Nonlinear MHD-equations: symmetries, solutions and conservation laws

International Nuclear Information System (INIS)

Samokhin, A.V.

1985-01-01

To investigate stability and nonlinear effects in a high-temperature plasma the system of two scalar nonlinear equations is considered. The algebra of classical symmetries of this system and a certain natural part of its conservation laws are described. It is shown that first, with symmetries one can derive invariant (self-similar) solutions, second, acting with symmetry on the known solution the latter can be included into parametric family

On a quantum version of conservation laws for derivative nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Sen, S.; Chowdhury, A.R.

1988-01-01

The authors derived the quantum mechanical versions of infinite number of conservation laws associated with Derivative Nonlinear Schrodinger equation with the help of a methodology used in string theory. The renormalised version of the conserved quantities are obtained with explicit forms of the counter terms

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

Science.gov (United States)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Symmetries, Traveling Wave Solutions, and Conservation Laws of a (3+1-Dimensional Boussinesq Equation

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Letlhogonolo Daddy Moleleki

2014-01-01

Full Text Available We analyze the (3+1-dimensional Boussinesq equation, which has applications in fluid mechanics. We find exact solutions of the (3+1-dimensional Boussinesq equation by utilizing the Lie symmetry method along with the simplest equation method. The solutions obtained are traveling wave solutions. Moreover, we construct the conservation laws of the (3+1-dimensional Boussinesq equation using the new conservation theorem, which is due to Ibragimov.

Reductions and conservation laws for BBM and modified BBM equations

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Khorshidi Maryam

2016-01-01

Full Text Available In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM and modified Benjamin-Bona-Mahony equations (MBBM to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry properties are given too.

Conservation laws derived by the Neutral-Action Method. A simple application to the Schroedinger equation

International Nuclear Information System (INIS)

Nordbrock, U.; Kienzler, R.

2007-01-01

Conservation laws are a recognized tool in physical and engineering sciences. The classical procedure to construct conservation laws is to apply Noether's Theorem. It requires the existence of a Lagrange-function for the system under consideration. Two unknown sets of functions have to be found. A broader class of such laws is obtainable, if Noether's Theorem is used together with the Bessel-Hagen extension, raising the number of sets of unknown functions to three. By using the recently developed Neutral-Action Method, the same conservation laws can be obtained by calculating only one unknown set of functions. Moreover the Neutral Action Method can also be applied in the absence of a Lagrangian, since only the governing differential equations are required for this procedure. In the paper, an application of this method to the Schroedinger equation is presented. (authors)

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

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Emrullah Yaşar

Full Text Available In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI equation with Riemann–Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi–Kober sense. Furthermore, adapting the Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method. Keywords: Fractional Sawada–Kotera–Ito equation, Lie symmetry, Riemann–Liouville fractional derivative, Conservation laws, Exact solutions

Local instant conservation equations

International Nuclear Information System (INIS)

Delaje, Dzh.

1984-01-01

Local instant conservation equations for two-phase flow are derived. Derivation of the equation starts from the recording of integral laws of conservation for a fixed reference volume, containing both phases. Transformation of the laws, using the Leibniz rule and Gauss theory permits to obtain the sum of two integrals as to the volume and integral as to the surface. Integrals as to the volume result in local instant differential equations, in particular derivatives for each phase, and integrals as to the surface reflect local instant conditions of a jump on interface surface

AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Zhao Dun; Zhang Yujuan; Lou Weiwei; Luo Honggang

2011-01-01

By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLS systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.

Conservation properties and potential systems of vorticity-type equations

International Nuclear Information System (INIS)

Cheviakov, Alexei F.

2014-01-01

Partial differential equations of the form divN=0, N t +curl M=0 involving two vector functions in R 3 depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R 4 (t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations, it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented

Symmetry Reductions, Exact Solutions and Conservation Laws of Asymmetric Nizhnik-Novikov-Veselov Equation

International Nuclear Information System (INIS)

Wang Ling; Dong Zhongzhou; Liu Xiqiang

2008-01-01

By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation (ANNV). Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.

Equations of motion and conservation laws in a theory of stably stratified turbulence

Energy Technology Data Exchange (ETDEWEB)

L' vov, Victor S; Rudenko, Oleksii [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)], E-mail: oleksii.rudenko@weizmann.ac.il

2008-12-15

This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider non-isothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of state including both non-ideal gases as well as liquids. The proposed approach is based on a suggested general definition of potential temperature. Special attention is paid to the energy conservation principle: the proposed approximation exactly preserves the total mechanical energy by approximate equations of motion. It is emphasized explicitly the importance for any turbulent boundary layer model to respect the conservation laws.

Conservation laws for certain time fractional nonlinear systems of partial differential equations

Science.gov (United States)

Singla, Komal; Gupta, R. K.

2017-12-01

In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.

Diffusion Processes Satisfying a Conservation Law Constraint

Directory of Open Access Journals (Sweden)

J. Bakosi

2014-01-01

Full Text Available We investigate coupled stochastic differential equations governing N nonnegative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires a set of fluctuating variables to be nonnegative and (if appropriately normalized sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the nonnegativity and the unit-sum conservation law constraints are satisfied as the variables evolve in time. We investigate the consequences of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.

Conservation laws and self-consistent sources for a super-CKdV equation hierarchy

International Nuclear Information System (INIS)

Li Li

2011-01-01

From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy.

Conservation laws and self-consistent sources for a super-CKdV equation hierarchy

Energy Technology Data Exchange (ETDEWEB)

Li Li, E-mail: li07099@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2011-03-14

From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy.

Theoretical Maxwell's Equations, Gauge Field and Their Universality Based on One Conservation Law

Institute of Scientific and Technical Information of China (English)

Liu Changmao

2005-01-01

The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codifferential forms are pointed out: they represent the tangent surface and the normal surface fluxes of a tensor, respectively. The definitions of the divergence and the curl of a 2D surface flux of a tensor are obtained.Maxwell's equations, namely, the construction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law ( mass or fluid flux quantity and so on) and the feature of central field ( or its composition). By the feature of central field ( or its composition), the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory ( a magnetic monopole has no effect on electric current just like a couple basing no effect on the sum of forces) are presented: magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell's equations.

An Analysis of the Invariance and Conservation Laws of Some Classes of Nonlinear Ostrovsky Equations and Related Systems

International Nuclear Information System (INIS)

Fakhar, K.; Kara, A. H.

2011-01-01

A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties (through the Lie point symmetry generators) and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ‘multipliers’ associated with the conservation laws with a stronger emphasis on the ‘higher-order’ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers. (general)

Variational approaches to conservation laws for a nonlinear ...

African Journals Online (AJOL)

The conservation laws of a nonlinear evolution equation of time dependent variable coefficients of damping and dispersion is studied. The equation under consideration is not derivable from a variational principle which means that one cannot appeal to the Noether theorem to determine the conservation laws. We utilize the ...

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

Science.gov (United States)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Nonlinear Conservation Laws and Finite Volume Methods

Science.gov (United States)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Asymptotic Conservation Laws in Classical Field Theory

International Nuclear Information System (INIS)

Anderson, I.M.; Torre, C.G.

1996-01-01

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. copyright 1996 The American Physical Society

Discontinuous Galerkin Method for Hyperbolic Conservation Laws

KAUST Repository

Mousikou, Ioanna

2016-11-11

Hyperbolic conservation laws form a special class of partial differential equations. They describe phenomena that involve conserved quantities and their solutions show discontinuities which reflect the formation of shock waves. We consider one-dimensional systems of hyperbolic conservation laws and produce approximations using finite difference, finite volume and finite element methods. Due to stability issues of classical finite element methods for hyperbolic conservation laws, we study the discontinuous Galerkin method, which was recently introduced. The method involves completely discontinuous basis functions across each element and it can be considered as a combination of finite volume and finite element methods. We illustrate the implementation of discontinuous Galerkin method using Legendre polynomials, in case of scalar equations and in case of quasi-linear systems, and we review important theoretical results about stability and convergence of the method. The applications of finite volume and discontinuous Galerkin methods to linear and non-linear scalar equations, as well as to the system of elastodynamics, are exhibited.

Discontinuous Galerkin Method for Hyperbolic Conservation Laws

KAUST Repository

Mousikou, Ioanna

2016-01-01

Hyperbolic conservation laws form a special class of partial differential equations. They describe phenomena that involve conserved quantities and their solutions show discontinuities which reflect the formation of shock waves. We consider one-dimensional systems of hyperbolic conservation laws and produce approximations using finite difference, finite volume and finite element methods. Due to stability issues of classical finite element methods for hyperbolic conservation laws, we study the discontinuous Galerkin method, which was recently introduced. The method involves completely discontinuous basis functions across each element and it can be considered as a combination of finite volume and finite element methods. We illustrate the implementation of discontinuous Galerkin method using Legendre polynomials, in case of scalar equations and in case of quasi-linear systems, and we review important theoretical results about stability and convergence of the method. The applications of finite volume and discontinuous Galerkin methods to linear and non-linear scalar equations, as well as to the system of elastodynamics, are exhibited.

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

Science.gov (United States)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

On the coupling of systems of hyperbolic conservation laws with ordinary differential equations

International Nuclear Information System (INIS)

Borsche, Raul; Colombo, Rinaldo M; Garavello, Mauro

2010-01-01

Motivated by applications to the piston problem, to a manhole model, to blood flow and to supply chain dynamics, this paper deals with a system of conservation laws coupled with a system of ordinary differential equations. The former is defined on a domain with boundary and the coupling is provided by the boundary condition. For each of the examples considered, numerical integrations are provided

Conservation Laws for Partially Conservative Variable Mass Systems via d'Alembert's Principle

Institute of Scientific and Technical Information of China (English)

AFTAB Ahmed; NASEER Ahmed; QUDRAT Khan

2008-01-01

Conservation laws for partially conservative variable mass dynamical systems under symmetric infinitesimal transformations are determined. A generalization of Lagrange-d'Alembert's principle for a variable mass system in terms of asynchronous virtual variation is presented. The generalized Killing equations are obtained such that their solution yields the transformations and the associated conservation laws. An example illustrative of the theory is furnished at the end as well.

The conservation laws for deformed classical models

International Nuclear Information System (INIS)

Klimek, M.

1994-01-01

The problem of deriving the conservation laws for deformed linear equations of motion is investigated. The conserved currents are obtained in explicit form and used in the construction of constants of motion. The equations for the set of non-interacting oscillators with arbitrary scale-time as well as the κ-Klein-Gordon equation are considered as an example of application of the method. (author) 9 refs

Higher order supersymmetries and fermionic conservation laws of the supersymmetric extension of the KdV equation

NARCIS (Netherlands)

Kersten, P.H.M.

1988-01-01

By the introduction of nonlocal basonic and fermionic variables we construct a recursion symmetry of the super KdV equation, leading to a hierarchy of bosonic symmetries and one of fermionic symmetries. The hierarchies of bosonic and fermionic conservation laws arise in a natural way in the

Discrete conservation laws and the convergence of long time simulations of the mkdv equation

Science.gov (United States)

Gorria, C.; Alejo, M. A.; Vega, L.

2013-02-01

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

Conservation Laws for Partially Conservative Variable Mass Systems via d'Alembert's Principle

International Nuclear Information System (INIS)

Ahmed, Aftab; Ahmed, Naseer; Khan, Qudrat

2008-01-01

Conservation laws for partially conservative variable mass dynamical systems under symmetric infinitesimal transformations are determined. A generalization of Lagrange-d'Alembert's principle for a variable mass system in terms of asynchronous virtual variation is presented. The generalized Killing equations are obtained such that their solution yields the transformations and the associated conservation laws. An example illustrative of the theory is furnished at the end as well. (the physics of elementary particles and fields)

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

Science.gov (United States)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

ADM pseudotensors, conserved quantities and covariant conservation laws in general relativity

International Nuclear Information System (INIS)

Fatibene, L.; Ferraris, M.; Francaviglia, M.; Lusanna, L.

2012-01-01

The ADM formalism is reviewed and techniques for decomposing generic components of metric, connection and curvature are obtained. These techniques will turn out to be enough to decompose not only Einstein equations but also covariant conservation laws. Then a number of independent sets of hypotheses that are sufficient (though not necessary) to obtain standard ADM quantities (and Hamiltonian) from covariant conservation laws are considered. This determines explicitly the range in which standard techniques are equivalent to covariant conserved quantities. The Schwarzschild metric in different coordinates is then considered, showing how the standard ADM quantities fail dramatically in non-Cartesian coordinates or even worse when asymptotically flatness is not manifest; while, in view of their covariance, covariant conservation laws give the correct result in all cases. - Highlights: ► In the paper ADM conserved quantities for GR are obtained from augmented conservation laws. ► Boundary conditions for this to be possible are considered and compared with the literature. ► Some different forms of Schwarzschild solutions are considered as simple examples of different boundary conditions.

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

Science.gov (United States)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-11-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

International Nuclear Information System (INIS)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-01-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations. 6 references

Conserved quantities for generalized KdV equations

International Nuclear Information System (INIS)

Calogero, F.; Rome Univ.; Degasperis, A.; Rome Univ.

1980-01-01

It is noted that the nonlinear evolution equation usub(t) = α(t)usub(xxx) - 6ν(t) usub(x)u, u is identical to u(x,t), possesses three (and, in some cases, four) conserved quantities, that are explicitly displayed. These results are of course relevant only to the cases in which this evolution equation is not known to possess an infinite number of conserved quantities. Purpose and scope of this paper is to report three or four simple conservation laws possessed by the evolution equation usub(t) = α(t)usub(xxx) - 6ν(t)usub(x)u, u is identical to u(x,t). (author)

Negatons, positons, rational-like solutions and conservation laws of the Korteweg-de Vries equation with loss and non-uniformity terms

International Nuclear Information System (INIS)

Zhang Dajun; Chen Dengyuan

2004-01-01

Solitons, negatons, positons, rational-like solutions and mixed solutions of a non-isospectral equation, the Korteweg-de Vries equation with loss and non-uniformity terms, are obtained through the Wronskian technique. The non-isospectral characteristics of the motion behaviours of some solutions are described with some figures made by using Mathematica. We also derive an infinite number of conservation laws of the equation

The conservation laws of nonrelativistic classical and quantum mechanics for a system of interacting particles

International Nuclear Information System (INIS)

Havas, P.

1978-01-01

The various classical or quantum mechanical equations describing a system of N particles with central two-body interactions are invariant under the 10 transformations of the Galilei group, and for interaction potential inversely proportional to the squares of the particle separations also under two further transformations. From the invariance of the corresponding classical and quantum mechanical variation principles under this 12-parameter conformal extension of the Galilei group, the 'Jacobi-Schroedinger group', the 12 well-known conservation laws of Newtonian dynamics as well as 12 local conservation laws implied by the Schroedinger equation are obtained via Noether's theorem. Under appropriate conditions on the wave functions, these local laws yield 12 global conservation laws which are analogous to the Newtonian ones. The Hamiltonian-Jacobi equation implies a classical equation differing from the Schroedinger equation only by a potential-like term involving the Van Vleck determinant, from which 12 local balance equations and the corresponding global equations are obtained, which under certain conditions reduce the true conservation laws. (Auth.)

Bianchi-Baecklund transformations, conservation laws, and linearization of various field theories

International Nuclear Information System (INIS)

Chau Wang, L.L.

1980-01-01

The discussion includes: the Sine-Gordon equation, parametric Bianchi-Baecklund transformations and the derivation of local conservation laws; chiral fields, parametric Bianchi-Baecklund transformations, local and non-local conservation laws, and linearization; super chiral fields, a parallel development similar to the chiral field; and self-dual Yang-Mills fields in 4-dimensional Euclidean space; loop-cpace chiral equations, parallel development but with subtlety

Invariance analysis and conservation laws of the wave equation on ...

Indian Academy of Sciences (India)

in [7], the more interesting case being the latter since these lead to conservation laws via ... obtained and, hence, more conservation laws are classified. .... −2r2 sin θurt − 2r sin θut + 2r sin θ. (. 1 −. 2t r. ) ur + 2t sin θur. +r2 sin θ. (. 1 −. 2t r. ) urr + cos θuθ + sin θuθθ = 0,. (15) and then ¯X2 = u∂u + t∂t + r∂r leads to dt t. = dr.

Massively parallel computation of conservation laws

Energy Technology Data Exchange (ETDEWEB)

Garbey, M [Univ. Claude Bernard, Villeurbanne (France); Levine, D [Argonne National Lab., IL (United States)

1990-01-01

The authors present a new method for computing solutions of conservation laws based on the use of cellular automata with the method of characteristics. The method exploits the high degree of parallelism available with cellular automata and retains important features of the method of characteristics. It yields high numerical accuracy and extends naturally to adaptive meshes and domain decomposition methods for perturbed conservation laws. They describe the method and its implementation for a Dirichlet problem with a single conservation law for the one-dimensional case. Numerical results for the one-dimensional law with the classical Burgers nonlinearity or the Buckley-Leverett equation show good numerical accuracy outside the neighborhood of the shocks. The error in the area of the shocks is of the order of the mesh size. The algorithm is well suited for execution on both massively parallel computers and vector machines. They present timing results for an Alliant FX/8, Connection Machine Model 2, and CRAY X-MP.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅵ)-CONSERVATION LAWS OF MASS AND INERTIA

Institute of Scientific and Technical Information of China (English)

戴安民

2003-01-01

The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the line element, the surface element and the volume element were derived and the generalized Reynolds transport theorem was presented. Combining these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum and energy may be obtained by the usual localization.

New Positive and Negative Hierarchies of Integrable Differential-Difference Equations and Conservation Laws

International Nuclear Information System (INIS)

Li Xinyue; Zhao Qiulan

2009-01-01

Two hierarchies of nonlinear integrable positive and negative lattice equations are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws about the positive hierarchy.

Conservation laws with coinciding smooth solutions but different conserved variables

Science.gov (United States)

Colombo, Rinaldo M.; Guerra, Graziano

2018-04-01

Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

Conservation laws for two (2 + 1)-dimensional differential-difference systems

International Nuclear Information System (INIS)

Yu Guofu; Tam, H.-W.

2006-01-01

Two integrable differential-difference equations are considered. One is derived from the discrete BKP equation and the other is a symmetric (2 + 1)-dimensional Lotka-Volterra equation. An infinite number of conservation laws for the two differential-difference equations are deduced

On conserved densities and asymptotic behaviour for the potential Kadomtsev-Petviashvili equation

International Nuclear Information System (INIS)

Rosenhaus, V

2006-01-01

We study local conservation laws with non-vanishing conserved densities and corresponding boundary conditions for the potential Kadomtsev-Petviashvili equation. We analyse an infinite symmetry group of the equation, and generate a finite number of conserved densities corresponding to infinite symmetries through appropriate boundary conditions

Hyperbolic Conservation Laws and Related Analysis with Applications

CERN Document Server

Holden, Helge; Karlsen, Kenneth

2014-01-01

This book presents thirteen papers, representing the most significant advances and current trends in nonlinear hyperbolic conservation laws and related analysis with applications. Topics covered include a survey on multidimensional systems of conservation laws as well as novel results  on liquid crystals, conservation laws with discontinuous flux functions, and applications to sedimentation.  Also included are articles on recent advances in the Euler equations and the Navier-Stokes-Fourier-Poisson system, in addition to new results on collective phenomena described by the Cucker-Smale model.    The Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications at the International Centre for Mathematical Sciences (Edinburgh, UK) held in Edinburgh, September 2011, produced this fine collection of original research and survey articles. Many leading mathematicians attended the event and submitted their contributions for this volume. It is addressed to researchers and graduate students inter...

Conservation laws for multidimensional systems and related linear algebra problems

International Nuclear Information System (INIS)

Igonin, Sergei

2002-01-01

We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for the existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A t S and SA=-A t S for a quadratic matrix A and its transpose A t , which may be of independent interest

Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form

Science.gov (United States)

Delzanno, G. L.

2015-11-01

A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.

Front tracking for hyperbolic conservation laws

CERN Document Server

Holden, Helge

2002-01-01

Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet "I have read the book with great pleasure, and I can recommend it to experts as well as students. It can also be used for reliable and very exciting basis for a one-semester graduate course." S. Noelle, Book review, German Math. Soc. "Making it an ideal first book for the theory of nonlinear partial differential equations...an excellent reference for a graduate course on nonlinear conservation laws." M. Laforest, Comp. Phys. Comm.

The symmetries and conservation laws of some Gordon-type

Indian Academy of Sciences (India)

Conservation laws; Milne space-time; Gordon-type equations. Abstract. In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented ... Pramana – Journal of Physics | News.

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

Science.gov (United States)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

Lagrange and Noether analysis of polarization laws of conservation for electromagnetic field

International Nuclear Information System (INIS)

Krivskij, I.Yu.; Simulik, V.M.

1988-01-01

Both well-known Bessel-Hagen conservation laws and conservation laws of polarized character are derived for electromagnetic field in the Lagrange approach to electrodynamics in terms of intensities (without using the A μ potentials as variation variables). The laws mentioned are derived according to Noether theorem because symmetry to which such concervation laws correspond is lost during the transition from intensities to potentials. Based on Noether theorem (and its generalization for Naeik's symmetries) and Lagrange function scalar in relation to complete Poincare group in terms of intensity tensor, a convenient formula for calculating and values conserved for electromagnetic field is derived which sets up a physically adequate symmetry operator -conservation law correlation and thus links the presence of conservation laws of polarized character with symmetry properties of Maxwell equations. Adiabaticity of conservation laws of polarized character under the presence of interaction with currents and charges is indicated

Conservation laws for steady flow and solitons in a multifluid plasma revisited

International Nuclear Information System (INIS)

Mace, R. L.; McKenzie, J. F.; Webb, G. M.

2007-01-01

The conservation laws used in constructing the governing equations for planar solitons in multifluid plasmas are revisited. In particular, the concept of generalized vorticity facilitates the derivation of some general ''Bernoulli theorems,'' which reduce, in specific instances, to conservation laws previously deduced by other means. These theorems clarify the underlying physical principles that give rise to the conserved quantities. As an example of the usefulness of the techniques, even for relatively simple flows and progressive waves, the equations governing stationary nonlinear whistler waves propagating parallel to an ambient magnetic field are derived using generalized vorticity concepts

Front tracking for hyperbolic conservation laws

CERN Document Server

Holden, Helge

2015-01-01

This is the second edition of a well-received book providing the fundamentals of the theory hyperbolic conservation laws. Several chapters have been rewritten, new material has been added, in particular, a chapter on space dependent flux functions, and the detailed solution of the Riemann problem for the Euler equations. Hyperbolic conservation laws are central in the theory of nonlinear partial differential equations and in science and technology. The reader is given a self-contained presentation using front tracking, which is also a numerical method. The multidimensional scalar case and the case of systems on the line are treated in detail. A chapter on finite differences is included. From the reviews of the first edition: "It is already one of the few best digests on this topic. The present book is an excellent compromise between theory and practice. Students will appreciate the lively and accurate style." D. Serre, MathSciNet  "I have read the book with great pleasure, and I can recommend it to experts ...

Power-law and runaway growth in conserved aggregation systems

International Nuclear Information System (INIS)

Yamamoto, Hiroshi; Ohtsuki, Toshiya; Fujihara, Akihiro; Tanimoto, Satoshi

2006-01-01

The z-transform technique is used to analyze the Smoluchowski coagulation equation for conserved aggregation systems. A universal power law with the exponent -5/2 appears when a total 'mass' has a certain critical value. Below the threshold, ordinary scaling relations hold and the system exhibits a behavior like usual critical phenomena. Above the threshold, in contrast, the excess amount of mass coagulates into a runaway member, and remaining members follow the power law. Here the runaway growth coexists with the power law. It is argued that these behaviors are observed universally in conserved aggregation processes

Kac-Moody-Virasoro Symmetries and Related Conservation Laws

International Nuclear Information System (INIS)

Lou, S. Y.; Jia, M.; Tang, X. Y.

2010-01-01

In this report, some important facts on the symmetries and conservation laws of high dimensional integrable systems are discussed. It is summarized that almost all the known (2+1)-dimensional integrable models possess the Kac-Moody-Virasoro (KMV) symmetry algebras. One knows that infinitely many partial differential equations may possess a same KMV symmetry algebra. It is found that the KMV symmetry groups can be explicitly obtained by using some direct methods. For some quite general variable coefficient nonlinear systems, their sufficient and necessary condition for the existence of the KMV symmetry algebra is they can be changed to the related known constant coefficient models. Finally, it is found that every one symmetry may be related to infinitely many conservation laws and then infinitely many models may possess a same set of infinitely many conservation laws.

Rarefaction and shock waves for multi-dimensional hyperbolic conservation laws

International Nuclear Information System (INIS)

Dening, Li

1991-01-01

In this paper, the author wants to show the local existence of a solution of combination of shock and rarefaction waves for the multi-dimensional hyperbolic system of conservation laws. The typical example he has in mind is the Euler equations for compressible fluid. More generally, he studies the hyperbolic system of conservation laws ∂ t F 0 (u) + Σ j=1 n ∂ x j F j (u)=0 where u=(u 1 ....,u m ) and F j (u), j=0,...,n are m-dimensional vector-valued functions. He'll impose some conditions in the following on the systems (1.2). All these conditions are satisfied by the Euler equations

Effects of collisions on conservation laws in gyrokinetic field theory

Energy Technology Data Exchange (ETDEWEB)

Sugama, H.; Nunami, M. [National Institute for Fusion Science, Toki 509-5292 (Japan); Department of Fusion Science, SOKENDAI (The Graduate University for Advanced Studies), Toki 509-5292 (Japan); Watanabe, T.-H. [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan)

2015-08-15

Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether's theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novel gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations.

Infinitely many conservation laws for two integrable lattice hierarchies associated with a new discrete Schroedinger spectral problem

International Nuclear Information System (INIS)

Zhu, Zuo-nong; Tam, Hon-Wah; Ding, Qing

2003-01-01

In this Letter, by means of considering matrix form of a new Schroedinger discrete spectral operator equation, and constructing opportune time evolution equations, and using discrete zero curvature representation, two discrete integrable lattice hierarchies proposed by Boiti et al. [J. Phys. A: Math. Gen. 36 (2003) 139] are re-derived. From the matrix Lax representations, we demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes by means of formulae. Thus their integrability is further confirmed. Specially we obtain the infinitely many conservation laws for a new discrete version of the KdV equation. A connection between the conservation laws of the discrete KdV equation and the ones of the KdV equation is discussed by two examples

Propagation of multidimensional nonlinear waves and kinematical conservation laws

CERN Document Server

Prasad, Phoolan

2017-01-01

This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1–4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved sho...

