Fundamental Law Of Dynamics Research Articles

Re‐derivation and mathematical analysis for linear peridynamics model for arbitrary Poisson ratio's material

AbstractThis paper is concerned with the modeling and mathematical analysis of linear peridynamic model for arbitrary Poisson ratio's material. Based on the fundamental laws of dynamics, we re‐derive the bond‐based peridynamic model for anisotropic materials by relaxing certain assumptions. Through this process, we draw several significant conclusions, such as the relationship between the equivalent strain energy density hypothesis and the convergence of the peridynamic operator to the classical Navier operator. Additionally, the well‐posedness of time‐dependent peridynamic equations of motion is established. Finally, some necessary conditions for the material stability of anisotropic material are given.

The Decoherent Arrow of Time and the Entanglement Past Hypothesis

If an asymmetry in time does not arise from the fundamental dynamical laws of physics, it may be found in special boundary conditions. The argument normally goes that since thermodynamic entropy in the past is lower than in the future according to the Second Law of Thermodynamics, then tracing this back to the time around the Big Bang means the universe must have started off in a state of very low thermodynamic entropy: the Thermodynamic Past Hypothesis. In this paper, we consider another boundary condition that plays a similar role, but for the decoherent arrow of time, i.e. the subsystems of the universe are more mixed in the future than in the past. According to what we call the Entanglement Past Hypothesis, the initial quantum state of the universe had very low entanglement entropy. We clarify the content of the Entanglement Past Hypothesis, compare it with the Thermodynamic Past Hypothesis, and identify some challenges and open questions for future research.

Spontaneous Collapse Theories and Temporal Primitivism about Time’s Direction

Two views on the direction of time can be distinguished—primitivism and non-primitivism. According to the former, time’s direction is an in-built, fundamental property of the physical world. According to the latter, time’s direction is a derivative property of a fundamentally directionless reality. In the literature, non-primitivism has been widely supported since most (if not all) our fundamental dynamical laws are time-reversal invariant. In this paper, I offer a way out to the primitivist. I argue that we do have good grounds to support a primitive direction of time in the quantum realm. The rationale depends on exploiting the metaphysical and dynamical underdetermination of quantum theories to make a case in favor of primitivism. In particular, primitivism can be grounded in spontaneous collapse theories (e.g., GRW and CSL). The specific sense in which these theories capture a primitive direction of time is that, when the ontology of the theory is seriously taken into account, it does not remain invariant under time reversal. In taking GRW with a matter-density field (GRWm), I will argue that primitivism about the direction of time can be defended in the quantum case.

Time's arrow and self‐locating probability

AbstractOne of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low‐entropy state. Unfortunately, in a universe where there are many copies of us (in the distant “past” or the distant “future”), the Past Hypothesis is not enough; we also need to postulate self‐locating (de se) probabilities. However, I show that we can similarly use self‐locating probabilities to strengthen its rival—the Fluctuation Hypothesis, leading to in‐principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to ‘empirical coherence’ or ‘simplicity.’ That is a serious problem for the vision of providing a completely scientific explanation of time's arrow.

The equations of Lagrange for a continuous deformable body with rigid body degrees of freedom, written in a momentum based formulation

The present paper is concerned with Lagrange׳s Equations, applied to a deformable body in the presence of rigid body degrees of freedom. The Lagrange description of Continuum Mechanics is used. An exact version of the Equations is derived first. This version, which represents an identical extension of the Fundamental Law of Dynamics, does involve the idea of virtual motions. The virtual motion is described in the framework of the Ritz-Ansatz, but our derivation does not make use of D׳Alemberts principle, the principle of virtual work, or variational principles. From the exact version, by involving arguments related to the Galerkin approximation technique, we derive an approximate Ritz type version of Lagrange׳s Equations. This approximate version coincides with the traditional one, which is based on the notion of kinetic energy. However, since our derivation stems from the Fundamental Law of Dynamics, we have at our disposal an alternative formulation, which is based on the notion of local momentum. This momentum based version, which is the main topic of the present contribution, can be used for the purpose of performing independent checks of the energy based version of Lagrange׳s Equations. The momentum based version also clarifies that and how certain terms in the energy based version do cancel out. The momentum based version is worked out in the framework of the Floating Frame of Reference Formulation of Multibody Dynamics. Explicit formulas for the single terms of Lagrange׳s Equations are derived for the translational, rotational and flexible degrees of freedom of the deformable body, respectively. Corresponding Lagrange׳s Equations are explained in the light of the relations of Balance of Total Momentum, Balance of Total Moment of Momentum, of the Mean Stress Theorem and the notion of Virial of Forces. An embedding into the literature is given.

