Showing papers on "Conservation law published in 1971"
TL;DR: If the additional conserved quantity is a convex function of the original ones, the original system can be put into symmetric hyperbolic form and an entropy inequality is derived.
Abstract: We discuss first-order systems of nonlinear conservation laws which have as a consequence an additional conservation law. We show that if the additional conserved quantity is a convex function of the original ones, the original system can be put into symmetric hyperbolic form. Next we derive an entropy inequality, which has also been suggested by I. Kružhkov, for discontinuous solutions of the given system of conservation laws.
609 citations
TL;DR: In this paper, the conservation laws of nonlocal continuum mechanics are derived from the conservation of energy and the invariance conditions under superposed rigid body motions, and the theory of non-local thermoelasticity is reconsidered in the light of recent developments in thermodynamics.
Abstract: : It is shown in this paper that the conservation laws of nonlocal continuum mechanics are equivalent to, and can be derived from, the conservation of energy and the invariance conditions under superposed rigid body motions. Also, the theory of nonlocal thermoelasticity is reconsidered in the light of recent developments in thermodynamics, taking invariance conditions fully into account. (Author)
182 citations
TL;DR: In this paper, it is shown that in the limit of vanishing electron mass m transitions forbidden by γ 5 invariance give a non-vanishing contribution to the imaginary part of the triangle graph.
131 citations
TL;DR: In this paper, the authors proposed a new Lorentz-Dirac equation of motion for a charge, which conserves energy and momentum in a modified form in which the energy-momentum tensor contains a part made of a new field-charge interaction.
Abstract: With the intuitive new ideas that (1) in classical electrodynamics, radiation reaction should be expressible by the external field and the charge's kinematics, (2) a charge experiences, in addition to the Lorentz forces, another "small" external force e_1F^(μλ)u_λ proportional to its acceleration, and (3) inertia plus radiation is balanced by these two external forces, we propose the new equation of motion,
mu^μ − ((2e^3)/3m)F^(λα)_(ext)u_λu_αu^μ = eF^(μλ)_(ext)u_λ + e_1F^(μλ)_(ext)u_λ, where mass conservation requires e_1 = (2e^3)/3m. (The particle's spin is not considered in this work.) This equation for a classical charge is free from all the well-known difficulties of the Lorentz-Dirac equation. It conserves energy and momentum in a modified form in which the energy-momentum tensor contains a part t^(μν)(x) made of a new field-charge interaction
φ^μ(x), in addition to the conventional "local" part made of
F^(μν)_(ret)(x) and F^(μν)_(ext)(x) only, and therefore it no longer satisfies the conventional "local" conservation laws. It predicts correct radiation damping, as demonstrated here by applying it to various cases of basic physical importance. Also, it implies that a massless particle follows a null geodesic and cannot interact with the electromagnetic field whether it be charged or not; this implication may add a new degree of freedom to the charge-conservation law.
73 citations
TL;DR: The importance of considering non-invariant Lagrangians and the associated conservation laws is illustrated by several examples: energy conservation, Galilean invariance, dynamical symmetries (harmonic oscillator and Kepler's problem), motion in a uniform electric field as discussed by the authors.
Abstract: When a physical system has some symmetry properties, it is described by equations of motion invariant under the corresponding transformation group. Its Lagrangian however need not be invariant and may be “gauge-variant,” that is, vary by the addition of a total time derivative. A slightly generalized form of Noether's theorem nevertheless exists in such cases, still leading to conservation laws. The importance of considering such noninvariant Lagrangians and the associated conservation laws is illustrated by several examples: energy conservation, Galilean invariance, dynamical symmetries (harmonic oscillator and Kepler's problem), motion in a uniform electric field.
69 citations
TL;DR: Lorentz invariant theory for relativistic gravity testing, deriving conservation laws and parameter constraints from parametrized post-Newtonian equations of motion, is presented in this paper.
Abstract: Lorentz invariant theory for relativistic gravity testing, deriving conservation laws and parameter constraints from parametrized post-Newtonian equations of motion
62 citations
TL;DR: In this article, the authors used linear response theory to derive generalized nonlocal macroscopic equations which descibe the free relaxation of a system initially constrained to be in a state not far from its unperturbed equilibrium state.
