# Dynamical Sentence Examples

The R2 algorithm is specifically for simulating 2+1 flavors of

**dynamical**staggered fermions of different masses.Devoting himself next to optics, he produced memoirs which entitle him to a high place among the early, searchers after a true

**dynamical**theory of light.Though we may allow that the results obtained by Rumford and Davy demonstrate satisfactorily that heat is in some way due to motion, yet they do not tell us to what particular

**dynamical**quantity heat corresponds.Therefore, according to Kekule, the double linkages are in a state of continual oscillation, and if his

**dynamical**notion of valency, or a similar hypothesis, be correct, then the difference between the 1.2 and 1.6 di-derivatives rests on the insufficiency of his formula, which represents the configuration during one set of oscillations only.The heading "Measurement of

**Dynamical**Quantities" includes the topics units, measurements, and the constant of gravitation.Mechanics (including

**dynamical**astronomy) is that subject among those traditionally classed as "applied" which has been most completely transfused by mathematics - that is to say, which is studied with the deductive spirit of the pure mathematician, and not with the covert inductive intention overlaid with the superficial forms of deduction, characteristic of the applied mathematician.The

**dynamical**equivalent of the calorie is 4.18 X Io 7 ergs or C.G.S.Thomson (Applications of Dynamics to Physics and Chemistry, 47) that on

**dynamical**principles there must be a reciprocal relation between the changes of dimensions produced by magnetization and the changes of magnetization attending mechanical strain.Besides this most important contribution to the general fabric of

**dynamical**science, we owe to Lagrange several minor theorems of great elegance, - among which may be mentioned his theorem that the kinetic energy imparted by given impulses to a material system under given constraints is a maximum.Although the matter can be fully treated only upon the basis of a

**dynamical**theory, it is proper to point out at once that there is an element of assumption in the application of Huygens's principle to the calculation of the effects produced by opaque screens of limited extent.AdvertisementCalling the sum of the pressure and potential head the statical head, surfaces of constant statical and

**dynamical**head intersect in lines on H, and the three surfaces touch where the velocity is stationary.Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the

**dynamical**equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..When no external force acts, the case which we shall consider, there are three integrals of the equations of motion (i.) T =constant, x 2 +x 2 +x 2 =F 2, a constant, (iii.) x1y1 +x2y2+x3y3 =n = GF, a constant; and the

**dynamical**equations in (3) express the fact that x, x, xs.Social physics will consist of the conditions and relations of the facts of society, and will have two departments, - one, statical, containing the laws of order; the other

**dynamical**, containing the laws of progress.In later memoirs Reynolds followed up this subject by proceeding to establish definitions of the velocity and the momentum and the energy at an element of volume of the molecular medium, with the precision necessary in order that the

**dynamical**equations of the medium in bulk, based in the usual manner on these quantities alone, without directly considering thermal stresses, shall be strictly valid - a discussion in which the relation of ordinary molar mechanics to the more complete molecular theory is involved.AdvertisementA number of molecules moving in obedience to

**dynamical**laws will pass through a series of configurations which can be theoretically determined as soon as the structure of each molecule and the initial position and velocity of every part of it are known.We begin with a general

**dynamical**theorem, whose special application, when the**dynamical**system is identified with a gas, will appear later.The planetary theory and other particular

**dynamical**problems likewise occupied his attention from time to time.Lamb, The

**Dynamical**Theory of Sound (1910), is intended as a stepping-stone to the study of-the writings of Helmholtz and Rayleigh.These antinomies are four - two mathematical, two

**dynamical**- connected with (I) the limitation of the universe in respect of space and time, (2) the theory that the whole consists of indivisible atoms (whereas, in fact, none such exist), (3) the problem of freedom in relation to universal causality, (4) the existence of a universal being - about each of which pure reason contradicts the empirical, as thesis and antithesis.AdvertisementThe wider view, according to which the hypothesis of direct transmission of physical influences expresses only part of the facts, is that all space is filled with physical activity, and that while an influence is passing across from a body, A, to another body, B, there is some

**dynamical**process in action in the intervening region, though it appears to the senses to be mere empty space.MacCullagh's hands the correct equations were derived from a single energy formula by the principle of least action; and while the validity of this

**dynamical**method was maintained, it was frankly admitted that no mechanical analogy was forthcoming.In this place it must suffice to indicate the gist of the more recent developments of the electro-optical theory, which involve the

**dynamical**verification of Fresnel's hypothesis regarding optical convection and the other relations above described.The

**dynamical**series of stages in nature, the forms in which the ideal structure of nature is realized, are matter, as the equilibrium of the fundamental expansive and contractive forces; light, with its subordinate processes - magnetism, electricity, and chemical action; organism, with its component phases of reproduction, irritability and sensibility.'Just as nature exhibits to us the series of

**dynamical**stages of processes by which spirit struggles towards consciousness of itself, so the world of intelligence and practice, the world of mind, exhibits the series of stages through which self-consciousness with its inevitable oppositions and reconciliations develops in its ideal form.AdvertisementLord Rayleigh,' who has also investigated vibrating systems giving series of lines approaching a definite limit of " root," remarks that by

**dynamical**reasoning we are always led to equations giving the square of the period and not the period, while in the equation representing spectral series the simplest results are obtained for the first power of the period.The discovery of the magnetic rotation of the plane of polarized light, though it did not lead to such important practical applications as some of Faraday's earlier discoveries, has been of the highest value to science, as furnishing complete

**dynamical**evidence that wherever magnetic force exists there is matter, small portions of which are rotating about axes parallel to the direction of that force.A definition of the measurement dependent on

**dynamical**theory has Time.Nevertheless, the theoretical possibility, and its realization in many cases, has brought considerations to the front which have recently become of predominant interest; consequently the possible transformations of isomers and polymers will be considered later under the denomination of reversible or

