from (II) we see that while the nodal conditions of b, with Co' and u=o, travel with velocity 1/(E/p), the crests exceed that velocity by 1(7 + i)u, and the hollows fall short of it by 1(7 + I)u, with the result that the fronts of the pressure waves become steeper and steeper, and the train b changes into something like c. If the steepness gets very great our investigation ceases to apply, and neither experiment nor theory has yet shown what happens.

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  • In ordinary sound-waves the effect of the particle velocity in affecting the velocity of transmission must be very small.

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  • The maximum particle velocity is 21rna (where n is the frequency and a the amplitude), or 27raU/X.

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  • The maximum velocity of a particle in the wave-train is the amplitude of dy/dt.

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  • When two trains of sound waves travel through the same medium, each particle of the air, being simultaneously affected by the disturbances due to the different waves, moves in a different manner than it would if only acted on by each wave singly.

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  • The infinitive is not found; as in Greek, Rumanian and Bulgarian, it is replaced by the subjunctive with a particle.

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  • 656s, a way, and yp&4*t y, to write), a curve of which the radius vector is proportional to the velocity of a moving particle.

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  • The motion of a particle of air is, as represented in these illustrations, to and fro in the direction of propagation, i.e.

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  • But the waves on the surface of a liquid, which are not of the sound kind, are both longitudinal and transverse, the compound nature being easily seen in watching the motion of a floating particle.

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  • let a line be drawn perpendicular to AD and proportional to the displacement of the particle which was at the point before the disturbance began.

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  • Thus let the particle which was at L be at to the right or forwards, at a given instant.

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  • Let MP =y represent the forward displacement of the particle originally at M, and NQ = y +dy that of the particle originally at N.

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  • Let U be the velocity of the wave and let u be the velocity of the particle originally at N.

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  • In the time dt which the wave takes to travel over MN the particle displacement at N changes by QR, and QR= - udt, so that QR/MN = - u/U.

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  • Then u/U = - dy/dx (2) This gives the velocity of any particle in terms of the displacement.

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  • Equating (I) and (2) u/U = wÆ (3) which gives the particle velocity in terms of the pressure excess.

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  • Every particle in the plane will have the same displacement and the same velocity, and these will be perpendicular to the plane and parallel to the line of propagation.

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  • Whatever the form of a wave, we could always force it to travel on with that form unchanged, and with any velocity we chose, if we could apply any " external " force we liked to each particle, in addition to the " internal " force called into play by the compressions or extensions.

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  • on in time dt to A'B'C', where AA' = Udt, the displacement of the particle originally at M must change from PM to P'M or by PP'.

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  • It is easily shown that after a time we shall have to superpose on the original displacement a displacement proportional to the square of the particle velocity, and this will introduce just the same set of combination tones.

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  • Probably the size of the particle will be slightly reduced.

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  • 4 So Aquila, the disciple of `Agiba, translates the accusative particle by ow; see W.

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  • 13, where the singular use of the restrictive particle ak (EV " verily ") supported the teaching that other Sabbaths need not be observed.

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  • This cement is nothing else than the actual life of the sacred and kindred animal, which is conceived as residing in its flesh, but specially in its blood, and so, in the sacred meal, is actually distributed among all the participants, each of whom incorporates a particle of it with his own individual life."

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  • Newton assumed the possibility of choosing a base such that, relatively to it, the motion of any particle would have only such divergence from uniform velocity in a straight line as could be expressed by laws of acceleration dependent on its relation to other bodies.

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  • It is found that this gives a consistent result; that is to say, if by an experiment with two particles A and B we get the ratio of their masses, and by an experiment with B and a third particle C we get the ratio of the masses of B and C, and thus the ratio of the masses of A and C, we should get the same ratio by a direct experiment with A and C. For the numerical measure of mass that of some standard body is chosen as a unit, and the masses of other bodies are obtained by comparison with this.

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  • The total acceleration of any particle is that obtained by the superposition of the component accelerations derived from its association with the other particles of the system severally in accordance with this law.

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  • A force is said to act upon each of two particles forming a pair, its magnitude being the product of mass and component acceleration of the particle on which it acts, and its direction that of this component acceleration.

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  • Each particle may react in some way on the solvent in its neighbourhood, but if the solution be so dilute that each of these spheres of influence is unaffected by the rest, no further addition of solvent will change the connexion between one particle of solute and its associated solvent.

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  • The only effect of adding solvent will be to separate further from each other the systems composed of solute particle as nucleus and solvent as atmosphere; it will not affect the action of each nucleus on its atmosphere.

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  • It confers the nobiliary particle von.

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  • But, as no particle of evidence on his side was advanced, the protest of his representative was rejected, and Bothwell, acquitted in default of witnesses against him, was free to challenge any persistent accuser to the ancient ordeal of battle.

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  • Now if a be the amplitude expressed in millimetres, and t the period expressed in seconds, then the maximum velocity of an earth particle as it vibrates to and fro equals 27ra/t, whilst the maximum acceleration equals 4,r 2 0 2.

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  • By this motion things are gradually constructed not entirely of homogeneous particles (the homoeomere, oµoLo t ccpi 7) but in each thing with a majority of a certain kind of particle.

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  • Statics of a particle.

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  • Statics of a Particle.By a particle is meant a body whose position can for the purpose in hand be sufficiently specified by a mathematical point.

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  • The fundamental postulate of this part of our subject is that the two forces acting on a particle may be compounded by the parallelogram rule.

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  • By successive applications of the above rule any number of forces acting on a particle may be replaced by a single force which is the vector-sum of the given forces; this single force -~ ~-~ -~

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  • the particle could remain permanently at rest under its action.

