Showing papers on "Conservation law published in 1973"

Conservation Laws and Energy-Release Rates

Abstract: New path-independent integrals recently discovered by Knowles and Sternberg are related to energy-release rates associated with cavity or crack rotation and expansion. Complex-variable forms are presented for the conservation laws in the cases of linear, isotropic, plane elasticity. A special point concerning plastic stress distributions around cracks is discussed briefly.

Double charge transfer spectroscopy of diatomic molecules

Abstract: Translational energy spectra of H- ions arising from single- and double-collision double charge transfer of 4 keV protons on N2, O2 and NO have been measured. The energy values of some double ionized states of these molecules were determined. The spin conservation rule is shown to hold strictly for these processes. Approximate selection rules bearing on the symmetry of the involved states are proposed and used for the discussion of the results.

On an asymptotic solution of the Korteweg–de Vries equation with slowly varying coefficients

Abstract: The variable-coefficient Korteweg–de Vries equation \[ H_X + {\textstyle\frac{3}{2}}d^{-\frac{7}{4}}HH_{\xi} + {\textstyle\frac{1}{6}}\kappa d^{\frac{1}{2}}H_{\xi\xi\xi} = 0 \] with d = d (e X ) is discussed for solitary-wave initial profiles. A straightforward asymptotic solution for e → 0 is constructed and is shown to be non-uniform both ahead of and behind the solitary wave. The behaviour ahead is rectified by matching to the appropriate exponential form and, together with the use of conservation laws for the equation, the nature of the solution behind the solitary wave is discussed. This leads to the formulation of the solution in the oscillatory ‘tail’, which is again matched directly. The results are applied to the development of the solitary wave into variable-depth water, and the predictions are compared with those obtained, for example, by Grimshaw (1970, 1971). Finally, the asymptotic behaviour of both the solitary wave and the oscillatory tail are assessed in the light of some numerical integrations of the equation.

Classical Electromagnetic Interaction of a Charged Particle with a Constant-Current Solenoid

Abstract: The classical electromagnetic interaction for a charged particle with a long, constant-current solenoid is investigated in the context of classical electromagnetism. The conservation laws connected with energy, linear momentum, and angular momentum are first verified. Then the changes in the electromagnetic field quantities are evaluated explicitly, and the values are seen to have interesting connections with the solenoid vector potential. The calculations are of interest in connection with the Aharonov-Bohm effect involving the passage of electrons past a solenoid, and the classical expressions for energy and momentum are reminiscent of terms in the quantum-mechanical calculations.

Remark on Baryon Conservation

Abstract: The Higgs mechanism can serve to implement baryon conservation via an extension of the local weak-electromagnetic gauge group by a local factor U(1) without conflict with the E\"otv\"os experiments.

Generalization of Hamilton's principle to continuous dissipative systems

Abstract: Some variational principles describing the behavior of nonstationary dissipative processes are presented. These criteria appear as an extension of Hamilton's principle to dissipative systems. Firstly, processes with vanishing barycentric velocity, i.e., of purely dissipative nature, are considered. The principle proposed is a slight modification of a criterion derived previously by the authors: The central quantity in the expression of the principle is however no longer the Legendre transform of the entropy per unit mass but is here the Legendre transform of the internal energy per unit volume. As an illustrative example, thermodiffusion is considered. Afterwards, the principle is generalized to describe the flow of a compressible, Newtonian fluid in which temperature effects are not neglected. After having shown that the Euler‐Lagrange equations are equivalent to the conservation laws, some particular expressions of the principle, corresponding to special situations like the stationary case and fixed boundary conditions, are given.

On steady wave profiles in solids

Abstract: A presentation is given of a new and novel way of expressing the three conservation laws of mass, linear momentum and energy in terms of specific volume and time as the independent variables. This choice of coordinates appears to be fundamental to the description of shock wave propagation in solids. From these equations the following result is derived : the strain derivative of the total stress in an arbitrary dissipative medium plays the same role in the propagation of a density profile as does the strain derivative in isentropic flow, provided the density profile is near to the steady profile. An analysis is presented of the development of arbitrary profiles into the steady wave. The paper concludes with a linearized stability analysis of the steady wave profile for a material with a special form of equation of state. This analysis shows that the steady profile is asymptotically stable.

The conservative “flow” method and the calculation of the flow of a viscous heat-conducting gas past a body of finite size

Abstract: A METHOD for the numerical solution of gas dynamical problems, based on a difference approximation of the conservation laws, is presented. Examples of calculations of the flow past a body of finite size are given. This paper presents a numerical method, based on a difference approximation of the conservation laws, recorded for each cell of the difference grid. In the field variables the method generates an explicit difference scheme which, as is shown by calculations and studies of a model example, is conditionally stable and monotonic. From the method of construction, the scheme is conservative with respect to mass, the momentum components and the total energy. The method is used to calculate the flow past a sphere of a viscous, heat conducting gas at a given surface temperature. Various formulations of this problem have been considered in [1–3]. In [1] the “shortened” Navier—Stokes equations were solved by the method of integral ratios; in [2] a numerical solution of the complete Navier—Stokes equations was found by a finite-difference method. In [3] the method of integral ratios was also used for the complete system of Navier-Stokes equations.