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian

2015-01-01

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean

2015-02-03

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Scaling symmetries, conservation laws and action principles in one-dimensional gas dynamics

International Nuclear Information System (INIS)

Webb, G M; Zank, G P

2009-01-01

Scaling symmetries of the planar, one-dimensional gas dynamic equations with adiabatic index γ are used to obtain Lagrangian and Eulerian conservation laws associated with the symmetries. The known Eulerian symmetry operators for the scaling symmetries are converted to the Lagrangian form, in which the Eulerian spatial position of the fluid element is given in terms of the Lagrangian fluid labels. Conditions for a linear combination of the three scaling symmetries to be a divergence or variational symmetry of the action are established. The corresponding Lagrangian and Eulerian form of the conservation laws are determined by application of Noether's theorem. A nonlocal conservation law associated with the scaling symmetries is obtained by applying a nonlocal symmetry operator to the scaling symmetry-conserved vector. An action principle incorporating known conservation laws using Lagrangian constraints is developed. Noether's theorem for the constrained action principle gives the same formulas for the conserved vector as the classical Noether theorem, except that the Lie symmetry vector field now includes the effects of nonlocal potentials. Noether's theorem for the constrained action principle is used to obtain nonlocal conservation laws. The scaling symmetry conservation laws only apply for special forms of the entropy of the gas.

Nearly auto-parallel maps and conservation laws on curved spaces

International Nuclear Information System (INIS)

Vacaru, S.

1994-01-01

The theory of nearly auto-parallel maps (na-maps, generalization of conformal transforms) of Einstein-Cartan spaces is formulated. The transformation laws of geometrical objects and gravitational and matter field equations under superpositions of na-maps are considered. A special attention is paid to the very important problem of definition of conservation laws for gravitational fields. (Author)

Waves, conservation laws and symmetries of a third-order nonlinear ...

African Journals Online (AJOL)

order is under consideration. Important properties concerning advanced character such like conservation laws and the equation of continuity are given. Characteristic wave properties such like dispersion relations and both the group and phase ...

Frequency modulation at a moving material interface and a conservation law for wave number. [acoustic wave reflection and transmission

Science.gov (United States)

Kleinstein, G. G.; Gunzburger, M. D.

1976-01-01

An integral conservation law for wave numbers is considered. In order to test the validity of the proposed conservation law, a complete solution for the reflection and transmission of an acoustic wave impinging normally on a material interface moving at a constant speed is derived. The agreement between the frequency condition thus deduced from the dynamic equations of motion and the frequency condition derived from the jump condition associated with the integral equation supports the proposed law as a true conservation law. Additional comparisons such as amplitude discontinuities and Snells' law in a moving media further confirm the stated proposition. Results are stated concerning frequency and wave number relations across a shock front as predicted by the proposed conservation law.

Lax pairs and conservation laws for two differential-difference systems

International Nuclear Information System (INIS)

Li Chunxia

2003-01-01

A coupled extended Lotka-Volterra lattice and a special Toda lattice are derived from the existing bilinear equations. Starting from the corresponding bilinear Baecklund transformation, Lax pairs for these two differential-difference systems are obtained. Furthermore, an infinite number of conservation laws for the differential-difference equations are deduced from the Lax pairs in a systematic way

Unsplit schemes for hyperbolic conservation laws with source terms in one space dimension

International Nuclear Information System (INIS)

Papalexandris, M.V.; Leonard, A.; Dimotakis, P.E.

1997-01-01

The present work is concerned with an application of the theory of characteristics to conservation laws with source terms in one space dimension, such as the Euler equations for reacting flows. Space-time paths are introduced on which the flow/chemistry equations decouple to a characteristic set of ODE's for the corresponding homogeneous laws, thus allowing the introduction of functions analogous to the Riemann invariants in classical theory. The geometry of these paths depends on the spatial gradients of the solution. This particular decomposition can be used in the design of efficient unsplit algorithms for the numerical integration of the equations. As a first step, these ideas are implemented for the case of a scalar conservation law with a nonlinear source term. The resulting algorithm belongs to the class of MUSCL-type, shock-capturing schemes. Its accuracy and robustness are checked through a series of tests. The stiffness of the source term is also studied. Then, the algorithm is generalized for a system of hyperbolic equations, namely the Euler equations for reacting flows. A numerical study of unstable detonations is performed. 57 refs

Hyperbolic conservation laws in continuum physics

CERN Document Server

Dafermos, Constantine M

2016-01-01

This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conser...

A closed set of conservation laws and the evolution of the electron magnetic moment in the collisionless solar wind

International Nuclear Information System (INIS)

Alexander, P.

1993-01-01

A hydromagnetic equation system for the interplanetary collisionless solar wind is used to derive a set of conservation laws for that medium. It is found that every equation of the original system, including the closure relation, is related to one conservation law. The set that has been derived does not only include the traditional laws, but also a new one for the magnetic moment of the electrons. The conservation set is then used to obtain the space constants for the solar coronal expansion. The new law yields a constant that has not been predicted by other models

Enforcing conservation laws in nonequilibrium cluster perturbation theory

Science.gov (United States)

Gramsch, Christian; Potthoff, Michael

2017-05-01

Using the recently introduced time-local formulation of the nonequilibrium cluster perturbation theory (CPT), we construct a generalization of the approach such that macroscopic conservation laws are respected. This is achieved by exploiting the freedom for the choice of the starting point of the all-order perturbation theory in the intercluster hopping. The proposed conserving CPT is a self-consistent propagation scheme which respects the conservation of energy, particle number, and spin, which treats short-range correlations exactly up to the linear scale of the cluster, and which represents a mean-field-like approach on length scales beyond the cluster size. Using Green's functions, conservation laws are formulated as local constraints on the local spin-dependent particle and the doublon density. We consider them as conditional equations to self-consistently fix the time-dependent intracluster one-particle parameters. Thanks to the intrinsic causality of the CPT, this can be set up as a step-by-step time propagation scheme with a computational effort scaling linearly with the maximum propagation time and exponentially in the cluster size. As a proof of concept, we consider the dynamics of the two-dimensional, particle-hole-symmetric Hubbard model following a weak interaction quench by simply employing two-site clusters only. Conservation laws are satisfied by construction. We demonstrate that enforcing them has strong impact on the dynamics. While the doublon density is strongly oscillating within plain CPT, a monotonic relaxation is observed within the conserving CPT.

Mei Symmetry and New Conserved Quantities of Tzénoff Equations for the Variable Mass Higher-Order Nonholonomic System

Institute of Scientific and Technical Information of China (English)

ZHENG Shi-Wang; WANG Jian-Bo; CHEN Xiang-Wei; XIE Jia-Fang

2012-01-01

Operational systems of spacecraft are general variable mass mechanics systems,and their symmetries and conserved quantities imply profound physical rules of the space system.We study the Mei symmetry of Tzénoff equations for a variable mass nonholonomic system and the new conserved quantities derived.The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented.This result has some theoretical values in further research of conservation laws obeyed by the variable mass system.%Operational systems of spacecraft are general variable mass mechanics systems, and their symmetries and conserved quantities imply profound physical rules of the space system. We study the Mei symmetry of Tzenoff equations for a variable mass nonholonomic system and the new conserved quantities derived. The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented. This result has some theoretical values in further research of conservation laws obeyed by the variable mass system.

Family of two-dimensional Born-Infeld equations and a system of conservation laws

International Nuclear Information System (INIS)

Koiv, M.; Rosenhaus, V.

1979-01-01

Lower-order conserved quantities, the ''currents'', for two-dimensional Lorentz-invariant Born-Infeld equation are considered. The currents are divided into pairs, which contain a class (basic currents) leading to the family equations. The basic currents determine the transformations between the solutions of the Born-Infeld eqution family. The equations belonging to the family are fully hodograph-invariant, partly hodograph-invariant, and effectively linear, i.e. non-linear equations with linear image of hodograph transformation

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

Science.gov (United States)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

Conservation Laws in Biochemical Reaction Networks

DEFF Research Database (Denmark)

Mahdi, Adam; Ferragut, Antoni; Valls, Claudia

2017-01-01

We study the existence of linear and nonlinear conservation laws in biochemical reaction networks with mass-action kinetics. It is straightforward to compute the linear conservation laws as they are related to the left null-space of the stoichiometry matrix. The nonlinear conservation laws...... are difficult to identify and have rarely been considered in the context of mass-action reaction networks. Here, using the Darboux theory of integrability, we provide necessary structural (i.e., parameterindependent) conditions on a reaction network to guarantee the existence of nonlinear conservation laws...

LETTER TO THE EDITOR: Bicomplexes and conservation laws in non-Abelian Toda models

Science.gov (United States)

Gueuvoghlanian, E. P.

2001-08-01

A bicomplex structure is associated with the Leznov-Saveliev equation of integrable models. The linear problem associated with the zero-curvature condition is derived in terms of the bicomplex linear equation. The explicit example of a non-Abelian conformal affine Toda model is discussed in detail and its conservation laws are derived from the zero-curvature representation of its equation of motion.

Notes on Conservation Laws, Equations of Motion of Matter, and Particle Fields in Lorentzian and Teleparallel de Sitter Space-Time Structures

Directory of Open Access Journals (Sweden)

Waldyr A. Rodrigues

2016-01-01

Full Text Available We discuss the physics of interacting fields and particles living in a de Sitter Lorentzian manifold (dSLM, a submanifold of a 5-dimensional pseudo-Euclidean (5dPE equipped with a metric tensor inherited from the metric of the 5dPE space. The dSLM is naturally oriented and time oriented and is the arena used to study the energy-momentum conservation law and equations of motion for physical systems living there. Two distinct de Sitter space-time structures MdSL and MdSTP are introduced given dSLM, the first equipped with the Levi-Civita connection of its metric field and the second with a metric compatible parallel connection. Both connections are used only as mathematical devices. Thus, for example, MdSL is not supposed to be the model of any gravitational field in the General Relativity Theory (GRT. Misconceptions appearing in the literature concerning the motion of free particles in dSLM are clarified. Komar currents are introduced within Clifford bundle formalism permitting the presentation of Einstein equation as a Maxwell like equation and proving that in GRT there are infinitely many conserved currents. We prove that in GRT even when the appropriate Killing vector fields exist it is not possible to define a conserved energy-momentum covector as in special relativistic theories.

Baeklund transformations, conservation laws and linearization of the self-dual Yang-Mills and chiral fields

International Nuclear Information System (INIS)

Wang, L.C.

1980-01-01

Baecklund Transformations (BT) and the derivation of local conservation laws are first reviewed in the classic case of the Sine-Gordon equation. The BT, conservation laws (local and nonlocal), and the inverse-scattering formulation are discussed for the chiral and the self-dual Yang-Mills fields. Their possible applications to the loop formulation for the Yang-Mills fields are mentioned. 55 references, 1 figure

On 2X2 systems of conservation laws with fluxes that are entropies

Directory of Open Access Journals (Sweden)

Michael Junk

2003-03-01

Full Text Available In this article, we study systems of conservation laws with two dependent and two independent variables which have the property that the fluxes are entropies. Several characterizations of such flux functions are presented. It turns out, that the corresponding systems automatically possess a large class of additional entropies, they are closely related to a kinetic equation, and, in the case of strict hyperbolicity, they can be decoupled into two independent Burgers' equations. The isentropic Euler equations with zero or cubic pressure laws are the most prominent examples of such systems, but other examples are also presented.

Higher conservation laws for ten-dimensional supersymmetric Yang-Mills theories

International Nuclear Information System (INIS)

Abdalla, E.; Forger, M.; Freiburg Univ.; Jacques, M.

1988-01-01

It is shown that ten-dimensional supersymmetric Yang-Mills theories are integrable systems, in the (weak) sense of admitting a (superspace) Lax representation for their equations of motion. This is achieved by means of an explicit proof that the equations of motion are not only a consequence of but in fact fully equivalent to the superspace constraint F αβ =0. Moreover, a procedure for deriving infinite series of non-local conservation laws is outlined. (orig.)

Helicity and other conservation laws in perfect fluid motion

Science.gov (United States)

Serre, Denis

2018-03-01

In this review paper, we discuss helicity from a geometrical point of view and see how it applies to the motion of a perfect fluid. We discuss its relation with the Hamiltonian structure, and then its extension to arbitrary space dimensions. We also comment about the existence of additional conservation laws for the Euler equation, and its unlikely integrability in Liouville's sense.

Gravitation SL(2,C) gauge theory and conservation laws

CERN Document Server

Carmeli, Moshe; Nissani, Noah

1990-01-01

This monograph gives a comprehensive presentation of the SL(2,C) Gauge Theory of Gravitation along with some recent developments in the problem of Conservation Laws in General Relativity. Emphasis is put on quadratic Lagrangians which yield the Einstein field equations, as compared with Hilbert's original linear Langrangian, thus gravitation follows the other Gauge Fields all of which are derived from nonlinear Lagrangians.

Three-parameter relativistic dynamics. 1. Equation of motion, energy conservation

International Nuclear Information System (INIS)

Rogachevskii, A.G.

1995-01-01

A formally geometric analog of the relativistic dynamics of a point charged particle is constructed. Time as a function of the spatial coordinates is taken as the trajectory equation, i.e., the trajectory is a hypersurface in Minkowski space. The dynamics is presented. The law of open-quotes energyclose quotes conservation is examined

Construction of local and non-local conservation laws for non-linear field equations

International Nuclear Information System (INIS)

Vladimirov, V.S.; Volovich, I.V.

1984-08-01

A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)

From conservation laws to port-Hamiltonian representations of distributed-parameter systems

NARCIS (Netherlands)

Maschke, B.M.; van der Schaft, Arjan; Piztek, P.

Abstract: In this paper it is shown how the port-Hamiltonian formulation of distributed-parameter systems is closely related to the general thermodynamic framework of systems of conservation laws and closure equations. The situation turns out to be similar to the lumped-parameter case where the

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

KAUST Repository

Guermond, J. L.

2010-09-17

A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

KAUST Repository

Guermond, J. L.; Pasquetti, R.

2010-01-01

A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.

A generalized variational algebra and conserved densities for linear evolution equations

International Nuclear Information System (INIS)

Abellanas, L.; Galindo, A.

1978-01-01

The symbolic algebra of Gel'fand and Dikii is generalized to the case of n variables. Using this algebraic approach a rigorous characterization of the polynomial kernel of the variational derivative is given. This is applied to classify all the conservation laws for linear polynomial evolution equations of arbitrary order. (Auth.)

Relativistic dynamics without conservation laws

OpenAIRE

Rothenstein, Bernhard; Popescu, Stefan

2006-01-01

We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The derivations are based on the principle of relativity and on its direct consequence, the addition law of relativistic velocities.

Searching for Conservation Laws in Brain Dynamics—BOLD Flux and Source Imaging

Directory of Open Access Journals (Sweden)

Henning U. Voss

2014-07-01

Full Text Available Blood-oxygen-level-dependent (BOLD imaging is the most important noninvasive tool to map human brain function. It relies on local blood-flow changes controlled by neurovascular coupling effects, usually in response to some cognitive or perceptual task. In this contribution we ask if the spatiotemporal dynamics of the BOLD signal can be modeled by a conservation law. In analogy to the description of physical laws, which often can be derived from some underlying conservation law, identification of conservation laws in the brain could lead to new models for the functional organization of the brain. Our model is independent of the nature of the conservation law, but we discuss possible hints and motivations for conservation laws. For example, globally limited blood supply and local competition between brain regions for blood might restrict the large scale BOLD signal in certain ways that could be observable. One proposed selective pressure for the evolution of such conservation laws is the closed volume of the skull limiting the expansion of brain tissue by increases in blood volume. These ideas are demonstrated on a mental motor imagery fMRI experiment, in which functional brain activation was mapped in a group of volunteers imagining themselves swimming. In order to search for local conservation laws during this complex cognitive process, we derived maps of quantities resulting from spatial interaction of the BOLD amplitudes. Specifically, we mapped fluxes and sources of the BOLD signal, terms that would appear in a description by a continuity equation. Whereas we cannot present final answers with the particular analysis of this particular experiment, some results seem to be non-trivial. For example, we found that during task the group BOLD flux covered more widespread regions than identified by conventional BOLD mapping and was always increasing during task. It is our hope that these results motivate more work towards the search for conservation

On the structure on non-local conservation laws in the two-dimensional non-linear sigma-model

International Nuclear Information System (INIS)

Zamolodchikov, Al.B.

1978-01-01

The non-local conserved charges are supposed to satisfy a special multiplicative law in the space of asymptotic states of the non-linear sigma-model. This supposition leads to factorization equations for two-particle scattering matrix elements and determines to some extent the action of these charges in the asymptotic space. Their conservation turns out to be consistent with the factorized S-matrix of the non-linear sigma-model. It is shown also that the factorized sine-Gordon S-matrix is consistent with a similar family of conservation laws

A Note on Weak Solutions of Conservation Laws and Energy/Entropy Conservation

Science.gov (United States)

Gwiazda, Piotr; Michálek, Martin; Świerczewska-Gwiazda, Agnieszka

2018-03-01

A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such cases most often related to the second law of thermodynamics. This observation easily generalizes to any symmetrizable system of conservation laws; they are endowed with nontrivial companion conservation laws, which are immediately satisfied by classical solutions. Not surprisingly, weak solutions may fail to satisfy companion laws, which are then often relaxed from equality to inequality and overtake the role of physical admissibility conditions for weak solutions. We want to answer the question: what is a critical regularity of weak solutions to a general system of conservation laws to satisfy an associated companion law as an equality? An archetypal example of such a result was derived for the incompressible Euler system in the context of Onsager's conjecture in the early nineties. This general result can serve as a simple criterion to numerous systems of mathematical physics to prescribe the regularity of solutions needed for an appropriate companion law to be satisfied.

Entropy viscosity method for nonlinear conservation laws

KAUST Repository

Guermond, Jean-Luc

2011-05-01

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

Entropy viscosity method for nonlinear conservation laws

KAUST Repository

Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan

2011-01-01

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

Averaged multivalued solutions and time discretization for conservation laws

International Nuclear Information System (INIS)

Brenier, Y.

1985-01-01

It is noted that the correct shock solutions can be approximated by averaging in some sense the multivalued solution given by the method of characteristics for the nonlinear scalar conservation law (NSCL). A time discretization for the NSCL equation based on this principle is considered. An equivalent analytical formulation is shown to lead quite easily to a convergence result, and a third formulation is introduced which can be generalized for the systems of conservation laws. Various numerical schemes are constructed from the proposed time discretization. The first family of schemes is obtained by using a spatial grid and projecting the results of the time discretization. Many known schemes are then recognized (mainly schemes by Osher, Roe, and LeVeque). A second way to discretize leads to a particle scheme without space grid, which is very efficient (at least in the scalar case). Finally, a close relationship between the proposed method and the Boltzmann type schemes is established. 14 references

Mei Symmetry and New Conserved Quantities of Tzénoff Equations for the Variable Mass Higher-Order Nonholonomic System

International Nuclear Information System (INIS)

Zheng Shi-Wang; Wang Jian-Bo; Chen Xiang-Wei; Xie Jia-Fang

2012-01-01

Operational systems of spacecraft are general variable mass mechanics systems, and their symmetries and conserved quantities imply profound physical rules of the space system. We study the Mei symmetry of Tzénoff equations for a variable mass nonholonomic system and the new conserved quantities derived. The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented. This result has some theoretical values in further research of conservation laws obeyed by the variable mass system. (general)

Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves

Science.gov (United States)

Barker, Blake; Jung, Soyeun; Zumbrun, Kevin

2018-03-01

Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability in conservation laws and (ii) use these conditions to find families of periodic solutions bifurcating from uniform states, numerically continuing these families into the large-amplitude regime. For the examples studied, numerical stability analysis suggests that stable periodic waves can emerge either from supercritical Turing bifurcations or, via secondary bifurcation as amplitude is increased, from subcritical Turing bifurcations. This answers in the affirmative a question of Oh-Zumbrun whether stable periodic solutions of conservation laws can occur. Determination of a full small-amplitude stability diagram - specifically, determination of rigorous Eckhaus-type stability conditions - remains an interesting open problem.

Conservation laws arising in the study of forward-forward Mean-Field Games

KAUST Repository

Gomes, Diogo A.; Nurbekyan, Levon; Sedjro, Marc

2017-01-01

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models.

Conservation laws arising in the study of forward-forward Mean-Field Games

KAUST Repository

Gomes, Diogo A.

2017-04-24

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models.

Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

International Nuclear Information System (INIS)

Zhao Gang-Ling; Chen Li-Qun; Fu Jing-Li; Hong Fang-Yu

2013-01-01

In this paper, Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated. Firstly, the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices. Secondly, for cases of the two lattices, based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates, we present the quasi-extremal equation, the discrete analogues of Noether identity, Noether theorems, and the Noether conservation laws of the systems. Thirdly, in cases of the two lattices, we study the Mei symmetry in which we give the discrete analogues of the criterion, the theorem, and the conservative laws of Mei symmetry for the systems. Finally, an example is discussed for the application of the results

Violations of conservation laws in viscous liquid dynamics

DEFF Research Database (Denmark)

Dyre, Jeppe

2007-01-01

The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring equipment over the long times needed to study the dynamics. Moreover,......, although particle number conservation applies strictly for any liquid, the solidity of viscous liquids implies that even this conservation law is apparently violated in coarse-grained descriptions of density fluctuations.......The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring equipment over the long times needed to study the dynamics. Moreover...

Layer-Mean Quantities, Local Conservation Laws, and Vorticity

International Nuclear Information System (INIS)

Camassa, R.; Levermore, C.D.

1997-01-01

We derive local conservation laws for layer-mean quantities in two general settings. When applied to Euler flows, the first of these settings yields well-known local conservation laws for quantities averaged between material surfaces. The second, however, leads to new local conservation laws for quantities involving the vorticity that are averaged between arbitrary surfaces. These produce the crucial vorticity conservation laws in shallow water models that admit nonhydrostatic and noncolumnar motion. Moreover, they seem to lie outside the Hamiltonian paradigm of fluid dynamics. The formalism generalizes to skew-symmetric matrix fields; applications to electromagnetism are suggested. copyright 1997 The American Physical Society

Numerical solutions of conservation laws

International Nuclear Information System (INIS)

Shu, C.W.

1986-01-01

In the computation of conservation laws u/sub t/ + f(u)/sub x/ 0, TVD (total-variation-diminishing) schemes have been very successful. TVB (total-variation-bounded) schemes share most the advantages and may remove some of the disadvantages (e.g. local degeneracy of accuracy at critical points) TVD schemes. Included in this dissertation are a class of m-step Runge-Kutta type TVD schemes with CFL number equaling m; a procedure to obtain uniformly high order in space TVB schemes; a class of TVD high order time discretizations; a special boundary treatment which keeps the high order of the scheme up to the boundary and preserves the TVB properties in the nonlinear scalar and linear system cases; a discrete entropy inequality for a modified Lax-Wendroff scheme applied to Burgers' equation; and discusses about error propagation in large regions

A conservative local discontinuous Galerkin method for the solution of nonlinear Schr(o)dinger equation in two dimensions

Institute of Scientific and Technical Information of China (English)

ZHANG RongPei; YU XiJun; LI MingJun; LI XiangGui

2017-01-01

In this study,we present a conservative local discontinuous Galerkin (LDG) method for numerically solving the two-dimensional nonlinear Schr(o)dinger (NLS) equation.The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux.The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central,alternative and upwind-based flux.We will propose two kinds of time discretization methods for the semi-discrete formulation.One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation.The other one is Krylov implicit integration factor (ⅡF) method which demands much less computational effort.Various numerical experiments are presented to demonstrate the conservation law of mass and energy,the optimal rates of convergence,and the blow-up phenomenon.

A Kinematic Conservation Law in Free Surface Flow

OpenAIRE

Gavrilyuk , Sergey; Kalisch , Henrik; Khorsand , Zahra

2015-01-01

The Green-Naghdi system is used to model highly nonlinear weakly dispersive waves propagating at the surface of a shallow layer of a perfect fluid. The system has three associated conservation laws which describe the conservation of mass, momentum, and energy due to the surface wave motion. In addition, the system features a fourth conservation law which is the main focus of this note. It will be shown how this fourth conservation law can be interpreted in terms of a concrete kinematic quanti...

On the Incompleteness of Ibragimov’s Conservation Law Theorem and Its Equivalence to a Standard Formula Using Symmetries and Adjoint-Symmetries

Directory of Open Access Journals (Sweden)

Stephen C. Anco

2017-02-01

Full Text Available A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law through a well-known Fréchet derivative identity. Furthermore, the connection of this formula (and of Ibragimov’s theorem to the standard action of symmetries on conservation laws is explained, which accounts for a number of major drawbacks that have appeared in recent work using the formula to generate conservation laws. In particular, the formula can generate trivial conservation laws and does not always yield all non-trivial conservation laws unless the symmetry action on the set of these conservation laws is transitive. It is emphasized that all local conservation laws for any given system of differential equations can be found instead by a general method using adjoint-symmetries. This general method is a kind of adjoint version of the standard Lie method to find all local symmetries and is completely algorithmic. The relationship between this method, Noether’s theorem and the symmetry/adjoint-symmetry formula is discussed.

Quasilocal conservation laws in the quantum Hirota model

International Nuclear Information System (INIS)

Zadnik, Lenart; Prosen, Tomaž

2017-01-01

The extensivity of the quantum Hirota model’s conservation laws on a 1  +  1 dimensional lattice is considered. This model can be interpreted in terms of an integrable many-body quantum Floquet dynamics. We establish the procedure to generate a continuous family of quasilocal conservation laws from the conserved operators proposed by Faddeev and Volkov. The Hilbert–Schmidt kernel which allows the calculation of inner products of these new conservation laws is explicitly computed. This result has potential applications in quantum quench and transport problems in integrable quantum field theories. (paper)

Mathematical Model Based on Newton’s Laws and in First Thermodynamic Law of a Gas Turbine

Directory of Open Access Journals (Sweden)

Ottmar Rafael Uriza Gosebruch

2017-09-01

Full Text Available The present article explains the modeling of a Gas Turbine system; the mathematical modeling is based on fluid mechanics applying the principal energy laws such as Euler’s Law, Newton’s second Law and the first thermodynamic law to obtain the equations for mass, momentum and energy conservation; expressed as the continuity equation, the Navier-Stokes equation and the energy conservation using Fourier’s Law. The purpose of this article is to establish a precise mathematical model to be applied in control applications, for future works, within industry applications.

Renormalization, averaging, conservation laws and AdS (in)stability

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg; Vanhoof, Joris

2015-01-01

We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.