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  • If three forces acting on a particle are represented as to magnitude and direction by the sides of a triangle taken in order, they are in equilibrium.

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  • if three forces acting on a particle be in equilibrium, and any triangle be constructed whose sides are respectively parallel to the forces, the magnitudes of the forces will be to ope another as the corresponding sides of the triangle.

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  • As a simple example of the geometrical method of treating statical problems we may consider the equilibrium of a particle on a rough inclined plane.

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  • lhe usual empirical law of sliding friction is that the mutual action between two plane surfaces in contact, or between a particle and a curve or surface, cannot make with the normal an angle exceeding a certain limit X called the angle of friction.

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  • This leads to formulae for the analytical ~ reduction of a system of co planar forces acting on a ~ particle.

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  • the force exerted by a particle A on a particle B, and the force exerted by B on A, are equal and opposite in the line AB.

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  • The problem of determining the possible configurations of equilibrium of a system of particles subject to extraneous forces which are known functions of the positions of the particles, and to internal forces which are known functions of the distances of the pairs of particles between which they act, is in general determinate For if n be the number of particles, the 3n conditions of equilibrium (three for each particle) are equal in number to the 351 Cartesian (or other) co-ordinates of the particles, which are to be found.

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  • The relation between the three forces acting on any particle, viz, the extraneous force and the tensions in the two adjacent portions of the string can be exhibited by means of a triangle of forces; and if the successive triangles be drawn to the same scale they can be fitted together so as to constitute a single force-diagram, as shown in fig.

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  • Work.The work done by a force acting on a particle, in any infinitely small displacement, is defined as the product of the force into the orthogonal projection of the displacement on the direction of the force; i.e.

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  • The total work done by two concurrent forces acting on a particle, or on a rigid body, in any infinitely small displacement, is equal to the work of their resultant.

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  • For example, in the case of a particle lying on a smooth curve, or on a smooth surface, if it be displaced along the curve, or on the surface, the virtual work of the normal component of the pressure may be ignored, since it is of the second order.

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  • It is easily seen that, in the process of determining the masscentre, any group of particles may be replaced by a single particle whose mass isequal to that of the group, situate at the mass-centre of the group.

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  • 3I) that the linear moment of each particle about the line may be found by means of a funicular polygon.

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  • If we replace the mass of each particle by its moment, as thus found, we can in like manner obtain the quadratic moment of the system with respect to the line.

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  • The quadratic moment of the first particle will then be represented by twice the area FIG.

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  • In our ideal representation of natural phenomena this is allowed for by endowing each material particle with a suitable mass or inertiacoefficient m.

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  • On the Newtonian system the motion of a particle entirely uninfluenced by other bodies, when referred to a suitable base, would be rectilinear, with constant velocity.

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  • We may take it as an experimental result, although the best evidence is indirect, that a particle falling freely under gravity experiences a constant acceleration which at the same place is the same for all bodies.

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  • We take next the case of a particle attracted towards a fixed point 0 in the line of motion with a force varying as the distance from that point.

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  • The particle oscifiates between the two positions x= ~a, and the same point is passed through in the same direction with the same velocity at equal intervals of time 21r/o.

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  • If the inclination of the string to the vertical does not exceed a few degrees, the vertical displacement of the particle is of the second order, so that the vertical acceleration may be neglected, and the tension of the string may be equated to the gravity mg of the particle.

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  • In the case of a particle falling directly towards the earth from rest at a very great distance we have C=o and, by Newtons Law of Gravitation, p/ai=g, where a is the earths radius.

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  • We find that the velocity with which the particle would arrive at the earths surface (x=a)is ~ (2ga).

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  • We recognize the right-hand member as the work done by the force X on the particle as the latter moves from the position x0 to the position Xi.

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  • The product 4muf is called the kinetic energy of the particle, and the equation.

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  • (21) is therefore equivalent to the statement that the increment of the kinetic energy is equal to the work done on the particle.

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  • If the force, X be always the same in the same position, the particle may be regarded as moving in a certain invariable field of force.

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  • The work which would have to be supplied by other forces, extraneous to the field, in order to bring the particle from rest in some standard position P0 to rest in any assigned position P, will depend only on the position of P; it is called the statical or potential energy of the particle with respect to the field, in the position P. Denoting this by V, we have VX~x=o, whence X=--~.

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  • It appears then that this sum is a measure of the total capacity for doing work against extraneous resistances which the particle possesses in virtue of its motion and its position; this is in fact the origin of the term energy.

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  • If the positiv~ direction of x be downwards, the equation of motion of a falling particle will be of the form ~l=gku2 (24)

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  • if the particle start from rest in the position x = o at the instant =o.

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  • In the case of a particle projected vertically upwards we have (26)

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  • The particle comes to rest when V us Vf I Uo2\

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  • The momentum of a particle is the vector obtained by multiplying the velocity by the mass in.

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  • For example, the path of a particle projected anyhow under gravity will obviously be confined to the vertical plane through the initial direction of motion.

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  • Thus if the particle start at time t=o from the origin, with the component velocities uf, Vo, we have x=u~t, y_~vct~1/8gt5.

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  • Another important example is that of a particle subject to an acceleration which is directed always towards a fixed point 0 and is proportional to the distance from 0.

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  • If P be the initial position of the particle, we may conveniently take OP as axis of x, and draw Oy parallel to the direction of motion at P. If OP=a, and ~ be the velocity at P, we have, initially, x=a, y=o, x=o, y=.f0 whence x=a cos at, y=b sin nt, (10)

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  • The above problem is identical with that of the oscillation of a particle in a smooth spherical bowl, in the neighborhood of the lowest point, If the bowl has any other shape, the axes Ox, Oy may, ..--7 be taken tangential to the lines tof curvature ~ / at the lowest point 0; the equations of small A motion then are dix xdiy (II) c where P1, P2, are the principal radii of curvature at 0.