Critique of fluid theory of magnetospheric phenomena

Abstract: It is pointed out that the fluid theory has been successful in magnetospheric problems (such as the shape of the magnetopause) which involve basic considerations such as the conservation of particles, of momentum, and of energy, but that it is inadequate for other problems (such as the energization of auroral particles). Difficulties arise from the fact that it is not always possible to specify ‘a volume of plasma’ because particles do not remain as neighbours. Misuse of the fluid theory has led to a number of fallacies, such as the idea that the causal order of physical events in cosmic electrodynamics is the reverse of that in the familiar laboratory electrodynamics. This mistaken idea comes from a confusion of a mathematical sequence of calculations with the causal order. Also, the importance of the magnetic field as an active element is over-emphasized. Appreciation of the fact that kinetic theory is the more fundamental seems to be widely lacking. A plea is made for a common sense approach to magnetospheric and auroral problems wherein the fluid theory is used whenever it can, but where it is not expected to be adequate for all purposes.

Theorems on symmetries and flux conservation in radiative transfer using the matrix operator theory.

Abstract: The matrix operator approach to radiative transfer is shown to be a very powerful technique in establishing symmetry relations for multiple scattering in inhomogeneous atmospheres. Symmetries are derived for the reflection and transmission operators using only the symmetry of the phase function. These results will mean large savings in computer time and storage for performing calculations for realistic planetary atmospheres using this method. The results have also been extended to establish a condition on the reflection matrix of a boundary in order to preserve reciprocity. Finally energy conservation is rigorously proven for conservative scattering in inhomogeneous atmospheres.

A study of the global solutions for quasi-linear hyperbolic systems of conservation laws

Abstract: The present paper is divided into two parts. In Part 1 we deal with a special initial value problem of the gas dynamics system with initial values more general than those in [6]. In this paper we shall prove the existence theorem in the large, the invariability with respeet to t of the properties of the initial values. Moreover, we have studied some properties of the solutions. For example, suppose that the Riemann problem with initial values (u_0(±∞), v_0(±∞)) contains a forward shock wave, then the solution must contain a forward shock wave. The interactions of the shock and rarefaction wave of the same direction are special eases of our initial value problems. In Part 2 we extend the main results of Part 1 to the systems studied in [7].

Mathematical formulation of the laws of conservation of mass and energy and the equation of motion for a moving thread

Abstract: The general mathematical formulation of the laws of conservation of mass and energy and the equation of motion are derived for a moving thread. Within the thread only forces in tangential direction are considered: internal stresses perpendicular to the tangential direction are left out of consideration. The equations as formulated here can easily be applied to many problems in the various stages of fibre processing.

Higher Order Accuracy Finite Difference Algorithms for Quasi-Linear, Conservation Law Hyperbolic Systems*

Abstract: An explicit algorithm that yields finite difference schemes of any desired order of accuracy for solving quasi-linear hyperbolic systems of partial differential equations in several space dimensions is presented. These schemes are shown to be stable under certain conditions. The stability conditions in the one-dimensional case are derived for any order of accuracy. Analytic stability proofs for two and d (d > 2) space dimensions are also ob- tained up to and including third order accuracy. A conjecture is submitted for the highest accuracy schemes in the multi-dimensional cases. Numerical examples show that the above schemes have the stipulated accuracy and stability.

Apparent Loss of Angular Momentum in the Earth–Moon System

Abstract: PANNELLA1,2 and others3,4 have presented palaeontological counts of the number of days per solar year (N) and per synodic month (n) during geologic time. This method is based on the cyclic growth increments of various fossils and has been confirmed in their modern counterparts1,5. The observations extend back to 1.7 × 109 yr with some incomplete data to 2.8 × 109 yr.

Derivation of general conservation laws and Ward--Takahashi identities in the functional integration method

Abstract: The functional integration method is applied to derive Ward-Takahashi identities involving the energy-momentum tensor, currents, and fields. In the process of the derivation, we have introduced a variational method to derive conservation laws, in which the improved energy-momentum tensor of Callan, Coleman, and Jackiw is obtained. Establishing the correspondence between the c- number relations obtained in the functional integration method and the q-number ones resulting from the conventional way, we demonstrated that the two approaches of quantum field theory give identical results for the perturbation expansion, canonical equal-time commutation relations, etc. They are, therefore, equivalent. (auth)

Properties of inclusive reactions in a unitarized dual model of production amplitudes

Abstract: Inclusive cross-sections are studied in the planar dual model by first constructing a unitarized set of production amplitudes. Total cross-sections, and single- and many-particle spectra are then constructed, and conservation laws are imposed through a set of sum rules. A weak form of the Harari-Freund conjecture for total cross-sections is derived and is easily generalized to single- (and many-) particle spectra. A large number of predictions is obtained for single-particle spectra, many of which are capable of experimental verification. Inclusive experiments on deuterium targets are urged in order to provide a crucial test of the model. Using a stronger form of the Harari-Freund conjecture as an input, we obtain predictions for the way single-particle spectra approach scaling. Criteria for early scaling, and for rising and falling inclusive cross-sections, are discussed in detail. Diffraction dissociation is included in a very natural way. Effects of interference terms, cuts and absorption are briefly discussed, and it is argued that they cannot change the general results discussed in this paper.

Investigation of laminar flow in a porous pipe with variable wall suction

Abstract: An analytical model has been developed to provide an analogy for and predict flow property distributions in the condensing regions of a heat pipe. The model incorporates the phenomenon of incompressibl e, steady, laminar flow through a uniformly-poro us-wall pipe with a closed end-wall. A Karman-Pohlhau sen momentum integral technique was employed to reduce the axisymmetric Navier-Stokes equation to a nonlinear second-order ordinary differential equation. The axial pressure gradient, suction velocity at the porous wall, and wall friction coefficient were computed over a range of Reynolds numbers and wall permeabilities. These flow property distributions were not constrained a priori, but were allowed to vary in accordance with the conservation laws. The calculated flow property distributions for the condenser region of the heat pipe model are compared with published experimental data and several other theoretical models cited in the literature.