1/N perturbation theory and quantum conservation laws for supersymmetrical chiral field. 2

International Nuclear Information System (INIS)

Aref'eva, I.Ya.; Krivoshchekov, V.K.; Medvedev, P.B.; Gosudarstvennyj Komitet Standartov Soveta Ministrov SSSR, Moscow; Gosudarstvennyj Komitet po Ispol'zovaniyu Atomnoj Ehnergii SSSR, Moscow. Inst. Teoreticheskoj i Ehksperimental'noj Fiziki)

1980-01-01

The renormalizability of the supersymmetric chiral model (supersymmetric nonlinear σ-model) is proved in the framework of the 1/N perturbation theory expansion proposed in the previous paper. The renormalizability proof is essentially based on the quantum supersymmetric chirality condition. The supersymmetric formulation of equations of motion is given. The first non-trivial quantum conservation laws are derived

Conservation Laws for Gyrokinetic Equations for Large Perturbations and Flows

Science.gov (United States)

Dimits, Andris

2017-10-01

Gyrokinetic theory has proved to be very useful for the understanding of magnetized plasmas, both to simplify analytical treatments and as a basis for efficient numerical simulations. Gyrokinetic theories were previously developed in two extended orderings that are applicable to large fluctuations and flows as may arise in the tokamak edge and scrapeoff layer. In the present work, we cast the resulting equations in a field-theoretical variational form, and derive, up to second order in the respective orderings, the associated global and local energy and (linear and toroidal) momentum conservation relations that result from Noether's theorem. The consequences of these for the various possible choices of numerical discretization used in gyrokinetic simulations are considered. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and supported by the U.S. DOE, OFES.

Tests of conservation laws

International Nuclear Information System (INIS)

Goldhaber, M.

1988-01-01

For quite a while it has been realized that some discrete quantum numbers are conserved in some interactions but not in others. The most conspicuous cases are parity P, charge conjugation C, and the product CP which are conserved in strong and electromagnetic interactions but not in weak interactions. The question arises whether for some of the other conserved quantities, which are conserved in strong, electromagnetic and weak interactions, there is an interaction intermediate in strength between weak and gravitational which violates these quantum numbers, e.g., baryon number B and lepton number L. The possibility exists that these conservation laws, if they are broken at all, are only broken by the gravitational force which would make the mass of an intermediate boson which induces the break-down equal to the Planck mass. (orig.)

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

Science.gov (United States)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

Science.gov (United States)

Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles

2011-01-01

Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

Truncated Wigner dynamics and conservation laws

Science.gov (United States)

Drummond, Peter D.; Opanchuk, Bogdan

2017-10-01

Ultracold Bose gases can be used to experimentally test many-body theory predictions. Here we point out that both exact conservation laws and dynamical invariants exist in the topical case of the one-dimensional Bose gas, and these provide an important validation of methods. We show that the first four quantum conservation laws are exactly conserved in the approximate truncated Wigner approach to many-body quantum dynamics. Center-of-mass position variance is also exactly calculable. This is nearly exact in the truncated Wigner approximation, apart from small terms that vanish as N-3 /2 as N →∞ with fixed momentum cutoff. Examples of this are calculated in experimentally relevant, mesoscopic cases.

Solutions and conservation laws of Benjamin–Bona–Mahony

Indian Academy of Sciences (India)

In this paper, exact solutions of Benjamin–Bona–Mahony–Peregrine equation are obtained with power-law and dual power-law nonlinearities. The Lie group analysis as well as the simplest equation method are used to carry out the integration of these equations. The solutions obtained are cnoidal waves, periodic solutions ...

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

Science.gov (United States)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

Residual distribution for general time-dependent conservation laws

International Nuclear Information System (INIS)

Ricchiuto, Mario; Csik, Arpad; Deconinck, Herman

2005-01-01

We consider the second-order accurate numerical solution of general time-dependent hyperbolic conservation laws over unstructured grids in the framework of the Residual Distribution method. In order to achieve full conservation of the linear, monotone and first-order space-time schemes of (Csik et al., 2003) and (Abgrall et al., 2000), we extend the conservative residual distribution (CRD) formulation of (Csik et al., 2002) to prismatic space-time elements. We then study the design of second-order accurate and monotone schemes via the nonlinear mapping of the local residuals of linear monotone schemes. We derive sufficient and necessary conditions for the well-posedness of the mapping. We prove that the schemes obtained with the CRD formulation satisfy these conditions by construction. Thus the nonlinear schemes proposed in this paper are always well defined. The performance of the linear and nonlinear schemes are evaluated on a series of test problems involving the solution of the Euler equations and of a two-phase flow model. We consider the resolution of strong shocks and complex interacting flow structures. The results demonstrate the robustness, accuracy and non-oscillatory character of the proposed schemes. d schemes

Reduced energy conservation law for magnetized plasma

International Nuclear Information System (INIS)

Sosenko, P.P.; Decyk, V.K.

1994-01-01

A global energy conservation law for a magnetized plasma is studied within the context of a quasiparticle description. A reduced energy conservation law is derived for low-frequency, as compared to the gyromagnetic frequency, plasma motions with regard to both non-uniform mean flows and fluctuations in the plasma. The mean value of plasma energy is calculated and sufficient stability conditions for non-equilibrium plasmas are derived. (orig.)

Integrating factors and conservation theorems for Hamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems

Institute of Scientific and Technical Information of China (English)

李仁杰; 乔永芬; 刘洋

2002-01-01

We present a general approach to the construction of conservation laws for variable mass nonholonomic noncon-servative systems. First, we give the definition of integrating factors, and we study in detail the necessary conditionsfor the existence of the conserved quantities. Then, we establish the conservation theorem and its inverse theorem forHamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems. Finally,we give an example to illustrate the application of the results.

Uniqueness of Mass-Conserving Self-similar Solutions to Smoluchowski's Coagulation Equation with Inverse Power Law Kernels

Science.gov (United States)

Laurençot, Philippe

2018-03-01

Uniqueness of mass-conserving self-similar solutions to Smoluchowski's coagulation equation is shown when the coagulation kernel K is given by K(x,x_*)=2(x x_*)^{-α } , (x,x_*)\\in (0,∞)^2 , for some α >0.

Reduced Braginskii equations

International Nuclear Information System (INIS)

Yagi, M.; Horton, W.

1994-01-01

A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation

Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations

International Nuclear Information System (INIS)

Hong Jialin; Li Chun

2006-01-01

In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law

Local conservation laws for principle chiral fields (d=1)

International Nuclear Information System (INIS)

Cherednik, I.V.

1979-01-01

The Beklund transformation for chiral fields in the two-dimensional Minkovski space is found. As a result an infinite series of conservation laws for principle chiral Osub(n) fields (d=1) has been built. It is shown that these laws are local, the infinite series of global invariants which do not depend on xi, eta, and which is rather rapidly decrease along xi (or along eta) solutions being connected with these laws (xi, eta - coordinates of the light cone). It is noted that with the help of the construction proposed it is possible to obtain conservation laws of principle chiral G fields, including G in the suitable ortogonal groups. Symmetry permits to exchange xi and eta. The construction of conservation laws may be carried out without supposition that lambda has a multiplicity equal to 1, however the proof of the locality applied does not transfer on the laws obtained

Weak self-adjoint differential equations

International Nuclear Information System (INIS)

Gandarias, M L

2011-01-01

The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006 J. Math. Anal. Appl. 318 742-57; 2007 Arch. ALGA 4 55-60). In Ibragimov (2007 J. Math. Anal. Appl. 333 311-28), a general theorem on conservation laws was proved. In this paper, we generalize the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. We find a class of weak self-adjoint quasi-linear parabolic equations. The property of a differential equation to be weak self-adjoint is important for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)

Reduced Braginskii equations

International Nuclear Information System (INIS)

Yagi, M.; Horton, W.

1993-11-01

A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0

Conservation laws with non-convex flux and applications to two-phase flow in porous media

Energy Technology Data Exchange (ETDEWEB)

Tegnander, Cathrine

1998-12-31

This thesis deals with conservation laws, which form a family of partial differential equations (PDEs) describing conservation of mass, momentum and energy. The first part studies some theoretical aspects of conservation laws: (1) Scalar hyperbolic conservation laws with a non-convex flux function, where time dependent decay estimates are mainly obtained by a front tracking technique, (2) Convergence of solutions for a finite difference scheme given by a class of one dimensional parabolic systems. The second part of the thesis applies the theory to multiphase flow in porous media. A number of mathematical models for multiphase flow in groundwater are studied. Techniques to improve the study of simulations of oil, gas and water phases in reservoirs such as in the North Sea are discussed. Upscaling of a refinement of the permeability field is evaluated using a flow simulation. This is done by a study of the preserving of the rank of a number of realizations with respect to the cumulative production parameter. Finally, the importance of selection of numerical methods in the simulations are exemplified by considering various splitting techniques. The numerical methods of front tracking and finite difference schemes and finite element methods are used. 98 refs., 24 figs., 18 tabs.

Italian energy conservation laws: Implementation problems

International Nuclear Information System (INIS)

Anon.

1993-01-01

Italian energy conservation Law No. 9 was designed to reduce Italy's worrisome 82% dependency on foreign energy supplies by encouraging the development and use of renewable energy sources, fuel diversification and auto-production/cogeneration by private industry. Law No. 10 was intended to promote energy conservation initiatives especially with regard to the efficient use of energy for space heating in public buildings. Both of these legal incentives have encountered great difficulties in implementation due to the inability of the Government to provide the necessary timely and sufficient start-up funds, as well as, due to the excessive bureaucratism that was built into the administrative procedures

Demonstrations of the Action and Reaction Law and the Energy Conservation Law Using Fine Spherical Plastic Beads

Science.gov (United States)

Khumaeni, A.; Tanaka, S.; Kobayashi, A.; Lee, Y. I.; Kurniawan, K. H.; Ishii, K.; Kagawa, K.

2008-01-01

Equipment for demonstrating Newton's third law and the energy conservation law in mechanics have successfully been constructed utilizing fine spherical plastic beads in place of metal ball bearings. To demonstrate Newton's third law, special magnetized Petri dishes were employed as objects, while to examine the energy conservation law, a…

Solitons, Lie Group Analysis and Conservation Laws of a (3+1)-Dimensional Modified Zakharov-Kuznetsov Equation in a Multicomponent Magnetised Plasma

Science.gov (United States)

Du, Xia-Xia; Tian, Bo; Chai, Jun; Sun, Yan; Yuan, Yu-Qiang

2017-11-01

In this paper, we investigate a (3+1)-dimensional modified Zakharov-Kuznetsov equation, which describes the nonlinear plasma-acoustic waves in a multicomponent magnetised plasma. With the aid of the Hirota method and symbolic computation, bilinear forms and one-, two- and three-soliton solutions are derived. The characteristics and interaction of the solitons are discussed graphically. We present the effects on the soliton's amplitude by the nonlinear coefficients which are related to the ratio of the positive-ion mass to negative-ion mass, number densities, initial densities of the lower- and higher-temperature electrons and ratio of the lower temperature to the higher temperature for electrons, as well as by the dispersion coefficient, which is related to the ratio of the positive-ion mass to the negative-ion mass and number densities. Moreover, using the Lie symmetry group theory, we derive the Lie point symmetry generators and the corresponding symmetry reductions, through which certain analytic solutions are obtained via the power series expansion method and the (G'/G) expansion method. We demonstrate that such an equation is strictly self-adjoint, and the conservation laws associated with the Lie point symmetry generators are derived.

Reduced Braginskii equations

Energy Technology Data Exchange (ETDEWEB)

Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies

1993-11-01

A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.

Hamiltonian structures of some non-linear evolution equations

International Nuclear Information System (INIS)

Tu, G.Z.

1983-06-01

The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

Unimodular Einstein-Cartan gravity: Dynamics and conservation laws

Science.gov (United States)

Bonder, Yuri; Corral, Cristóbal

2018-04-01

Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the most general matter Lagrangian allowed by the symmetries is considered, dynamical restrictions arise on their functional dependence. The field equations are obtained and the conservation laws associated with the symmetries are derived. It is found that, analogous to torsion-free unimodular gravity, the field equation for the vierbein is traceless; nevertheless, torsion is algebraically related to the spin density as in standard Einstein-Cartan theory. The particular example of massless Dirac spinors is studied, and comparisons with standard Einstein-Cartan theory are shown.

Solutions and conservation laws of Benjamin–Bona–Mahony ...

Indian Academy of Sciences (India)

obtained with power-law and dual power-law nonlinearities. The Lie group analysis as ... The notion of conservation laws plays an important role in the solution process of differential ... For the theory and applications of Lie group analysis the ...

Super-Hamiltonian Structures and Conservation Laws of a New Six-Component Super-Ablowitz-Kaup-Newell-Segur Hierarchy

Directory of Open Access Journals (Sweden)

Fucai You

2014-01-01

Full Text Available A six-component super-Ablowitz-Kaup-Newell-Segur (-AKNS hierarchy is proposed by the zero curvature equation associated with Lie superalgebras. Supertrace identity is used to furnish the super-Hamiltonian structures for the resulting nonlinear superintegrable hierarchy. Furthermore, we derive the infinite conservation laws of the first two nonlinear super-AKNS equations in the hierarchy by utilizing spectral parameter expansions. PACS: 02.30.Ik; 02.30.Jr; 02.20.Sv.

Conservation laws and nuclear transport models

International Nuclear Information System (INIS)

Gale, C.; Das Gupta, S.

1990-01-01

We discuss the consequences of energy and angular momentum conservation for nucleon-nucleon scattering in a nuclear environment during high-energy heavy-ion collisions. We describe algorithms that ensure stricter enforcement of such conservation laws within popular microscopic models of intermediate-energy heavy-ion collisions. We find that the net effects on global observables are small

Constitutive equations for two-phase flows

International Nuclear Information System (INIS)

Boure, J.A.

1974-12-01

The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr

Statistically derived conservation equations for fluid particle flows

International Nuclear Information System (INIS)

Reyes, J.N. Jr.

1989-01-01

The behavior of water droplets in a heated nuclear fuel channel is of significant interest to nuclear reactor safety studies pertaining to loss-of-coolant accidents. This paper presents the derivation of the mass, momentum, and energy conservation equations for a distribution of fluid particles (bubbles or droplets) transported by a continuous fluid medium. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior

Modified Van der Waals equation and law of corresponding states

Science.gov (United States)

Zhong, Wei; Xiao, Changming; Zhu, Yongkai

2017-04-01

It is well known that the Van der Waals equation is a modification of the ideal gas law, yet it can be used to describe both gas and liquid, and some important messages can be obtained from this state equation. However, the Van der Waals equation is not a precise state equation, and it does not give a good description of the law of corresponding states. In this paper, we expand the Van der Waals equation into its Taylor's series form, and then modify the fourth order expansion by changing the constant Virial coefficients into their analogous ones. Via this way, a more precise result about the law of corresponding states has been obtained, and the law of corresponding states can then be expressed as: in terms of the reduced variables, all fluids should obey the same equation with the analogous Virial coefficients. In addition, the system of 3 He with quantum effects has also been taken into consideration with our modified Van der Waals equation, and it is found that, for a normal system without quantum effect, the modification on ideal gas law from the Van der Waals equation is more significant than the real case, however, for a system with quantum effect, this modification is less significant than the real case, thus a factor is introduced in this paper to weaken or strengthen the modification of the Van der Waals equation, respectively.

The structure of additive conservation laws

International Nuclear Information System (INIS)

Helmut Reen

1979-01-01

All additive conserved quantities are listed for a system with short range central force interaction between the particles: a special case shows up in Boltzmann H-theorem and his derivation of the Maxwell velocity distribution. It is concluded that in classical mechanics of mass points there are no other additive conservation laws besides of energy, momentum, angular momentum and center of mass motion. A generator is considered of a symmetry transformation defined as integral over a conserved local current density where the latter, in general, needs not be covariant under translations

Symmetries and Conservation Laws in Classical and Quantum ...

Indian Academy of Sciences (India)

sriranga

and conservation principles in the Lagrangian and. Hamiltonian ... theory. V Balakrishnan – his research interests are statistical phys- ics, stochastic .... We can appreciate this difference in yet another way: ... principles and conservation laws.

Conservation laws for voter-like models on random directed networks

International Nuclear Information System (INIS)

Ángeles Serrano, M; Klemm, Konstantin; Vazquez, Federico; Eguíluz, Víctor M; San Miguel, Maxi

2009-01-01

We study the voter model, under node and link update, and the related invasion process on a single strongly connected component of a directed network. We implement an analytical treatment in the thermodynamic limit using the heterogeneous mean-field assumption. From the dynamical rules at the microscopic level, we find the equations for the evolution of the relative densities of nodes in a given state on heterogeneous networks with arbitrary degree distribution and degree–degree correlations. We prove that conserved quantities as weighted linear superpositions of spin states exist for all three processes and, for uncorrelated directed networks, we derive their specific expressions. We also discuss the time evolution of the relative densities that decay exponentially to a homogeneous stationary value given by the conserved quantity. The conservation laws obtained in the thermodynamic limit for a system that does not order in that limit determine the probabilities of reaching the absorbing state for a finite system. The contribution of each degree class to the conserved quantity is determined by a local property. Depending on the dynamics, the highest contribution is associated with influential nodes reaching a large number of outgoing neighbors, not too influenceable ones with a low number of incoming connections, or both at the same time

The laws of conservation of physics and the β-decay of atomic nuclei

International Nuclear Information System (INIS)

Bagge, E.R.

1976-01-01

The laws of conservation of energy, the momentum of translation and the angular momentum of a system form a closed unit according to Noether's theorem. A generalisation of these laws taking into account the states of negative energies must therefore comprise all laws of conservation. A new interpretation of the β-decay without neutrinos should thus take the law of conservation of energy at the β-continuum for the world and anti-world as motivation to demand corresponding laws of conservation for the linear momentum and the spin and it will be shown that this new interpretation of the laws of conservation exactly suffices to interpret all characteristic phenomena of β-decay in a manner free of contradiction. (orig.) [de

Invariant relations in Boussinesq-type equations

International Nuclear Information System (INIS)

Meletlidou, Efi; Pouget, Joeel; Maugin, Gerard; Aifantis, Elias

2004-01-01

A wide class of partial differential equations have at least three conservation laws that remain invariant for certain solutions of them and especially for solitary wave solutions. These conservation laws can be considered as the energy, pseudomomentum and mass integrals of these solutions. We investigate the invariant relation between the energy and the pseudomomentum for solitary waves in two Boussinesq-type equations that come from the theory of elasticity and lattice models

A Kirchhoff-like conservation law in Regge calculus

International Nuclear Information System (INIS)

Gentle, Adrian P; Kheyfets, Arkady; McDonald, Jonathan R; Miller, Warner A

2009-01-01

Simplicial lattices provide an elegant framework for discrete spacetimes. The inherent orthogonality between a simplicial lattice and its circumcentric dual yields an austere representation of spacetime which provides a conceptually simple form of Einstein's geometric theory of gravitation. A sufficient understanding of simplicial spacetimes has been demonstrated in the literature for spacetimes devoid of all non-gravitational sources. However, this understanding has not been adequately extended to non-vacuum spacetime models. Consequently, a deep understanding of the diffeomorphic structure of the discrete theory is lacking. Conservation laws and symmetry properties are attractive starting points for coupling matter with the lattice. We present a simplicial form of the contracted Bianchi identity which is based on the E Cartan moment of rotation operator. This identity manifests itself in the conceptually simple form of a Kirchhoff-like conservation law. This conservation law enables one to extend Regge calculus to non-vacuum spacetimes and provides a deeper understanding of the simplicial diffeomorphism group.

Integrating factors and conservation theorems for Hamilton‘s canonical equations of motion of variable mass nonholonmic nonconservative dynamical systems

Institute of Scientific and Technical Information of China (English)

李仁杰; 刘洋; 等

2002-01-01

We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton's canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results.

Magnetohydrodynamics and fluid dynamics action principles and conservation laws

CERN Document Server

Webb, Gary

2018-01-01

This text focuses on conservation laws in magnetohydrodynamics, gasdynamics and hydrodynamics. A grasp of new conservation laws is essential in fusion and space plasmas, as well as in geophysical fluid dynamics; they can be used to test numerical codes, or to reveal new aspects of the underlying physics, e.g., by identifying the time history of the fluid elements as an important key to understanding fluid vorticity or in investigating the stability of steady flows. The ten Galilean Lie point symmetries of the fundamental action discussed in this book give rise to the conservation of energy, momentum, angular momentum and center of mass conservation laws via Noether’s first theorem. The advected invariants are related to fluid relabeling symmetries – so-called diffeomorphisms associated with the Lagrangian map – and are obtained by applying the Euler-Poincare approach to Noether’s second theorem. The book discusses several variants of helicity including kinetic helicity, cross helicity, magnetic helici...

Integrable covariant law of energy-momentum conservation for a gravitational field with the absolute parallelism structure

International Nuclear Information System (INIS)

Asanov, G.S.

1979-01-01

It is shown the description of gravitational field in the riemannian space-time by means of the absolute parallelism structure makes it possible to formulate an integrable covariant law of energy-momentum conservation for gravitational field, by imposing on the energy-momentum tensor the condition of vanishing of the covariant divergence (in the sense of the absolute parallelism). As a result of taking into account covariant constraints for the tetrads of the absolute parallelism, the Lagrangian density turns out to be not geometrised anymore and leads to the unambiguous conservation law of the type mentioned in the N-body problem. Covariant field equations imply the existence of the special euclidean coordinates outside of static neighbourhoods of gravitationing bodies. In these coordinates determined by the tetrads of the absolute parallelism, the linear approximation is not connected with any noncovariant assumptions

Newton's laws of motion in form of Riccati equation

OpenAIRE

Nowakowski, M.; Rosu, H. C.

2001-01-01

We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential $V(r)=k r^{\\epsilon}$. For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, ...

Analysis of self-similar solutions of multidimensional conservation laws

Energy Technology Data Exchange (ETDEWEB)

Keyfitz, Barbara Lee [The Ohio State Univ., Columbus, OH (United States)

2014-02-15

This project focused on analysis of multidimensional conservation laws, specifically on extensions to the study of self-siminar solutions, a project initiated by the PI. In addition, progress was made on an approach to studying conservation laws of very low regularity; in this research, the context was a novel problem in chromatography. Two graduate students in mathematics were supported during the grant period, and have almost completed their thesis research.

Electromagnetic equations based on the law of Biot and Savart

International Nuclear Information System (INIS)

Yan, C.-C.

1983-01-01

The law of Biot and Savart is given some interpretations that may be of some help in presenting the law. Some possible consequences and the whole set of Maxwell-Lorentz equations are shown to be derivable from the law of Biot and Savart. It is pointed out that the failure or success of deriving the set of Maxwell-Lorentz equation from the law of Biot and Savart is intimately connected to the basic ideas of the theory of special relativity of Einstein. (Author) [pt

A general qualitative theory of conservation laws, their violation and other spontaneous phenomena

International Nuclear Information System (INIS)

Tahir Shah, K.

1976-10-01

A general theory of conservation laws and other invariants for a physical system through equivalence relations are formulated. The conservation laws are classified according to the type of equivalence relation; group equivalence, homotopical equivalence and other types of equivalence relations giving respective kinds of conservation laws. The stability properties in the topological (and differentiable) sense are discussed using continuous deformations with respect to control parameters. The conservation laws due to the abelian symmetries are shown to be stable through application of well-known theorems

Hall magnetohydrodynamics: Conservation laws and Lyapunov stability

International Nuclear Information System (INIS)

Holm, D.D.

1987-01-01

Hall electric fields produce circulating mass flow in confined ideal-fluid plasmas. The conservation laws, Hamiltonian structure, equilibrium state relations, and Lyapunov stability conditions are presented here for ideal Hall magnetohydrodynamics (HMHD) in two and three dimensions. The approach here is to use the remarkable array of nonlinear conservation laws for HMHD that follow from its Hamiltonian structure in order to construct explicit Lyapunov functionals for the HMHD equilibrium states. In this way, the Lyapunov stability analysis provides classes of HMHD equilibria that are stable and whose linearized initial-value problems are well posed (in the sense of possessing continuous dependence on initial conditions). Several examples are discussed in both two and three dimensions

Expanding Newton Mechanics with Neutrosophy and Quadstage Method ──New Newton Mechanics Taking Law of Conservation of Energy as Unique Source Law

Directory of Open Access Journals (Sweden)

Fu Yuhua

2014-06-01

Full Text Available Neutrosophy is a new branch of philosophy, and "Quad-stage" (Four stages is the expansion of Hegel’s triad thesis, antithesis, synthesis of development. Applying Neutrosophy and "Quad-stage" method, the purposes of this paper are expanding Newton Mechanics and making it become New Newton Mechanics (NNW taking law of conservation of energy as unique source law. In this paper the examples show that in some cases other laws may be contradicted with the law of conservation of energy. The original Newton's three laws and the law of gravity, in principle can be derived by the law of conservation of energy. Through the example of free falling body, this paper derives the original Newton's second law by using the law of conservation of energy, and proves that there is not the contradiction between the original law of gravity and the law of conservation of energy; and through the example of a small ball rolls along the inclined plane (belonging to the problem cannot be solved by general relativity that a body is forced to move in flat space, derives improved Newton's second law and improved law of gravity by using law of conservation of energy. Whether or not other conservation laws (such as the law of conservation of momentum and the law of conservation of angular momentum can be utilized, should be tested by law of conservation of energy. When the original Newton's second law is not correct, then the laws of conservation of momentum and angular momentum are no longer correct; therefore the general forms of improved law of conservation of momentum and improved law of conservation of angular momentum are presented. In the cases that law of conservation of energy cannot be used effectively, New Newton Mechanics will not exclude that according to other theories or accurate experiments to derive the laws or formulas to solve some specific problems. For example, with the help of the result of general relativity, the improved Newton's formula of universal

Identifying all moiety conservation laws in genome-scale metabolic networks.

Science.gov (United States)

De Martino, Andrea; De Martino, Daniele; Mulet, Roberto; Pagnani, Andrea

2014-01-01

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

Identifying all moiety conservation laws in genome-scale metabolic networks.

Directory of Open Access Journals (Sweden)

Andrea De Martino

Full Text Available The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

Symmetries, conservation laws and least action

International Nuclear Information System (INIS)

Maher, P.J.

1982-01-01

This article is a non-technical account of some recent work on the connection between symmetries and conservation laws. This recent work-which uses the modern algebraic concept of naturality-yields a new interpretation of the variational, or least action, principle. (author)

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

Energy Technology Data Exchange (ETDEWEB)

Delhaye, J M [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

Energy Technology Data Exchange (ETDEWEB)

Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

Hunting, law enforcement, and African primate conservation.