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  • Take, for example, the case of a particle moving on a smooth curve in a vertical plane, under the action of gravity and the pressure R of the curve.

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  • Hodograph.The motion of a particle subject to a force which passes always through a fixed point 0 is necessarily in a plane orbit.

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  • No~ it appears from (6) that 2/s/r is the square of the velocity whici would be acquired by a particle faffing from rest at infinity to the distance r.

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  • If A, B have the same sign, this is equivalent to au = cosh mO, (23) if the origin of 0 be suitably adjusted; hence r has a maximum value a, and the particle ultimately approaches the pole asymptotically by an infinite number of convolutions.

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  • In the case of a particle oscillating under gravity on a smooth cycloid from rest at the cusp the hotlograph is a circle through the pole, described with constant velocity.

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  • For the velocity of a particle m at P may be replaced by two components one of which (ii) is identical in magnitude and direction with the velocity of G, whilst the other (v) is the velocity relative to G.

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  • If the equations of motion of each particle be formed separately, each such internal force will appear twice over, with opposite signs for its components, viz, as affecting the motion of each of the two particles between which it acts.

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  • In the time ~5t a certain impulse is given to the first particle in the direction (say) from P to Q, whilst an equal and opposite impulse is given to the second in the, direction from Q to P. Since these impulses produce equal and opposite momenta in the two particles, the resultant lineal momentumof the system is unaltered.

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  • The angular momentum of a particle m at a distance r from the axis is mwr.

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  • This may be compared with the equation of rectilinear motion of a particle, viz.

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  • The angular velocity being constant, the effective force on a particle m at a distance r from Oz is snw2r toward& this axis, and its components are accordingly w2mx, wfmy, 0.

    0
    0
  • If q be any variable co-ordinate defining the position or (in the case of a system of bodies) the configuration, the velocity of each particle at any instant will be proportional to 4, and the total kinetic energy may be expressed in the form 1/8A42, where A is in general a function of q The special case where both cones are right circular and a is constant is important ~n astronomy and also in mechanism (theory of bevel wheels).

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  • If m be the mass of a particle at P, and PN the perpendicular to the instantaneous axis, the kinetic energy T is given by 2T=2~{m(w.

    0
    0
  • It is implied in the above description of the system that the Cartesian co-ordinates x, y, z of any particle of the system are known functions of the qs, varying in form (of course) from particle to particle.

    0
    0
  • As a first application of Lagranges formula (II) we may form the equations of motion of a particle in spherical polar co-ordinates.

    0
    0
  • The component velocities in these directions are therefore t, rO, r sin Oil, and if m be the mass of a moving particle at P we have 2T = n1(~1 + rfEi + r2 sin2 8 ~l,2).

    0
    0
  • If the particle describes a horizontal circle of angular radius a with constant angular velocity f~, we have 0=0, h=c~ sin a, and therefore f~f-cosa, (25)

    0
    0
  • To apply the equations (11) to the case of the top we start with the expression (15) of 22 for the kinetic energy, the simplified form (i) of 20 being for the present purpose inadmissible, since it is essential that the generalized co-ordinates employed should be competent to specify the position of every particle.

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    0
  • This solution, taken by itself, represents a motion in which each particle of the system (since its displacements parallel to Cartesian co-ordinate axes are linear functions of the qs) executes a simple vibration of period 21r/u.

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  • The oscillation of M then resembles that of a particle at a distance a from one end of a string of length a+b fixed at the ends and subject to a tension mg.

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    0
  • Every particle of the system executes in general a simple vibration of the imposed period 27r/il, and all the particles pass simultaneously through their equilibrium positions.

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  • ed., Cambridge, 1896), Dynamics of a Particle (Cambridge, 1898), Rigid Dynamics (6th ed., Cambridge 1905); G.

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  • An example of a force distributed throughout a volume is the weight of the body itself, which acts on every particle, however small.

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  • For a given link, this force isthe resultant of all the accelerating forces distributed through the substance of the material of the link required to produce the requisite acceleration of each particle, and the determination of this force depends upon the principles of the two preceding sections.

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  • In addition to the particle Homer has another, hardly distinguishable in meaning.

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  • He also made many experiments with the tourmaline when cut into thin slices, and reduced to the finest powder, in which state each particle preserved its pyro-electricity; and he showed that scolezite and mesolite, even when deprived of their water of crystallization and reduced to powder, retain their property of becoming electrical by heat.

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  • The verb may be preceded by an affirmative, a negative, or an interrogative particle.

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  • In a simple interrogative sentence the introductory particle before the verb is a, and the positive answer consists in a repetition of the verb; a ddaw Dafydd ?

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    0
  • As an instance of misdirection, we may take the irritation which remains in the eye after a particle of dust has been removed, or the itching of the skin which occurs in eczema.

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  • The irritation of the conjunctiva caused by dust leads to winking of the eyelids, lachrymation and rubbing, which tend to remove it; but after the dust has been removed violent rubbing tends rather to keep up the irritation; and sometimes, if the particle of dust remains under the eyelid and is sharp and angular, the process of rubbing may cause it to injure the conjunctiva much more than if it were left alone.

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  • In everything that exists, therefore, even the smallest particle, there are these two principles.

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  • We saw that virtue is a law which governs the universe: that which Reason and God ordain must be accepted as binding upon P g P the particle of reason which is in each one of us.

