On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions
Directory of Open Access Journals (Sweden)
P. Masemola
2014-01-01
results in a scalar cubic Schrödinger equation. We investigate the relationship between the conservation laws and Lie symmetries and investigate a Lagrangian, corresponding Noether symmetries, conserved vectors, and exact solutions via “double reductions.”
Conservation laws and symmetries in stochastic thermodynamics.
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.
Conservation laws and symmetries in stochastic thermodynamics
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 Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
Sharapov, Alexey A.
2016-10-01
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are represented by on-shell closed forms of various degrees. This extends the usual Noether's correspondence between global symmetries and conservation laws to the case of lower-degree conservation laws and not necessarily variational equations of motion. Finally, we equip the space of conservation laws of a given degree with a Lie bracket and establish a homomorphism of the resulting Lie algebra to the Lie algebra of global symmetries.
Variational tricomplex, global symmetries and conservation laws of gauge systems
Sharapov, A A
2016-01-01
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are represented by on-shell closed forms of various degrees. This extends the usual Noether's correspondence between global symmetries and conservation laws to the case of lower-degree conservation laws and not necessarily variational equations of motion. Finally, we equip the space of conservation laws of a given degree with a Lie bracket and establish a homomorphism of the resulting Lie algebra to the Lie algebra of global symmetries.
Symmetries, Conservation Laws, and Wave Equation on the Milne Metric
Directory of Open Access Journals (Sweden)
Ahmad M. Ahmad
2012-01-01
representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determining Noether symmetries and conserved vectors for a Lagrangian constructed from a Lorentzian metric of interest in mathematical physics. For completeness, we give Lie point symmetries and conservation laws admitted by the wave equation on this Lorentzian metric.
On Symmetry Analysis and Conservation Laws of the AKNS System
Zhao, Zhonglong; Han, Bo
2016-08-01
The Lie symmetry analysis is applied to study the Ablowitz-Kaup-Newell-Segur (AKNS) system of water wave model. The AKNS system can be obtained from a dispersive-wave system via a variable transformation. Lie point symmetries and corresponding point transformations are determined. The optimal system of one-dimensional subalgebras is presented. On the basis of the optimal system, the similarity reductions and the invariant solutions are obtained. Some conservation laws are derived using the multipliers. In addition, the AKNS system is quasi self-adjoint. The conservation laws associated with the symmetries are also constructed.
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
Amitava Choudhuri; Subrata Ghosh; B Talukdar
2008-04-01
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 variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.
Symmetries and conservation laws of a damped Boussinesq equation
Gandarias, María Luz; Rosa, María
2016-08-01
In this work, we consider a damped equation with a time-independent source term. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. We also present some exact solutions. Conservation laws for this equation are constructed by using the multiplier method.
Uniform Projectile Motion: Dynamics, Symmetries and Conservation Laws
Swaczyna, Martin; Volný, Petr
2014-04-01
A geometric nonholonomic theory is applied to the problem of uniform projectile motion, i.e. motion of a projectile with constant instantaneous speed. The problem is investigated from the kinematic and dynamic point of view. Corresponding kinematic parameters of classical and uniform projectile motion are compared, nonholonomic Hamilton equations are derived and their solvability is discussed. Symmetries and conservation laws of the considered system are studied, the nonholonomic formulation of a conservation law of generalized energy is found as one of the corresponding Noetherian first integrals of this nonholonomic system.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The symmetries and non-Noether conservation laws of Birkhoffian system with unilateral constraints are studied. The differential equations of motion of the system are established, and the criterions of Noether symmetry,Lie symmetry and Mei symmetry of the system are given. Two types of new conservation laws, called the Hojman conservation law and the Mei conservation law respectively, are obtained, and the intrinsic relations among the symmetries and the new conservation laws are researched. At the end of the paper, an example is given to illustrate the application of the results.
Conservation laws and symmetries of Hunter-Saxton equation: revisited
Tian, Kai; Liu, Q. P.
2016-03-01
Through a reciprocal transformation {{T}0} induced by the conservation law {{\\partial}t}≤ft(ux2\\right)={{\\partial}x}≤ft(2uux2\\right) , the Hunter-Saxton (HS) equation {{u}xt}=2u{{u}2x}+ux2 is shown to possess conserved densities involving arbitrary smooth functions, which have their roots in infinitesimal symmetries of {{w}t}={{w}2} , the counterpart of the HS equation under {{T}0} . Hierarchies of commuting symmetries of the HS equation are studied under appropriate changes of variables initiated by {{T}0} , and two of these are linearized while the other is identical to the hierarchy of commuting symmetries admitted by the potential modified Korteweg-de Vries equation. A fifth order symmetry of the HS equation is endowed with a sixth order hereditary recursion operator, which is proved to have a bi-Hamiltonian factorization, by its connection with the Fordy-Gibbons equation. These results reveal the origin for the rich and remarkable structures of the HS equation and partially answer the questions raised by Wang (2010 Nonlinearity 23 2009).
Scaling symmetries, conservation laws and action principles in one-dimensional gas dynamics
Energy Technology Data Exchange (ETDEWEB)
Webb, G M; Zank, G P [Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL 35805 (United States)], E-mail: gary.webb@uah.edu
2009-11-27
Scaling symmetries of the planar, one-dimensional gas dynamic equations with adiabatic index {gamma} 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.
Schaft, Arjan van der
1981-01-01
The definitions of symmetries and conservation laws for autonomous (i.e. without external forces) Hamiltonian systems are generalized to Hamiltonian systems with inputs and outputs. It is shown that a symmetry implies the existence of a conservation law and vice versa; thereby generalizing Noether's
Xi-Zhong, Liu
2012-01-01
In this paper, We derive the symmetry group theorem to the Lin-Tsien equation by using the modified CK's direct method, from which we obtain the corresponding symmetry group. More importantly, conservation laws corresponding to the Kac-Moody-Virasoro symmetry algebra of Lin-Tsien equation is obtained up to second order group invariants.
Symmetry and conservation laws in semiclassical wave packet dynamics
Energy Technology Data Exchange (ETDEWEB)
Ohsawa, Tomoki, E-mail: tomoki@utdallas.edu [Department of Mathematical Sciences, The University of Texas at Dallas, 800 W Campbell Rd., Richardson, Texas 75080-3021 (United States)
2015-03-15
We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether’s theorem. We consider two slightly different formulations of Gaussian wave packet dynamics; one is based on earlier works of Heller and Hagedorn and the other based on the symplectic-geometric approach by Lubich and others. In either case, we reveal the symplectic and Hamiltonian nature of the dynamics and formulate natural symmetry group actions in the setting to derive the corresponding conserved quantities (momentum maps). The semiclassical angular momentum inherits the essential properties of the classical angular momentum as well as naturally corresponds to the quantum picture.