Science.gov (United States)

N'Goran, Paul K; Boesch, Christophe; Mundry, Roger; N'Goran, Eliezer K; Herbinger, Ilka; Yapi, Fabrice A; Kühl, Hjalmar S

2012-06-01

Primates are regularly hunted for bushmeat in tropical forests, and systematic ecological monitoring can help determine the effect hunting has on these and other hunted species. Monitoring can also be used to inform law enforcement and managers of where hunting is concentrated. We evaluated the effects of law enforcement informed by monitoring data on density and spatial distribution of 8 monkey species in Taï National Park, Côte d'Ivoire. We conducted intensive surveys of monkeys and looked for signs of human activity throughout the park. We also gathered information on the activities of law-enforcement personnel related to hunting and evaluated the relative effects of hunting, forest cover and proximity to rivers, and conservation effort on primate distribution and density. The effects of hunting on monkeys varied among species. Red colobus monkeys (Procolobus badius) were most affected and Campbell's monkeys (Cercopithecus campbelli) were least affected by hunting. Density of monkeys irrespective of species was up to 100 times higher near a research station and tourism site in the southwestern section of the park, where there is little hunting, than in the southeastern part of the park. The results of our monitoring guided law-enforcement patrols toward zones with the most hunting activity. Such systematic coordination of ecological monitoring and law enforcement may be applicable at other sites. ©2012 Society for Conservation Biology.

The Conservation Principles and Kepler's Laws of Planetary Motion

Science.gov (United States)

Motz, Lloyd

1975-01-01

Derives Kepler's three laws of planetary motion algebraically from conservation principles without introducing Newton's law of force explicitly. This procedure can be presented to students who have had no more than high school algebra. (Author)

Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations

International Nuclear Information System (INIS)

Hof, Bas van’t; Veldman, Arthur E.P.

2012-01-01

The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting ‘MaMEC’ discretizations conserve mass, momentum as well as energy, although no explicit conservation law for the total energy is present. Essential ingredients are (i) discrete convection that leaves the discrete energy invariant, and (ii) discrete consistency between the thermodynamic terms. Of particular relevance is the way in which finite volume fluxes are related to nodal values. The method is an extension of existing methods based on skew-symmetry of discrete operators, because it allows arbitrary equations of state and a larger class of grids than earlier methods. The method is first illustrated with a one-dimensional example on a highly stretched staggered grid, in which the MaMEC method calculates qualitatively correct results and a non-skew-symmetric finite volume method becomes unstable. A further example is a two-dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid. The conservation of mass, momentum and energy is checked, and losses are found negligible up to machine accuracy.

Post-Newtonian conservation laws in rigid quasilocal frames

International Nuclear Information System (INIS)

McGrath, Paul L; Chanona, Melanie; Epp, Richard J; Mann, Robert B; Koop, Michael J

2014-01-01

In recent work we constructed completely general conservation laws for energy (McGrath et al 2012 Class. Quantum Grav. 29 215012) and linear and angular momentum (Epp et al 2013 Class. Quantum Grav. 30 195019) of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level that these RQF conservation laws are superior to conservation laws based on the local stress–energy–momentum tensor of matter because (1) they do not rely on spacetime symmetries and (2) they properly account for both matter and gravitational effects. Moreover, they provide simple, exact, operational expressions for fluxes of gravitational energy and linear and angular momentum. In this paper we derive the form of these laws in a general first post-Newtonian (1PN) approximation, and then apply these approximate laws to the problem of gravitational tidal interactions. We obtain formulas for tidal heating and tidal torque that agree with the literature, but without resorting to the use of pseudotensors. We describe the physical mechanism of these tidal interactions not in the traditional terms of a Newtonian gravitational force, but in terms of a much simpler and universal mechanism that is an exact, quasilocal manifestation of the equivalence principle in general relativity. As concrete examples, we look at the tidal heating of Jupiter’s moon Io and angular momentum transfer in the Earth–Moon system that causes a gradual spin-down of the Earth and recession of the Moon. In both examples we find agreement with observation. (paper)

Conservation laws and geometry of perturbed coset models

CERN Document Server

Bakas, Ioannis

1994-01-01

We present a Lagrangian description of the $SU(2)/U(1)$ coset model perturbed by its first thermal operator. This is the simplest perturbation that changes sign under Krammers--Wannier duality. The resulting theory, which is a 2--component generalization of the sine--Gordon model, is then taken in Minkowski space. For negative values of the coupling constant $g$, it is classically equivalent to the $O(4)$ non--linear $\\s$--model reduced in a certain frame. For $g > 0$, it describes the relativistic motion of vortices in a constant external field. Viewing the classical equations of motion as a zero curvature condition, we obtain recursive relations for the infinitely many conservation laws by the abelianization method of gauge connections. The higher spin currents are constructed entirely using an off--critical generalization of the $W_{\\infty}$ generators. We give a geometric interpretation to the corresponding charges in terms of embeddings. Applications to the chirally invariant $U(2)$ Gross--Neveu model ar...

Tendril perversion-a physical implication of the topological conservation law

International Nuclear Information System (INIS)

Pieranski, Piotr; Baranska, Justyna; Skjeltorp, Arne

2004-01-01

Tendril perversion-a phenomenon ruled by the topological conservation law-is presented. A contemporary, quantitative analysis of the phenomenon is confronted with its qualitative, intuitive analysis carried out by Charles Darwin. The linking number, twist and writhe are defined. The topological conservation law is introduced. The Gauss formula for calculating the linking number and the Calugareanu formula for calculating writhe are derived and discussed using physical arguments

Tendril perversion-a physical implication of the topological conservation law

Energy Technology Data Exchange (ETDEWEB)

Pieranski, Piotr [Laboratory of Computational Physics and Semiconductors, Poznan University of Technology, Nieszawska 13A, 60 965 Poznan (Poland); Baranska, Justyna [Laboratory of Computational Physics and Semiconductors, Poznan University of Technology, Nieszawska 13A, 60 965 Poznan (Poland); Skjeltorp, Arne [Institute for Energy Technology, Kjeller (Norway)

2004-09-10

Tendril perversion-a phenomenon ruled by the topological conservation law-is presented. A contemporary, quantitative analysis of the phenomenon is confronted with its qualitative, intuitive analysis carried out by Charles Darwin. The linking number, twist and writhe are defined. The topological conservation law is introduced. The Gauss formula for calculating the linking number and the Calugareanu formula for calculating writhe are derived and discussed using physical arguments.

Convergence of finite differences schemes for viscous and inviscid conservation laws with rough coefficients

Energy Technology Data Exchange (ETDEWEB)

Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik

2000-09-01

We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a ''rough'' coefficient function k(x). we show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k' is in BV, thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations as well as new convergence results for their finite difference approximations. In the inviscid case, we also provide a rate of convergence. Our convergence proofs are based on deriving a series of a priori estimates and using a general L{sup p} compactness criterion. (author)

Nonlinearity, Conservation Law and Shocks

Indian Academy of Sciences (India)

However, genuine nonlinearity is always present in an ideal gas. The conservation form of the equation (25) brings in shocks which cut off the growing part of the amplitUde as shown in. Figure 15. Acknowledgements. The author sincerely thanks the two referees whose valuable comments led to an improvement of the ...

An exactly conservative particle method for one dimensional scalar conservation laws

International Nuclear Information System (INIS)

Farjoun, Yossi; Seibold, Benjamin

2009-01-01

A particle scheme for scalar conservation laws in one space dimension is presented. Particles representing the solution are moved according to their characteristic velocities. Particle interaction is resolved locally, satisfying exact conservation of area. Shocks stay sharp and propagate at correct speeds, while rarefaction waves are created where appropriate. The method is variation diminishing, entropy decreasing, exactly conservative, and has no numerical dissipation away from shocks. Solutions, including the location of shocks, are approximated with second order accuracy. Source terms can be included. The method is compared to CLAWPACK in various examples, and found to yield a comparable or better accuracy for similar resolutions.

Geometric approach to soliton equations

International Nuclear Information System (INIS)

Sasaki, R.

1979-09-01

A class of nonlinear equations that can be solved in terms of nxn scattering problem is investigated. A systematic geometric method of exploiting conservation laws and related equations, the so-called prolongation structure, is worked out. The nxn problem is reduced to nsub(n-1)x(n-1) problems and finally to 2x2 problems, which have been comprehensively investigated recently by the author. A general method of deriving the infinite numbers of polynomial conservation laws for an nxn problem is presented. The cases of 3x3 and 2x2 problems are discussed explicitly. (Auth.)

Symmetry Principles and Conservation Laws in Atomic and ...

Indian Academy of Sciences (India)

Symmetry Principles and Conservation Laws in. Atomic and Subatomic Physics – 2. P C Deshmukh .... dicated that parity conservation, though often assumed, had not been verified in weak interactions. Acting on ... The gauge bosons W§ have a charge of +1 and −1 unit, but the Z0 boson of the standard model is neutral.

Generalized Laws of Black Hole Thermodynamics and Quantum Conservation Laws on Hawking Radiation Process

OpenAIRE

Wu, S. Q.; Cai, X.

2000-01-01

Four classical laws of black hole thermodynamics are extended from exterior (event) horizon to interior (Cauchy) horizon. Especially, the first law of classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to those in quantum form. Then five quantum conservation laws on the KNBH evaporation effect are derived in virtue of thermodynamical equilibrium conditions. As a by-product, Bekenstein-Hawking's relation $ S=A/4 $ is exactly recovered.

Generalized laws of black-hole thermodynamics and quantum conservation laws on Hawking radiation process

International Nuclear Information System (INIS)

Wu, S.Q.; Cai, X.

2000-01-01

Four classical laws of black-hole thermodynamics are extended from exterior (event) horizon to interior (Cauchy) horizon. Especially, the first law of classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to those in quantum form. Then five quantum conservation laws on the KNBH evaporation effect are derived in virtue of thermodynamical equilibrium conditions. As a by-product, Bekenstein-Haw king's relation S=A/4 is exactly recovered

Numerical methods for Eulerian and Lagrangian conservation laws

CERN Document Server

Després, Bruno

2017-01-01

This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.

Derivation of Grad’s Thirteen Regularized Moment Equations Using a Hermite Polynomial Representation of Velocity Distribution Function (Preprint)

Science.gov (United States)

2010-06-16

B4) Substituting tui  / and tVT  /2 from the momentum and energy conservation law equations, Eqs...B9) Substituting tui  / and tVT  /2 from the momentum and energy conservation law equations, Eqs. (15...Substituting tui  / and tVT  /2 from the momentum and energy conservation law equations, Eqs. (15) and (16), into Eq. (B13) and then dropping all

Conservation law of plants' energy value dependence of plants ...

African Journals Online (AJOL)

The plants differences in biochemical composition are analyzed, and the conservation law of energy value in plants is obtained. The link between the need for the nutrients and the plants biochemical composition is examined, Liebig's law is specified. Keywords: plant's biochemical composition, biochemistry, energy value in ...

The tensorial conservation law in general relativity

International Nuclear Information System (INIS)

Zhao, M.G.

1984-01-01

A general tensorial conservation law is formulated by starting from the invariance of the gravitational Lagrangian density. Utilising this new formula, the author derives some reasonable results for the mass-energy distribution which are in accordance with the Newtonian formulae. (author)

Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

International Nuclear Information System (INIS)

Jia Liqun; Cui Jinchao; Zhang Yaoyu; Luo Shaokai

2009-01-01

Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results. (general)

Compensatory Measures in European Nature Conservation Law

Directory of Open Access Journals (Sweden)

Geert Van Hoorick

2014-05-01

Full Text Available The Birds and Habitats Directives are the cornerstones of EU nature conservation law, aiming at the conservation of the Natura 2000 network, a network of protected sites under these directives, and the protection of species. The protection regime for these sites and species is not absolute: Member States may, under certain conditions, allow plans or projects that can have an adverse impact on nature. In this case compensatory measures can play an important role in safeguarding the Natura 2000 network and ensuring the survival of the protected species.This contribution analyses whether taking compensatory measures is always obligatory, and discusses the aim and the characteristics of compensatory measures, in relation to other kinds of measures such as mitigation measures, usual nature conservation measures, and former nature development measures, and to the assessment of the adverse impact caused by the plan or project and of the alternative solutions. The questions will be discussed in light of the contents of the legislation, the guidance and practice by the European Commission, (legal doctrine and case law, mainly of the Court of Justice of the European Union.

Hojman's theorem of the third-order ordinary differential equation

International Nuclear Information System (INIS)

Hong-Sheng, Lü; Hong-Bin, Zhang; Shu-Long, Gu

2009-01-01

This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results. (general)

Conservation properties of numerical integration methods for systems of ordinary differential equations

Science.gov (United States)

Rosenbaum, J. S.

1976-01-01

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks

International Nuclear Information System (INIS)

Delhaye, J.M.

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

Lie symmetry analysis, optimal system, exact solutions and conservation laws of a class of high-order nonlinear wave equations%一类高阶非线性波方程的李群分析、最优系统、精确解和守恒律∗

Institute of Scientific and Technical Information of China (English)

李凯辉; 刘汉泽; 辛祥鹏

2016-01-01

The symmetries, conservation laws and exact solutions to the nonlinear partial differential equations play a signif-icant role in nonlinear science and mathematical physics. Symmetry is derived from physics, and it is a mathematical description for invariance. Symmetry group theory plays an important role in constructing explicit solutions, whether the equations are integrable or not. By using the symmetry method, an original nonlinear system can be reduced to a system with fewer independent variables through any given subgroup. But, since there are almost always an infinite number of such subgroups, it is usually not feasible to list all possible group invariant solutions to the system. It is anticipated to find all those equivalent group invariant solutions, that is to say, to construct the one-dimensional optimal system for the Lie algebra. Construction of explicit forms of conservation laws is meaningful, as they are used for developing the appropriate numerical methods and for making mathematical analyses, in particular, of existence, uniqueness and stability. In addition, the existence of a large number of conservation laws of a partial differential equation (system) is a strong indication of its integrability. The similarity solutions are of importance for investigating the long-time behavior, blow-up profile and asymptotic phenomena of a non-linear system. For instance, in some circumstance, the asymptotic behaviors of finite-mass solutions of non-linear diffusion equation with non-linear source term are described by an explicit self-similar solution, etc. However, how to tackle these matters is a complicated problem that challenges researchers to be solved. In this paper, by using the symmetry method, we obtain the symmetry reduction, optimal systems, and many new exact group invariant solution of a fifth-order nonlinear wave equation. By Lie symmetry analysis method, the point symmetries and an optimal system of the equation are obtained. The exact power

Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics

Directory of Open Access Journals (Sweden)

Lorenzo Fatibene

2010-04-01

Full Text Available We review the Lagrangian formulation of (generalised Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called “Natural Theories” and “Gauge-Natural Theories” that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.. It is discussed how the use of Poincar´e–Cartan forms and decompositions of natural (or gauge-natural variational operators give rise to notions such as “generators of Noether symmetries”, energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-calledADMlaws in General Relativity with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.. A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer; one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation “à la Palatini” and in its extensions to Non-Linear Gravity Theories; one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero–Immirzi connections.

Application of polynomial preconditioners to conservation laws

NARCIS (Netherlands)

Geurts, Bernardus J.; van Buuren, R.; Lu, H.

2000-01-01

Polynomial preconditioners which are suitable in implicit time-stepping methods for conservation laws are reviewed and analyzed. The preconditioners considered are either based on a truncation of a Neumann series or on Chebyshev polynomials for the inverse of the system-matrix. The latter class of

Conservation laws and rogue waves for a higher-order nonlinear Schrödinger equation with variable coefficients in the inhomogeneous fiber

Science.gov (United States)

Du, Zhong; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Sun, Yan

2017-07-01

Subpicosecond or femtosecond optical pulse propagation in the inhomogeneous fiber can be described by a higher-order nonlinear Schrödinger equation with variable coefficients, which is investigated in the paper. Via the Ablowitz-Kaup-Newell-Segur system and symbolic computation, the Lax pair and infinitely-many conservation laws are deduced. Based on the Lax pair and a modified Darboux transformation technique, the first- and second-order rogue wave solutions are constructed. Effects of the groupvelocity dispersion and third-order dispersion on the properties of the first- and second-order rouge waves are graphically presented and analyzed: The groupvelocity dispersion and third-order dispersion both affect the ranges and shapes of the first- and second-order rogue waves: The third-order dispersion can produce a skew angle of the first-order rogue wave and the skew angle rotates counterclockwise with the increase of the groupvelocity dispersion, when the groupvelocity dispersion and third-order dispersion are chosen as the constants; When the groupvelocity dispersion and third-order dispersion are taken as the functions of the propagation distance, the linear, X-shaped and parabolic trajectories of the rogue waves are obtained.

Notes on Well-Posed, Ensemble Averaged Conservation Equations for Multiphase, Multi-Component, and Multi-Material Flows

International Nuclear Information System (INIS)

Ray A. Berry

2005-01-01

At the INL researchers and engineers routinely encounter multiphase, multi-component, and/or multi-material flows. Some examples include: Reactor coolant flows Molten corium flows Dynamic compaction of metal powders Spray forming and thermal plasma spraying Plasma quench reactor Subsurface flows, particularly in the vadose zone Internal flows within fuel cells Black liquor atomization and combustion Wheat-chaff classification in combine harvesters Generation IV pebble bed, high temperature gas reactor The complexity of these flows dictates that they be examined in an averaged sense. Typically one would begin with known (or at least postulated) microscopic flow relations that hold on the ''small'' scale. These include continuum level conservation of mass, balance of species mass and momentum, conservation of energy, and a statement of the second law of thermodynamics often in the form of an entropy inequality (such as the Clausius-Duhem inequality). The averaged or macroscopic conservation equations and entropy inequalities are then obtained from the microscopic equations through suitable averaging procedures. At this stage a stronger form of the second law may also be postulated for the mixture of phases or materials. To render the evolutionary material flow balance system unique, constitutive equations and phase or material interaction relations are introduced from experimental observation, or by postulation, through strict enforcement of the constraints or restrictions resulting from the averaged entropy inequalities. These averaged equations form the governing equation system for the dynamic evolution of these mixture flows. Most commonly, the averaging technique utilized is either volume or time averaging or a combination of the two. The flow restrictions required for volume and time averaging to be valid can be severe, and violations of these restrictions are often found. A more general, less restrictive (and far less commonly used) type of averaging known as

Convergence of a continuous BGK model for initial boundary-value problems for conservation laws

Directory of Open Access Journals (Sweden)

Driss Seghir

2001-11-01

Full Text Available We consider a scalar conservation law in the quarter plane. This equation is approximated in a continuous kinetic Bhatnagar-Gross-Krook (BGK model. The convergence of the model towards the unique entropy solution is established in the space of functions of bounded variation, using kinetic entropy inequalities, without special restriction on the flux nor on the equilibrium problem's data. As an application, we establish the hydrodynamic limit for a $2imes2$ relaxation system with general data. Also we construct a new family of convergent continuous BGK models with simple maxwellians different from the $chi$ models.

Different realizations of Cooper-Frye sampling with conservation laws

Science.gov (United States)

Schwarz, C.; Oliinychenko, D.; Pang, L.-G.; Ryu, S.; Petersen, H.

2018-01-01

Approaches based on viscous hydrodynamics for the hot and dense stage and hadronic transport for the final dilute rescattering stage are successfully applied to the dynamic description of heavy ion reactions at high beam energies. One crucial step in such hybrid approaches is the so-called particlization, which is the transition between the hydrodynamic description and the microscopic degrees of freedom. For this purpose, individual particles are sampled on the Cooper-Frye hypersurface. In this work, four different realizations of the sampling algorithms are compared, with three of them incorporating the global conservation laws of quantum numbers in each event. The algorithms are compared within two types of scenarios: a simple ‘box’ hypersurface consisting of only one static cell and a typical particlization hypersurface for Au+Au collisions at \\sqrt{{s}{NN}}=200 {GeV}. For all algorithms the mean multiplicities (or particle spectra) remain unaffected by global conservation laws in the case of large volumes. In contrast, the fluctuations of the particle numbers are affected considerably. The fluctuations of the newly developed SPREW algorithm based on the exponential weight, and the recently suggested SER algorithm based on ensemble rejection, are smaller than those without conservation laws and agree with the expectation from the canonical ensemble. The previously applied mode sampling algorithm produces dramatically larger fluctuations than expected in the corresponding microcanonical ensemble, and therefore should be avoided in fluctuation studies. This study might be of interest for the investigation of particle fluctuations and correlations, e.g. the suggested signatures for a phase transition or a critical endpoint, in hybrid approaches that are affected by global conservation laws.

Some current topics on nonlinear conservation laws lectures at the morningside center of mathematics, 1

CERN Document Server

Hsiao, Ling

2000-01-01

This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research. A. Bressan's theory of L^1-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results in the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave-a major focus of research in...

An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws

Science.gov (United States)

Borges, Rafael; Carmona, Monique; Costa, Bruno; Don, Wai Sun

2008-03-01

In this article we develop an improved version of the classical fifth-order weighted essentially non-oscillatory finite difference scheme of [G.S. Jiang, C.W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228] (WENO-JS) for hyperbolic conservation laws. Through the novel use of a linear combination of the low order smoothness indicators already present in the framework of WENO-JS, a new smoothness indicator of higher order is devised and new non-oscillatory weights are built, providing a new WENO scheme (WENO-Z) with less dissipation and higher resolution than the classical WENO. This new scheme generates solutions that are sharp as the ones of the mapped WENO scheme (WENO-M) of Henrick et al. [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542-567], however with a 25% reduction in CPU costs, since no mapping is necessary. We also provide a detailed analysis of the convergence of the WENO-Z scheme at critical points of smooth solutions and show that the solution enhancements of WENO-Z and WENO-M at problems with shocks comes from their ability to assign substantially larger weights to discontinuous stencils than the WENO-JS scheme, not from their superior order of convergence at critical points. Numerical solutions of the linear advection of discontinuous functions and nonlinear hyperbolic conservation laws as the one dimensional Euler equations with Riemann initial value problems, the Mach 3 shock-density wave interaction and the blastwave problems are compared with the ones generated by the WENO-JS and WENO-M schemes. The good performance of the WENO-Z scheme is also demonstrated in the simulation of two dimensional problems as the shock-vortex interaction and a Mach 4.46 Richtmyer-Meshkov Instability (RMI) modeled via the two dimensional Euler equations.

Convergence of spectral methods for nonlinear conservation laws. Final report

International Nuclear Information System (INIS)

Tadmor, E.

1987-08-01

The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows

Newton's laws of motion in the form of a Riccati equation

International Nuclear Information System (INIS)

Nowakowski, Marek; Rosu, Haret C.

2002-01-01

We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr ε . For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems

Newton's laws of motion in the form of a Riccati equation.

Science.gov (United States)

Nowakowski, Marek; Rosu, Haret C

2002-04-01

We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.

A generalised groundwater flow equation using the concept of non ...

African Journals Online (AJOL)

The classical Darcy law is generalised by regarding the water flow as a function of a non-integer order derivative of the piezometric head. This generalised law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Numerical solutions of this equation for various fractional orders of ...

Symmetries and conservation laws in the single-time Lagrangian form of the Fokker-type relativistic dynamics

International Nuclear Information System (INIS)

Tretyak, V.I.; Gaida, R.P.

1980-01-01

Symmetry properties of the single-time relativistic Lagrangian of an N-particle-system corresponding to the many-time action of the Fokker-type, which are a function of derivatives of particle coordinates with respect to time up to infinite order, are investigated. The conditions for quasi-invariance for such a Lagrangian, with respect to a representation of an arbitrary group in infinite continuation of configuration space of the system, are discussed. Using these conditions a general expression for the Lagrangian, securing Poincare covariance of corresponding equations of motion, is found, and the conservation laws related to this covariance are formulated. In the case of tensor interaction, the expansion of conserved quantities in c -1 up to terms of the order c -4 is performed. (author)

Fractional Schroedinger equation

International Nuclear Information System (INIS)

Laskin, Nick

2002-01-01

Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

Infinite set of conservation laws for relativistic string

International Nuclear Information System (INIS)

Isaev, A.P.

1981-01-01

The solution of the Cauchy problem has been found. An infinite class of conserving values Jsub(α) for a free closed relativistic string has been constructed. Jsub(α) values characterize three-parametric generating functions of conservation laws. It is shown using particular examples that it is necessary to order subintegral expressions of quantum values Jsub(α) and do not disturb a property of commutativity with a hamiltonian to attach sense to these values [ru

New formulation of Hardin-Pope equations for aeroacoustics

DEFF Research Database (Denmark)

Ekaterinaris, J.A.

1999-01-01

Dynamics, Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed information about the unsteady aerodynamic flowfield, which usually is obtained from a computational fluid dynamics solution. A new, conservative formulation of the equations governing acoustic disturbances is presented....... The conservative form of the governing equations is obtained after application of a transformation of variables that produces a set of inhomogeneous equations similar to the conservation-law form of the compressible Euler equations. The source term of these equations depends only on the derivatives...... of the hydrodynamic variables. Explicit time marching is performed. A high-order accurate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-biased formulas and flux-vector splitting. Solutions are obtained for the acoustic...

Is Yang-Mills equation a totally integrable system. Lecture III

International Nuclear Information System (INIS)

Chau Wang, L.L.

1981-01-01

Topics covered include: loop-space formulation of gauge theory - loop-space chiral equation; two dimensional chiral equation - conservation laws, linear system and integrability; and parallel development for the loop-space chiral equation - subtlety

The Fourier law in a momentum-conserving chain

NARCIS (Netherlands)

Giardinà, C.; Kurchan, J.

2005-01-01

We introduce a family of models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases the Fourier law is verified in one dimension.

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

Science.gov (United States)

Wang, D.

2017-12-01

The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

Physical conservation laws and the β-decay of nuclei

International Nuclear Information System (INIS)

Bagge, E.

1975-04-01

The law of conservation of energy is extended to the region of the Dirac states of negative energy. When particles are produced or disappear, energy changes occur in the negative energy region which can be seen in the positive energy region. The law of conservation of energy then says that the total change in energy is equal to naught. The same is valid for translations and angular momentum. The way in which completely occupied states change energy and momentum is not shown. The β-decay of the neutron is considered as pair production in which an electron is emitted and a positron is bonded to the neutron. Neutrinos are not produced. The latest results on neutrino experiments on accelerators are not discussed. (BJ/LH) [de

On the classical theory of ordinary linear differential equations of the second order and the Schroedinger equation for power law potentials

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1983-01-01

The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author) [pt

Comment on ''Boltzmann equation and the conservation of particle number''

International Nuclear Information System (INIS)

Zanette, D.