The emergence of time's arrows and special science laws from physics

In this paper, I will argue that there is an important connection between two questions concerning how certain features of the macro world emerge from the laws and processes of fundamental microphysics and suggest an approach to answering these questions. The approach involves a kind of emergence but quite different from 'top-down' emergence discussed at the conference, for which an earlier version of this paper was written. The two questions are (i) How do 'the arrows of time' emerge from microphysics? (ii) How do macroscopic special science laws and causation emerge from microphysics? Answering these questions is especially urgent for those, who like myself, think that a certain version of physicalism, which I call 'micro-physical completeness' (MC), is true. According to MC, there are fundamental dynamical laws that completely govern (deterministically or probabilistically), the evolution of all micro-physical events and there are no additional ontologically independent dynamical or causal special science laws. In other words, there is no ontologically independent 'top-down' causation. Of course, MC does not imply that physicists now or ever will know or propose the complete laws of physics. Or even if the complete laws were known we would know how special science properties and laws reduce to laws and properties of fundamental physics. Rather, MC is a contingent metaphysical claim about the laws of our world. After a discussion of the two questions, I will argue the key to showing how it is possible for the arrows of time and the special science laws to emerge from microphysics and a certain account of how thermodynamics is related to fundamental dynamical laws.

The Metaphysics Within Physics - Tim Maudlin

This is a slim, lively volume, packed with intriguing argument, a collation of thematically unified essays composed over a number of years. It will, I think, be read by many with interest, profit and surprise, in gently varying proportion. The general theme is a call for metaphysical discussions to engage more realistically and more substantively with what our fundamental physical theories have to say about what the world is like; the doctrine – or hypothesis? – of Humean supervenience is one metaphysical position which particularly comes in for stick. The general theme is certainly a timely one (vide the recent book by Ladyman and Ross), as is the more specific target of Humean supervenience (e.g., recent papers by Jeremy Butterfield). The first chapter, ‘Fundamental Laws of Temporal Evolution’, argues for primitivism about laws of nature. Following the practice of physics, we should not seek to explain fundamental dynamical laws in terms of anything else. There follows a straightforward and appealing proposal for how counterfactuals should then be understood on the back of laws. Ch. 5 picks up this theme again and argues that rather than analysing causation in terms of counterfactuals (or vice versa), both should be explained in terms of laws.

Simulation of Surface Mesh Deformation in Orthodontics by Mass-Spring Model

The mass-spring model has been used to describe elastically deformable models such as skin, textiles, and soft tissue in computer graphics. A mass-spring mesh is composed of a network of masses and springs, in which each edge is a spring. We apply the mass spring system to mesh deformation in 3D orthodontic simulation, the movement of which is evaluated using the numerical integration of the fundamental law of dynamics based on the 4th-order Runge-Kutta method. Computational quantity and accuracy is demonstrated on test and dental cast model examples. The experimental results show that it can simulate the deformation change in real time and display the results vividly.

Physical modeling for underwater flexible systems dynamic simulation

Fishing gear systems and aquaculture facilities are generally considered as a flexible system in which many mass points are connected with elastic lines. A physically based calculation model to simulate the flexible structures' behavior is presented in order to understand the movements and design an appropriate system. The flexible system described is composed of a network of masses and springs, the behavior of which is calculated using the implicit integration method of the fundamental law of dynamics. This method offers low computational times and a stable solution. Also, this paper is characterized by automatic modeling methods using a computer graphic user interface and application examples on the netting and fishing gear system behaviors.