Munteanu, Florian
2016-01-01
In this paper, we will present Lagrangian and Hamiltonian k-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will obtain new kinds of conservation laws for k-symplectic Hamiltonian systems and k-symplectic Lagrangian systems.
Symmetries and conservation laws for the wave equations of scalar statistical optics
Energy Technology Data Exchange (ETDEWEB)
Mitofsky, A M; Carney, P S [Department of Electrical and Computer Engineering and the Beckman Institute for Science and Technology, University of Illinois at Urbana-Champaign, 405 N Mathews Avenue, Urbana, IL 61801 (United States)
2008-10-17
The Lie method and Noether's theorem are applied to the double wave equations for the correlation functions of statistical optics. Generalizations of the deterministic conservation laws are found and seen to correspond to the usual laws in the deterministic limit. The statistically stationary wave equations are shown to contain fewer symmetries than for the nonstationary case, so the corresponding conservation laws differ from the conservation laws of the nonstationary, two-time, wave equations.
Noether-Type Symmetries and Associated Conservation Laws of Some Systems of Nonlinear PDEs
Institute of Scientific and Technical Information of China (English)
MEI Jian-Qin
2009-01-01
The algorithm for constructing conservation laws of Etder-Lagrange--type equations via Noether-type symmetry operators associated with partial Lagrangian has been presented. As applications, many new conservation laws of some important systems of nonlinear partial differential equations have been obtained.
A New Conservation Law Derived from Mei Symmetry for the System of Generalized Classical Mechanics
Institute of Scientific and Technical Information of China (English)
ZHANGYi
2004-01-01
A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under irdinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finadly, an example is given to illustrate the application of the results.
A New Conservation Law Derived from Mei Symmetry for the System of Generalized Classical Mechanics
Institute of Scientific and Technical Information of China (English)
ZHANG Yi
2004-01-01
A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under infinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finally, an example is given to illustrate the application of the results.
Symmetry and conservation law structures of some anti-self-dual (ASD) manifolds
Indian Academy of Sciences (India)
J BASINGWA; A H KARA; ASHFAQUE H BOKHARI; R A MOUSA; F D ZAMAN
2016-11-01
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.
Symmetry Analysis and Conservation Laws for the Hunter-Saxton Equation
Institute of Scientific and Technical Information of China (English)
Mehdi Nadjafikhah; Fatemeh Ahangari
2013-01-01
In this paper,the problem of determining the most generalLie point symmetries group and conservation laws of a well known nonlinear hyperbolic PDE in mathematical physics called the Hunter-Saxton equation (HSE) is analyzed.By applying the basic Lie symmetry method for the HSE,the classical Lie point symmetry operators are obtained.Also,the algebraic structure of the Lie algebra of symmetries is discussed and an optimal system of one-dimensional subalgebras of the HSE symmetry algebra which creates the preliminary classification of group invariant solutions is constructed.Particularly,the Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained.Mainly,the conservation laws of the HSE are computed via three different methods including Boyer's generalization of Noether's theorem,first homotopy method and second homotopy method.
Institute of Scientific and Technical Information of China (English)
ZHANG Li-Hua; WANG Ling; LIU Xi-Qiang; DONG Zhong-Zhou; BAI Cheng-Lin; LIU Xi-Qiang
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.
Symmetry analysis and conservation laws of the Drinfeld-Sokolov-Wilson system
Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong
2014-07-01
In this paper, Lie symmetry analysis is performed on the Drinfeld-Sokolov-Wilson system. We get the corresponding Lie algebra and similarity reductions of the system. In addition, we utilize Noether's approach and the new conservation theorem deriving the conservation laws of this system.
The symmetries and conservation laws of some Gordon-type equations in Milne space-time
Indian Academy of Sciences (India)
S Jamal; A H Kara; A H Bokhari; F D Zaman
2013-05-01
In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented and analysed. Using the Lie point symmetries, it is showed how to reduce Gordon-type wave equations using the method of invariants, and to obtain exact solutions corresponding to some boundary values. The Noether point symmetries and conservation laws are obtained for the Klein–Gordon equation in one case. Finally, the existence of higher-order variational symmetries of a projection of the Klein–Gordon equation is investigated using the multiplier approach.
Institute of Scientific and Technical Information of China (English)
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.
Symmetries, conservation laws, and time reversibility for Hamiltonian systems with external forces
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 def
Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation
Rui, Wenjuan; Zhang, Xiangzhi
2016-05-01
This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.
Directory of Open Access Journals (Sweden)
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.
Higher-order symmetries and conservation laws of multi-dimensional Gordon-type equations
Indian Academy of Sciences (India)
S Jamal; A H Kara
2011-09-01
In this paper a class of multi-dimensional Gordon-type equations are analysed using a multiplier and homotopy approach to construct conservation laws. The main focus is the analysis of the classical versions of the Gordon-type equations and obtaining higher-order variational symmetries and corresponding conserved quantities. The results are extended to the multi-dimensional Gordontype equations with the two-dimensional Klein–Gordon equation in particular yielding interesting results.
Bua, Lucía; Salgado, Modesto
2012-01-01
In this paper we study symmetries, Newtonoid vector fields, conservation laws, Noether Theorem and its converse, in the framework of the $k$-symplectic formalism, using the Fr\\"olicher-Nijenhuis formalism on the space of $k^1$ velocities of the configuration manifold. For the $k=1$ case it is well known that Cartan symmetries induce and are induced by constants of motions, and these results are known as Noether Theorem and its converse. For $k>1$, we provide a new proof that Noether Theorem is true, and hence each Cartan symmetry induces a conservation law. We show that under some assumptions, the converse of Noether Theorem is also true and provide examples when this is not the case. We also study the relations between dynamical symmetries, Newtonoid vector fields, Cartan symmetries and conservation laws, showing when one of them will imply the others. We use several examples of partial differential equations to illustrate when these concepts are related and when they are not.