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  • He thus showed that at a curved part of the surface, a superficial particle would be urged towards the centre of curvature of the surface, and he gave reasons for concluding that this force is proportional to the sum of the curvatures of the surface in two normal planes at right angles to each other.

    0
    0
  • In the Supplement to the Theory of Capillary Action, Laplace deduced the equation of the surface of the fluid from the condition that the resultant force on a particle at the surface must be normal to the surface.

    0
    0
  • Instead of calculating the direction and magnitude of the resultant force on each particle arising from the action of neighbouring particles, he formed a single expression which is the aggregate of all the potentials arising from the mutual action between pairs of particles.

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    0
  • We have next to determine the value of x in terms of the action between one particle and another.

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    0
  • If we next introduce a new function of f and write f .f 4(f) d f =Il (f), (23) then m m' II(f) will represent - (I) The work done by the attractive force on the particle m, while it is brought from an infinite distance from m' to the distance f from m'; or (2) The attraction of a particle m on a narrow straight rod resolved in the direction of the length of the rod, one extremity of the rod being at a distance f from m, and the other at an infinite distance, the mass of unit of length of the rod being m'.

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    0
  • If we next write f II (f) d f =, P(z), (24) then 27rmagz) will represent - (I) The work done by the attractive force while a particle m is brought from an infinite distance to a distance z from an infinitely thin stratum of the substance whose mass per unit of area is Z o; (2) The attraction of a particle m placed Q 2 at a distance z from the plane surface of an infinite solid whose density is a.

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  • Let us examine the case in which the particle m is placed at a distance z from a curved stratum of the substance, whose principal radii of curvature are R 1 and R2.

    0
    0
  • 2) be the particle and PB a normal to the surface.

    0
    0
  • We may also write ur 1 = I +zu 1+ &c., since z is very small compared with u, and expressing u in terms of w by (25), (we find l 21- mv i fi(z) i I +z(c R w + ' R 2 w) do) = 27rmoti(z) I -f-ZZ (Ki + R2/ This then expresses the work done by the attractive forces when a particle m is brought from an infinite distance to the point P at a distance z from a stratum whose surface-density is a, and whose principal radii of curvature are R 1 and R2.

    0
    0
  • This expression, when integrated, gives (I) the work done on a particle m while it is brought from an infinite distance to the point P, or (2) the attraction on a long slender column normal to the surface and terminating at P, the mass of unit of length of the column being m.

    0
    0
  • Now 2 7rmpi,t(c) represents the attraction between a particle m and the plane surface of an infinite mass of the liquid, when the distance of the particle outside the surface is c. Now, the force between the particle and the liquid is certainly, on the whole, attractive; but if between any two small values of c it should be repulsive, then for films whose thickness lies between these values the tension will increase as the thickness diminishes, but for all other cases the tension will diminish as the thickness diminishes.

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  • A particle of soap rising accidentally to the surface would spread itself with rapidity.

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    0
  • " The smoker assumes a comfortable attitude (lying down of course) at a proper distance from the lamp. He now puts the stem to his lips, and holds the bowl over the lamp. The heat causes the opium to frizzle, and the smoker takes three or four long inhalations, all the time using the dipper to bring every particle of the opium to the orifice as it burns away, but not taking his lips from the end of the stem, or the opium pellet from the lamp till all is finished.

    0
    0
  • The universe is in motion in every particle of every part; rock and metal merely a transition stage between crystallization and dissolution.

    0
    0
  • Like all spiders, the tarantula possesses poison glands in its jaws, but there is not a particle of trustworthy evidence that the secretion of these glands is more virulent than that of other spiders of the same size, and the medieval belief that the bite of the spider gave rise to tarantism has long been abandoned.

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    0
  • There were those who neither believed the predictions nor looked for success in war, but destroyed their last particle of food in unquestioning obedience to their chiefs command.

    0
    0
  • Serious leakage at once began between c and b and washed out the clay, particle by particle, but did not wash out the sand associated with it, which remained rench.

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    0
  • (3) Feeding of birds (auspicia ex tripudiis), which consisted in observing whether a bird - usually a fowl - on grain being thrown before it, let fall a particle from its mouth (tripudium sollistimum).

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    0
  • The exercise of wisdom was now viewed as the pure life of that particle of divine substance which was in very truth the " god within him "; the reason whose supremacy he maintained was the reason of Zeus, and of all gods and reasonable men, no less than his own; its realization in any one individual was thus the common good of all rational beings as such; " the sage could not stretch out a finger rightly without thereby benefiting all other sages," - nay, it might even be said that he was " as useful to Zeus as Zeus to him."

    0
    0
  • At the outset, the position of each body, considered as a material particle, is defined by reference to a system of co-ordinate axes, and not by any verbal description.

    0
    0
  • The process of discovering the laws of motion of the particle then consists in the integration of these equations.

    0
    0
  • The earth, for example, may be regarded as a particle attracted by another more massive particle, the sun.

    0
    0
  • The general equations expressing the motion of a planet considered as a material particle round a centre of attraction lead to theorems the more interesting of which will now be enunciated.

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    0
  • Almost any word may be made into a verb by using with it a verbal particle.

    0
    0
  • 13, we suppose that a diffracting particle of such fineness is placed at 0 that the diffracted pencils of the 1st order make an angle w with the axis; the principal maximum of the Fraunhofer diffraction phenomena lies in F' 1; and the two diffraction maxima of the 1st order in P' and P' 1.

    0
    0
  • acceleration of a particle moving in a circle.

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    0
  • These features are formed as a result of particle acceleration in the hairpin field structure of the distant tail.

    0
    0
  • accelerator physics research in particle physics in UK universities.