1990-09-01

In a recent paper (Z. Banggu, Phys. Rev. A 42, 761 (1990)) it is argued that some solutions of the Boltzmann equation do not satisfy particle conservation as a consequence of the independence of velocity on position. In this comment, the arguments and conclusions of that paper are discussed. In particular, it is stressed that the temporal series used for solving the kinetic equation are generally divergent. A discussion about the particle conservation in its solutions is also provided. (author). 4 refs

Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods - Part 1: Derivation and properties

Science.gov (United States)

Eldred, Christopher; Randall, David

2017-02-01

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.

Computational partial differential equations using Matlab

CERN Document Server

Li, Jichun

2008-01-01

Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

Energy conservation law for randomly fluctuating electromagnetic fields

International Nuclear Information System (INIS)

Gbur, G.; Wolf, E.; James, D.

1999-01-01

An energy conservation law is derived for electromagnetic fields generated by any random, statistically stationary, source distribution. It is shown to provide insight into the phenomenon of correlation-induced spectral changes. The results are illustrated by an example. copyright 1999 The American Physical Society

The Conservation Status of Eagles in South African Law

Directory of Open Access Journals (Sweden)

JC Knobel

2013-12-01

Full Text Available This contribution is an introductory survey and preliminary evaluation of the conservation status of eagles in South African law. The methodology is primarily an interdisciplinary literature study of legal texts and texts from the natural sciences. Eagles are some of the largest and most powerful avian predators, and the human response to their presence is dualistic and polarised. At the one extreme, many people admire eagles, while at the other extreme they are perceived as a threat to economic and other interests, and may even be actively persecuted in a conviction that they are vermin. This duality in the human perception of eagles is also prevalent in South Africa and complicates their conservation. The mobility of eagles and other birds of prey means that they cannot be restrained by fencing national parks and other protected areas, and this heightens the likelihood of their entering into conflict with human interests. The conservation problems faced by eagles in South Africa can broadly be divided into direct and indirect threats. Direct threats include the intentional killing of eagles, and trade in eagles and their eggs. Indirect threats include non-targeted poisoning (where poisoned bait is used to control other predators, but eagles find the bait, feed on it, and succumb; habitat loss; mortality induced by dangerous structures; and disturbance. The legal status of eagles is influenced by a large body of legislative provisions, ranging from international and regional legal instruments, through national legislation, to provincial legislative measures. An overview of these provisions is given, with concise explanations of how they apply to the legal status of eagles and other birds of prey in South Africa. The conservation status of eagles in South African law is subsequently evaluated by considering the contribution of the applicable laws to three main types of conservation interventions. In respect of the first, habitat preservation

Conservation of energy and momentum in nonrelativistic plasmas

International Nuclear Information System (INIS)

Sugama, H.; Watanabe, T.-H.; Nunami, M.

2013-01-01

Conservation laws of energy and momentum for nonrelativistic plasmas are derived from applying Noether's theorem to the action integral for the Vlasov-Poisson-Ampère system [Sugama, Phys. Plasmas 7, 466 (2000)]. The symmetric pressure tensor is obtained from modifying the asymmetric canonical pressure tensor with using the rotational symmetry of the action integral. Differences between the resultant conservation laws and those for the Vlasov-Maxwell system including the Maxwell displacement current are clarified. These results provide a useful basis for gyrokinetic conservation laws because gyrokinetic equations are derived as an approximation of the Vlasov-Poisson-Ampère system.

Self-consistent perturbation expansion for Bose-Einstein condensates satisfying Goldstone's theorem and conservation laws

International Nuclear Information System (INIS)

Kita, Takafumi

2009-01-01

Quantum-field-theoretic descriptions of interacting condensed bosons have suffered from the lack of self-consistent approximation schemes satisfying Goldstone's theorem and dynamical conservation laws simultaneously. We present a procedure to construct such approximations systematically by using either an exact relation for the interaction energy or the Hugenholtz-Pines relation to express the thermodynamic potential in a Luttinger-Ward form. Inspection of the self-consistent perturbation expansion up to the third order with respect to the interaction shows that the two relations yield a unique identical result at each order, reproducing the conserving-gapless mean-field theory [T. Kita, J. Phys. Soc. Jpn. 74, 1891 (2005)] as the lowest-order approximation. The uniqueness implies that the series becomes exact when infinite terms are retained. We also derive useful expressions for the entropy and superfluid density in terms of Green's function and a set of real-time dynamical equations to describe thermalization of the condensate.

International energy conservation: comparative law and policy

Energy Technology Data Exchange (ETDEWEB)

1979-02-01

Ernest C. Baynard III, in the Foreword to the conference, told of the purpose of the conference - to compare and discuss the policies and laws that highly industrialized nations have used and considered to meet the challenge of energy conservation. The following countries participated in the conference: U.K.; Australia; Federal Republic of Germany; Japan; France; Canada; Sweden; Italy; the Netherlands; and the U.S. The IEA and the Commission of the European Communities also participated. The conference format consisted of ministerial addresses to the conference, interspersed with panel discussions focusing on energy conservation in transportation, industry, agriculture, and utilities; residential, commercial, and industrial buildings; and emergency situations. There was also a panel discussion on the role of government in energy conservation and energy information collection. The panels were composed of participating countries' representatives. (MCW)

Finite difference techniques for nonlinear hyperbolic conservation laws

International Nuclear Information System (INIS)

Sanders, R.

1985-01-01

The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

Science.gov (United States)

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

Cayley number and conservation laws for elementary particles

International Nuclear Information System (INIS)

Vollendorf, F.

1975-01-01

It is shown that the five conservation laws of charge, hyper-charge, barion number and the two lepton numbers lead to the construction of a commutative non-associative 24 dimensional linear algebra. Each element of the algebra is an ordered set of three Cayley numbers. (orig.) [de

High-resolution finite-difference algorithms for conservation laws

International Nuclear Information System (INIS)

Towers, J.D.

1987-01-01

A new class of Total Variation Decreasing (TVD) schemes for 2-dimensional scalar conservation laws is constructed using either flux-limited or slope-limited numerical fluxes. The schemes are proven to have formal second-order accuracy in regions where neither u/sub x/ nor y/sub y/ vanishes. A new class of high-resolution large-time-step TVD schemes is constructed by adding flux-limited correction terms to the first-order accurate large-time-step version of the Engquist-Osher scheme. The use of the transport-collapse operator in place of the exact solution operator for the construction of difference schemes is studied. The production of spurious extrema by difference schemes is studied. A simple condition guaranteeing the nonproduction of spurious extrema is derived. A sufficient class of entropy inequalities for a conservation law with a flux having a single inflection point is presented. Finite-difference schemes satisfying a discrete version of each entropy inequality are only first-order accurate

Non-Noether conserved quantity for differential equations of motion in the phase space

Institute of Scientific and Technical Information of China (English)

无

2002-01-01

A non-Noether conserved quantity for the differential equations of motion of mechanical systems in the phase space is studied. The differential equations of motion of the systems are established and the determining equations of Lie symmetry are given. An existence theorem of non-Noether conserved quantity is obtained. An example is given to illustrate the application of the result.

Multidimensional Riemann problem with self-similar internal structure. Part II - Application to hyperbolic conservation laws on unstructured meshes

Science.gov (United States)

Balsara, Dinshaw S.; Dumbser, Michael

2015-04-01

Multidimensional Riemann solvers that have internal sub-structure in the strongly-interacting state have been formulated recently (D.S. Balsara (2012, 2014) [5,16]). Any multidimensional Riemann solver operates at the grid vertices and takes as its input all the states from its surrounding elements. It yields as its output an approximation of the strongly interacting state, as well as the numerical fluxes. The multidimensional Riemann problem produces a self-similar strongly-interacting state which is the result of several one-dimensional Riemann problems interacting with each other. To compute this strongly interacting state and its higher order moments we propose the use of a Galerkin-type formulation to compute the strongly interacting state and its higher order moments in terms of similarity variables. The use of substructure in the Riemann problem reduces numerical dissipation and, therefore, allows a better preservation of flow structures, like contact and shear waves. In this second part of a series of papers we describe how this technique is extended to unstructured triangular meshes. All necessary details for a practical computer code implementation are discussed. In particular, we explicitly present all the issues related to computational geometry. Because these Riemann solvers are Multidimensional and have Self-similar strongly-Interacting states that are obtained by Consistency with the conservation law, we call them MuSIC Riemann solvers. (A video introduction to multidimensional Riemann solvers is available on http://www.elsevier.com/xml/linking-roles/text/html". The MuSIC framework is sufficiently general to handle general nonlinear systems of hyperbolic conservation laws in multiple space dimensions. It can also accommodate all self-similar one-dimensional Riemann solvers and subsequently produces a multidimensional version of the same. In this paper we focus on unstructured triangular meshes. As examples of different systems of conservation laws we

Modulational instability: Conservation laws and bright soliton solution of ion-acoustic waves in electron-positron-ion-dust plasmas

Science.gov (United States)

EL-Kalaawy, O. H.

2018-02-01

We consider the nonlinear propagation of non-planar (cylindrical and spherical) ion-acoustic (IA) envelope solitary waves in an unmagnetized plasma consisting of electron-positron-ion-dust plasma with two-electron temperature distributions in the context of the non-extensive statistics. The basic set of fluid equations is reduced to the modified nonlinear Schrödinger (MNLS) equation in cylindrical and spherical geometry by using the reductive perturbation method (RPM). It is found that the nature of the modulational instabilities would be significantly modified due to the effects of the non-extensive and other plasma parameters as well as cylindrical and spherical geometry. Conservation laws of the MNLS equation are obtained by Lie symmetry and multiplier method. A new exact solution (envelope bright soliton) is obtained by the extended homogeneous balance method. Finally, we study the results of this article.

Conservative numerical schemes for Euler-Lagrange equations

Energy Technology Data Exchange (ETDEWEB)

Vazquez, L. [Universidad Complutense, Madrid (Spain). Dept. de Matematica Aplicada; Jimenez, S. [Universidad Alfonso X El Sabio, Madrid (Spain). Dept. de Matematica Aplicada

1999-05-01

As a preliminary step to study magnetic field lines, the authors seek numerical schemes that reproduce at discrete level the significant feature of the continuous model, based on an underling Lagrangian structure. The resulting scheme give discrete counterparts of the variation law for the energy as well of as the Euler-Lagrange equations and their symmetries.

Statistical mechanical foundation of the peridynamic nonlocal continuum theory: energy and momentum conservation laws.

Science.gov (United States)

Lehoucq, R B; Sears, Mark P

2011-09-01

The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics.

Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

Science.gov (United States)

Morita, Satoru

2018-05-01

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. For discrete-time systems, the power-law exponent is known to decrease as the autocorrelation time of the multiplier increases. However, for continuous-time systems, it is not yet clear how the temporal correlation affects the power-law behavior. Herein, we analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.

Weak asymptotic solution for a non-strictly hyperbolic system of conservation laws-II

Directory of Open Access Journals (Sweden)

Manas Ranjan Sahoo

2016-04-01

Full Text Available In this article we introduce a concept of entropy weak asymptotic solution for a system of conservation laws and construct the same for a prolonged system of conservation laws which is highly non-strictly hyperbolic. This is first done for Riemann type initial data by introducing $\\delta,\\delta',\\delta''$ waves along a discontinuity curve and then for general initial data by piecing together the Riemann solutions.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅱ)-MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

Institute of Scientific and Technical Information of China (English)

戴天民

2003-01-01

The purpose is to reestablish the balance laws of momentum, angular momentumand energy and to derive the corresponding local and nonlocal balance equations formicromorphic continuum mechanics and couple stress theory. The desired results formicromorphic continuum mechanics and couple stress theory are naturally obtained via directtransitions and reductions from the coupled conservation law of energy for micropolarcontinuum theory, respectively. The basic balance laws and equation s for micromorphiccontinuum mechanics and couple stress theory are constituted by combining these resultsderived here and the traditional conservation laws and equations of mass and microinertiaand the entropy inequality. The incomplete degrees of the former related continuum theoriesare clarified. Finally, some special cases are conveniently derived.

Relativistic phenomenological equations and transformation laws of relative coefficients

Directory of Open Access Journals (Sweden)

Patrizia Rogolino

2017-06-01

Full Text Available The aim of this paper is to derive the phenomenological equations in the context of special relativistic non-equilibrium thermodynamics with internal variables. In particular, after introducing some results developed in our previous paper, by means of classical non-equilibrium thermodynamic procedure and under suitable assumptions on the entropy density production, the phenomenological equations and transformation laws of phenomenological coefficients are derived. Finally, some symmetries of aforementioned coefficients are obtained.

Calorimeter energy calibration using the energy conservation law

Indian Academy of Sciences (India)

A new calorimeter energy calibration method was developed for the proposed ILC detectors. The method uses the center-of-mass energy of the accelerator as the reference. It has been shown that using the energy conservation law it is possible to make ECAL and HCAL cross calibration to reach a good energy resolution ...

Notes on the Mass Definition with Covariant Conservation Law

OpenAIRE

Fujimura, Jun

1990-01-01

Mass definition based on the conservation law of some physical quantities is investigated, adopting the 2nd rank tensor in four space world as the conserving quantity. It is shown that the scalar function appeared as coefficients in the general expression of this tensor quantity should be independent on s, s being the line element of the world line, under the postulate that the trajectories of free particle must be geodesic lines of the world. Discussions are made on this constant factor whic...

Application of an analytical method for solution of thermal hydraulic conservation equations

Energy Technology Data Exchange (ETDEWEB)

Fakory, M.R. [Simulation, Systems & Services Technologies Company (S3 Technologies), Columbia, MD (United States)

1995-09-01

An analytical method has been developed and applied for solution of two-phase flow conservation equations. The test results for application of the model for simulation of BWR transients are presented and compared with the results obtained from application of the explicit method for integration of conservation equations. The test results show that with application of the analytical method for integration of conservation equations, the Courant limitation associated with explicit Euler method of integration was eliminated. The results obtained from application of the analytical method (with large time steps) agreed well with the results obtained from application of explicit method of integration (with time steps smaller than the size imposed by Courant limitation). The results demonstrate that application of the analytical approach significantly improves the numerical stability and computational efficiency.

On the structure of the new electromagnetic conservation laws

International Nuclear Information System (INIS)

Edgar, S Brian

2004-01-01

New electromagnetic conservation laws have recently been proposed: in the absence of electromagnetic currents, the trace of the Chevreton superenergy tensor, H ab is divergence free in four-dimensional (a) Einstein spacetimes for test fields, and (b) Einstein-Maxwell spacetimes. Subsequently it has been pointed out, in analogy with flat spaces, that for Ricci-flat spacetimes the trace of the Chevreton superenergy tensor H ab can be rearranged in the form of a generalized wave operator □ L acting on the energy-momentum tensor T ab of the test fields, i.e., H ab □ L T ab /2. In this letter we show, for Einstein-Maxwell spacetimes in the full nonlinear theory, that, although, the trace of the Chevreton superenergy tensor H ab can again be rearranged in the form of a generalized wave operator □ G acting on the electromagnetic energy-momentum tensor, in this case the result is also crucially dependent on Einstein's equations; hence we argue that the divergence-free property of the tensor H ab = □ G T ab /2 has significant independent content beyond that of the divergence-free property of T ab . (letter to the editor)

Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models

International Nuclear Information System (INIS)

Eyink, Gregory L.

2009-01-01

We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.

Generalization of the Biot--Savart law to Maxwell's equations using special relativity

International Nuclear Information System (INIS)

Neuenschwander, D.E.; Turner, B.N.

1992-01-01

Maxwell's equations are obtained by generalizing the laws of magnetostatics, which follow from the Biot--Savart law and superposition, to be consistent with special relativity. The Lorentz force on a charged particle and its rate of energy change also follow by making Newton's second law for a particle in a magnetostatic field consistent with special relativity

The general conservation principle. Absolute validity of conservation laws and their role as source of entanglement, topology changes, and generation of masses

International Nuclear Information System (INIS)

Basini, Giuseppe; Capozziello, Salvatore; Longo, Giuseppe

2003-01-01

We propose a new approach in which several paradoxes and shortcomings of modern physics can be solved because conservation laws are always conserved. Directly due to the fact that conservation laws can never be violated, the symmetry of the theory leads to the very general consequence that backward and forward time evolution are both allowed. The generalization of the approach to five dimensions, each one with real physical meaning, leads to the derivation of particle masses as a result of a process of embedding

Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact ...

African Journals Online (AJOL)

Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact solutions and conservation laws. ... In this paper we study the combined sinh-cosh-Gordon equation, which arises in mathematical physics and has a wide range of scientific applications that range from chemical reactions to water surface gravity waves.

Background Killing vectors and conservation laws in Rosen's bimetric theories of gravitation

International Nuclear Information System (INIS)

Israelit, M.

1979-01-01

The problem of global energy, linear momentum, and angular momentum in Rosen's bimetric theories of gravitation is considered from the point of view of motions of the background space-time. It turns out that by means of background Killing vectors global mechanical integrals for matter and field can be defined in a correct manner. For the flat-background bimetric theory conditions are obtained which have been imposed on the algebraic structure of the matter tensor Tsub(μ)sup(ν) in order to get global mechanical conservation laws. For bimetric gravitation theories based on a cosmological (nonflat) background the set of Killing vectors is found. For these theories the obtained restrictions on the algebraic structure of Tsub(μ)sup(ν) lead to global generation laws (instead of conservation laws in the flat-background theory) for mechanical quantities. In particular cases the generation effect vanishes and then conservation laws exist. By means of the method developed in this paper, Rosen's homogeneous isotropic universe in the framework of the cosmological-background bimetric theory with k = 1 is considered. It turns out that such a universe does not generate globally, but will generate locally. The global energy of this universe is found to be zero. (author)

On the method of inverse scattering problem and Baecklund transformations for supersymmetric equations

International Nuclear Information System (INIS)

Chaichian, M.; Kulish, P. P.

1978-04-01

Supersymmetric Liouville and sine-Gordon equations are studied. We write down for these models the system of linear equations for which the method of inverse scattering problem should be applicable. Expressions for an infinite set of conserved currents are explicitly given. Supersymmetric Baecklund transformations and generalized conservation laws are constructed. (author)

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning

2014-03-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning; Canepa, Edward S.; Claudel, Christian

2014-01-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

Symmetries and conservation laws of the damped harmonic oscillator

Indian Academy of Sciences (India)

We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the ...

Angular momentum in general relativity. 1. Definition and asymptotic behaviour. [axisymmetric space-times, infinity, conservation law, spin coefficient formalism

Energy Technology Data Exchange (ETDEWEB)

Prior, C R [Cambridge Univ. (UK). Dept. of Applied Mathematics and Theoretical Physics

1977-06-27

Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptotically-flat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.

Quasiclassical deformation in KP hierarchy and Benney's long wave equations

International Nuclear Information System (INIS)

Kolokol'tsov, V.N.; Lebedev, D.R.

1987-01-01

In the paper by means of the formal variant of Zakharov-Shabat ''dressing'' method various formulas are obtained for the generating functions of the conservation laws of Kadomtsev-Petvias hierarchy which turn into analogous formulas for Benney hierarchy in the quasiclassical limit. The generating fucntion of the conservation laws of Miura type is constructed for higher Benney equations and the simple proof of the related identities is given

Tsunami risk assessment for facility group over a wide area using inundation assessment method considering energy conservation law

International Nuclear Information System (INIS)

Fukutani, Yo; Imamura, Fumihiko; Tokunaga, Takeshi; Sato, Ichiro

2015-01-01

We propose a quantitative evaluation method of overall tsunami risk that the entire facility group over a wide area holds. We considerably reduced the calculation cost for tsunami inundation depth by adopting the evaluation method using energy conservation law as compared with the evaluation method using non-linear long wave equation. For financial institutions such as banks and insurance companies with contractors over a wide area and business companies with multiple their assets and facilities in various places, the proposed evaluation method in this study could be a useful approach to implement their risk-based management decisions for tsunami risk. (author)

Noether's theorem and Steudel's conserved currents for the sine-Gordon equation

International Nuclear Information System (INIS)

Shadwick, W.F.

1980-01-01

A version of Noether's theorem appropriate for the extended Hamilton-Cartan formalism for regular first-order Lagrangians is proposed. Steudel's derivation of an infinite collection of conserved currents for the sine-Gordon equation is presented in this context and it is demonstrated that, as a consequence of the commutativity of the sine-Gordon Baecklund transformations, the conserved charges corresponding to these currents are in involution with respect to the natural Poisson bracket provided by the formalism. Thus one obtains the formal 'complete integrability' of the sine-Gordon equation as a consequence of the properties of the Baecklund transformation. (orig.)

On conservation laws in geometrically nonlinear elasto-dynamic field of non-homogenous materials%论非均匀材料几何非线性弹性动力学场的守恒律

Institute of Scientific and Technical Information of China (English)

施伟辰; 高庆海; 李欢欢

2006-01-01

对基于Lagrange框架描述的非均匀弹性材料的Lagrange泛函应用Noether原理,开展材料的几何非线性弹性动力学场守恒律的研究,并给出其物质空间守恒律与物质平衡定律之间关系的清晰图景.研究发现,质量密度和弹性系数需满足一组一阶线性偏微分方程,该组方程不但包含来自Newton力学时-空观的全部时-空对称变换,而且控制着材料物质空间守恒律的存在性和存在的形式.特别需指出的是,惯性坐标系的平移和旋转是Lagrange泛函的对称变换,这些对称变换可导致均匀材料的物质空间守恒律和非均匀材料的物质平衡定律,但是时-空坐标的标度改变并不是对称变换.然而,若质量密度和弹性系数满足由上述方程简化而来的一组特殊的一阶线性偏微分方程,则时-空坐标的标度改变可成为Lagrange泛函的对称变换并导致相关守恒律的存在,但此时与该守恒律关联的物质平衡定律仍然不存在.为构造适合力学分析的功能梯度材料的物质空间守恒律,进行了质量密度和弹性系数需满足的方程的应用研究.对于粘合于基底的功能梯度材料层,给出全部非平凡的物质空间守恒律.%By applying Noether's theorem to the Lagrangian density of non-homogenous elastic materials in the so-called Lagrangian framework, conservation laws in geometrically nonlinear elasto-dynamic field have been studied, and a clear picture of relations between the conservation laws in material space and the material balance laws is given. It is found that the mass density and Lamé's moduli have to satisfy a set of first-order linear partial differential equations, which contain all the symmetry-transformations of space-time based on Newtonian viewpoint of mechanics. The existence and existent forms of conservation laws in material space are governed by these equations. Especially, translation and rotation of coordinates are symmetry

The role of angular momentum conservation law in statistical mechanics

Directory of Open Access Journals (Sweden)

I.M. Dubrovskii

2008-12-01

Full Text Available Within the limits of Khinchin ideas [A.Y. Khinchin, Mathematical Foundation of Statistical Mechanics. NY, Ed. Dover, 1949] the importance of momentum and angular momentum conservation laws was analyzed for two cases: for uniform magnetic field and when magnetic field is absent. The law of momentum conservation does not change the density of probability distribution in both cases, just as it is assumed in the conventional theory. It is shown that in systems where the kinetic energy depends only on particle momenta canonically conjugated with Cartesian coordinates being their diagonal quadric form,the angular momentum conservation law changes the density of distribution of the system only in case the full angular momentum of a system is not equal to zero. In the gas of charged particles in a uniform magnetic field the density of distribution also varies if the angular momentum is zero [see Dubrovskii I.M., Condensed Matter Physics, 2206, 9, 23]. Two-dimensional gas of charged particles located within a section of an endless strip filled with gas in magnetic field is considered. Under such conditions the angular momentum is not conserved. Directional particle flows take place close to the strip boundaries, and, as a consequence, the phase trajectory of the considered set of particles does not remain within the limited volume of the phase space. In order to apply a statistical thermodynamics method, it was suggested to consider near-boundary trajectories relative to a reference system that moves uniformly. It was shown that if the diameter of an orbit having average thermal energy is much smaller than a strip width, the corrections to thermodynamic functions are small depending on magnetic field. Only the average velocity of near-boundary particles that form near-boundary electric currents creating the paramagnetic moment turn out to be essential.

Conservation laws and symmetries in stochastic thermodynamics.

Science.gov (United States)

Polettini, Matteo; Bulnes-Cuetara, Gregory; Esposito, Massimiliano

2016-11-01

Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities, such as matter, energy, and charge, flow from outer reservoirs across a system and how they irreversibly degrade from one form to another. Stochastic thermodynamics is formulated in terms of probability fluxes circulating in the system's configuration space. The consistency of the two frameworks is granted by the condition of local detailed balance, which specifies the amount of physical quantities exchanged with the reservoirs during single transitions between configurations. We demonstrate that the topology of the configuration space crucially determines the number of independent thermodynamic affinities (forces) that the reservoirs generate across the system and provides a general algorithm that produces the fundamental affinities and their conjugate currents contributing to the total dissipation, based on the interplay between macroscopic conservations laws for the currents and microscopic symmetries of the affinities.

Variational symmetries, conserved quantities and identities for several equations of mathematical physics

Energy Technology Data Exchange (ETDEWEB)

Donchev, Veliko, E-mail: velikod@ie.bas.bg [Laboratory “Physical Problems of Electron and Ion Technologies,” Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko shosse, 1784 Sofia (Bulgaria)

2014-03-15

We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.

Error Analysis of Explicit Partitioned Runge–Kutta Schemes for Conservation Laws

KAUST Repository

Hundsdorfer, Willem

2014-08-27

An error analysis is presented for explicit partitioned Runge–Kutta methods and multirate methods applied to conservation laws. The interfaces, across which different methods or time steps are used, lead to order reduction of the schemes. Along with cell-based decompositions, also flux-based decompositions are studied. In the latter case mass conservation is guaranteed, but it will be seen that the accuracy may deteriorate.

Error Analysis of Explicit Partitioned Runge–Kutta Schemes for Conservation Laws

KAUST Repository

Hundsdorfer, Willem; Ketcheson, David I.; Savostianov, Igor

2014-01-01

An error analysis is presented for explicit partitioned Runge–Kutta methods and multirate methods applied to conservation laws. The interfaces, across which different methods or time steps are used, lead to order reduction of the schemes. Along with cell-based decompositions, also flux-based decompositions are studied. In the latter case mass conservation is guaranteed, but it will be seen that the accuracy may deteriorate.

Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz—Ladik—Lattice system

International Nuclear Information System (INIS)

Fu Jing-Li; He Yu-Fang; Hong Fang-Yu; Song Duan; Fu Hao

2013-01-01

In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz—Ladik—Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz—Ladik—Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz—Ladik—Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz—Ladik—Lattice method is verified. (general)

Partial differential equations

CERN Document Server

Evans, Lawrence C

2010-01-01

This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

On 'conflict of conservation laws in cyclotron radiation'

International Nuclear Information System (INIS)

White, S.M.; Parle, A.J.