Laws of conservation as related to brain growth, aging, and evolution: symmetry of the minicolumn
Directory of Open Access Journals (Sweden)
Manuel F. Casanova
2011-12-01
Full Text Available Development, aging, and evolution offer different time scales regarding possible anatomical transformations of the brain. This article expands on the perspective that the cerebral cortex exhibits a modular architecture with invariant properties in regards to these time scales. These properties arise from morphometric relations of the ontogentic minicolumn as expressed in Noether’s first theorem, i.e., that for each continuous symmetry there is a conserved quantity. Whenever minicolumnar symmetry is disturbed by either developmental or aging processes the principle of least action limits the scope of morphometric alterations. Alternatively, local and global divergences from these laws apply to acquired processes when the system is no longer isolated from its environment. The underlying precepts to these physical laws can be expressed in terms of mathematical equations that are conservative of quantity. Invariant properties of the brain include the rotational symmetry of minicolumns, a scaling proportion or even expansion between pyramidal cells and core minicolumnar size, and the translation of neuronal elements from the main axis of the minicolumn. It is our belief that a significant portion of the architectural complexity of the cerebral cortex, its response to injury, and its evolutionary transformation, can all be captured by a small set of basic physical laws dictated by the symmetry of minicolumns. The putative preservations of parameters related to the symmetry of the minicolumn suggest that the development and final organization of the cortex follows a deterministic process.
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.
Lie Symmetry Analysis and Conservation Laws of a Generalized Time Fractional Foam Drainage Equation
Wang, Li; Tian, Shou-Fu; Zhao, Zhen-Tao; Song, Xiao-Qiu
2016-07-01
In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann—Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method. Supported by the National Training Programs of Innovation and Entrepreneurship for Undergraduates under Grant No. 201410290039, the Fundamental Research Funds for the Central Universities under Grant Nos. 2015QNA53 and 2015XKQY14, the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Mines, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2015M570498, and Natural Sciences Foundation of China under Grant No. 11301527
Lie Symmetries, Conservation Laws and Explicit Solutions for Time Fractional Rosenau–Haynam Equation
Qin, Chun-Yan; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian
2017-02-01
Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation. Supported by the Fundamental Research Fund for Talents Cultivation Project of the China University of Mining and Technology under Grant No. YC150003
Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model
Directory of Open Access Journals (Sweden)
M.C. Nucci
2015-09-01
Full Text Available Basener and Ross (2005 proposed a mathematical model that describes the dynamics of growth and sudden decrease in the population of Easter Island. We have applied Lie group analysis to this system and found that it can be integrated by quadrature if the involved parameters satisfy certain relationships. We have also discerned hidden linearity. Moreover, we have determined a Jacobi last multiplier and, consequently, a Lagrangian for the general system and have found other cases independently and dependently on symmetry considerations in order to construct a corresponding variational problem, thus enabling us to find conservation laws by means of Noether’s theorem. A comparison with the qualitative analysis given by Basener and Ross is provided.
Asymptotic symmetry and conservation laws in 2d Poincaré gauge theory of gravity
Blagojevic, M; Vukasinac, T
1996-01-01
The structure of the asymptotic symmetry in the Poincar\\'e gauge theory of gravity in 2d is clarified by using the Hamiltonian formalism. The improved form of the generator of the asymptotic symmetry is found for very general asymptotic behaviour of phase space variables, and the related conserved quantities are explicitly constructed.
Conservation laws and symmetries of the shallow water system above rough bottom
Aksenov, A. V.; Druzhkov, K. P.
2016-06-01
The system of one-dimensional shallow water equations above the rough bottom is considered. All its hydrodynamic conservation laws are found, and a group classification is performed. A new conservation law additional to the two basic conservation laws is found. It is shown that the system of shallow water equations can be linearized by a point change of variables only in cases of constant and linear bottom profiles.
Ahangari, Fatemeh
2017-01-01
Scalar-field cosmology can be regarded as one of the significant fields of research in recent years. This paper is dedicated to a thorough investigation of the symmetries and conservation laws of the geodesic equations associated to a specific exact cosmological solution of a scalar-field potential which was originally motivated by six-dimensional Einstein-Maxwell theory. The mentioned string inspired Friedmann-Robertson-Lamai ^tre-Walker (FRLW) solution is one of the noteworthy solutions of Einstein field equations. For this purpose, first of all the Christoffel symbols and the corresponding system of geodesic equations are computed and then the associated Lie symmetries are totally analyzed. Moreover, the algebraic structure of the Lie algebra of local symmetries is briefly investigated and a complete classification of the symmetry subalgebras is presented. Besides by applying the resulted symmetry operators the invariant solutions of the system of geodesic equations are discussed. In addition, the Noether symmetries and the Killing vector fields of the geodesic Lagrangian are determined and the corresponding optimal system of one-dimensional subalgebras is constructed. Mainly, an entire set of local conservation laws is computed for our analyzed scalar-field cosmological solution. For this purpose, two distinct procedures are applied: the celebrated Noether's theorem and the direct method which is fundamentally based on a systematic application of Euler differential operators which annihilate any divergence expression identically.
Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian
2017-03-01
In this article, a generalised Whitham-Broer-Kaup-Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham-Broer-Kaup-Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.
Institute of Scientific and Technical Information of China (English)
DONG Zhong-Zhou; LIU Xi-Qiang; BAI Cheng-Lin
2006-01-01
Using the classical Lie method of infinitesimals, we first obtain the symmetry of the (2+1)-dimensional Burgers-Korteweg-de-Vries (3D-BKdV) equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.
Pitts, J Brian
2016-01-01
Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? Einstein used an identity from his assumed linear coordinate covariance x'= Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf La...
Pitts, J. Brian
2016-05-01
Recent work on the history of General Relativity by Renn et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911-1914) of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance xμ‧ = Mνμ xν to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit). Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom (later called "ghosts" in particle physics). Thus the Entwurf theory fails a 1920s-1930s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting
Energy Technology Data Exchange (ETDEWEB)
Bostrem, I.G. [Department of Physics, Ural State University, Ekaterinburg 620083 (Russian Federation); Kishine, J. [Faculty of Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550 (Japan); Lavrov, R.V. [Department of Physics, Ural State University, Ekaterinburg 620083 (Russian Federation); Ovchinnikov, A.S. [Department of Physics, Ural State University, Ekaterinburg 620083 (Russian Federation)], E-mail: alexander.ovchinnikov@usu.ru
2009-01-26
An appearance of the transport spin current in chiral helimagnet is mathematically justified based on the symmetry arguments. Although the starting Lagrangian of the chiral magnet with the Berry phase term and the parity-violating Dzyaloshinskii-Morya coupling is not manifestly Galilean invariant, the Lie point group symmetry analysis and the variational symmetry analysis elucidate the hidden Galilean symmetry and the existence of the linear momentum as a conserved Noether current, respectively.