45 citations
TL;DR: In this article, the equilibrium and nonequilibrium statistical mechanics of a two-dimensional plasma in a uniform dc magnetic field are investigated, where the charges are assumed to interact only through electrostatic potentials.
Abstract: Several features of the equilibrium and nonequilibrium statistical mechanics of a two-dimensional plasma in a uniform dc magnetic field are investigated. The charges are assumed to interact only through electrostatic potentials. The problem is considered both with and without the guiding-center approximation. With the guiding-center approximation, an appropriate Liouville equation and BBGKY hierarchy predict no approach to thermal equilibrium for the spatially uniform case. For the spatially nonuniform situation, a guiding-center Vlasov equation is discussed and solved in special cases. For the nonequilibrium, nonguiding-center case, a Boltzmann equation, and a Fokker-Planck equation are derived in the appropriate limits. The latter is more tractable than the former, and can be shown to obey conservation laws and an H-theorem, but contains a divergent integral which must be cut off on physical grounds. Several unsolved problems are posed.
35 citations
24 citations
01 Jan 1971
TL;DR: Newton's mechanics of point particles has served as a model of physical theory for two centuries as mentioned in this paper, and this particular form of Newtonian mechanics is invariant under a ten-parameter group, the inhomogeneous Galilei group, and possesses ten integrals which are algebraic functions of the positions and velocities.
Abstract: Newton’s mechanics of point particles has served as a model of physical theory for two centuries. In its usual formulation, the forces considered are two-body forces depending on the mutual separation of the particles at the same time. The third law implies that these forces are derivable from a potential also depending only on this separation, which allows a Lagrangean formulation of the theory. As was gradually recognized during the past century, this particular form of Newtonian mechanics is invariant under a ten-parameter group, the inhomogeneous Galilei group [1], and possesses ten integrals which are algebraic functions of the positions and velocities; one of these corresponds to the conservation of energy, three to the conservation of linear momentum, three to the conservation of angular momentum, and three express the uniform motion of the center of mass.
21 citations
TL;DR: In this paper, a conservation law is derived in nonrelativistic mechanics with a homogeneous potential and the virial theorem is an immediate consequence of this conservation law, which can also be applied to the relativistic Coulomb problem.
Abstract: As a consequence of scale invariance, a conservation law is derived in nonrelativistic mechanics with a homogeneous potential. The virial theorem is an immediate consequence of this conservation law. A slightly different scale transformation is then presented, which yields the same conservation law but which can also be applied to the relativistic Coulomb problem. Finally, both the conservation law and the virial theorem are derived for relativistic two-body theory in the Wheeler-Feynman formalism, where they provide a generalization of the expression for the energy of a two-body system with circular orbits.
TL;DR: In this paper, it was shown that for quasi-linear hyperbolic systems of the conservation form W sub t = -(F sub x) = -A(W sub x), it is possible to build up relatively simple finite difference numerical schemes accurate to 3rd and 4th order provided that the matrix A satisfies commutativity relations with its partial-derivative-matrices.
Abstract: : It is shown that for quasi-linear hyperbolic systems of the conservation form W sub t = -(F sub x) = -A(W sub x), it is possible to build up relatively simple finite difference numerical schemes accurate to 3rd and 4th order provided that the matrix A satisfies commutativity relations with its partial-derivative-matrices. This requirement is not fulfilled by any known physical systems of equations. These schemes generalize the Lax-Wendroff 2nd order one, and are written down explicitly. As found by Strang, odd order schemes are linearly unstable unless modified by adding a term containing the next higher space derivative. Thus stabilized, the schemes, both odd and even, can be made to meet the C.F.L. (Courant-Friedrichs-Lewy) criterion. Numerical calculations were made with a 3rd order and a 4th order scheme for scalar equations with continuous and discontinuous solutions. The results are compared with analytic solutions and the predicted improvement is verified.
CERN1
TL;DR: In this article, sum rules for n -particle distributions are obtained resulting from energy-momentum conservation, which imply an average limiting behavior for single particle distributions and average factorization for n-particle distribution.
