Showing papers on "Conservation law published in 1975"

Relationships among Inverse Method, Bäcklund Transformation and an Infinite Number of Conservation Laws

Abstract: It is shown that inverse method, Backlund transformation and an infinite number of conservation laws are closely related. The derivation of Backlund transformation from the fundamental equations of inverse method is explicitly shown. Also it is shown that conser· vation la~ is obtained in a simple way from the. Riccati form of inverse method and the derivation of conservation law from Backlund transformation is possible.

An introduction to invariant imbedding

Abstract: 1. Fundamental Concepts 2. Additional Illustrations of the Invariant Imbedding Method 3. Functional Equations and Related Matters 4. Existence, Uniqueness, and Conservation Relations 5. Random Walk 6. Wave Propagation 7. Time-Dependent Problems 8. The Calculation of Eigenvalues for Sturm-Liouville Type Systems 9. Schrodinger-Like Equations 10. Applications to Equations with Periodic Coefficients 11. Transport Theory and Radiative Transfer 12. Integral Equations Author index Subject index.

Evidence for Delta S = - Delta Q Currents or Charmed Baryon Production by Neutrinos

Abstract: We report on the production by neutrinos of an event with negative strangeness. In an exposure of the Brookhaven National Laboratory 7-ft cryogenic bubble chamber to a broad-band neutrino beam 335 events were observed, one of which fits the reaction vj p A &+&+&+& . Alternative explanations are examined and none found with a probability greater than 3x 10 . The event thus represents a large violation of the M =~@ rule or alternatively the production and decay of a charmed baryon state. The most plausible mass for this state is found to be 2426+ 12 MeV.

Adiabatic evolution of plasma equilibrium.

Abstract: A new theory of plasma equilibrium is introduced in which adiabatic constraints are specified. This leads to a mathematically nonstandard structure, as compared to the usual equilibrium theory, in which prescription of pressure and current profiles leads to an elliptic partial differential equation. Topologically complex configurations require further generalization of the concept of adiabaticity to allow irreversible mixing of plasma and magnetic flux among islands. Matching conditions across a boundary layer at the separatrix are obtained from appropriate conservation laws. Applications are made to configurations with planned islands (as in Doublet) and accidental islands (as in Tokamaks). Two-dimensional, axially symmetric, helically symmetric, and closed line equilibria are included.

Consistency in the formulation of the Dirac, Pauli, and Schrödinger theories

Abstract: Properties of observables in the Pauli and Schrodinger theories and first order relativistic approximations to them are derived from the Dirac theory. They are found to be inconsistent with customary interpretations in many respects. For example, failure to identify the ’’Darwin term’’ as the s−state spin−orbit energy in conventional treatments of the hydrogen atom is traced to a failure to distinguish between charge and momentum flow in the theory. Consistency with the Dirac theory is shown to imply that the Schrodinger equation describes not a spinless particle as universally assumed, but a particle in a spin eigenstate. The bearing of spin on the interpretation of the Schrodinger theory is discussed. Conservation laws of the Dirac theory are formulated in terms of relative variables, and used to derive virial theorems and the corresponding conservation laws in the Pauli−Schrodinger theory.

Field-theoretic techniques and critical dynamics. I. Ginzburg-Landau stochastic models without energy conservation

Abstract: The critical dynamics of a stochastic Ginzburg-Landau model of an $N$-component order parameter coupled to a conserved-energy-density field is studied with the help of field-theoretical techniques introduced in previous work. Our results essentially confirm and refine upon those of Halperin, Hohenberg, and Ma. Scaling laws are derived (whenever they hold). A better knowledge of the domain structure of the ($N, d$) plane and the corresponding critical exponents is obtained, in particular one additional region is shown to be present. Stability criteria lead to a characterization of the leading corrections to dynamical scaling by extra exponents which, except for one of them, are related to known static exponents.

Bäcklund Transformation for the Exponential Lattice

Abstract: A Backlund transformation associated with the equation of motion for an exponential lattice is found. It is shown that recursive application of the transformation provides an algebraic recursion formula for the solutions. Using the recursion formula, two-soliton solution is obtained and a method for constructing N -soliton solution is presented. It is also shown that the fundamental equations of inverse method and conservation laws can be derived from the transformation.