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    0
  • I switched on the particle accelerator in my basement.

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    0
  • The amount of water adsorbed on the surface of Perlite is a function of particle size.

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    0
  • Here the spherical glyphs represent particle advection of heated air around a room.

    0
    0
  • Another important practice in analyzing nonlinear water waves is to study the water particle advection in the history of a simulation.

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    0
  • adverb particle, e.g. up, off, out.

    0
    0
  • adverbial particle - preposition.

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  • Additionally, moisture sorption can lead to particle agglomeration and powder caking.

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    0
  • Second, it is a potent radioactive carcinogen, emitting a relatively heavy alpha particle composed of 2 protons and 2 neutrons.

    0
    0
  • The center of the particle appears amorphous in negatively stained EM preps, the nucleocapsid being in a loosely wound rather disordered state.

    0
    0
  • The location where particle displacement is at a maximum is called a displacement antinode.

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    0
  • antiparticle of an electron is a particle of positive electric charge called the positron.

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    0
  • They can be used very generally to study the angular momentum and spectroscopic factors associated with specific single particle states.

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    0
  • astronomy cosmology particle physics WATER ON THE SUN.

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    0
  • Proven record of high quality research in experimental particle physics or particle astrophysics.

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    0
  • One was a new neutral particle called the axion, less than one-millionth of the mass of an electron.

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    0
  • boson particle.

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    0
  • The measurements of the guage boson properties enables the Standard Model of particle physics to be tested to incredibly high precision.

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    0
  • This is called magnetic bremsstrahlung or synchrotron radiation (after radiation observed from particle accelerators by that name ).

    0
    0
  • Next on its outward journey the particle passes through a detector called the " electromagnetic calorimeter " .

    0
    0
  • The powder from which tantalum capacitors are made is of pure tantalum metal, with a typical particle size of 10µm.

    0
    0
  • The protein subunits in a virus capsid are multiply redundant, i.e. present in many copies per particle.

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    0
  • carbonaceous particles to overall particle mass, the sources of such particles are not clearly known.

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    0
  • A supported heterogeneous catalyst prepared by traditional methods will not normally have this tightly-controlled a particle size distribution.

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    0
  • Soil acidity and pH; cation exchange capacity and exchangeable cation exchange capacity and exchangeable cations; particle size analysis; soil salinity.

    0
    0
  • NIST Recommended Practice Guide " particle size characterization " .

    0
    0
  • collider experiments, addressing a broad range of issues in modern particle physics.

    0
    0
  • collider physics, particle theory is nowadays also studied in the context of the early universe.

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    0
  • Many aspects of quantum chromodynamics are presently probed in particle collider experiments.

    0
    0
  • It is clear, however, that the flow is severely perturbed by the enhanced ionospheric conductivity caused by particle precipitation into the E-region.

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    0
  • correlation coefficient value, the more similiar the particle will look to the reference projection.

    0
    0
  • cosmology particle physics WATER ON THE SUN.

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    0
  • Rev. Lett.) astronomy cosmology particle physics WATER ON THE SUN.

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    0
  • The recent abundance of results from such observations has made the subject of particle cosmology blossom.

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    0
  • cuspate forelands, patterned vegetation develops, due to the differing particle size and hydrology.

    0
    0
  • A particle physics Grid for the UK GridPP is the UK's contribution to analyzing this data deluge.

    0
    0
  • At the onset of soot inception, the PSDF was found to follow a power-law dependence on particle diameter.

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    0
  • devised to overcome this problem of particle activity.

    0
    0
  • particle Size Characterization Dynamic Light Scattering (DLS) is a non-invasive method for measuring the size of molecules and particle dispersions.

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    0
  • Auto wash between particle size distribution measurements eliminates cross contamination.

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    0
  • dungeon walls, and also implemented a particle system.

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    0
  • electron micrograph normally displays a wide range of particle views.

    0
    0
  • The use of the particle mesh Ewald method for treating the long range electrostatics also reduces the effect of the cutoff.

    0
    0
  • electroweak interactions in particle physics.

    0
    0
  • elementary particle physics must get a copy.

    0
    0
  • The advent of positron emission particle tracking (PEPT) has now made this possible.

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    0
  • enclitic particle ' A ', even.

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    0
  • Of course, it is theoretically possible that a hugely energetic particle could come blasting through your memory and take out multiple bits.

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    0
  • entrained in the particle flow.

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    0
  • The quantum eraser also works by seeking an entanglement of the particle motion with the detector.

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    0
  • evaporatelight from the emission of radiation from the ionized gas and from the white hot evaporating particle.

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    0
  • Particle physics experiments are performed at accelerators where the products of head-on collisions between matter and antimatter are studied with huge detectors.

    0
    0
  • On the parallel ridges of cuspate forelands, patterned vegetation develops, due to the differing particle size and hydrology.

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    0
  • formalism used in particle physics.

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    0
  • This includes the graviton, a hypothetical particle thought to be responsible for gravity.

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    0
  • In quantum gravity, the role of the gage coupling, is played by the energy of a particle.

    0
    0
  • For every particle except the neutrinos there is an antiparticle of the opposite handedness.

    0
    0
  • prophylactic quadrivalent human papillomavirus (types 6, 11, 16, and 18) L1 virus-like particle vaccine in young women.

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    0
  • Thus new material models and innovative methods such as smooth particle hydrodynamics are utilized.

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    0
  • Disparity of particle sizes following crushing has also been shown to relate to the strong hysteresis observed in unloading and reloading tests on soils.

    0
    0
  • The emphasis of the study was to follow the evolution of the PSDF from the onset of particle inception to particle mass growth.

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  • indivisible particle.