Are There Dynamical Laws

The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to a final state then depends on the quantum geometry that is determined by symmetries, which may exist as relations between states in the absence of dynamical laws. This enables the experimentally well-confirmed quantum probabilities to be derived from the geometry of Hilbert space and gives rise to effective probabilistic laws. An arrow of time which is consistent with the one given by the second law of thermodynamics, regarded as an effective law, is obtained. Symmetries are used as the basis for a new proposed paradigm of physics. This naturally gives rise to the gravitational and gauge fields from the symmetry group of the standard model and a general procedure for obtaining interactions from any symmetry group.

The second law of thermodynamics: entropy, irreversibility and dynamics

Irreversibility is at once a profound and an elusive concept. We are all aware of the directed, irreversible arrow of time which dominates our own existence. Until recently, however, it had been thought that the fundamental dynamical laws were incompatible with the objective existence of the irreversible processes that thermodynamics purports to describe.

Pattern recognition in molecular quantum mechanics

It is shown that the classical concept of an open system does not encompass quantal systems but has to be replaced by the non-Boolean notion of an entangled system. Molecular, chemical, or biological phenomena can be considered to be reduced to a fundamental theory like quantum mechanics only if the fundamental and the phenomenological theories are formally and interpretatively connected, and if the classifications used in the empirical sciences are shown to follow from a single set of fundamental dynamical laws. These conditions enforce a non-statistical and ontic interpretation of quantum mechanics, hence a non-Boolean calculus of propositions. In this interpretation the notion of a world state is well-defined, its Schmidt-decomposition defines a background-dependent model state for molecular systems and creates the phenomena we can observe. To any molecular system there is associated in an objective way a nonnegative number which we call the integrity. The integrity measures the inherent fuzziness of the system concept in a holistic theory, and is used to define recognizable molecular patterns.

Effects of Major Seismic Events on the Rotation of the Earth

S-Y A spherical theory is advanced for perturbations of the Earth‘s rotation by major earthquakes and explosions. Explicit expressions are obtained for the dependence of the secular polar shift on the dimensions, depth, and location of the seismic event. Numerical results show that a single shallow earthquake of magnitude 8.5, occurring at a suitable latitude and with a favourable strike-azimuth, may suffice to maintain the Chandler wobble for about one year. Hence, it is deduced that earthquakes may at most 8ccouIlt for 30 per cent of the observed secular polar shift. 1. Introdoction The equations of rigid gyroscopic motion were given by Euler in 1758. On the basis of this theory, he suggested in 1765 that the Earth might undergo a free precession with period of A/(C-A) sideral days. Assuming this to be true, a spectator partaking in the Earth’s motion should observe periodic changes in latitude with a period of about 10 months. However, no such period could be found. Instead, Chandler established in 1891 the existence of a 428-days period in the spectrum of the latitude variation. The lengthening of the period was explained by Newcomb, in 1892, to be the result of the Earth’s elasticity. A theoretical veriiication was given by Love (1909), based on first-order theory of the figure of the Earth. This 14-month precessional motion of the instantaneous axis of rotation about the Earth’s axis of figure is known today as the Chandler Wobble. (Fig. 1.) Spectral analyses of latitude time series disclosed that the motion is damped with a ‘ Q ’ value between 30 and 40. The wobble must therefore be maintained by a certain source of energy. Munk & Macdonald (1960, p. 174) conclude that: ‘The statistical properties of the latitude time series are those associated with a damped oscillator excited at random. . . . Irregular variations of the atmosphere are the most likely cause of the wobble.’ Recently, however, observational evidence has been presented in support of the hypothesis that earthquakes may excite the wobble and produce the observed polar shift. To explain these arguments we shall recapitulate the theoretical background of the subject: The fundamental law of dynamics as experienced by earth-bound spectators is given by the Liouville equation (Munk & Macdonald 1960)

Dynamics of Compressible Saturated Two-Phase Flow : Critical Flow-sequel, and Flow in a Pipe

Improving the analysis of the author's previous report on a few points of importance, an exact analysis based on fundamental laws of dynamics and thermodynamics is accomplished on a simple but clearly defined model of compressible saturated two-phase flow. As the result, fundamental matters such as the behavior of energy within the two phases, the change of phase, the change of entropy, the variation of pressure near the exit of pipe in critical flow and others are clarified with physical distinctness. Besides, numerical computation is carried out for critical flow of the model afore-mentioned in case of water / steam system, and the results are presented. Distinction between critical flow with evaporation and that with condensation has an important effect on the analysis.