Invariance transformations, invariance group transformations, and invariance groups of the sine-Gordon equations

Abstract: We investigate a structure of continuous invariance transformations connected to the identity transformation. The transformations considered do not necessarily form a group. We clarify the relationship between the infinitesimal invariance transformation and the finite invariance transformation by showing explicitly how the infinitesimal transformations are woven into the finite one. The analysis leads to a new method of finding generators of the invariance group transformation. The results are useful in the study of symmetry properties, or group theoretic structure, of differential equations. We use the results in studying the group properties of the sine‐Gordon equation uxt=sinu, and indicate that the equation is invariant under an infinite number of one‐parameter groups; the groups obtained are of a more general type than that dealt with by Lie. These findings are used to prove the group theoretic origin of the well‐known conservation laws associated with the sine‐Gordon equation.

Upwind second-order difference schemes and applications in unsteady aerodynamic flows

Abstract: Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock waves. The general utility of the operational approach for combining schemes is emphasized by deriving a second-order conservative scheme for the steady transonic small-disturbance potential equation.

Gravitational theories with nonzero divergence of the energy-momentum tensor

Abstract: Assuming that the divergence of the energy-momentum tensor is nonzero leads to a class of theories with consistent field equations and gauge conditions as well as compatibility with the Newtonian limit of the conservation laws. Both the Einstein and the Brans-Dicke theories are used as models, but the extension to other viable theories such as vector-metric and two-metric theories is possible. One particularly interesting theory emerges that agrees with the ordinary Brans-Dicke theory except for the post-Newtonian parameter zeta sub 2, which predicts nonconservation of total momentum. Unfortunately, no accurate experimental limits for this parameter are known. It thus remains for future experiments in lunar-laser ranging to test this theory.

On the equations governing the axisymmetric perturbations of the Kerr black hole

Abstract: It is shown how Teukolsky's equation, governing the perturbations of the Kerr black hole, can be reduced, in the axisymmetric case, to a one-dimensional wave equation with four possible potentials. The potentials are implicitly, dependent on the frequency; and besides, depending on circumstances, they can be complex. In all cases (i.e. whether or not the potentials are real or complex), the problem of the reflexion and the transmission of gravitational waves by the potential barriers can be formulated, consistently, with the known conservation laws. It is, further, shown that all four potentials lead to the same reflexion and transmission coefficients.

NOETHER'S Theorem and Higher Conservation Laws in Ultrashort Pulse Propagation

Abstract: LAMB has constructed a number of local conservation laws for the differential equation στ = sin σ describing ultrashort pulse propagation in a resonant medium. On the other hand it is known that from any solution of this equation others may be found by BACKLUND transformation. In this paper we introduce extended BACKLUND transformations Ba and compose them to form infinitesimal invariance transformations Ba+e B from which via NOETHER'S theorem a system of conservation laws follows. Some of them are recognized as LAMB'S conservation laws. Another conservation law results from a scale invariance called LIE'S transformation. LAMB hat eine Anzahl von lokalen Erhaltungssatzen fur die Differentialgleichung στ = sin σ konstruiert, welche die Ausbreitung eines ultrakurzen Lichtimpulses im resonanten Medium beschreibt. Andererseits ist bekannt, das aus einer Losung dieser Gleichung weitere Losungen durch BACKLUND-Transformation gefunden werden konnen. In der vorliegenden Arbeit definieren wir erweiterte BACKLUND-Transformationen Ba, setzen diese zu infinitesimalen Invarianztransformationen Ba+e B zusammen und finden nach dem NOETHERschen Satz ein System von Erhaltungssatzen, von denen einige als die von LAMB angegebenen erkannt werden. Ein weiterer Erhaltungssatz folgt aus einer Skaleninvarianz, der sog. LIEschen Transformation.

On Rosen's bi-metric theory of gravitation

Abstract: The field equations of Rosen's bi-metric theory of gravitation [1] are solved exactly. The solutions are the same as in the author's theory of gravitation [2]. These solutions are, however, incompatible with Rosen's conservation laws and his second (flat) metric. Incompatibility with the conservation laws arises in second order. Incompatibility with the flat metric arises in first order but only for time-dependent fields. Rosen's theory is defensible only as a static first order theory and predicts the red shift light deflection and time-delay correctly.