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    0
  • Figure 4: Low loss spectra from the unirradiated SiO 2, heavily irradiated SiO 2, heavily irradiated silicon particle and nanoporous silicon.

    0
    0
  • kinematics of a particle in a plane including the case when velocity or acceleration depends on time (but excluding use of acceleration.

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  • As with most enveloped viruses, the particle is relatively labile.

    0
    0
  • In order to then find those final leptons, we have used a standard detector in particle physics: the DØ detector.

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  • lint particle.

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  • magnetosphere particle showers finally the field the depression i'm.

    0
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  • Particle physics experiments so far directly establish only values for the square of neutrino mass differences.

    0
    0
  • Envelope: A lipid membrane enveloping a virus particle.

    0
    0
  • Also quantitative methods to describe particle shape etc. by image analysis have been developed.

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    0
  • Thus, the electron micrograph normally displays a wide range of particle views.

    0
    0
  • Polypropylene can be made auxetic by compacting ultra high molecular weight PP powder, with a particle size of 30 to 120 microns.

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  • momentum of the particle.

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  • This angular momentum leads to a magnetic moment of fixed size for each particle.

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  • Many of their applications utilize the ability of these particles to stay firmly attached to oil-water interfaces, thus forming particle monolayers.

    0
    0
  • Martin Turner takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.

    0
    0
  • The movement and deposition of rocks and particle debris by glaciers to form moraines is also discussed.

    0
    0
  • For example, there is a particle called the muon which is a heavier cousin of the electron.

    0
    0
  • Early in 1932 James Chadwick discovered the neutron, a particle in the nuclei of most atoms.

    0
    0
  • The neutron fluence rate depends upon factors such as target thickness, charged particle beam current, geometry and required neutron fluence rate depends upon factors such as target thickness, charged particle beam current, geometry and required neutron energy resolution.

    0
    0
  • Gasoline vehicles are better for human health with their lower NOx and particle emissions.

    0
    0
  • The alpha particle is a helium nucleus - one of the products of a nuclear fission.

    0
    0
  • As the particle passes through the beam, a secondary " pulse " signal is generated by a single optical fiber.

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    0
  • For example, in the bulk palladium, less than 4% of the palladium atoms were on surface of the particle.

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  • paradoxical situation arises: we obtain information about some region of space without any particle being there.

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  • Particle Accelerators are devices used to accelerate charged elementary particle Accelerators are devices used to accelerate charged elementary particles or ions to high energies.

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  • particle physics Grid.

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  • particle physics must get a copy.

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  • particle accelerator.

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  • particle physicists.

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  • particle size?

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  • Some speculate that the high-energy particles are not protons at all but some exotic new particle.

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  • The LHC will be the world's most powerful particle accelerator.

    0
    0
  • Next year the nuclear research institute at CERN will start using the largest particle accelerator in the world.

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  • However, it is widely felt that the standard model is incomplete (hence the need to build ever more powerful particle accelerators ).

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  • particle acceleratorenergy frontier of the present and future generation of particle physics accelerators is the TeV regime.

    0
    0
  • Particle physicists are waiting for 2007 when a new particle accelerator opens in the world's largest particle physics laboratory, CERN.

    0
    0
  • About GridPP UK particle physicists are builing a computing Grid, to analyze the data deluge from CERN's next particle accelerator.

    0
    0
  • Fermi Lab: Fermilab operates the world's highest-energy particle accelerator, the Tevatron.

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    0
  • It is a proposed 33 kilometer long superconducting particle accelerator with built-in X-ray lasers planned to begin operating in 2012.

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  • particle accelerator in the world.

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    0
  • Keywords: elementary, particle physics, Hadrons, Phase space, Monte carlo, Rapidity, Integration, Importance sampling.

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    0
  • particle physics experiments relys on large scale distributed computing systems.

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  • particle physics laboratory supported by PPARC.

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  • particle physics community has been at the cutting-edge of Grid development.

    0
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  • particle physics detectors ever built, ATLAS will also pose a computing challenge of monumental scale.

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    0
  • particle physics today.

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  • percentile of fixed daily mean ' other ' particle concentrations estimated within the model.

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  • It aims to foster world-class research in particle physics phenomenology.

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    0
  • We do not offer an MSc course in particle physics.

    0
    0
  • A particle physicist in the family is a rare occurrence.

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    0
  • They are all part of the GridPP project, which runs the UK particle physics Grid.

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    0
  • neutrino physics This has been one of the most exciting areas in particle physics in recent years.

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    0
  • The end of the particle attached to the F pilus flares open, exposing the phage DNA.

    0
    0
  • ploughge of average particle speed in the cross-sectional plane of a plow blade mixer.

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    0
  • The electric charge may be positive, in which case the beta particle is called a positron.

    0
    0
  • positron emission particle tracking (PEPT) has now made this possible.

    0
    0
  • The supersymmetric theories postulate that every particle we observe has a massive " shadow " particle partner.

    0
    0
  • poxvirus particle click here.

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    0
  • Previously, there were only two choices of convection patterns and particle precipitation inputs, with a limited number of standard configurations.

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    0
  • provisional timetable for all of the postgraduate lectures in Particle Physics.

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    0
  • quadrivalent human papillomavirus (types 6, 11, 16, and 18) L1 virus-like particle vaccine in young women.

    0
    0
  • This is what RHIC set out to show. nuclear physics particle physics quarks forces Let's look at what happened.

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  • reactant particle will hit the solid surface and react.

    0
    0
  • regeneratee clear benefits from Ultra Low Sulfur Diesel and ULSD with a continuously regenerating particle trap over standard diesel.