1985-01-01

The authors reconsider the apparent conflict of conservation laws in cyclotron radiation, and show that earlier workers in this field did not correctly include the effects of radiation reaction in their calculations. When a 'recoil' term, calculated using relativistic quantum theory, is included in the angular momentum of the particle the conflict disappears. It is found that the guiding centre of the particle drifts outwards during cyclotron radiation. (author)

Conservation laws in the quantum mechanics of closed systems

International Nuclear Information System (INIS)

Hartle, J.B.; Laflamme, R.; Marolf, D.

1995-01-01

We investigate conservation laws in the quantum mechanics of closed systems and begin by reviewing an argument that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian. However, we also show that decoherence limits the alternatives that can be included in sets of histories that assess the conservation of these quantities. In the case of charge and energy, these limitations would be severe were these quantities not coupled to a gauge field. However, for the realistic cases of electric charge coupled to the electromagnetic field and mass coupled to spacetime curvature, we show that when alternative values of charge and mass decohere they always decohere exactly and are exactly conserved. Further, while decohering histories that describe possible changes in time of the total charge and mass are also subject to the limitations mentioned above, we show that these do not, in fact, restrict physical alternatives and are therefore not really limitations at all

General Large Deviations and Functional Iterated Logarithm Law for Multivalued Stochastic Differential Equations

OpenAIRE

Ren, Jiagang; Wu, Jing; Zhang, Hua

2015-01-01

In this paper, we prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations. As an application, we derive a functional iterated logarithm law for the solutions of multivalued stochastic differential equations.

Multi-symplectic Preissmann methods for generalized Zakharov-Kuznetsov equation

International Nuclear Information System (INIS)

Wang Junjie; Yang Kuande; Wang Liantang

2012-01-01

Generalized Zakharov-Kuznetsov equation, a typical nonlinear wave equation, was studied based on the multi-symplectic theory in Hamilton space. The multi-symplectic formulations of generalized Zakharov-Kuznetsov equation with several conservation laws are presented. The multi-symplectic Preissmann method is used to discretize the formulations. The numerical experiment is given, and the results verify the efficiency of the multi-symplectic scheme. (authors)

Symmetry and conservation law structures of some anti-self-dual

Indian Academy of Sciences (India)

The ASD systems and manifolds have been studied via a number of approaches and their origins have been well documented. In this paper, we look at the symmetry structures, variational symmetries and related concepts around the associated conservation laws for a number of such manifolds.

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

Science.gov (United States)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

Integrability of an extended (2+1)-dimensional shallow water wave equation with Bell polynomials

International Nuclear Information System (INIS)

Wang Yun-Hu; Chen Yong

2013-01-01

We investigate the extended (2+1)-dimensional shallow water wave equation. The binary Bell polynomials are used to construct bilinear equation, bilinear Bäcklund transformation, Lax pair, and Darboux covariant Lax pair for this equation. Moreover, the infinite conservation laws of this equation are found by using its Lax pair. All conserved densities and fluxes are given with explicit recursion formulas. The N-soliton solutions are also presented by means of the Hirota bilinear method. (general)

Numerical viscosity of entropy stable schemes for systems of conservation laws. Final Report

International Nuclear Information System (INIS)

Tadmor, E.

1985-11-01

Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones

2×2 systems of conservation laws with L data

Science.gov (United States)

Bianchini, Stefano; Colombo, Rinaldo M.; Monti, Francesca

Consider a hyperbolic system of conservation laws with genuinely nonlinear characteristic fields. We extend the classical Glimm-Lax (1970) result [13, Theorem 5.1] proving the existence of solutions for L initial datum, relaxing the assumptions taken therein on the geometry of the shock-rarefaction curves.

A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

Science.gov (United States)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For

Contractive relaxation systems and interacting particles for scalar conservation laws

International Nuclear Information System (INIS)

Katsoulakis, M.A.; Tzavaras, A.E.

1996-01-01

We consider a class of semi linear hyperbolic systems with relaxation that are contractive in the L 1 -norm and admit invariant regions. We show that, as the relaxation parameter ξ goes to zero, their solutions converge to a weak solution of the scalar multidimensional conversation law that satisfies the Kruzhkov conditions. In the case of one space dimension, we propose certain interacting particle systems, whose mesoscopic limit is the systems with relaxation and their macroscopic dynamics is described by entropy solutions of a scalar conservation law. (author)

On dynamic equations for interaction of the affinor field with affine connection

International Nuclear Information System (INIS)

Pestov, A.B.

1987-01-01

The Lagrangian of interaction of an affinor field with an affine connection is constructed and the equations of motion and conservation laws are derived. It is shown that there exists a symmetric conserved tensor of the affine-connection energy-momentum

Simple connection between conservation laws in the Korteweg--de Vriesand sine-Gordon systems

International Nuclear Information System (INIS)

Chodos, A.

1980-01-01

An infinite sequence of conserved quantities follows from the Lax representation in both the Korteweg--de Vries and sine-Gordon systems. We show that these two sequences are related by a simple substitution. In an appendix, two different methods of deriving conservation laws from the Lax representation are presented

A novel study on Kepler’s law and inverse square law of gravitation

International Nuclear Information System (INIS)

Zhang, Bingzhan; Zhen, Shengchao; Zhao, Han; Huang, Kang; Deng, Bin; Chen, Ye-Hwa

2015-01-01

The Udwadia–Kalaba equation is a simple, aesthetic, and thought-provoking description of the world at a very fundamental level. It is about the way systems move. In this paper, we creatively apply the Udwadia–Kalaba approach to study heavenly bodies’ movements (especially on Kepler’s law and the inverse square law of gravitation). In an alternative way, we show that a heavenly body’s motion orbit can be an ellipse, a circle, a hyperbola, or a parabola and show the conservation of angular momentum. Furthermore, by applying the Udwadia–Kalaba approach, we use the constraint of motion orbit (ellipse, circle, hyperbola, or parabola) and the conservation of angular momentum constraint (or energy conservation constraint) and easily verify that any heavenly body’s motion complies with the inverse square law of gravitation. That is, we study Kepler’s law and Newton’s inverse square law in an analytical way, which makes the dynamicist more clear about the way heavenly bodies move and also makes the celestial mechanician more clear about the analytical mechanics (the Udwadia–Kalaba approach). Furthermore, for the students of dynamics and celestial physics, a different unique perspective is provided for them to study. At the end, we present the detailed process of applying the Udwadia–Kalaba approach to two imaginary cases to show its simplicity and efficiency. (paper)

A new look at the free electromagnetic field. The Gauss law as a hamiltonian equation of motion

International Nuclear Information System (INIS)

Aldaya, V.; Navarro-Salas, J.

1992-01-01

A new canonical formalism for the free electromagnetic field is proposed in terms of an infinite-dimensional Lie group. The Gauss law is derived as a hamiltonian equation of motion and the quantum theory is obtained by constructing the irreducible representation of the group. The quantum Gauss law thus appears as an additional polarization equation and not as a constraint equation. (orig.)

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN

OpenAIRE

Jiang, H.; Liu, F.; Meerschaert, M. M.; McGough, R. J.

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development.

On conservation laws for models in discrete, noncommutative and fractional differential calculus

International Nuclear Information System (INIS)

Klimek, M.

2001-01-01

We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1+1 dimensions are studied

Construction of elasto-plastic boundaries using conservation laws

OpenAIRE

Senashov, S.; Filyushina, E.; Gomonova, O.

2015-01-01

The solution of elasto-plastic problems is one of the most complicated and actual problems of solid mechanics. Traditionally, these problems are solved by the methods of complex analysis, calculus of variations or semi-inverse methods. Unfortunately, all these methods can be applied to a limited number of problems only. In this paper, a technique of conservation laws is used. This technique allows constructing analytical formulas to determine the elasto-plastic boundary for a wide class of pr...

The role of energy conservation in the BFKL equation

International Nuclear Information System (INIS)

Forshaw, J.R.; Harriman, P.N.; Sutton, P.J.

1993-01-01

We study a modification to the BFKL equation at zero momentum transfer due to the imposition of energy conservation. The significance of our modification, which enters in the form of an ultraviolet cutoff, is illustrated directly and is discussed within the context of the gluon diffusion in k T . (Author)

Trouble with the Lorentz law of force: incompatibility with special relativity and momentum conservation.

Science.gov (United States)

Mansuripur, Masud

2012-05-11

The Lorentz law of force is the fifth pillar of classical electrodynamics, the other four being Maxwell's macroscopic equations. The Lorentz law is the universal expression of the force exerted by electromagnetic fields on a volume containing a distribution of electrical charges and currents. If electric and magnetic dipoles also happen to be present in a material medium, they are traditionally treated by expressing the corresponding polarization and magnetization distributions in terms of bound-charge and bound-current densities, which are subsequently added to free-charge and free-current densities, respectively. In this way, Maxwell's macroscopic equations are reduced to his microscopic equations, and the Lorentz law is expected to provide a precise expression of the electromagnetic force density on material bodies at all points in space and time. This Letter presents incontrovertible theoretical evidence of the incompatibility of the Lorentz law with the fundamental tenets of special relativity. We argue that the Lorentz law must be abandoned in favor of a more general expression of the electromagnetic force density, such as the one discovered by Einstein and Laub in 1908. Not only is the Einstein-Laub formula consistent with special relativity, it also solves the long-standing problem of "hidden momentum" in classical electrodynamics.

Conservation laws in the SLsub(2,C) gauge theory of gravitation

International Nuclear Information System (INIS)

Nissani, N.

1983-01-01

A one-parameter family of new Lagrangian densities for the SLsub(2,C) gauge theory of gravitation is proposed. The relation between the laws of conservation and the SLsub(2,C) symmetry of general relativity through the Noether theorem is investigated

Wave equations on anti self dual (ASD) manifolds

Science.gov (United States)

Bashingwa, Jean-Juste; Kara, A. H.

2017-11-01

In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

Science.gov (United States)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

Polynomial chaos methods for hyperbolic partial differential equations numerical techniques for fluid dynamics problems in the presence of uncertainties

CERN Document Server

Pettersson, Mass Per; Nordström, Jan

2015-01-01

This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The approach described in the text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dime...

Conformal conservation laws for second-order scalar fields

International Nuclear Information System (INIS)

Blakeskee, J.S.; Logan, J.D.

1976-01-01

It is considered an action integral over space-time whose Lagrangian depends upon a scalar field an upon derivatives of the field function up to second order. From invariance identities obtained by the authors in an earlier work it is shown how a new proof of Noether's theorem for this second-order problem follows in the multiple integral case. Finally, conservation laws are written down in the case that the given action integral be invariant under the fifteen-parameter special conformal group

Vapor-droplet flow equations

International Nuclear Information System (INIS)

Crowe, C.T.

1975-01-01

General features of a vapor-droplet flow are discussed and the equations expressing the conservation of mass, momentum, and energy for the vapor, liquid, and mixture using the control volume approach are derived. The phenomenological laws describing the exchange of mass, momentum, and energy between phases are also reviewed. The results have application to development of water-dominated geothermal resources

Geometrical-integrability constraints and equations of motion in four plus extended super spaces

International Nuclear Information System (INIS)

Chau, L.L.

1987-01-01

It is pointed out that many equations of motion in physics, including gravitational and Yang-Mills equations, have a common origin: i.e. they are the results of certain geometrical integrability conditions. These integrability conditions lead to linear systems and conservation laws that are important in integrating these equations of motion

Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models

International Nuclear Information System (INIS)

Steinacker, Harold

2009-01-01

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.

Approximate spacetime symmetries and conservation laws

Energy Technology Data Exchange (ETDEWEB)

Harte, Abraham I [Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 (United States)], E-mail: harte@uchicago.edu

2008-10-21

A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincare and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is a generalized Komar integral that may be taken to define the linear and angular momenta of a spacetime volume as seen by a particular observer. This is evaluated explicitly for a gravitational plane wave spacetime.

Electromagnetic-field equations in the six-dimensional space-time R6

International Nuclear Information System (INIS)

Teli, M.T.; Palaskar, D.

1984-01-01

Maxwell's equations (without monopoles) for electromagnetic fields are obtained in six-dimensional space-time. The equations possess structural symmetry in space and time, field and source densities. Space-time-symmetric conservation laws and field solutions are obtained. The results are successfully correlated with their four-dimensional space-time counterparts

On the checking of electric charge conservation law and the pauli principle

International Nuclear Information System (INIS)

Okun', L.B.

1989-01-01

This is a short critical review of the attempts to check the accuracy with which are carried out in experiment the electric charge conservation law and the Pauli principle. The absence of the inwardly noncontradictory phenomenological theory is emphasized, which could describe the charge conservation and/or the Pauli principle violation. Under charge nonconservation longitudinal photons are of a principal importance. New suggestions concerning the principle Puli checking are discussed

First law of thermodynamics and Friedmann-like equations in braneworld cosmology

International Nuclear Information System (INIS)

Ge Xianhui

2007-01-01

We derive the Friedmann-like equations in braneworld cosmology by imposing the first law of thermodynamics and Bekenstein's area-entropy formula on the apparent horizon of a Friedmann-Robertson-Walker universe in both Randall-Sundrum II gravity and Dvali-Gabadadze-Porrati gravity models. Israel's boundary condition plays an important role in our calculations in both cases, besides the first law of thermodynamics and Bekenstein's area-entropy formula. The results indicate that thermodynamics on the brane world knows the behaviors of gravity

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

Generalized continuity equations from two-field Schrödinger Lagrangians

Science.gov (United States)

Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.

2016-11-01

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.

A Simple Derivation of Kepler's Laws without Solving Differential Equations

Science.gov (United States)

Provost, J.-P.; Bracco, C.

2009-01-01

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

Mass and energy-capital conservation equations to study the price evolution of non-renewable energy resources

International Nuclear Information System (INIS)

Gori, F.

2006-01-01

Mass conservation equation of non-renewable resources is employed to study the resources remaining in the reservoir according to the extraction policy. The energy conservation equation is transformed into an energy-capital conservation equation. The Hotelling rule is shown to be a special case of the general energy-capital conservation equation when the mass flow rate of extracted resources is equal to unity. Mass and energy-capital conservation equations are then coupled and solved together. It is investigated the price evolution of extracted resources. The conclusion of the Hotelling rule for non-extracted resources, i.e. an exponential increase of the price of non-renewable resources at the rate of current interest, is then generalized. A new parameter, called 'Price Increase Factor', PIF, is introduced as the difference between the current interest rate of capital and the mass flow rate of extraction of non-renewable resources. The price of extracted resources can increase exponentially only if PIF is greater than zero or if the mass flow rate of extraction is lower than the current interest rate of capital. The price is constant if PIF is zero or if the mass flow rate of extraction is equal to the current interest rate. The price is decreasing with time if PIF is smaller than zero or if the mass flow rate of extraction is higher than the current interest rate. (author)

Quantitative Compactness Estimates for Hamilton-Jacobi Equations

Science.gov (United States)

Ancona, Fabio; Cannarsa, Piermarco; Nguyen, Khai T.

2016-02-01

We study quantitative compactness estimates in {W^{1,1}_{loc}} for the map {S_t}, {t > 0} that is associated with the given initial data {u_0in Lip (R^N)} for the corresponding solution {S_t u_0} of a Hamilton-Jacobi equation u_t+Hbig(nabla_{x} ubig)=0, qquad t≥ 0,quad xinR^N, with a uniformly convex Hamiltonian {H=H(p)}. We provide upper and lower estimates of order {1/\\varepsilon^N} on the Kolmogorov {\\varepsilon}-entropy in {W^{1,1}} of the image through the map S t of sets of bounded, compactly supported initial data. Estimates of this type are inspired by a question posed by Lax (Course on Hyperbolic Systems of Conservation Laws. XXVII Scuola Estiva di Fisica Matematica, Ravello, 2002) within the context of conservation laws, and could provide a measure of the order of "resolution" of a numerical method implemented for this equation.

A discrete model on Sierpinski gasket substrate for a conserved current equation with a conservative noise

International Nuclear Information System (INIS)

Kim, Dae Ho; Kim, Jin Min

2012-01-01

A conserved discrete model on the Sierpinski gasket substrate is studied. The interface width W in the model follows the Family–Vicsek dynamic scaling form with growth exponent β ≈ 0.0542, roughness exponent α ≈ 0.240 and dynamic exponent z ≈ 4.42. They satisfy a scaling relation α + z = 2z rw , where z rw is the random walk exponent of the fractal substrate. Also, they are in a good agreement with the predicted values of a fractional Langevin equation where η c is a conservative noise. (paper)

Efficient robust control of first order scalar conservation laws using semi-analytical solutions

KAUST Repository

Li, Yanning; Canepa, Edward S.; Claudel, Christian G.

2014-01-01

This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using initial density control and boundary flow control, as a Linear Program. We then show that this framework can be extended to arbitrary control problems involving the control of subsets of the initial and boundary conditions. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP/MILP. Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality.

General relativistic continuum mechanics and the post-Newtonian equations of motion

International Nuclear Information System (INIS)

Morrill, T.H.

1991-01-01

Aspects are examined of general relativistic continuum mechanics. Perfectly elastic materials are dealt with but not exclusively. The derivation of their equations of motion is emphasized, in the post-Newtonian approximation. A reformulation is presented based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. A field Lagrangian is derived describing perfect material media; show that the usual covariant conservations law for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einstein's field equations. In addition, a version of this principle shows that the local mass density in curved space-time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. The total Lagrangian was also expanded in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. The results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law

Semi-discrete approximations to nonlinear systems of conservation laws; consistency and L(infinity)-stability imply convergence. Final report

International Nuclear Information System (INIS)

Tadmor, E.

1988-07-01

A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods)

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

On the Definition of Energy for a Continuum, Its Conservation Laws, and the Energy-Momentum Tensor

Directory of Open Access Journals (Sweden)

Mayeul Arminjon

2016-01-01

Full Text Available We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in Newtonian gravity. Next, we consider a continuum or a system of fields in special relativity: we recall that the conservation of the energy-momentum tensor contains two local conservation equations of the same kind as before. We show that both of these equations depend on the reference frame and that, however, they can be given a rigorous meaning. Then, we review the definitions of the canonical and Hilbert energy-momentum tensors from a Lagrangian through the principle of stationary action in general space-time. Using relatively elementary mathematics, we prove precise results regarding the definition of the Hilbert tensor field, its uniqueness, and its tensoriality. We recall the meaning of its covariant conservation equation. We end with a proof of uniqueness of the energy density and flux, when both depend polynomially on the fields.

Conservation laws in disordered electron systems: Thermodynamic limit and configurational averaging

Czech Academy of Sciences Publication Activity Database

Janiš, Václav; Kolorenč, Jindřich

2004-01-01

Roč. 241, č. 9 (2004), s. 2032-2042 ISSN 0370-1972 R&D Projects: GA ČR GA202/04/1055 Institutional research plan: CEZ:AV0Z1010914 Keywords : conservation laws * noninteracting disordered electrons * diffusion pole Subject RIV: BE - Theoretical Physics Impact factor: 0.982, year: 2004

Macroscopic law of conservation revealed in the population dynamics of Toll-like receptor signaling

Directory of Open Access Journals (Sweden)

Selvarajoo Kumar

2011-04-01

Full Text Available Abstract Stimulating the receptors of a single cell generates stochastic intracellular signaling. The fluctuating response has been attributed to the low abundance of signaling molecules and the spatio-temporal effects of diffusion and crowding. At population level, however, cells are able to execute well-defined deterministic biological processes such as growth, division, differentiation and immune response. These data reflect biology as a system possessing microscopic and macroscopic dynamics. This commentary discusses the average population response of the Toll-like receptor (TLR 3 and 4 signaling. Without requiring detailed experimental data, linear response equations together with the fundamental law of information conservation have been used to decipher novel network features such as unknown intermediates, processes and cross-talk mechanisms. For single cell response, however, such simplicity seems far from reality. Thus, as observed in any other complex systems, biology can be considered to possess order and disorder, inheriting a mixture of predictable population level and unpredictable single cell outcomes.

Symmetry and conservation law structures of some anti-self-dual ...

Indian Academy of Sciences (India)

2016-09-28

Sep 28, 2016 ... (2016) 87: 64 c Indian Academy of Sciences. DOI 10.1007/s12043-016-1258-y. Symmetry and conservation law structures of some anti-self-dual (ASD) manifolds. J BASINGWA1, A H KARA1,∗, ASHFAQUE H BOKHARI2, R A MOUSA2 and F D ZAMAN2. 1School of Mathematics, University of the ...

Determination of constants of factorized pairing force from conservation laws

International Nuclear Information System (INIS)

Voronkov, Yu.P.; Mikhajlov, V.M.

1975-01-01

The constants of a factorized interaction in the particle-particle channel are evaluated on the basis of average field parameters and Cooper pairing. The relations between the constants of multipole particle-particle forces are derived for the spherical nuclei. The constants of the quadrupole pairing are obtained for deformed nuclei from the angular momentum conservation law. The calculated constants are compared with empiricalones

A general nonlinear evolution equation for irreversible conservative approach to stable equilibrium

International Nuclear Information System (INIS)

Beretta, G.P.

1986-01-01

This paper addresses a mathematical problem relevant to the question of nonequilibrium and irreversibility, namely, that of ''designing'' a general evolution equation capable of describing irreversible but conservative relaxtion towards equilibrium. The objective is to present an interesting mathematical solution to this design problem, namely, a new nonlinear evolution equation that satisfies a set of very stringent relevant requirements. Three different frameworks are defined from which the new equation could be adopted, with entirely different interpretations. Some useful well-known mathematics involving Gram determinants are presented and a nonlinear evolution equation is given which meets the stringent design specifications

The centripetal force law and the equation of motion for a particle on a curved hypersurface

International Nuclear Information System (INIS)

Hu, L.D.; Lian, D.K.; Liu, Q.H.

2016-01-01

It is pointed out that the current form of the extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version; for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once this fact is taken into consideration, the equation takes the same form as that for the centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is preferable. (orig.)

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

Science.gov (United States)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Local conservation law and dark radiation in cosmological braneworld

International Nuclear Information System (INIS)

Minamitsuji, Masato; Sasaki, Misao

2004-01-01

In the context of the Randall-Sundrum (RS) single-brane scenario, we discuss the bulk geometry and dynamics of a cosmological brane in terms of the local energy conservation law which exists for the bulk that allows slicing with a maximally symmetric three-space. This conservation law enables us to define a local mass in the bulk. We show that there is a unique generalization of the dark radiation on the brane, which is given by the local mass. We find there also exists a conserved current associated with the Weyl tensor, and the corresponding local charge, which we call the Weyl charge, is given by the sum of the local mass and a certain linear combination of the components of the bulk energy-momentum tensor. This expression of the Weyl charge relates the local mass to the projected Weyl tensor, E μν , which plays a central role in the geometrical formalism of the RS braneworld. On the brane, in particular, this gives a decomposition of the projected Weyl tensor into the local mass and the bulk energy-momentum tensor. Then, as an application of these results, we consider a null dust model for the bulk energy-momentum tensor and discuss the black hole formation in the bulk. We investigate the causal structure by identifying the locus of the apparent horizon and clarify possible brane trajectories in the bulk. We find that the brane stays always outside the black hole as long as it is expanding. We also find an upper bound on the value of the Hubble parameter in terms of the matter energy density on the brane, irrespective of the energy flux emitted from the brane

Generalized equations of gravitational field

International Nuclear Information System (INIS)

Stanyukovich, K.P.; Borisova, L.B.

1985-01-01

Equations for gravitational fields are obtained on the basis of a generalized Lagrangian Z=f(R) (R is the scalar curvature). Such an approach permits to take into account the evolution of a gravitation ''constant''. An expression for the force Fsub(i) versus the field variability is obtained. Conservation laws are formulated differing from the standard ones by the fact that in the right part of new equations the value Fsub(i) is present that goes to zero at an ultimate passage to the standard Einstein theory. An equation of state is derived for cosmological metrics for a particular case, f=bRsup(1+α) (b=const, α=const)

Helmholtz solitons in power-law optical materials

International Nuclear Information System (INIS)

Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.

2007-01-01

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified

Sensitivity analysis of 1−d steady forced scalar conservation laws

Czech Academy of Sciences Publication Activity Database

Ersoy, M.; Feireisl, Eduard; Zuazua, E.

2013-01-01

Roč. 254, č. 9 (2013), s. 3817-3834 ISSN 0022-0396 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : sensitivity * scalar conservation law * control Subject RIV: BA - General Mathematics Impact factor: 1.570, year: 2013 http://www.sciencedirect.com/science/article/pii/S0022039613000892#

An improved front tracking method for the Euler equations

NARCIS (Netherlands)

Witteveen, J.A.S.; Koren, B.; Bakker, P.G.

2007-01-01

An improved front tracking method for hyperbolic conservation laws is presented. The improved method accurately resolves discontinuities as well as continuous phenomena. The method is based on an improved front interaction model for a physically more accurate modeling of the Euler equations, as

Relativistic dissipative hydrodynamic equations at the second order for multi-component systems with multiple conserved currents

International Nuclear Information System (INIS)

Monnai, Akihiko; Hirano, Tetsufumi

2010-01-01

We derive the second order hydrodynamic equations for the relativistic system of multi-components with multiple conserved currents by generalizing the Israel-Stewart theory and Grad's moment method. We find that, in addition to the conventional moment equations, extra moment equations associated with conserved currents should be introduced to consistently match the number of equations with that of unknowns and to satisfy the Onsager reciprocal relations. Consistent expansion of the entropy current leads to constitutive equations which involve the terms not appearing in the original Israel-Stewart theory even in the single component limit. We also find several terms which exhibit thermal diffusion such as Soret and Dufour effects. We finally compare our results with those of other existing formalisms.

Symmetries, conservation laws, and time reversibility for Hamiltonian systems with external forces

NARCIS (Netherlands)

Schaft, A.J. van der

1983-01-01

A system theoretic framework is given for the description of Hamiltonian systems with external forces and partial observations of the state. It is shown how symmetries and conservation laws can be defined within this framework. A generalization of Noether's theorem is obtained. Finally a precise

Nonlinear and linear wave equations for propagation in media with frequency power law losses

Science.gov (United States)

Szabo, Thomas L.