The Weyl tensor and shear‐free perfect fluids

Abstract: It is proved that a necessary and sufficient condition for a shear‐free perfect fluid to be irrotational is that the Weyl tensor be pure electric type. For shear‐free isentropic flow with unit tangent uα, we find the conservation law ∇α(n1/3iω uα) =0, where i is the relativistic specific enthalpy, n is the conserved particle number density, and ω is the vorticity scalar.

Noether's Theorem and the Conservation Laws of the KORTEWEG-DE VRIES Equation

Abstract: A method developed recently by the author to derive a continuum of conservation laws by Noether's theorem from the so-called extended Backlund transformations is applied to the KORTEWEG-DE VRIES equation that describes various nonlinear dispersive wave phenomena in hydrodynamics, plasma physics and solid state physics. Further applications of Noether's theorem concerning this equation are given. It is shown that the Galilean transformation in the present case has an analogous function as Lie's transformation has with respect to the sine-Gordon equation. Der Noethersche Satz und die Erhaltungssatze der Korteweg-de-Vries-Gleichung Eine kurzlich vom Verfasser entwickelte Methode zur Ableitung eines Kontinuums von Erhaltungssatzen nach dem Noetherschen Satz aus sog. erweiterten Backlundtransformationen wird auf die KORTEWEG-DE-VRIES-Gleichung angewendet, die verschiedene nichtlineare dispersive Wellenerscheinungen in der Hydrodynamik, der Plasmaphysik und der Festkorperphysik beschreibt. Weitere Anwendungen des Noetherschen Satzes in bezug auf diese Gleichung werden angegeben. Es wird gezeigt, das die Galileitransformation im vorliegenden Fall eine analoge Rolle spielt wie die Liesche Transformation bezuglich der Sinus-Gordon-Gleichung.

Self-consistent calculation of the longitudinal NMR for the Balian-Werthamer and Anderson-Brinkman-Morel states of superfluid3He

Abstract: The general equations of motion for the Green's functions and correlation functions and the associated conservation laws for an anisotropic superfluid are derived. This leads to a simple commutator relation for the total angular momentum of the system and thep-wave pair amplitude. The longitudinal NMR frequencies for both the Balian-Werthamer (BW) and Anderson-Brinkman-Morel (ABM) states are calculated rigorously within the self-consistent random phase approximation scheme, taking account of all the degrees of freedom of the complex fluctuations of the order parameter (18 components) and their couplings via the dipole interactions. The results for the low-frequency resonances (ω≪Δ) are in agreement with those of Leggett except in the vicinity ofTc. In addition, in the presence of the dipole interaction, we find longitudinal resonances at ω=(8/5)1/2Δ and ω=21/2Δ for the BW and ABM states, respectively.

Quantum action principle in curved space

Abstract: Schwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianLc(\(\dot x\), x)=(M/2)gij(x)\(\dot x\)i\(\dot x\)j−v(x). It is sufficient for the purpose of deriving the laws of quantum mechanics to consider onlyc-number variations of coordinates and time. The Euler-Lagrange equation, the canonical commutation relations, and the canonical equations of motion are derived from this principle in a consistent manner. Further, it is shown that an arbitrary point transformation leaves the forms of the fundamental equations invariant. The judicious choice of the quantal Lagrangian is essential in our formulation. A quantum mechanical analog of Noether's theorem, which relates the invariance of the quantal action with a conservation law, is established. The ambiguities in the quantal Lagrangian are also discussed and it is pointed out that the requirement of invariance is not sufficient to determine uniquely the quantal Lagrangian and the Hamiltonian.

Bäcklund Transformation for Equation of Motion for Nonlinear Lattice under Weak Dislocation Potential

Abstract: The Backlund transformation for the equation of the motion for the nonlinear lattice under the influence of the weak dislocation potential is discussed. It is found that Backlund transformation is derived from Riccati form of inverse method and that a recursion formula to obtain a ladder of kind solutions is constructed. An infinite number of conservation laws is obtained.

Action conservation in the presence of a high-frequency field

Abstract: Even in the presence of a high-frequency field, which strongly modifies the plasma normal modes and their coupling coefficients, the Manley-Rowe condition for action conservation remains valid.