The Using of Conservation Laws in Symmetry-Preserving Difference Scheme
Institute of Scientific and Technical Information of China (English)
XIN Xiang-Peng; CHEN Yong
2013-01-01
In this paper,by means of the potential systems of the giyen nonlinear evolution equations,a procedure of symmetry preserving discretization of differential equations is presented.The specific process will be given detailed in sec0tion 2.This extended method is effective for discreting the high-order (high-dimensional) nonlinear evolution equations.As examples,the invariant difference models of the mKdV equation and the Boussinesq equation are constructed.
Asymptotically anti-de Sitter space-times: symmetries and conservation laws revisited
Barnich, G.; Brandt, F.; Claes, K.
2004-02-01
In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat metric induced on the boundary. The fall-off conditions for the metric perturbations that guarantee finiteness of the associated conserved charges are derived.
Feng, Lian-Li; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian
2016-09-01
In this paper, the time fractional Fordy-Gibbons equation is investigated with Riemann-Liouville derivative. The equation can be reduced to the Caudrey-Dodd-Gibbon equation, Savada-Kotera equation and the Kaup-Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method. Supported by the Fundamental Research Funds for Key Discipline Construction under Grant No. XZD201602, the Fundamental Research Funds for the Central Universities under Grant Nos. 2015QNA53 and 2015XKQY14, the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Mines, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2015M570498, and Natural Sciences Foundation of China under Grant No. 11301527
The conservation of orbital symmetry
Woodward, R B
2013-01-01
The Conservation of Orbital Symmetry examines the principle of conservation of orbital symmetry and its use. The central content of the principle was that reactions occur readily when there is congruence between orbital symmetry characteristics of reactants and products, and only with difficulty when that congruence does not obtain-or to put it more succinctly, orbital symmetry is conserved in concerted reaction. This principle is expected to endure, whatever the language in which it may be couched, or whatever greater precision may be developed in its application and extension. The book ope
Conservation Laws of Differential Equations in Finance
Institute of Scientific and Technical Information of China (English)
QIN Mao-Chang; MEI Feng-Xiang; SHANG Mei
2005-01-01
Conservation laws of some differential equations in fiance are studied in this paper. This method does not involve the use or existence of a variational principle. As an alternative, linearize the given equation and find adjoint equation of the linearized equation, the conservation laws can be constructed directly from the symmetries and adjoint symmetries of the associated linearized equation and its adjoint equation.
Conserved quantities and symmetries related to stochastic Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Shang Mei; Mei Feng-Xiang
2007-01-01
In this paper symmetries and conservation laws for stochastic dynamical systems are discussed in detail.Determining equations for infinitesimal approximate symmetries of Ito and Stratonovich dynamical systems are derived. It shows how to derive conserved quantities for stochastic dynamical systems by using their symmetries without recourse to Noether's theorem.
Conservation laws for vacuum tetrad gravity
Energy Technology Data Exchange (ETDEWEB)
Estabrook, Frank B [Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 (United States)
2006-05-07
Ten conservation laws in useful polynomial form are derived from a Cartan form and exterior differential system (EDS) for the tetrad equations of vacuum general relativity. The Noether construction of conservation laws for well-posed EDSs is introduced first, and an illustration given, deriving 15 conservation laws of the free field Maxwell equations from symmetries of its EDS. The Maxwell EDS and tetrad gravity EDS have parallel structures, with their numbers of dependent variables, numbers of generating 2-forms and generating 3-forms, and Cartan character tables all in the ratio of 1 to 4. They have ten corresponding symmetries with the same Lorentz algebra and ten corresponding conservation laws.
Symmetry breaking in non conservative systems
Martínez-Pérez, N E
2016-01-01
We apply Noether's theorem to show how the invariances of conservative systems are broken for nonconservative systems, in the variational formulation of Galley. This formulation considers a conservative action, extended by the inclusion of a time reversed sector and a nonconservative generalized potential. We assume that this potential is invariant under the symmetries of the initial conservative system. The breaking occurs because the time reversed sector requires inverse symmetry transformations, under which the nonconservative potential is not invariant. The resulting violation of the conservation laws is consistent with the equations of motion. We generalize this formulation for fermionic and sypersymmetric systems. In the case of a supersymmetric oscillator, the effect of damping is that the bosonic and fermionic components become different frequencies. Considering that initially the nonconservative action is invariant under supersymmetry, and that the breaking is associated to an instability, this resul...
Conservation Laws with Dissipation,
1980-07-01
smooth, due to the formation of shock waves. However, global solutions exist in the class of functions of bounded variation ,/in the sense of Tonelli...hyperbolic conservation law (2.2) ut + f(u)x -0 The Cauchy problem for (2.2), with initial data u(x,O), of bounded variation , admits a solution in the class...BV of functions of bounded variation ,.in the sense of Tonelli-Cesari. No gain would be made by assuming that u(x,O) is smoother, even analytic! In
Student understanding of Symmetry and Gauss' law
Singh, Chandralekha
2016-01-01
Helping students learn why Gauss' law can or cannot be easily applied to determine the strength of the electric field at various points for a particular charge distribution, and then helping them learn to determine the shape of the Gaussian surfaces if sufficient symmetry exists can develop their reasoning and problem solving skills. We investigate the difficulties that students in calculus-based introductory physics courses have with the concepts of symmetry, electric field and electric flux that are pivotal to Gauss' law of electricity. Determination of the electric field using Gauss' law requires discerning the symmetry of a particular charge distribution and being able to predict the direction of the electric field everywhere if a high symmetry exists. It requires a good grasp of how to add the electric field vectors using the principle of superposition, and the concepts of area vector and electric flux. We administered free response and multiple-choice questions and conducted interviews with individual s...
CONSERVATION LAWS AND SIMILARITY REDUCTION OF THE ZOOMERON EQUATION
Directory of Open Access Journals (Sweden)
Hejazi S. Reza
2016-11-01
Full Text Available In this study, we consider a 4-th order (1+1-dimensional PDE called Zoomeron equation. Some conservation laws are derived based on direct method. We also derived some similarity solutions using the symmetries.
Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Li-Qun; Liu Rong-Wan
2004-01-01
This paper focuses on studying non-Noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-Noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry of the systems. The work also gives connections between the nonNoether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-Noether conserved quantity. Finally, an example is discussed to illustrate these results.
Symmetries and Mei Conserved Quantities of Nonholonomic Controllable Mechanical Systems
Institute of Scientific and Technical Information of China (English)
XIA Li-Li; LI Yuan-Cheng; WANG Jing; HOU Qi-Bao
2006-01-01
This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result.
Conservation Laws of a Class of Combined Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Zhi-Yong; YONG Xue-Lin; CHEN Yu-Fu
2009-01-01
In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx=H (x)utt.
Indian Academy of Sciences (India)
K Fakhar; A A Zainal; A H Kara
2011-09-01
We investigate the invariance properties, nontrivial conservation laws and interplay between these notions that underly the equations governing Stokes’ ﬁrst problem for third-grade rotating ﬂuids. We show that a knowledge of this leads to a number of different reductions of the governing equations and, thus, a number of exact solutions can be obtained and a spectrum of further analyses may be pursued.
Field equations or conservation laws?
Francaviglia, Mauro; Winterroth, Ekkehart
2013-01-01
We explicate some epistemological implications of stationary principles and in particular of Noether Theorems. Noether's contribution to the problem of covariance, in fact, is epistemologically relevant, since it moves the attention from equations to conservation laws.
Scaling symmetry and conserved charge for shape-invariant optical fields
El Gawhary, O.; Severini, S.
2013-01-01
In this work we present an extensive study of the scaling symmetry typical of a paraxial wave theory. In particular, by means of a Lagrangian approach we derive the conservation law and the corresponding generalized charge associated with the scale invariance symmetry. In general, such a conserved c
Scaling symmetry and conserved charge for shape-invariant optical fields
El Gawhary, O.; Severini, S.
2013-01-01
In this work we present an extensive study of the scaling symmetry typical of a paraxial wave theory. In particular, by means of a Lagrangian approach we derive the conservation law and the corresponding generalized charge associated with the scale invariance symmetry. In general, such a conserved c
An Effective Method for Seeking Conservation Laws of Partial Differential Equations
Institute of Scientific and Technical Information of China (English)
QIN Mao-Chang; MEI Feng-Xiang; FAN Gui-Hong
2006-01-01
This paper introduces an effective method for seeking localconservation laws of general partial differential equations (PDEs). The well-known variational principle does not involve in this method. Alternatively, the conservation laws can be derived from symmetries, which include the symmetries of the associated linearized equation of the PDEs,and the adjoint symmetries of the adjoint equation of the PDEs.
Conservation laws and exact solutions of system of Boussinesq-Burgers equations
Akbulut, Arzu; Kaplan, Melike; Taşcan, Filiz
2017-01-01
In this work, we study conservation laws that is one of the applications of symmetries. Conservation laws has important place for differential equations and their solutions, also in all physics applications. This study deals with conservation laws of Boussinessq-Burgers equation. We used Noether approach and conservation theorem approach for finding conservation laws for this equation. Also finally, we found exact solutions of this equation by using the modified simple equation method.
Conservation laws for Ablowitz-Kaup-Newell-Segur equation
Mothibi, Dimpho Millicent
2016-06-01
In this paper we study the Ablowitz-Kaup-Newell-Segur equation, which has many applications in several physical phenomena. We perform the Noether symmetries analysis for this equation. Thereafter we construct the conservation laws for those cases which admit the Noether operators.
Post-Newtonian Conservation Laws in Rigid Quasilocal Frames
McGrath, Paul L; Epp, Richard J; Koop, Michael J; Mann, Robert B
2013-01-01
In recent work we constructed completely general conservation laws for energy and linear and angular momentum 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...
Nonlinear self-adjointness and conservation laws
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H, E-mail: nib@bth.se [Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 Karlskrona (Sweden)
2011-10-28
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation u{sub t} - {Delta}u = 0 becomes strictly self-adjoint after multiplying by u{sup -1}. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems. (fast track communication)
Institute of Scientific and Technical Information of China (English)
A H Bokhari; F D Zaman; K Fakhar; A H Kara
2011-01-01
@@ First,we studied the invariance properties of the Kadomstev-Petviashvili equation with power law nonlinearity.Then,we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation.The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved flows.%First, we studied the invariance properties of the Kadomstev-Petviashvili equation with power law nonlinearity. Then, we determined the complete class of conservation laws and stated the corresponding conserved densities which are useful in finding the conserved quantities of the equation. The point symmetry generators were also used to reduce the equation to an exact solution and to verify the invariance properties of the conserved Bows.
Energy-Momentum and Gauge Conservation Laws
Giachetta, G; Sardanashvily, G
1999-01-01
We treat energy-momentum conservation laws as particular gauge conservation laws when generators of gauge transformations are horizontal vector fields on fibre bundles. In particular, the generators of general covariant transformations are the canonical horizontal prolongations of vector fields on a world manifold. This is the case of the energy-momentum conservation laws in gravitation theories. We find that, in main gravitational models, the corresponding energy-momentum flows reduce to the generalized Komar superpotential. We show that the superpotential form of a conserved flow is the common property of gauge conservation laws if generators of gauge transformations depend on derivatives of gauge parameters. At the same time, dependence of conserved flows on gauge parameters make gauge conservation laws form-invariant under gauge transformations.
Hyperbolic conservation laws and numerical methods
Leveque, Randall J.
1990-01-01
The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.
Conservation Laws in Gravitation and Cosmology
Fabris, J C
2012-01-01
The existence of conservation laws is one of the most important requirement of physical theories. Some of them, like energy conservation, knows no experimental exception. However, the generalization of these conservation laws to curved space presents many challenges. The implementation of conservation laws in the General Relativity theory is revised, and the possibility of the generalization of the usual expression is discussed. The Rastall's theory of gravity, which considers a modification of the usual conservation of the energy-momentum tensor, is discussed in more detail. Some applications of the Rastall's theory to cosmology are presented, showing that it can lead to competetive results with respect to the Standard Cosmological Model.