TL;DR: In this article, it was shown from a study of 16 GeV/c pp interactions that helicity cannot in general be conserved in the s-channel for pπ+π− systems produced diffractively and with spin-charge ΔJ ⩾ 1.6 GeV.
CERN1
TL;DR: In this paper, the behavior of π-nucleon and πΔ (1238) systems produced diffractively in high energy πp and Kp collisions is analyzed under the assumption of helicity conservation and parity rule ΔP = (−1)ΔJ.
TL;DR: The results established in the first series of this series of papers are then used to obtain necessary and sufficient conditions that a collection of vector fields generate weak coordinate or point invariance of a nonlocal functional relative to a given function in the domain of definition of the functional as mentioned in this paper.
TL;DR: In this paper, the authors considered Physically-based deterministic models, in which the models have a theoretical structure based primarily on the laws of conservation of mass, energy, or momentum.
Abstract: Physically-based, deterministic models, are considered in this paper. Physically-based, in that the models have a theoretical structure based primarily on the laws of conservation of mass, energy, or momentum; deterministic in the sense that when initial and boundary conditions and inputs are specified, the output is known with certainty. This type of model attempts to describe the structure of a particular hydrologic process and is therefore helpful in predicting what will happen when some change occurs in the system.
TL;DR: In this article, necessary and sufficient conditions are obtained in order that a collection of vector fields generate strong point and coordinate invariance transformations for functionals of functionals such vector fields are shown to lead to pointwise laws of balance and to global laws of conservation.
TL;DR: The first in a series of four papers dealing with the extensions of the Noether theorems on invariance and conservation laws to the nonlocal calculus of variations is.
TL;DR: The role of invariance considerations in conventional formulations of Noether's theorem in classical field theory is investigated and found weaker than is usually supposed in this article, where it is shown how nonfulfilment of the conventional assumptions going into Noethers theorem brings about nonconservation.
Abstract: The role of invariance considerations in conventional formulations of Noether's theorem in classical field theory is investigated and found weaker than is usually supposed. It is shown how nonfulfilment of the conventional assumptions going into Noether's theorem brings about nonconservation.
TL;DR: In this paper, the general form of covariant helicity-conserving couplings and their relation to the stress-tensor were discussed, and the relation between the two was discussed.
TL;DR: In this article, a new first-flight collision probability that takes into account the effect of the anisotropic scattering in the moderator is derived in a cylindrical cell under the condition that all neutrons impinging on the cell boundary should reflect with isotropic distribution back into the original cell.
Abstract: A new first-flight collision probability that takes into account the effect of the anisotropic scattering in the moderator is derived in a cylindrical cell. This probability is obtained by expanding the scattering kernel, angular flux and angular source into spherical harmonics series and retaining the first two terms in the integral Boltzmann equation. Making use of a new reciprocity relation and the conservation law, we introduce the probability relevant to a lattice cell under the condition that all neutrons impinging on the cell boundary should reflect with isotropic distribution back into the original cell. This probability also satisfies both the usual reciprocity theorem and the conservation law. Though we have here treated only a 2-medium problem, the method can be easily extended to the problem of a cell containing many regions. As an example of application, we calculate the flux ratios in a two region cell by one-group theory and the neutron spectra in fuel and moderator using the Fermi-age kern...
TL;DR: In this paper, it was shown that at 8.25 GeV/c, the reaction K − p→Q − p →p(K − K − π + π − ) at 8,25 GeVs/c favours t -channel helicity conservation over s -channel conservation.
CERN1
TL;DR: In this paper, the influence of s channel quantum numbers on inclusive distributions is investigated, and the way chosen by nature to enforce charge conservation is proposed as a test for production models.
TL;DR: In this paper, the semiclassical method for calculating collision induced vibrational transitions in diatomic molecules is extended to account for conservation of energy, and asymmetric distortions of the collision perturbation are found to have little effect on the transition probability.
Abstract: The semiclassical method for calculating collision induced vibrational transitions in diatomic molecules is extended to account for conservation of energy. Asymmetric distortions of the collision perturbation are found to have little effect on the transition probability, but symmetric distortions, associated with energy transiently stored in vibrational modes at the collision turning point, decrease the transition probability by factors of about 1.5 to 2. This correction does not significantly change the interaction potentials deduced from vibrational relaxation data.