**dynamical**isomerisms.But from the

**dynamical**standpoint it is obvious that equations which represent the facts correctly on one system of time-measurement might become seriously defective on another.In any general

**dynamical**equation the dimensions of each term in the fundamental units must be the same, for a change of units would otherwise alter the various terms in different ratios.For the determination of the motion it has only, been necessary to use one of the

**dynamical**equations.As in the case of (2), the equations are applicable to any

**dynamical**system whatever.These equations are due to Lagrange, with whom indeed the first conception, as well as the establishment, of a general

**dynamical**method applicable to all systems whatever appears to have originated.Free vibrations must of course be superposed on the forced vibrations given by (29) in order to obtain the complete solution of the

**dynamical**equations.Arago's previous investigations in the new science of electromagnetism, and crowned that labour by the announcement of his great discovery of the

**dynamical**action between conductors conveying the electric currents.This fruitful conception, however, Bacon does not work out; and though he uses the word cause, and identifies form with formal cause, yet it is perfectly apparent that the modern notions of cause as

**dynamical**, and of nature as in a process of flow or development, are foreign to him, and that in his view of the ultimate problem of science, cause meant causa immanens, or underlying substance, effects were not consequents but manifestations, and nature was regarded in a purely statical aspect.When a liquid is in thermal and

**dynamical**equilibrium with its vapour, then if p' and x' are the values of p and x for the vapour, and po and Xo those for the liquid, x' - xo=JL - p(I/p' - I/pc),.The Detachment Of The Drop Is A

**Dynamical**Effect, And It Is Influenced By Collateral Circumstances.But Although A Complete Solution Of The

**Dynamical**Problem Is Impracticable, Much Interesting Information May Be Obtained From The Principle Of**Dynamical**Similarity.**Dynamical**Similarity Requires That T/Gva 2 Be Constant; Or, If G Be Supposed To Be So, That A' Varies As T/V.But they contain what is far more valuable still, the greatest addition which

**dynamical**science had received since the grand strides made by Sir Isaac Newton and Joseph Louis Lagrange.Thus we feel it in its motion as wind, and observe the

**dynamical**effects of this motion in the quiver of the leaf or the motion of a sailing ship. It offers resistance to the passage of bodies through it, destroying their motion and transforming their energy - as is betrayed to our hearing in the whiz of the rifle bullet, to our sight in the flash of the meteor.The true foundations of a mechanical theory of the heavens were laid by Kepler's discoveries, and by Galileo's

**dynamical**demonstrations; its construction was facilitated by the development of mathematical methods.The analytic method sought to express the moon's motion by integrating the differential equations of the

**dynamical**theory.The interdependence of motion and force was not indeed formulated into definite laws by Galileo, but his writings on dynamics are everywhere suggestive of those laws, and his solutions of

**dynamical**problems involve their recognition.At first sight this period seemed to be inconsistent with

**dynamical**theory.These changes arise from two causes - the one statical, the other

**dynamical**.The

**dynamical**causes are atmospheric and oceanic currents.Mayer and Joule, and placed the

**dynamical**theory of heat and the fundamental principle of the conservation of energy in a position to command universal acceptance.According to his usual plan, Kant arranges these principles in conformity with the table of the categories, dividing the four classes, however, into two main groups, the mathematical and the

**dynamical**.The mathematical principles are the abstract expression of the necessary mode in which data of sense are determined by the category in the form of intuitions or representations of objects; the

**dynamical**are the abstract expression of the modes in which the existence of objects of intuition is determined.Under the

**dynamical**principles, the general modes in which the existence of objects are determined, fall the analogies of experience, or general rules according to which the existence of objects in relation to one another can be determined, and the postulates of experience, the general rules according to which the existence of objects for us or our own subjective existence can be determined.Finally, the

**dynamical**aspects of Bose condensation are further investigated by studying the evolution of excited atoms.The algorithm can also include

**dynamical**bosons, again with any number of flavors.In this

**dynamical**process the time delay between infrasonic pulses should reflect the gas nucleation interval of 1-2 s of basaltic magma.This work involves studies of the Hybrid Monte Carlo algorithm for generating

**dynamical**quarks.Dewar led him to see the true

**dynamical**explanation of the Crookes radiometer in the largeness of the free path of the molecule of the highly rarefied air.This was followed, in the second volume of the Miscellanea Taurinensia (1762) by his "Essai d'une nouvelle methode pour determiner les maxima et les minima des formules integrales indefinies," together with the application of this important development of analysis to the solution of several

**dynamical**problems, as well as to the demonstration of the mechanical principle of "least action."With the values above of u, v, w, u', v', w', the equations become of the form p x + 4 7rpAx -Fax -{-hy-}-gz =o, - p - dy+ 4?pBy + hx+ay+fz =o, P d p + TpCZ +f y + yz = o, and integrating p p 1+27rp(Ax2+By2+CZ2) +z ('ax e +ay e + yz2 2 f yz + 2gzx + 2 hx y) = const., (14) so that the surfaces of equal pressure are similar quadric surfaces, which, symmetry and

**dynamical**considerations show, must be coaxial surfaces; and f, g, h vanish, as follows also by algebraical reduction; and 4c2 (c 2 - a2)?It will at once be apparent that the kinetic theory of matter enables us to place the second law of thermodynamics upon a purely

**dynamical**basis.The latter force is, by Maxwell's hypothesis or by the

**dynamical**theory of an aether pervaded by electrons, the same as that which strair s the aether, and may be called the aethereal force; it thereby produces an aethereal electric displacement, say (f,g,h), according to the relation (f,g,h) = (41 r c 2) - 1(P',Q', RI), in which c is a constant belonging to the aether, which turns out to be the velocity of light.