2003-10-01

The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

Collisional drift fluid equations and implications for drift waves

International Nuclear Information System (INIS)

Pfirsch, Dieter; Correa-Restrepo, Dario

1996-01-01

The usual theoretical description of drift-wave turbulence (considered to be one possible cause of anomalous transport in a plasma), e.g. the Hasegawa-Wakatani theory, makes use of various approximations, the effects of which are extremely difficult to assess. This concerns in particular the conservation laws for energy and momentum. The latter law is important in relation to charge separation and the resulting electric fields, which are possibly related to the L-H transition. Energy conservation is crucial to the stability behaviour, it will be discussed by means of an example. New collisional multi-species drift-fluid equations were derived by a new method which yields, in a transparent way, conservation of energy and total angular momentum and the law for energy dissipation. Both electrostatic and electromagnetic field variations are considered. The only restriction involved is the validity of the drift approximation; in particular, there are no assumptions restricting the geometry of the system. The method is based primarily on a Lagrangian for dissipationless fluids in the drift approximation with isotropic pressures. The dissipative terms are introduced by adding corresponding terms to the ideal equations of motion and of the pressures. The equations of motion, of course, no longer result from a Lagrangian via Hamilton's principle. However, their relation to the ideal equations also implies a relation to the ideal Lagrangian, which can be used to advantage. Instead of introducing heat conduction one can also assume isothermal behaviour, e.g. T v (x) = constant. Assumptions of this kind are often made in the literature. The new method of introducing dissipation is not restricted to the present kind of theory; it can equally well be applied to theories such as multi-fluid theories without using the drift approximation of the present paper. (author)

Conservation laws for a system of two point masses in general relativity

International Nuclear Information System (INIS)

Damour, Thibaut; Deruelle, Nathalie

1981-01-01

We study the symmetries of the generalized lagrangian of two point masses, in the post-post newtonian approximation of General Relativity. We deduce, via Noether's theorem, conservation laws for energy, linear and angular momentum, as well as a generalisation of the center-of-mass theorem [fr

A simple derivation of Kepler's laws without solving differential equations

International Nuclear Information System (INIS)

Provost, J-P; Bracco, C

2009-01-01

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to an explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by undergraduates or by secondary school teachers (who might use it with their pupils), can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest

Lorentz invariance violation and charge (non)conservation: A general theoretical frame for extensions of the Maxwell equations

International Nuclear Information System (INIS)

Laemmerzahl, Claus; Macias, Alfredo; Mueller, Holger

2005-01-01

All quantum gravity approaches lead to small modifications in the standard laws of physics which in most cases lead to violations of Lorentz invariance. One particular example is the extended standard model (SME). Here, a general phenomenological approach for extensions of the Maxwell equations is presented which turns out to be more general than the SME and which covers charge nonconservation (CNC), too. The new Lorentz invariance violating terms cannot be probed by optical experiments but need, instead, the exploration of the electromagnetic field created by a point charge or a magnetic dipole. Some scalar tensor theories and higher dimensional brane theories predict CNC in four dimensions and some models violating special relativity have been shown to be connected with CNC. Its relation to the Einstein Equivalence Principle has been discussed. Because of this upcoming interest, the experimental status of electric charge conservation is reviewed. Up to now there seem to exist no unique tests of charge conservation. CNC is related to the precession of polarization, to a modification of the 1/r-Coulomb potential, and to a time dependence of the fine structure constant. This gives the opportunity to describe a dedicated search for CNC

Nonlocal symmetry generators and explicit solutions of some partial differential equations

International Nuclear Information System (INIS)

Qin Maochang

2007-01-01

The nonlocal symmetry of a partial differential equation is studied in this paper. The partial differential equation written as a conservation law can be transformed into an equivalent system by introducing a suitable potential. The nonlocal symmetry group generators of original partial differential equations can be obtained through their equivalent system. Further, new explicit solutions can be constructed from the newly obtained symmetry generators. The Burgers equation is chosen as an example; many new valuable explicit solutions and nonlocal symmetry generators are presented

Parametrized post-Newtonian approximation and Rastall's gravitational field equations

International Nuclear Information System (INIS)

Smalley, L.L.

1978-01-01

The parametrized post-Newtonian (PPN) approximation is generalized to accomodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield conserved energy-momentum and angular-momentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories

Student Interpretations of Equations Related to the First Law of Thermodynamics

Science.gov (United States)

Hadfield, Linda C.; Wieman, Carl E.

2010-01-01

Student interpretations of the equation for the first law of thermodynamics, [delta]U = q + w, an expression defining work done on or by a gas, w = -[image omitted]PdV, and an expression defining heat, q = [image omitted]C[subscript v]dT were investigated through a multiple-choice survey, a free-response written survey, and interviews. The…

Systems of conservation laws with third-order Hamiltonian structures

Science.gov (United States)

Ferapontov, Evgeny V.; Pavlov, Maxim V.; Vitolo, Raffaele F.

2018-02-01

We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in P^{n+2} satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n+2 , classify n-tuples of skew-symmetric 2-forms A^{α } \\in Λ ^2(W) such that φ _{β γ }A^{β }\\wedge A^{γ }=0, for some non-degenerate symmetric φ.

On the evolution equations, solvable through the inverse scattering method

International Nuclear Information System (INIS)

Gerdjikov, V.S.; Khristov, E.Kh.

1979-01-01

The nonlinear evolution equations (NLEE), related to the one-parameter family of Dirac operators are considered in a uniform manner. The class of NLEE solvable through the inverse scatterina method and their conservation laws are described. The description of the hierarchy of Hamiltonian structures and the proof of complete integrability of the NLEE is presented. The class of Baecklund transformations for these NLEE is derived. The general formulae are illustrated by two important examples: the nonlinear Schroedinger equation and the sine-Gordon equation

The zeroth law of thermodynamics and volume-preserving conservative system in equilibrium with stochastic damping

International Nuclear Information System (INIS)

Qian, Hong

2014-01-01

We propose a mathematical formulation of the zeroth law of thermodynamics and develop a stochastic dynamical theory, with a consistent irreversible thermodynamics, for systems possessing sustained conservative stationary current in phase space while in equilibrium with a heat bath. The theory generalizes underdamped mechanical equilibrium: dx=gdt+{−D∇ϕdt+√(2D)dB(t)}, with ∇⋅g=0 and {⋯} respectively representing phase-volume preserving dynamics and stochastic damping. The zeroth law implies stationary distribution u ss (x)=e −ϕ(x) . We find an orthogonality ∇ϕ⋅g=0 as a hallmark of the system. Stochastic thermodynamics based on time reversal (t,ϕ,g)→(−t,ϕ,−g) is formulated: entropy production e p # (t)=−dF(t)/dt; generalized “heat” h d # (t)=−dU(t)/dt, U(t)=∫ R n ϕ(x)u(x,t)dx being “internal energy”, and “free energy” F(t)=U(t)+∫ R n u(x,t)lnu(x,t)dx never increases. Entropy follows (dS)/(dt) =e p # −h d # . Our formulation is shown to be consistent with an earlier theory of P. Ao. Its contradistinctions to other theories, potential-flux decomposition, stochastic Hamiltonian system with even and odd variables, Klein–Kramers equation, Freidlin–Wentzell's theory, and GENERIC, are discussed.

Exact solutions to robust control problems involving scalar hyperbolic conservation laws using Mixed Integer Linear Programming

KAUST Repository

Li, Yanning

2013-10-01

This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.

Exact solutions to robust control problems involving scalar hyperbolic conservation laws using Mixed Integer Linear Programming

KAUST Repository

Li, Yanning; Canepa, Edward S.; Claudel, Christian G.

2013-01-01

This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.

On the application of subcell resolution to conservation laws with stiff source terms

International Nuclear Information System (INIS)

Chang, S.

1989-11-01

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented

Numerical solutions of incompressible Navier-Stokes equations using modified Bernoulli's law

Science.gov (United States)

Shatalov, A.; Hafez, M.

2003-11-01

Simulations of incompressible flows are important for many practical applications in aeronautics and beyond, particularly in the high Reynolds number regime. The present formulation is based on Helmholtz velocity decomposition where the velocity is presented as the gradient of a potential plus a rotational component. Substituting in the continuity equation yields a Poisson equation for the potential which is solved with a zero normal derivative at solid surfaces. The momentum equation is used to update the rotational component with no slip/no penetration surface boundary conditions. The pressure is related to the potential function through a special relation which is a generalization of Bernoulli's law, with a viscous term included. Results of calculations for two- and three-dimensional problems prove that the present formulation is a valid approach, with some possible benefits compared to existing methods.

On the constitutive law of environment assisted fatigue: The physical meaning of the Paris type equations. Pt. 1

International Nuclear Information System (INIS)

Krausz, K.; Wu Xijia; Krausz, A.S.; Lian Zhiwen

1992-01-01

Environment assisted fatigue crack growth is a complex of thermally activated processes. Accordingly, the framework for the expression of rational constitutive law is developed from fracture kinetics theory. The correlation of the constitutive law with the Paris equation is discussed and the empirical parameters in the Paris equation are expressed explicitly in terms of activation energy, stress intensity factor range, temperature, stress ratio, and other physically rigorous engineering quantities. The theory assures and facilitates, the rigorous quantitative evaluation of the effects of the microstructure: the constitutive law gives guidance to its measurement and expresses it in terms of energy-related quantities. (orig.) [de

Global conservation laws and femtoscopy of small systems

International Nuclear Information System (INIS)

Chajecki, Zbigniew; Lisa, Mike

2008-01-01

It is increasingly important to understand, in detail, two-pion correlations measured in p+p and d+A collisions. In particular, one wishes to understand the femtoscopic correlations to compare to similar measurements in heavy-ion collisions. However, in the low-multiplicity final states of these systems, global conservation laws generate significant N-body correlations that project onto the two-pion space in nontrivial ways and complicate the femtoscopic analysis. We discuss a formalism to calculate and account for these correlations in collisions dominated by a single particle species (e.g., pions). We also discuss effects on two-particle correlations between nonidentical particles, the understanding of which may be important in the study of femtoscopic space-time asymmetries

Horizon thermodynamics and gravitational field equations in Horava-Lifshitz gravity

International Nuclear Information System (INIS)

Cai Ronggen; Ohta, Nobuyoshi

2010-01-01

We explore the relationship between the first law of thermodynamics and gravitational field equation at a static, spherically symmetric black hole horizon in Horava-Lifshitz theory with/without detailed balance. It turns out that as in the cases of Einstein gravity and Lovelock gravity, the gravitational field equation can be cast to a form of the first law of thermodynamics at the black hole horizon. This way we obtain the expressions for entropy and mass in terms of black hole horizon, consistent with those from other approaches. We also define a generalized Misner-Sharp energy for static, spherically symmetric spacetimes in Horava-Lifshitz theory. The generalized Misner-Sharp energy is conserved in the case without matter field, and its variation gives the first law of black hole thermodynamics at the black hole horizon.

Symmetric truncations of the shallow-water equations

International Nuclear Information System (INIS)

Rouhi, A.; Abarbanel, H.D.I.

1993-01-01

Conservation of potential vorticity in Eulerian fluids reflects particle interchange symmetry in the Lagrangian fluid version of the same theory. The algebra associated with this symmetry in the shallow-water equations is studied here, and we give a method for truncating the degrees of freedom of the theory which preserves a maximal number of invariants associated with this algebra. The finite-dimensional symmetry associated with keeping only N modes of the shallow-water flow is SU(N). In the limit where the number of modes goes to infinity (N→∞) all the conservation laws connected with potential vorticity conservation are recovered. We also present a Hamiltonian which is invariant under this truncated symmetry and which reduces to the familiar shallow-water Hamiltonian when N→∞. All this provides a finite-dimensional framework for numerical work with the shallow-water equations which preserves not only energy and enstrophy but all other known conserved quantities consistent with the finite number of degrees of freedom. The extension of these ideas to other nearly two-dimensional flows is discussed

Equations of motion and conservation laws in a theory of stable stratified turbulence

NARCIS (Netherlands)

L'vov, V.S.; Rudenko, O.

2008-01-01

This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider non-isothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the Oberbeck–Boussinesq

(Non)local Hamiltonian and symplectic structures, recursions and hierarchies: a new approach and applications to the N = 1 supersymmetric KdV equation

International Nuclear Information System (INIS)

Kersten, P; Krasil'shchik, I; Verbovetsky, A

2004-01-01

Using methods of Kersten et al (2004 J. Geom. Phys. 50 273-302) and Krasil'shchik and Kersten (2000 Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations (Dordrecht: Kluwer)), we accomplish an extensive study of the N = 1 supersymmetric Korteweg-de Vries (KdV) equation. The results include a description of local and nonlocal Hamiltonian and symplectic structures, five hierarchies of symmetries, the corresponding hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. We stress that the main point of the paper is not just the results on super-KdV equation itself, but merely exposition of the efficiency of the geometrical approach and of the computational algorithms based on it

Exact solutions for a discrete unidimensional Boltzmann model satisfying all conservation laws

International Nuclear Information System (INIS)

Cornille, H.

1989-01-01

We consider a four-velocity discrete and unidimensional Boltzmann model. The mass, momentum and energy conservation laws being satisfied we can define a temperature. We report the exact positive solutions which have been found: periodic in the space and propagating or not when the time is growing, shock waves similarity solutions and (1 + 1)-dimensional solutions [fr

Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations

KAUST Repository

Bonito, Andrea; Guermond, Jean-Luc; Popov, Bojan

2013-01-01

We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method

The origin of the energy-momentum conservation law

Science.gov (United States)

Chubykalo, Andrew E.; Espinoza, Augusto; Kosyakov, B. P.

2017-09-01

The interplay between the action-reaction principle and the energy-momentum conservation law is revealed by the examples of the Maxwell-Lorentz and Yang-Mills-Wong theories, and general relativity. These two statements are shown to be equivalent in the sense that both hold or fail together. Their mutual agreement is demonstrated most clearly in the self-interaction problem by taking account of the rearrangement of degrees of freedom appearing in the action of the Maxwell-Lorentz and Yang-Mills-Wong theories. The failure of energy-momentum conservation in general relativity is attributed to the fact that this theory allows solutions having nontrivial topologies. The total energy and momentum of a system with nontrivial topological content prove to be ambiguous, coordinatization-dependent quantities. For example, the energy of a Schwarzschild black hole may take any positive value greater than, or equal to, the mass of the body whose collapse is responsible for forming this black hole. We draw the analogy to the paradoxial Banach-Tarski theorem; the measure becomes a poorly defined concept if initial three-dimensional bounded sets are rearranged in topologically nontrivial ways through the action of free non-Abelian isometry groups.

On the Riemann solutions of the balance equations for steam and water flow in a porous medium

NARCIS (Netherlands)

Lambert, W.; Marchesin, D.; Bruining, J.

2005-01-01

Conservation laws have been used to model a variety of physical phenomena and therefore the theory for this class of equations is well developed. However, in many problems, such as transport of hot fluids and gases undergoing mass transfer, balance laws are required to describe the flow. As an

Stochastic models with power-law tails the equation X = AX + B

CERN Document Server

Buraczewski, Dariusz; Mikosch, Thomas

2016-01-01

In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the c...

Symmetries and conservation laws in non-Hermitian field theories

Science.gov (United States)

Alexandre, Jean; Millington, Peter; Seynaeve, Dries

2017-09-01

Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for P T -symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the P T -conjugate variables, allowing for an unambiguous definition of the equations of motion. After discussing the resulting constraints on the consistency of the variational procedure, we show that the invariance of a non-Hermitian Lagrangian under a continuous symmetry transformation does not imply the existence of a corresponding conserved current. Conserved currents exist, but these are associated with transformations under which the Lagrangian is not invariant and which reflect the well-known interpretation of P T -symmetric theories in terms of systems with gain and loss. A formal understanding of this unusual feature of non-Hermitian theories requires a careful treatment of Noether's theorem, and we give specific examples for illustration.

Conservation laws of wave action and potential enstrophy for Rossby waves in a stratified atmosphere

Science.gov (United States)

Straus, D. M.

1983-01-01

The evolution of wave energy, enstrophy, and wave motion for atmospheric Rossby waves in a variable mean flow are discussed from a theoretical and pedagogic standpoint. In the absence of mean flow gradients, the wave energy density satisfies a local conservation law, with the appropriate flow velocity being the group velocity. In the presence of mean flow variations, wave energy is not conserved, but wave action is, provided the mean flow is independent of longitude. Wave enstrophy is conserved for arbitrary variations of the mean flow. Connections with Eliassen-Palm flux are also discussed.

Conservation laws and mass distribution in the planet formation process

International Nuclear Information System (INIS)

Farinella, P.; Paolicchi, P.

1977-01-01

Within the framework of the nebular theory of the origin of the solar system, conservation laws are applied to the condensation of a ring-shaped cloud of orbiting particles. The final configuration is assumed to be a point-like planet in a circular orbit around the Sun. On this ground, it is possible to relate the masses of the planets with the interplanetary distances. This relation is confirmed satisfactorily by the observed masses and orbital radii of several planets and satellites of the solar system. (Auth.)

Students' Understanding of Conservation of Matter, Stoichiometry and Balancing Equations in Indonesia

Science.gov (United States)

Agung, Salamah; Schwartz, Marc S.

2007-01-01

This study examines Indonesian students' understanding of conservation of matter, balancing of equations and stoichiometry. Eight hundred and sixty-seven Grade 12 students from 22 schools across four different cities in two developed provinces in Indonesia participated in the study. Nineteen teachers also participated in order to validate the…

Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids

KAUST Repository

Shen, Hua; Wen, Chih-Yung; Parsani, Matteo; Shu, Chi-Wang

2016-01-01

A maximum-principle-satisfying space-time conservation element and solution element (CE/SE) scheme is constructed to solve a reduced five-equation model coupled with the stiffened equation of state for compressible multifluids. We first derive a sufficient condition for CE/SE schemes to satisfy maximum-principle when solving a general conservation law. And then we introduce a slope limiter to ensure the sufficient condition which is applicative for both central and upwind CE/SE schemes. Finally, we implement the upwind maximum-principle-satisfying CE/SE scheme to solve the volume-fraction-based five-equation model for compressible multifluids. Several numerical examples are carried out to carefully examine the accuracy, efficiency, conservativeness and maximum-principle-satisfying property of the proposed approach.

Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids

KAUST Repository

Shen, Hua

2016-10-19

A maximum-principle-satisfying space-time conservation element and solution element (CE/SE) scheme is constructed to solve a reduced five-equation model coupled with the stiffened equation of state for compressible multifluids. We first derive a sufficient condition for CE/SE schemes to satisfy maximum-principle when solving a general conservation law. And then we introduce a slope limiter to ensure the sufficient condition which is applicative for both central and upwind CE/SE schemes. Finally, we implement the upwind maximum-principle-satisfying CE/SE scheme to solve the volume-fraction-based five-equation model for compressible multifluids. Several numerical examples are carried out to carefully examine the accuracy, efficiency, conservativeness and maximum-principle-satisfying property of the proposed approach.

Subchannel analysis program for boiling water reactor fuel bundles based on five conservation equations of two-phase flow

International Nuclear Information System (INIS)

Bessho, Y.; Uchikawa, S.

1985-01-01

A subchannel analysis program, MENUETT, is developed for evaluation of thermal-hydraulic characteristics in boiling water reactor fuel bundles. This program is based on five conservation equations of two-phase flow with the drift-flux correlation. The cross flows are calculated separately for liquid and vapor phases from the lateral momentum conservation equation. The effects of turbulent mixing and void drift are accounted for in the program. The conservation equations are implicitly differentiated with the convective terms by the donor-cell method, and are solved iteratively in the axial and lateral directions. Data of the 3 X 3 rod bundle experiments are used for program verification. The lateral distributions of equilibrium quality and mass flow rate at the bundle exit calculated by the program compare satisfactorily with the experimental results

Chirality conservation in the lattice gauge theory

International Nuclear Information System (INIS)

Peskin, M.E.

1978-01-01

The derivation of conservation laws corresponding to chiral invariance in quantum field theories of interacting quarks and gluons are studied. In particular there is interest in observing how these conservation laws are constrained by the requirement that the field theory be locally gauge invariant. To examine this question, a manifestly gauge-invariant definition of local operators in a quantum field theory is introduced, a definition which relies in an essential way on the use of the formulation of gauge fields on a lattice due to Wilson and Polyakov to regulate ultraviolet divergences. The conceptual basis of the formalism is set out and applied to a long-standing puzzle in the phenomenology of quark-gluon theories: the fact that elementary particle interactions reflect the conservation of isospin-carrying chiral currents but not of the isospin-singlet chiral current. It is well known that the equation for the isospin-singlet current contains an extra term, the operator F/sub mu neu/F/sup mu neu/, not present in the other chirality conservation laws; however, this term conventionally has the form of a total divergence and so still allows the definition of a conserved chiral current. It is found that, when the effects of maintaining gauge invariance are properly taken into account, the structure of this operator is altered by renormalization effects, so that it provides an explicit breaking of the unwanted chiral invariance. The relation between this argument, based on renormaliztion, is traced to a set of more heuristic arguments based on gauge field topology given by 't Hooft; it is shown that the discussion provides a validation, through short-distance analysis, of the picture 'Hooft has proposed. The formal derivation of conservation laws for chiral currents are set out in detail

Symmetry and conservation laws in particle physics in the fifties

International Nuclear Information System (INIS)

Michel, L.

1989-01-01

This paper puzzles over why symmetry, so central to particle physics today, was so little attended to in the 1950s when the need for it was becoming profound, with the notion of parity violation and other break-downs in conservation laws, such as angular momentum and charge conjugation. Group theory, including Lie groups, would also have helped understanding of the particle physics discoveries of the 1950s such as strange particles, resonances, and associated production. They were adopted ten years too late by the physics community. (UK)

Environmental law

International Nuclear Information System (INIS)

Anon.

1980-01-01

This pocketbook contains major federal regulations on environmental protection. They serve to protect and cultivate mankind's natural foundations of life, to preserve the environment. The environmental law is devided as follows: Constitutional law on the environment, common administrative law on the environment, special administrative law on the environment including conservation of nature and preservation of rural amenities, protection of waters, waste management, protection against nuisances, nuclear energy and radiation protection, energy conservation, protection against dangerous substances, private law relating to the environment, criminal law relating to the environment. (HSCH) [de

A novel hierarchy of differential—integral equations and their generalized bi-Hamiltonian structures

International Nuclear Information System (INIS)

Zhai Yun-Yun; Geng Xian-Guo; He Guo-Liang

2014-01-01

With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 × 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy

δ- and δ'-shock wave types of singular solutions of systems of conservation laws and transport and concentration processes

International Nuclear Information System (INIS)

Shelkovich, V M

2008-01-01

This is a survey of some results and problems connected with the theory of generalized solutions of quasi-linear conservation law systems which can admit delta-shaped singularities. They are the so-called δ-shock wave type solutions and the recently introduced δ (n) -shock wave type solutions, n=1,2,..., which cannot be included in the classical Lax-Glimm theory. The case of δ- and δ'-shock waves is analyzed in detail. A specific analytical technique is developed to deal with such solutions. In order to define them, some special integral identities are introduced which extend the concept of weak solution, and the Rankine-Hugoniot conditions are derived. Solutions of Cauchy problems are constructed for some typical systems of conservation laws. Also investigated are multidimensional systems of conservation laws (in particular, zero-pressure gas dynamics systems) which admit δ-shock wave type solutions. A geometric aspect of such solutions is considered: they are connected with transport and concentration processes, and the balance laws of transport of 'volume' and 'area' to δ- and δ'-shock fronts are derived for them. For a 'zero-pressure gas dynamics' system these laws are the mass and momentum transport laws. An algebraic aspect of these solutions is also considered: flux-functions are constructed for them which, being non-linear, are nevertheless uniquely defined Schwartz distributions. Thus, a singular solution of the Cauchy problem generates algebraic relations between its components (distributions).

The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation

Directory of Open Access Journals (Sweden)

Eitzinger B

2014-12-01

Full Text Available This study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.

The Reduction of Chazy Classes and Other Third-Order Differential Equations Related to Boundary Layer Flow Models

International Nuclear Information System (INIS)

Fakhar, K.; Kara, A. H.

2012-01-01

We study the symmetries, conservation laws and reduction of third-order equations that evolve from a prior reduction of models that arise in fluid phenomena. These could be the ordinary differential equations (ODEs) that are reductions of partial differential equations (PDEs) or, alternatively, PDEs related to given ODEs. In this class, the analysis includes the well-known Blasius, Chazy, and other associated third-order ODEs. (general)

Classical relativistic equations for particles with spin moving in external fields

NARCIS (Netherlands)

Dam, H. van; Ruijgrok, Th.W.

1980-01-01

We derive equations of motion for a point particle with spin in an external electromagnetic and in an external scalar field. The derivation is based on the ten conservation laws of linear and angular momentum and on a general expression for the current by which the particle interacts with the

The Law of Element Abundance Relationships in Igneous Rocks Petrogenetically Associated with Fractional Crystallization

Institute of Scientific and Technical Information of China (English)

汪云亮; 王旺章

1991-01-01

Reported in this paper are:1)the law of element abundance relationships:element abun-dances are of power function with each other in an igneous rock petrogenetically associated with fractional crystallization,2)deduction of the law and relevant parameters:abundance relationship constant(a°) and phase constant? from Henry's law and the law of mass conservation,3)the data basis and evidence of the law of element abundance relationships,4)establishment of the equa-bions for element abundance relationships in igneous rocks formed from the same parental magma during the same fractional crystallization stage ,and all measurable parameters involved in the equations.

Conservation laws and radiation in the scale covariant theory of gravitation

International Nuclear Information System (INIS)

Beesham, A.

1988-01-01

The conservation laws for mass, energy, and momentum are derived in the scale covariant theory of gravitation. The entropy problem which exists in the standard Friedmann-Lemaitre-Robertson-Walker models can be solved in the present context. Since the weak and strong energy conditions may be violated, a big bang singularity may be avoided, in contrast to general relativity. Since beta is shown to be constant during the radiation-dominated era, the difficulties in the theory associated with nucleosynthesis are avoided. 10 references

Binary Bell polynomial application in generalized (2+1)-dimensional KdV equation with variable coefficients

International Nuclear Information System (INIS)

Zhang Yi; Wei Wei-Wei; Cheng Teng-Fei; Song Yang

2011-01-01

In this paper, we apply the binary Bell polynomial approach to high-dimensional variable-coefficient nonlinear evolution equations. Taking the generalized (2+1)-dimensional KdV equation with variable coefficients as an illustrative example, the bilinear formulism, the bilinear Bäcklund transformation and the Lax pair are obtained in a quick and natural manner. Moreover, the infinite conservation laws are also derived. (general)

On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory

International Nuclear Information System (INIS)

Marrero, Juan Carlos; Roman-Roy, Narciso; Salgado, Modesto; Vilarino, Silvia

2011-01-01

This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating conservation laws to them by means of a suitable generalization of Noether's theorem.