Student understanding of symmetry and Gauss's law of electricity
Singh, Chandralekha
2016-01-01
We investigate the difficulties that students in calculus-based introductory physics courses have with the concepts of symmetry, electric field, and electric flux which are important for applying Gauss's law. The determination of the electric field using Gauss's law requires determining the symmetry of a particular charge distribution and predicting the direction of the electric field everywhere if a high symmetry exists. Effective application of Gauss's law implicitly requires understanding the principle of superposition for electric fields. Helping students learn when Gauss's law can be readily applied to determine the strength of the electric field, and then helping them learn to determine the appropriate shape of Gaussian surfaces if sufficient symmetry exists, can help develop their reasoning and problem-solving skills. We administered free-response and multiple-choice questions and conducted interviews with individual students using a think-aloud protocol to elucidate the difficulties that students have...
Optimal Regularizing Effect for Scalar Conservation Laws
Golse, François
2011-01-01
We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space.
A Kirchoff-like conservation law in Regge calculus
Gentle, Adrian P; McDonald, Jonathan R; Miller, Warner A
2008-01-01
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 identities which is based on the E. Cartan moment of rotation operator. These identities manifest themselves in the conceptually-simple form of a Kirchoff-like conservation law. This conservation law enables one to extend Re...
Lie Symmetry and Hojman Conserved Quantity of Maggi Equations
Institute of Scientific and Technical Information of China (English)
HU Chu-le; XIE Jia-fang
2007-01-01
Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An example is given to illustrate the application of the result.
Institute of Scientific and Technical Information of China (English)
K. Fakhar; A. H. Kara
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.
Group classification and conservation laws of anisotropic wave equations with a source
Ibragimov, N. H.; Gandarias, M. L.; Galiakberova, L. R.; Bruzon, M. S.; Avdonina, E. D.
2016-08-01
Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws.
Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Wang Xing-Zhong; Fu Hao; Fu Jing-Li
2012-01-01
This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems.Firstly,the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action.Secondly,the determining equations and structure equation of Lie symmetry of the system are obtained.Thirdly,the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems.Finally,an example is discussed to illustrate the application of the results.
Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems
Institute of Scientific and Technical Information of China (English)
Chen Rong; Xu Xue-Jun
2012-01-01
In this paper,the relation of the conformal invariance,the Noether symmetry,and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given.The relation between the conformal invariance and the Noether symmetry is discussed,the conformal factors of the determining expressions are found by using the Noether symmetry,and the Noether conserved quantity resulted from the conformal invariance is obtained.The relation between the conformal invariance and the Lie symmetry is discussed,the conformal factors are found by using the Lie symmetry,and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained.Two examples are given to illustrate the application of the results.
Momentum in general relativity: local versus quasilocal conservation laws
Epp, Richard J.; McGrath, Paul L.; Mann, Robert B.
2013-10-01
We construct a general relativistic conservation law for linear and angular momentum for matter and gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous construction of a general relativistic energy conservation law with the same features (McGrath et al 2012 Class. Quantum Grav. 29 215012). Our approach uses the Brown and York (1993 Phys. Rev. D 47 1407-19) quasilocal stress-energy-momentum tensor for matter and gravitational fields, plus the concept of a rigid quasilocal frame (RQF) introduced in (Epp et al 2009 Class. Quantum Grav. 26 035015; 2012 Classical and Quantum Gravity: Theory, Analysis, and Applications (Nova Science)). The RQF approach allows us to construct, in a generic spacetime, frames of reference whose boundaries are rigid (their shape and size do not change with time), and that have precisely the same six arbitrary time-dependent degrees of freedom as the accelerating and tumbling rigid frames we are familiar with in Newtonian mechanics. These RQFs, in turn, give rise to a completely general conservation law for the six components of momentum (three linear and three angular) of a finite system of matter and gravitational fields. We compare in detail this quasilocal RQF approach to constructing conservation laws with the usual local one based on spacetime symmetries, and discuss the shortcomings of the latter. These RQF conservation laws lead to a deeper understanding of physics in the form of simple, exact, operational definitions of gravitational energy and momentum fluxes, which in turn reveal, for the first time, the exact, detailed mechanisms of gravitational energy and momentum transfer taking place in a wide variety of physical phenomena, including a simple falling apple. As a concrete example, we derive a general relativistic version of Archimedes’ law that we apply to understand electrostatic weight and buoyant force in the context of a Reissner
An Unbroken Axial Vector Current Conservation Law
Sharafiddinov, Rasulkhozha S
2015-01-01
The mass, energy and momentum of the neutrino of a true flavor have an axial-vector nature. As a consequence, the left-handed truly neutral neutrino in an axial-vector field of emission can be converted into a right-handed one and vice versa. This predicts the unidenticality of masses, energies and momenta of neutrinos of the different components. Recognizing such a difference in masses, energies, momenta and accepting that the left-handed axial-vector neutrino and the right-handed antineutrino of true neutrality refer to long-lived C-odd leptons, and the right-handed truly neutral neutrino and the left-handed axial-vector antineutrino are of short-lived fermions of C-oddity, we would write a new CP-even Dirac equation taking into account the flavor symmetrical axial-vector mass, energy and momentum matrices. Their presence explains the spontaneous mirror symmetry violation, confirming that an axial-vector current conservation law has never violated. They reflect the availability of a mirror Minkowski space i...
Conserved symmetries in noncommutative quantum mechanics
Kupriyanov, V G
2014-01-01
We consider a problem of the consistent deformation of physical system introducing a new features, but preserving its fundamental properties. In particular, we study how to implement the noncommutativity of space-time without violation of the rotational symmetry in quantum mechanics or the Lorentz symmetry in f{i}eld theory. Since the canonical (Moyal) noncommutativity breaks the above symmetries one should work with more general case of coordinate-dependent noncommutative spaces, when the commutator between coordinates is a function of these coordinates. F{i}rst we describe in general lines how to construct the quantum mechanics on coordinate-dependent noncommutative spaces. Then we consider the particular examples: the Hydrogen atom on rotationally invariant noncommutative space and the Dirac equation on covariant noncommutative space-time.