Chapter 4. Quantum Mechanical Approach to the Composite Model of Elementary Particles

The structure of composite particles seem to be intimately connected with the nature of more fundamental dynamical laws which will reveal themselves beyond the limit of applicability of the point model. A general formulism for treating the Sakata model by means of quantum field theory is constructed and several consequences are derived, bearing in mind that the theory applied to the present model would have a physical reliability only in the corresponding- theoretical sense. (W.D.M.)

Application of Similarity Principles to Thermal Transport Systems

THE use of similarity laws is well established for mechanical transport systems, that is, systems in which the dependent variable (A) is the flow or transport of matter. Examples of dimensionless numbers (B) used in such systems are the Froude number for mechanical systems depending solely upon the action of gravity, the Reynolds number (Re) for mechanical systems depending upon the action of viscosity, and the number introduced by Davis1 for systems depending upon the action of density changes in hot gases. Although heat transfer is involved in the last of these three examples, it is really a mechanical system, since the heat is conveyed by the mechanical motion of the fluid concerned. The applicability of model results expressed in the form A = f(B) to the original system is based upon the fact that the motion of any element of the fluid obeys the fundamental law of dynamics, p = mf, even though the integration of this law for the three dimensional extended system is too complex for mathematical treatment.

An analysis of the electromagnetic field into moving elements

Introduction and Summary .—In Maxwell’s equations of the electromagnetic field, ∂e/∂t ═ curl h ( a ) ∂h/∂t ═ — curl e ( b ) div e ═ 0, div h ═ 0 ( c,d )} the properties of the field, in regions containing no charges, are described in terms of two vectors, e and h, which in the general case may have arbitrary magnitudes and directions at any given point of space and time. Although e and h are the quantities most closely related to experiment, they are not the only ones in terms of which the field can be described. The description can in fact be given in terms of any definite functions of e and h by making the appropriate substitutions in (1). The equations obtained by such a transformation cannot of course describe properties of the field which are not ultimately implied in Maxwell’s equations; they may nevertheless lend themselves more readily to determining what these properties are. It is shown in this paper that this is the case with a certain transformation in which, instead of in terms of e and h, vectors making an arbitrary angle with each other, the equations are expressed in terms of two vectors, R and u, at right angles to each other, and of a scalar function of position, α. The equations obtained reveal that the most general electromagnetic field in regions not containing charges can be represented by a vector R of invariant magnitude, the lines of which at each point are in motion at right angles to themselves with a definite velocity u relatively to the observer. They show further that small moving elements of the field can be constructed which can be regarded as keeping their identities permanently as they move. The movement of these elements takes place under the action of a simple form of stress in accordance with the fundamental laws of dynamics. In addition to their translatory motions and independent of them, the elements exhibit in the general case co-ordinated rotational movements. By their translatory and rotary movements, and the changes of shape which result from them, they fix definitely the local time rates of change of the field. In fact every property of the field can be specified directly in terms of these moving and rotating elements. A field element is a space section constructed in a natural way from, the four dimensional entity which constitutes the field in space-time. Considered in space-time as a four dimensional element, it appears as an element of action , and it is a result of the analysis that the general electromagnetic field can always be divided in a natural way into such elementary units of action. The properties which characterise them are of a kind which suggests and is consistent with the possibility that both field elements and the corresponding elements of action may have a finite magnitude in the field.

The Fundamental Axioms of Dynamics

As Prof. Lodge refers in the letter published in this week's NATURE, p. 101, to my remarks on his paper on the Fundamental Axiom of Dynamics, I shall be obliged if you will allow me to state my views in your columns. Apart from all minor questions it appears to me that the main issue raised by Prof. Lodge is whether the law of the conservation of energy can be proved from the fundamental laws of dynamics and the assumption of contact action.