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion

International Nuclear Information System (INIS)

Zhang Mei-Ling; Wang Xiao-Xiao; Xie Yin-Li; Jia Li-Qun; Sun Xian-Ting

2011-01-01

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results. (general)

Existence of traveling waves for diffusive-dispersive conservation laws

Directory of Open Access Journals (Sweden)

Cezar I. Kondo

2013-02-01

Full Text Available In this work we show the existence existence and uniqueness of traveling waves for diffusive-dispersive conservation laws with flux function in $C^{1}(mathbb{R}$, by using phase plane analysis. Also we estimate the domain of attraction of the equilibrium point attractor corresponding to the right-hand state. The equilibrium point corresponding to the left-hand state is a saddle point. According to the phase portrait close to the saddle point, there are exactly two semi-orbits of the system. We establish that only one semi-orbit come in the domain of attraction and converges to $(u_{-},0$ as $yo -infty$. This provides the desired saddle-attractor connection.

A Taylor weak-statement algorithm for hyperbolic conservation laws

Science.gov (United States)

Baker, A. J.; Kim, J. W.

1987-01-01

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

Application of the Binary Bell Polynomials Method to the Dissipative (2+1)-Dimensional AKNS Equation

International Nuclear Information System (INIS)

Liu Na; Liu Xi-Qiang

2012-01-01

Based on the binary Bell polynomials, the bilinear representation, bilinear Bäcklund transformation and the Lax pair for the dissipative (2+1)-dimensional Ablowitz—Kaup—Newell—Segur (AKNS) equation are obtained. Moreover, the infinite conservation laws are also derived

A discrete model on Sierpinski gasket substrate for a conserved current equation with a conservative noise

Science.gov (United States)

Kim, Dae Ho; Kim, Jin Min

2012-09-01

A conserved discrete model on the Sierpinski gasket substrate is studied. The interface width W in the model follows the Family-Vicsek dynamic scaling form with growth exponent β ≈ 0.0542, roughness exponent α ≈ 0.240 and dynamic exponent z ≈ 4.42. They satisfy a scaling relation α + z = 2zrw, where zrw is the random walk exponent of the fractal substrate. Also, they are in a good agreement with the predicted values of a fractional Langevin equation \\frac{\\partial h}{\\partial t}={\

Conservation laws and stress-energy-momentum tensors for systems with background fields

Energy Technology Data Exchange (ETDEWEB)

Gratus, Jonathan, E-mail: j.gratus@lancaster.ac.uk [Lancaster University, Lancaster LA1 4YB (United Kingdom); The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD (United Kingdom); Obukhov, Yuri N., E-mail: yo@thp.uni-koeln.de [Institute for Theoretical Physics, University of Cologne, 50923 Koeln (Germany); Tucker, Robin W., E-mail: r.tucker@lancaster.ac.uk [Lancaster University, Lancaster LA1 4YB (United Kingdom); The Cockcroft Institute, Daresbury Laboratory, Warrington WA4 4AD (United Kingdom)

2012-10-15

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields. - Highlights: Black-Right-Pointing-Pointer The role of background fields in diffeomorphism invariant actions is demonstrated. Black-Right-Pointing-Pointer Interrelations between different stress-energy-momentum tensors are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic tensors are discussed in this context. Black-Right-Pointing-Pointer Conservation laws in the presence of nondynamic background fields are formulated. Black-Right-Pointing-Pointer The discussion is facilitated by the development of a new variational calculus.

Irreversible thermodynamics of open chemical networks. I. Emergent cycles and broken conservation laws

International Nuclear Information System (INIS)

Polettini, Matteo; Esposito, Massimiliano

2014-01-01

In this paper and Paper II, we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks “in a box”, whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated with nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation a + b = s Y between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats s Y . We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction, and of thermodynamic constraints for network reconstruction

Irreversible thermodynamics of open chemical networks. I. Emergent cycles and broken conservation laws.

Science.gov (United States)

Polettini, Matteo; Esposito, Massimiliano

2014-07-14

In this paper and Paper II, we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks "in a box", whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated with nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation a + b = s(Y) between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats s(Y). We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction, and of thermodynamic constraints for network reconstruction.

Test of post-newtonian conservation laws in the binary system PSR 1913+16

International Nuclear Information System (INIS)

Will, C.M.

1976-01-01

Observations that set upper limits on secular changes in the pulsar period and orbital period in the binary system PSR 1913+16 may provide a test of post-Newtonian conservation laws. According to some metric theories of gravitation, the center of mass of a binary system may be accelerated in the direction of the periastron of the orbit because of a violation of post-Newtonian momentum conservation. In the binary system PSR 1913+16, this effect could produce secular changes in both pulsar and orbital periods (changing overall Doppler shift) as large as two parts in 10 6 per year. The size of the effect is proportional to the sine of the angle of periastron, to the difference in the masses of the components of the binary system, and to the combination of parametrized post-Newtonian parameters α 3 +zeta 2 -zeta/subw/. This combination is zero in any theory that predicts conserved total momentum for isolated systems (including general relativity and Brans-Dicke theory). Although solar-system experiments constrain α 3 and zeta/subw/ to be small, no decent direct limit has been placed on zeta 2 . Other possible sources of secular period changes in PSR 1913+16 are discussed and compared with this effect. It is also shown that a breakdown in the equality of active and passive gravitational masses (violation of ''Newton's third law'') leads only to periodic, unobservable orbital effects in a system like PSR 1913+16

Development of a Generalized Version of the Poisson-Nernst-Planck Equations Using the Hybrid Mixture Theory: Presentation of 2D Numerical Examples

DEFF Research Database (Denmark)

Johannesson, Björn

2010-01-01

A numerical scheme for the transient solution of generalized version of the Poisson-Nernst-Planck equations is presented. The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present problem iteratively. The Poisson......-scale and that it includes the volume fractions of phases in its structure. The background to the Poisson-Nernst-Planck equations can by the HMT approach be described by using the postulates of mass conservation of constituents together with the Gauss’ law used together with consistent constitutive laws. The HMT theory......-Nernst-Planck equations represent a set of diffusion equations for charged species, i.e. dissolved ions. These equations are coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst-Planck equations describing the diffusion of the ionic species and the Gauss’ law in used are...

Variational principle for nonlinear gyrokinetic Vlasov--Maxwell equations

International Nuclear Information System (INIS)

Brizard, Alain J.

2000-01-01

A new variational principle for the nonlinear gyrokinetic Vlasov--Maxwell equations is presented. This Eulerian variational principle uses constrained variations for the gyrocenter Vlasov distribution in eight-dimensional extended phase space and turns out to be simpler than the Lagrangian variational principle recently presented by H. Sugama [Phys. Plasmas 7, 466 (2000)]. A local energy conservation law is then derived explicitly by the Noether method. In future work, this new variational principle will be used to derive self-consistent, nonlinear, low-frequency Vlasov--Maxwell bounce-gyrokinetic equations, in which the fast gyromotion and bounce-motion time scales have been eliminated

Kepler's third law and the oscillator's isochronism

Science.gov (United States)

Gorringe, V. M.; Leach, P. G. L.

1993-11-01

Two classes of differential equations which have Kepler-like and oscillatorlike elliptical orbits are shown to have generalizations of the conserved angular momentum, energy, and Laplace-Runge-Lenz vector (Jauch-Hill-Fradkin tensor for the oscillator case). Both possess a generator of self-similar transformations and the related period-semimajor axis relation is a generalization of Kepler's third law in which the constant of proportionality depends explicitly on the eccentricity of the orbit.

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

Science.gov (United States)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

Neoclassical MHD equations for tokamaks

International Nuclear Information System (INIS)

Callen, J.D.; Shaing, K.C.

1986-03-01

The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion

Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations

NARCIS (Netherlands)

Hof, Bas van ’t; Veldman, Arthur E.P.

2012-01-01

The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting 'MaMEC' discretizations conserve mass, momentum as well as energy, although no

Modeling for cardiac excitation propagation based on the Nernst-Planck equation and homogenization.

Science.gov (United States)

Okada, Jun-ichi; Sugiura, Seiryo; Hisada, Toshiaki

2013-06-01

The bidomain model is a commonly used mathematical model of the electrical properties of the cardiac muscle that takes into account the anisotropy of both the intracellular and extracellular spaces. However, the equations contain self-contradiction such that the update of ion concentrations does not consider intracellular or extracellular ion movements due to the gradient of electric potential and the membrane charge as capacitive currents in spite of the fact that those currents are taken into account in forming Kirchhoff's first law. To overcome this problem, we start with the Nernst-Planck equation, the ionic conservation law, and the electroneutrality condition at the cellular level, and by introducing a homogenization method and assuming uniformity of variables at the microscopic scale, we derive rational bidomain equations at the macroscopic level.

BRST, generalized Maurer-Cartan equations and CFT

Energy Technology Data Exchange (ETDEWEB)

Zeitlin, Anton M. [Department of Mathematics, Yale University, 442 Dunham Lab, 10 Hillhouse Ave., New Haven, CT 06511 (United States); St. Petersburg Department of Steklov Mathematical Institute, Fontanka, 27, St. Petersburg 191023 (Russian Federation)]. E-mail: zam@math.ipme.ru

2006-12-25

The paper is devoted to the study of BRST charge in perturbed two-dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely algebraic operations on the corresponding operator algebra, which are defined via the OPE. The corresponding equations are constructed and their symmetries are studied up to the second order in formal coupling constant. It appears that the obtained equations can be interpreted as generalized Maurer-Cartan ones. We study two concrete examples in detail: the bosonic nonlinear sigma model and perturbed first order theory. In particular, we show that the Einstein equations, which are the conformal invariance conditions for both these perturbed theories, expanded up to the second order, can be rewritten in such generalized Maurer-Cartan form.

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

International Nuclear Information System (INIS)

Gamba, Irene M.; Haack, Jeffrey R.

2014-01-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation

Higher derivative extensions of 3d Chern-Simons models: conservation laws and stability

International Nuclear Information System (INIS)

Kaparulin, D.S.; Karataeva, I.Yu.; Lyakhovich, S.L.

2015-01-01

We consider the class of higher derivative 3d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability. (orig.)

A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation

Directory of Open Access Journals (Sweden)

Jinsong Hu

2013-01-01

Full Text Available We study the initial-boundary value problem for Rosenau-RLW equation. We propose a three-level linear finite difference scheme, which has the theoretical accuracy of Oτ2+h4. The scheme simulates two conservative properties of original problem well. The existence, uniqueness of difference solution, and a priori estimates in infinite norm are obtained. Furthermore, we analyze the convergence and stability of the scheme by energy method. At last, numerical experiments demonstrate the theoretical results.

Distilling free-form natural laws from experimental data.

Science.gov (United States)

Schmidt, Michael; Lipson, Hod

2009-04-03

For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the "alphabet" used to describe those systems.

Multicomponent fluid flow analysis using a new set of conservation equations

International Nuclear Information System (INIS)

Kamali, Reza; Emdad, Homayoon; Alishahi, Mohammad M

2008-01-01

In this work hydrodynamics of multicomponent ideal gas mixtures have been studied. Starting from the kinetic equations, the Eulerian approach is used to derive a new set of conservation equations for the multicomponent system where each component may have different velocity and kinetic temperature. The equations are based on the Grad's method of moment derived from the kinetic model in a relaxation time approximation (RTA). Based on this model which contains separate equation sets for each component of the system, a computer code has been developed for numerical computation of compressible flows of binary gas mixture in generalized curvilinear boundary conforming coordinates. Since these equations are similar to the Navier-Stokes equations for the single fluid systems, the same numerical methods are applied to these new equations. The Roe's numerical scheme is used to discretize the convective terms of governing fluid flow equations. The prepared algorithm and the computer code are capable of computing and presenting flow fields of each component of the system separately as well as the average flow field of the multicomponent gas system as a whole. Comparison of the present code results with those of a more common algorithm based on the mixture theory in a supersonic converging-diverging nozzle provides the validation of the present formulation. Afterwards, a more involved nozzle cooling problem with a binary ideal gas (helium-xenon) is chosen to compare the present results with those of the ordinary mixture theory. The present model provides the details of the flow fields of each component separately which is not available otherwise. It is also shown that the separate fluids treatment, such as the present study, is crucial when considering time scales on the order of (or shorter than) the intercollisions relaxation times.

Sn approach applied to the solution of transport equation

International Nuclear Information System (INIS)

Lopes, J.P.

1973-09-01

In this work the origin of the Transport Theory is considered and the Transport Equation for the movement of the neutron in a system is established in its more general form, using the laws of nuclear physics. This equation is used as the starting point for development, under adequate assumptions, of simpler models that render the problem suitable for numerical solution. Representation of this model in different geometries is presented. The different processes of nuclear physics are introduced briefly and discussed. In addition, the boundary conditions for the different cases and a general procedure for the application of the Conservation Law are stated. The last chapter deals specifically with the S n method, its development, definitions and generalities. Computational schemes for obtaining the S n solution in spherical and cylindrical geometry, and convergence acceleration methods are also developed. (author)

Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation

Directory of Open Access Journals (Sweden)

V. O. Vakhnenko

2016-01-01

Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.

Fokker-Planck equation in the presence of a uniform magnetic field

International Nuclear Information System (INIS)

Dong, Chao; Zhang, Wenlu; Li, Ding

2016-01-01

The Fokker-Planck equation in the presence of a uniform magnetic field is derived which has the same form as the case of no magnetic field but with different Fokker-Planck coefficients. The coefficients are calculated explicitly within the binary collision model, which are free from infinite sums of Bessel functions. They can be used to investigate relaxation and transport phenomena conveniently. The kinetic equation is also manipulated into the Landau form from which it is straightforward to compare with previous results and prove the conservation laws.

Fokker-Planck equation in the presence of a uniform magnetic field

Energy Technology Data Exchange (ETDEWEB)

Dong, Chao, E-mail: chaodong@iphy.ac.cn [Center for Plasma Theory and Computation, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Department of Nuclear Engineering, Seoul National University, Seoul 151-744 (Korea, Republic of); Zhang, Wenlu [Center for Plasma Theory and Computation, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Li, Ding, E-mail: dli@ustc.edu.cn [Center for Plasma Theory and Computation, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Department of Modern Physics, University of Science and Technology of China, Anhui Hefei 230026 (China)

2016-08-15

The Fokker-Planck equation in the presence of a uniform magnetic field is derived which has the same form as the case of no magnetic field but with different Fokker-Planck coefficients. The coefficients are calculated explicitly within the binary collision model, which are free from infinite sums of Bessel functions. They can be used to investigate relaxation and transport phenomena conveniently. The kinetic equation is also manipulated into the Landau form from which it is straightforward to compare with previous results and prove the conservation laws.

Revisiting Wiedemann-Franz law through Boltzmann transport equations and ab-initio density functional theory

Science.gov (United States)

Nag, Abhinav; Kumari, Anuja; Kumar, Jagdish

2018-05-01

We have investigated structural, electronic and transport properties of the alkali metals using ab-initio density functional theory. The electron energy dispersions are found parabolic free electron like which is expected for alkali metals. The lattice constants for all the studied metals are also in good agreement within 98% with experiments. We have further computed their transport properties using semi-classical Boltzmann transport equations with special focus on electrical and thermal conductivity. Our objective was to obtain Wiedemann-Franz law and hence Lorenz number. The motivation to do these calculations is to see that how the incorporation of different interactions such as electron-lattice, electron-electron interaction affect the Wiedeman-Franz law. By solving Boltzmann transport equations, we have obtained electrical conductivity (σ/τ) and thermal conductivity (κ0 /τ) at different temperatures and then calculated Lorenz number using L = κ0 /(σT). The obtained value of Lorenz number has been found to match with value derived for free electron Fermi gas 2.44× 10-8 WΩK-2. Our results prove that the Wiedemann-Franz law as derived for free electron gas does not change much for alkali metals, even when one incorporates interaction of electrons with atomic nuclei and other electrons. However, at lower temperatures, the Lorenz number, was found to be deviating from its theoretical value.

Effects of zonal flows on correlation between energy balance and energy conservation associated with nonlinear nonviscous atmospheric dynamics in a thin rotating spherical shell

Science.gov (United States)

Ibragimov, Ranis N.

2018-03-01

The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.

Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations

KAUST Repository

Bonito, Andrea

2013-10-03

We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.

A maximum-principle preserving finite element method for scalar conservation equations

KAUST Repository

Guermond, Jean-Luc; Nazarov, Murtazo

2014-01-01

This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.

A maximum-principle preserving finite element method for scalar conservation equations

KAUST Repository

Guermond, Jean-Luc

2014-04-01

This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.

A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions

Czech Academy of Sciences Publication Activity Database

Zborovský, Imrich

2018-01-01

Roč. 33, č. 10 (2018), č. článku 1850057. ISSN 0217-751X R&D Projects: GA MŠk(CZ) LG15052 Institutional support: RVO:61389005 Keywords : Hadron interactions * self-similarity * fractality * conservation laws * quanta Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.597, year: 2016

Charge-conserving FEM-PIC schemes on general grids

International Nuclear Information System (INIS)

Campos Pinto, M.; Jund, S.; Salmon, S.; Sonnendruecker, E.

2014-01-01

Particle-In-Cell (PIC) solvers are a major tool for the understanding of the complex behavior of a plasma or a particle beam in many situations. An important issue for electromagnetic PIC solvers, where the fields are computed using Maxwell's equations, is the problem of discrete charge conservation. In this article, we aim at proposing a general mathematical formulation for charge-conserving finite-element Maxwell solvers coupled with particle schemes. In particular, we identify the finite-element continuity equations that must be satisfied by the discrete current sources for several classes of time-domain Vlasov-Maxwell simulations to preserve the Gauss law at each time step, and propose a generic algorithm for computing such consistent sources. Since our results cover a wide range of schemes (namely curl-conforming finite element methods of arbitrary degree, general meshes in two or three dimensions, several classes of time discretization schemes, particles with arbitrary shape factors and piecewise polynomial trajectories of arbitrary degree), we believe that they provide a useful roadmap in the design of high-order charge-conserving FEM-PIC numerical schemes. (authors)

Environmental law

International Nuclear Information System (INIS)

Bender, B.; Sparwasser, R.

1988-01-01

Environmental law is discussed exhaustively in this book. Legal and scientific fundamentals are taken into account, a systematic orientation is given, and hints for further information are presented. The book covers general environmental law, plan approval procedures, protection against nuisances, atomic law and radiation protection law, water protection law, waste management law, laws on chemical substances, conservation law. (HSCH) [de

A simple mass-conserved level set method for simulation of multiphase flows

Science.gov (United States)

Yuan, H.-Z.; Shu, C.; Wang, Y.; Shu, S.

2018-04-01

In this paper, a modified level set method is proposed for simulation of multiphase flows with large density ratio and high Reynolds number. The present method simply introduces a source or sink term into the level set equation to compensate the mass loss or offset the mass increase. The source or sink term is derived analytically by applying the mass conservation principle with the level set equation and the continuity equation of flow field. Since only a source term is introduced, the application of the present method is as simple as the original level set method, but it can guarantee the overall mass conservation. To validate the present method, the vortex flow problem is first considered. The simulation results are compared with those from the original level set method, which demonstrates that the modified level set method has the capability of accurately capturing the interface and keeping the mass conservation. Then, the proposed method is further validated by simulating the Laplace law, the merging of two bubbles, a bubble rising with high density ratio, and Rayleigh-Taylor instability with high Reynolds number. Numerical results show that the mass is a well-conserved by the present method.

A Summary of the Space-Time Conservation Element and Solution Element (CESE) Method

Science.gov (United States)

Wang, Xiao-Yen J.

2015-01-01

The space-time Conservation Element and Solution Element (CESE) method for solving conservation laws is examined for its development motivation and design requirements. The characteristics of the resulting scheme are discussed. The discretization of the Euler equations is presented to show readers how to construct a scheme based on the CESE method. The differences and similarities between the CESE method and other traditional methods are discussed. The strengths and weaknesses of the method are also addressed.

Interactions of Delta Shock Waves for Zero-Pressure Gas Dynamics with Energy Conservation Law

OpenAIRE

Wei Cai; Yanyan Zhang

2016-01-01

We study the interactions of delta shock waves and vacuum states for the system of conservation laws of mass, momentum, and energy in zero-pressure gas dynamics. The Riemann problems with initial data of three piecewise constant states are solved case by case, and four different configurations of Riemann solutions are constructed. Furthermore, the numerical simulations completely coinciding with theoretical analysis are shown.

Green`s function of Maxwell`s equations and corresponding implications for iterative methods

Energy Technology Data Exchange (ETDEWEB)

Singer, B.S. [Macquarie Univ., Sydney (Australia); Fainberg, E.B. [Inst. of Physics of the Earth, Moscow (Russian Federation)

1996-12-31

Energy conservation law imposes constraints on the norm and direction of the Hilbert space vector representing a solution of Maxwell`s equations. In this paper, we derive these constrains and discuss the corresponding implications for the Green`s function of Maxwell`s equations in a dissipative medium. It is shown that Maxwell`s equations can be reduced to an integral equation with a contracting kernel. The equation can be solved using simple iterations. Software based on this algorithm have successfully been applied to a wide range of problems dealing with high contrast models. The matrix corresponding to the integral equation has a well defined spectrum. The equation can be symmetrized and solved using different approaches, for instance one of the conjugate gradient methods.

Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

Science.gov (United States)

Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

Symmetries, integrals, and three-dimensional reductions of Plebanski's second heavenly equation

International Nuclear Information System (INIS)

Neyzi, F.; Sheftel, M. B.; Yazici, D.

2007-01-01

We study symmetries and conservation laws for Plebanski's second heavenly equation written as a first-order nonlinear evolutionary system which admits a multi-Hamiltonian structure. We construct an optimal system of one-dimensional subalgebras and all inequivalent three-dimensional symmetry reductions of the original four-dimensional system. We consider these two-component evolutionary systems in three dimensions as natural candidates for integrable systems

Federal energy conservation programs pursuant to section 381 of the Energy Policy and Conservation Act (Public Law 94-163). Annual report to Congress

Energy Technology Data Exchange (ETDEWEB)

1979-02-21

This report provides an overview of the activities and achievements of the executive branch of the Federal Government in implementing the energy conservation requirements and provisions of section 381 of the Energy Policy and Conservation Act (EPCA) of 1975 (Public Law 94-163). The report describes Federal actions to develop procurement policies that promote energy conservation and efficiency, develop a Federal 10-Year Buildings Energy Conservation Plan, develop responsible public education and information programs, encourage energy conservation and energy efficiency, and promote vanpooling and carpooling arrangements. About half of the Nation's energy is used in our homes and automobiles. Another 48 percent is used by State and local governments, business and insutry, in providing needed goods and services. The Federal Government is the Nation's largest energy user, accouting for 2.2 percent of the total national energy used in 1977. This energy is used by nearly 6 million people in more than 400 thousand buildings and in the operation of more than 600 thousand vehicles. While energy conservation and energy efficiency measures alone cannot solve our immediate problems, they are an essential part of our transition to an era of scarce and expensive energy supplies.

The Robotic Scientist: Distilling Natural Laws from Experimental Data, from Cognitive Robotics to Computational Biology

Energy Technology Data Exchange (ETDEWEB)

Lipson, Hod [Cornell University

2011-10-25

Can machines discover analytical laws automatically? For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. By seeking dynamical invariants and symmetries, we show how we can go from finding just predictive models to finding deeper conservation laws. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the “alphabet” used to describe those systems. Application to modeling physical and biological systems will be shown.

A mass conservative numerical solution of vertical water flow and mass transport equations in unsaturated porous media

International Nuclear Information System (INIS)

Lim, S.C.; Lee, K.J.

1993-01-01

The Galerkin finite element method is used to solve the problem of one-dimensional, vertical flow of water and mass transport of conservative-nonconservative solutes in unsaturated porous media. Numerical approximations based on different forms of the governing equation, although they are equivalent in continuous forms, can result in remarkably different solutions in an unsaturated flow problem. Solutions given by a simple Galerkin method based on the h-based Richards equation yield a large mass balance error and an underestimation of the infiltration depth. With the employment of the ROMV (restoration of main variable) concept in the discretization step, the mass conservative numerical solution algorithm for water flow has been derived. The resulting computational schemes for water flow and mass transport are applied to sandy soil. The ROMV method shows good mass conservation in water flow analysis, whereas it seems to have a minor effect on mass transport. However, it may relax the time-step size restriction and so ensure an improved calculation output. (author)

Interactions of Delta Shock Waves for Zero-Pressure Gas Dynamics with Energy Conservation Law

Directory of Open Access Journals (Sweden)

Wei Cai

2016-01-01

Full Text Available We study the interactions of delta shock waves and vacuum states for the system of conservation laws of mass, momentum, and energy in zero-pressure gas dynamics. The Riemann problems with initial data of three piecewise constant states are solved case by case, and four different configurations of Riemann solutions are constructed. Furthermore, the numerical simulations completely coinciding with theoretical analysis are shown.

Basic conservation laws in the electromagnetic theory of cyclotron radiation: further analysis

International Nuclear Information System (INIS)

Lieu, R.; Leahy, D.A.

1984-01-01

The conflict of basic conservation laws in cyclotron radiation is considered in more general terms, taking into account relativistic effects of the electron. Also investigated are the effects due to the most important approximation in cyclotron theory, viz the omission of radiation back reaction. The conclusions are (i) the disagreement is of a magnitude considerably larger than any errors introduced by the approximation; (ii) the 'degree of conflict' attains its maximum in relativistic velocities, when the energy loss to radiation can approach the total energy of the electron. (author)

Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion

KAUST Repository

Cañizo, J.A.

2010-03-01

We present a new a priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case. © 2009 Elsevier Masson SAS. All rights reserved.

Divergence-Measure Fields, Sets of Finite Perimeter, and Conservation Laws

Science.gov (United States)

Chen, Gui-Qiang; Torres, Monica

2005-02-01

Divergence-measure fields in L∞ over sets of finite perimeter are analyzed. A notion of normal traces over boundaries of sets of finite perimeter is introduced, and the Gauss-Green formula over sets of finite perimeter is established for divergence-measure fields in L∞. The normal trace introduced here over a class of surfaces of finite perimeter is shown to be the weak-star limit of the normal traces introduced in Chen & Frid [6] over the Lipschitz deformation surfaces, which implies their consistency. As a corollary, an extension theorem of divergence-measure fields in L∞ over sets of finite perimeter is also established. Then we apply the theory to the initial-boundary value problem of nonlinear hyperbolic conservation laws over sets of finite perimeter.