Conserved symmetries in noncommutative quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Kupriyanov, V.G. [CMCC, Universidade Federal do ABC, Santo Andre, SP (Brazil)
2014-09-11
We consider a problem of the consistent deformation of physical system introducing a new features, but preserving its fundamental properties. In particular, we study how to implement the noncommutativity of space-time without violation of the rotational symmetry in quantum mechanics or the Lorentz symmetry in field theory. Since the canonical (Moyal) noncommutativity breaks the above symmetries one should work with more general case of coordinate-dependent noncommutative spaces, when the commutator between coordinates is a function of these coordinates. First we describe in general lines how to construct the quantum mechanics on coordinate-dependent noncommutative spaces. Then we consider the particular examples: the Hydrogen atom on rotationally invariant noncommutative space and the Dirac equation on covariant noncommutative space-time. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
SYMMETRIES AND CONSERVED QUANTITIES FOR SYSTEMS OF GENERALIZED CLASSICAL MECHANICS
Institute of Scientific and Technical Information of China (English)
Zhang Yi; Shang Mei; Mei Feng-xiang
2000-01-01
In this paper, the symmetries and the conserved quantities for systemsof generalized classical mechanics are studied. First, the generalizedNoether's theorem and the generalized Noether's inverse theorem of thesystems are given, which are based upon the invariant properties of thecanonical action with respect to the action of the infinitesimaltransformation of r-parameter finite group of transformation; second,the Lie symmetries and conserved quantities of the systems are studiedin accordance with the Lie's theory of the invariance of differentialequations under the transformation of infinitesimal groups; and finally,the inner connection between the two kinds of symmetries of systems isdiscussed.
Conservation laws and thermodynamic efficiencies.
Benenti, Giuliano; Casati, Giulio; Wang, Jiao
2013-02-15
We show that generic systems with a single relevant conserved quantity reach the Carnot efficiency in the thermodynamic limit. Such a general result is illustrated by means of a diatomic chain of hard-point elastically colliding particles where the total momentum is the only relevant conserved quantity.
Directory of Open Access Journals (Sweden)
Farhad Ali
2016-08-01
Full Text Available In this paper we find the Noether symmetries of the Lagrangian of cylindrically symmetric static spacetimes. Using this approach we recover all cylindrically symmetric static spacetimes appeared in the classification by isometries and homotheties. We give different classes of cylindrically symmetric static spacetimes along with the Noether symmetries of the corresponding Lagrangians and conservation laws.
Generalized conservation laws in non-local field theories
Kegeles, Alexander; Oriti, Daniele
2016-04-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Generalised conservation laws in non-local field theories
Kegeles, Alexander
2015-01-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalised conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalisation of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Diffusion processes satisfying a conservation law constraint
Bakosi, J
2014-01-01
We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative 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 non-negativity and the unit-sum conservation law constraint 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 di...
Energy Technology Data Exchange (ETDEWEB)
Barbosa, Gabriel Duarte; Ferreira, Renata Rosa; Thibes, Ronaldo [Universidade Estadual do Sudoeste da Bahia (UESB), BA (Brazil)
2011-07-01
Full text: We consider a classical particle minimally coupled to an external electromagnetic field, in both non-relativistic and relativistic regimes. The coupling is constructed via the electromagnetic potential which is assumed to satisfy the classical Maxwell equations. We review Noether's theorem at classical level associating infinitesimal symmetries to conserved quantities. The fundamental space-time symmetries are investigated considering a non-relativistic action, a relativistic action in a particular reference frame and an explicitly Lorentz invariant Lagrangian. We work out in detail the corresponding conserved quantities for each case. The well-known Noether's theorem establishes a connection between continuous infinitesimal symmetries of the action and conserved quantities - given a particular action, for each infinitesimal symmetry there exists an explicit conserved quantity. In particular, a single particle subjected to an external electromagnetic field gives rise to an action which may enjoy space-time symmetries. For the non-relativistic particle, we analyze translations in space and time and spatial rotations, calculating the conserved quantities - linear momentum, energy and angular momentum. The relativistic particle enjoys space-time Lorentz symmetry. Thus we check the six symmetries of the homogeneous Lorentz group, corresponding to three spatial rotations and three boosts, and the four space-time translations extending to the non-homogeneous Lorentz group (Poincare group). We consider two distinct actions describing the relativistic particle minimally coupled to an external electromagnetic field - the first one describes the particle in a particular frame of reference enforcing the relativistic generalization of Newton's second law with the Lorentz force while the second one is obtained from a Lorentz scalar Lagrangian. In all cases the conserved quantities are explicitly calculated via Noether's theorem. (author)
Symmetry conserving configuration mixing method with cranked states
Borrajo, Marta; Egido, J Luis
2015-01-01
We present the first calculations of a symmetry conserving configuration mixing method (SCCM) using time-reversal symmetry breaking Hartree-Fock-Bogoliubov (HFB) states with the Gogny D1S interaction. The method includes particle number and tridimensional angular momentum symmetry restorations as well as configuration mixing within the generator coordinate method (GCM) framework. The nucleus $^{32}$Mg is chosen to show the performance and reliability of the calculations. Additionally, $0^{+}_{1}$, $2^{+}_{1}$ and $4^{+}_{1}$ states are computed for the magnesium isotopic chain, where a noticeable compression of the spectrum is obtained by including cranked states, leading to a very good agreement with the known experimental data.
Symmetry conserving configuration mixing method with cranked states
Directory of Open Access Journals (Sweden)
Marta Borrajo
2015-06-01
Full Text Available We present the first calculations of a symmetry conserving configuration mixing method (SCCM using time-reversal symmetry breaking Hartree–Fock–Bogoliubov (HFB states with the Gogny D1S interaction. The method includes particle number and tridimensional angular momentum symmetry restorations as well as configuration mixing within the generator coordinate method (GCM framework. The nucleus 32Mg is chosen to show the performance and reliability of the calculations. Additionally, 01+, 21+ and 41+ states are computed for the magnesium isotopic chain, where a noticeable compression of the spectrum is obtained by including cranked states, leading to a very good agreement with the known experimental data.
Feinberg, G.; Weinberg, S.
1961-02-01
A multiplicative selection rule for mu meson-electron transitions is proposed. A "muon parity" = -1 is considered for the muon and its neutrino, while the "muon parity" for all other particles is +1. The selection rule then states that (-1) exp(no. of initial (-1) parity particles) = (-1) exp(no. of final (-1) parity particles). Several reactions that are forbidden by an additive law but allowed by the multiplicative law are suggested; these reactions include mu{sup +} .> e{sup +} + nu{sub mu} + {ovr nu}{sub e}, e{sup -} + e{sup -} .> mu{sup -} + mu{sup -}, and muonium .> antimuonium (mu{sup +} + e{sup -} .> mu{sup -} + e{sup +}). An intermediate-boson hypothesis is suggested. (T.F.H.)