    0
    0
  • Particle physicists at CERN have published the results of an experiment that conclusively proves Jimmy Saville cannot exist on Thursdays.

    0
    0
  • running time: Typical running times mostly depend on the shape of the tracer particle.

    0
    0
  • Each sensor consists of a CsI scintillator, which is bonded to a shell of Pilot B plastic scintillator used for charged particle suppression.

    0
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  • self-sufficient dynamic entity, a " thing " displaying many properties of a particle.

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  • Its ease of body contact and entry: particle size and solubility.

    0
    0
  • soot particle size distribution function (PSDF ).

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  • stratification based on particle size possibly, the larger particles being at the base.

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  • subatomic particle which circles the nucleus of the atom in a cloud.

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  • subatomic particle physics is a little more tenuous.

    0
    0
  • subpopulations identified in our original 15,650 particle data set.

    0
    0
  • sulfur emissions lead to new particle formation or increase the mass of existing particles?

    0
    0
  • A particle viewed down, for example, the three-fold symmetry axis can be readily identified by the three-fold symmetry of the projection.

    0
    0
  • talcum (powder)ahra talcum power has the smallest particle size commercially available in the world.

    0
    0
  • The powder from which tantalum capacitors are made is of pure tantalum capacitors are made is of pure tantalum metal, with a typical particle size of 10µm.

    0
    0
  • We investigate the stability of self-gravitating accretion disks using three-dimensional, global, smoothed particle hydrodynamic (SPH) simulations.

    0
    0
  • Failure to find the top quark would distrupt the current theory of basic particle physics.

    0
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  • tracer particle.

    0
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  • trajectoryhat Heisenberg's rule may not apply to past trajectories of a particle.

    0
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  • trajectoryw the end parts of alpha particle trajectories at these depths.

    0
    0
  • Piezoelectric impact transducers are used to detect large particle events.

    0
    0
  • With a diesel particulate trap, particle mass and accumulation mode particles were reduced by several orders of magnitude.

    0
    0
  • Estimating suspended sediment concentrations from ocean color measurements in moderately turbid waters; the impact of variable particle scattering properties.

    0
    0
  • ultrasonic cleaning, buffer roller cleaners and particle transfer rollers.

    0
    0
  • It was originally known as a V particle, due to the characteristic vee.

    0
    0
  • The plasma membrane envelopes the particle and buds off to form an intracellular vesicle, the phagosome.

    0
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  • virion particle.

    0
    0
  • A wide particle size distribution usually gives a lower viscosity than narrow due to better particle packing.

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  • However, the particle cluster motion could be clearly visualized.

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  • visualized using a constrained particle method.

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    0
  • Fast thorough washing should follow the fixing, in order to eliminate every particle of hyposulphite from the film.

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  • waterworks sludge treatment and particle removal.

    0
    0
  • c.royos, indivisible, from aprivative, and, uvEiv, to cut), the term given in physical science to the ultimate indivisible particle of matter, and so by analogy to something minutely small in size.

    0
    0
  • The table here given contains some of Dalton's diagrams of atoms. They are not all considered to be correct at the present time; for example, we now think that the ultimate particle of water is made up of two atoms of hydrogen and one of oxygen, and that that of ammonia contains three atoms of hydrogen to one of nitrogen.

    0
    0
  • The intensity of the light scattered by a small particle is constant, and a maximum, for rays which lie in the vertical plane running east and west, while there is no scattered ray along the north and south line.

    0
    0
  • The number (i) expressing the ratio of the two amplitudes is a function of the following quantities: - (T) the volume of the disturbing particle; (r) the distance of the point under consideration from it; (A) the wave-length; (b) the velocity of propagation of light; (D) and (D') the original and altered densities: of which the first three depend only upon space, the fourth on space and time, while the fifth and sixth introduce the consideration of mass.

    0
    0
  • Moreover, since the same amount of energy is propagated across all spheres concentric with the particle, we recognize that i varies as r.

    0
    0
  • Let the particle be at the origin of coordinates, and let the expression for the primary vibration be =sin (nt - kx).

    0
    0
  • To obtain the total force which must be supposed to act, the factor T (representing the volume of the particle) must be introduced.

    0
    0
  • The opposite of this, conceived to act at the origin, would give the same disturbance as is actually caused by the presence of the particle.

    0
    0
  • In order to find the whole emission of energy from one particle (T), we have to integrate the square of (3) over the surface of a sphere of radius r.

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  • By Brewster's law (see Polarization of light) this angle in the case of regular reflection from a plate is less than a right angle; so that not only is the law of polarization for a very small particle different from that applicable to a plate, but the first effect of an increase of size is to augment the difference.

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  • As the movement of one particle in a closely-packed universe is only possible if all other parts move simultaneously, so that the last in the series steps into the place of the first; and as the figure and division of the particles varies in each point in the universe, there will inevitably at the same instant result throughout the universe an innumerable host of more or less circular movements, and of vortices or whirlpools of material particles varying in size and velocity.

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  • For instance, the well-known description (in chap. xlvii.) of the preposition " in " occurring in a theological dogma as a " momentous particle which the memory rather than the understanding must retain " is taken directly from the first Provincial Letter.

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  • Ostwald) form so obtained being immediately solidified on the introduction of a particle of the solid modification; and supersaturated solutions behave in a similar manner.

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  • These particles, which were termed by their discoverer corpuscles, are more commonly spoken of as electrons,' the particle thus being identified with the charge which it carries.

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  • To determine the component acceleration of a particle, suppose F to denote any function of x, y, z, t, and investigate the time rate of F for a moving particle; denoting the change by DF/dt, DF = 1t F(x+uSt, y+vIt, z+wSt, t+St) - F(x, y, z, t) dt at = d + u dx +v dy+ w dz and D/dt is called particle differentiation, because it follows the rate of change of a particle as it leaves the point x, y, z; but dF/dt, dF/dx, dF/dy, dF/dz (2) represent the rate of change of F at the time t, at the point, x, y, z, fixed in space.

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  • d - K dK dK _ dK dK dK ?dx n dyd °, udx dz - ° and K=fdp/o+V+2q 2 =H (3) is constant along a vortex line, and a stream line, the path of a fluid particle, so that the fluid is traversed by a series of H surfaces, each covered by a network of stream lines and vortex lines; and if the motion is irrotational H is a constant throughout the fluid.

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  • Now if k denotes the component of absolute velocity in a direction fixed in space whose direction cosines are 1, m, n, k=lu+mv+nw; (2) and in the infinitesimal element of time dt, the coordinates of the fluid particle at (x, y, z) will have changed by (u', v', w')dt; so that Dk dl, do dt dt dt dt + dtw +1 (?t +u, dx +v, dy +w, dz) +m (d +u dx + v dy +w' dz) dw, dw +n (dt ?dx+v?dy +w dz) But as 1, m, n are the direction cosines of a line fixed in space, dl= m R-n Q, d m = nP-lR an =1Q-mP dt dt ' dt ' so that Dk __ du, du, du, du dt l (dt -vR+ wQ+u + v dy + w dz) +m(..

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  • This is continued until the particle freely swims, and then the density of the mixture is determined by the ordinary methods (see Mineralogy).

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  • This work included the "Logometria," the trigonometrical theorem known as "Cotes' Theorem on the Circle" (see TRIGONOMETRY), his theorem on harmonic means, subsequently developed by Colin Maclaurin, and a discussion of the curves known as "Cotes' Spirals," which occur as the path of a particle described under the influence of a central force varying inversely as the cube of the distance.

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  • From the literate minority, therefore, agency has to be drawn in sufficient strength to take down every particle of the information dictated by the heads of families.

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  • Equating (I) and (2) u/U = wÆ (3) which gives the particle velocity in terms of the pressure excess.

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  • Instead of the operation of superposing accelerations, we may compound the several forces acting on a particle by the parallelogram law (see Mechanics) into what may be called the resultant force, the total acceleration of the particle being the same as if this alone acted.

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  • But this Nous, or Mind, is not incorporeal; it is the thinnest of all things; its action on the particle is conceived materially.

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  • It will be seen that unless the conditions be exactly adjusted for a circular orbit the particle will either recede to infinity or approach the pole asymptotically.

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  • Whatever the ratio M/m, the twc values of o~ can never be exactly equal, but they are approximately equal if a, b are nearly equal and u is very small A curious phenomenon is then to be observed; the motion of each particle, being made up, (in general) of two superposed simple vibrations of nearly equal period, is seen to fluctuate greatly in extent, and if the amplitudes be equal we have periods of approximate rest, as in the case 01 beats in acoustics.

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  • In sentences in which a noun comes first, the interrogative particle is ai, and the answer is always, positive tie, negative nage; as ai Dafydd a ddaw ?

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  • Hence if we write K =27rf o,/i(z)dz, H =27rf o zi/i(z)dz, the pressure of a column of the fluid itself terminating at the surface will be p2{K+1H(I/Rid-I/R2)}, and the work done by the attractive forces when a particle m is brought to the surface of the fluid from an infinite distance will be mp{K+zH(I/Ri+I/Ro)} If we write (.0 J then 27rmpo(z) will express the work done by the attractive forces, while a particle m is brought from an infinite distance to a distance z from the plane surface of a mass of the substance of density p and infinitely thick.

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  • The curve has important mechanical relations, in particular it is the orbit of a particle moving under the influence of a central force which varies inversely as the square of the distance of the particle; this is the gravitational law of force, and the curve consequently represents the orbits of the planets if only an individual planet and the sun be considered; the other planets, however, disturb this orbit (see Mechanics).

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  • According to Huygens's principle (see Diffraction) each aether particle, set vibrating by an incident wave, can itself act as a new centre of excitement, emitting a spherical wave; and similarly each particle on this wave itself produces wave systems. All systems which are emitted from a single source can by a suitable optical device be directed that they simultaneously influence one and the same aether particle.

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  • This is what RHIC set out to show. nuclear physics particle physics quarks forces Let 's look at what happened.

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  • Therefore, there is more chance that a reactant particle will hit the solid surface and react.

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  • There are clear benefits from Ultra Low Sulfur Diesel and ULSD with a continuously regenerating particle trap over standard diesel.

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  • Running time: Typical running times mostly depend on the shape of the tracer particle.

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  • He viewed the solitary wave as a self-sufficient dynamic entity, a " thing " displaying many properties of a particle.

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  • Unsolved Puzzles in Particle Physics Field theory in all its glory, there are numerous shortcomings of the present models.

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  • The model involves keeping track of the moments of the soot particle size distribution function (PSDF).

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  • It would have cause essentially one layer with some stratification based on particle size possibly, the larger particles being at the base.

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  • Electron: A negatively charged subatomic particle which circles the nucleus of the atom in a cloud.

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  • Particle physics The link between the plaque and subatomic particle physics is a little more tenuous.

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  • In order to do so we have also calculated 3D maps of two additional subpopulations identified in our original 15,650 particle data set.

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  • For example, do anthropogenic sulfur emissions lead to new particle formation or increase the mass of existing particles?

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  • The surface of the particle shows a monolayer of bound surfactant molecules (far right).

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  • For example Zahra talcum power has the smallest particle size commercially available in the world.

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