Kersten, Paul 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 construc
Directory of Open Access Journals (Sweden)
N. Mindu
2014-01-01
Full Text Available The derivation of conservation laws for the magma equation using the multiplier method for both the power law and exponential law relating the permeability and matrix viscosity to the voidage is considered. It is found that all known conserved vectors for the magma equation and the new conserved vectors for the exponential laws can be derived using multipliers which depend on the voidage and spatial derivatives of the voidage. It is also found that the conserved vectors are associated with the Lie point symmetry of the magma equation which generates travelling wave solutions which may explain by the double reduction theorem for associated Lie point symmetries why many of the known analytical solutions are travelling waves.
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
Fractional conservation laws in optimal control theory
Frederico, Gastao S F
2007-01-01
Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define anymore a conservation law. Instead, it is proved that the fractional conservation law adds to the Hamiltonian a new term which depends on the fractional-order of differentiation, the generalized momentum, and the fractional derivative of the state variable.
Notes on conservation laws in chiral hydrodynamics
Zakharov, V I
2016-01-01
We consider chiral fluids within the standard framework of a chiral-invariant underlying field theory, anomalous in presence of electromagnetic fields. Apart from the Noether axial current of the underlying theory, in the limit of ideal fluid there exist extra conserved currents, corresponding to classical helical motions. The extra conservation laws are known to break down once viscosity is non-vanishing. Which looks puzzling, as if introduction of viscosity were inconsistent with chiral invariance. As a resolution of the puzzle, we argue that locally one can introduce an inertial frame where an extra conservation law still holds. In other words, the extra currents are covariantly conserved. The emergent gravitational field is determined by dynamics of the viscous fluid. We turn then to instabilities of chiral plasma against decays into helical magnetic or vortical configurations. We emphasise similarity between the two cases in the far infrared region, responsible for the decays. This similarity is not appa...
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.
Renormalization, averaging, conservation laws and AdS (in)stability
Energy Technology Data Exchange (ETDEWEB)
Craps, Ben [Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Evnin, Oleg [Department of Physics, Faculty of Science, Chulalongkorn University,Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Vanhoof, Joris [Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium)
2015-01-21
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.
Wigner-Araki-Yanase theorem beyond conservation laws
Tukiainen, Mikko
2017-01-01
The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables. Such limitations are imposed by the theorem of Wigner, Araki, and Yanase (WAY). In this paper a formulation of the WAY theorem is presented rephrasing the measurability limitations in terms of quantum incompatibility. This broader mathematical basis enables us to both capture and generalize the WAY theorem by allowing us to drop the assumptions of additivity and even conservation of the involved quantities. Moreover, we extend the WAY theorem to the general level of positive operator-valued measures.
Relativistic pseudospin symmetry and shell model Hamiltonians that conserve pseudospin symmetry
Energy Technology Data Exchange (ETDEWEB)
Ginocchio, Joseph N [Los Alamos National Laboratory
2010-09-21
Professor Akito Arima and his colleagues discovered 'pseudospin' doublets forty-one years ago in spherical nuclei. These doublets were subsequently discovered in deformed nuclei. We show that pseudospin symmetry is an SU(2) symmetry of the Dirac Hamiltonian which occurs when the scalar and vector potentials are opposite in sign but equal in magnitude. This symmetry occurs independent of the shape of the nucleus: spherical, axial deformed, triaxial, and gamma unstable. We survey some of the evidence that pseudospin symmetry is approximately conserved for a Dirac Hamiltonian with realistic scalar and vector potentials by examining the energy spectra, the lower components of the Dirac eigenfunctions, the magnetic dipole and Gamow-Teller transitions in nuclei, the upper components of the Dirac eigenfunctions, and nucleon-nucleus scattering. We shall also suggest that pseudospin symmetry may have a fundamental origin in chiral symmetry breaking by examining QCD sum rules. Finally we derive the shell model Hamiltonians which conserve pseudospin and show that they involve tensor interactions.
Application of polynomial preconditioners to conservation laws
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
The Hartwick rule as a conservation law
Heijnen, P.
2008-01-01
Using conservation laws, we provide a new proof of the Hartwick result, i.e. there is intergenerational equity if and only if net investment is constant. Subsequently, the technique is used to show that constant net investment does not indicate intergenerational equity if consumers value the existen
Noether-Lie symmetry and conserved quantities of mechanical system in phase space
Institute of Scientific and Technical Information of China (English)
Fang Jian-Hui; Liao Yong-Pan; Ding Ning; Wang Peng
2006-01-01
In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether-Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the NoetherLie symmetry of the system are obtained. The Noether-Lie symmetry contains the Nocthcr symmetry and the Lie symmetry, and has more generalized significance.
Momentum in General Relativity: Local versus Quasilocal Conservation Laws
Epp, Richard J; Mann, Robert B
2013-01-01
We construct a general relativistic conservation law for linear and angular momentum for matter and gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous construction of a general relativistic energy conservation law with the same features. Our approach uses the Brown and York quasilocal stress-energy-momentum tensor for matter and gravitational fields, plus the concept of a rigid quasilocal frame (RQF) introduced in previous work. The RQF approach allows us to construct, in a generic spacetime, frames of reference whose boundaries are rigid (their shape and size do not change with time), and that have precisely the same six arbitrary time-dependent degrees of freedom as the accelerating and tumbling rigid frames we are familiar with in Newtonian mechanics. These RQFs, in turn, give rise to a completely general conservation law for the six components of momentum (three linear and three angular) of a finite system of matter and gravita...
Discontinuous Galerkin Method for Hyperbolic Conservation Laws
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.
Hunting, law enforcement, and African primate conservation.
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.
Rosandić, Marija; Vlahović, Ines; Glunčić, Matko; Paar, Vladimir
2016-07-01
For almost 50 years the conclusive explanation of Chargaff's second parity rule (CSPR), the equality of frequencies of nucleotides A=T and C=G or the equality of direct and reverse complement trinucleotides in the same DNA strand, has not been determined yet. Here, we relate CSPR to the interstrand mirror symmetry in 20 symbolic quadruplets of trinucleotides (direct, reverse complement, complement, and reverse) mapped to double-stranded genome. The symmetries of Q-box corresponding to quadruplets can be obtained as a consequence of Watson-Crick base pairing and CSPR together. Alternatively, assuming Natural symmetry law for DNA creation that each trinucleotide in one strand of DNA must simultaneously appear also in the opposite strand automatically leads to Q-box direct-reverse mirror symmetry which in conjunction with Watson-Crick base pairing generates CSPR. We demonstrate quadruplet's symmetries in chromosomes of wide range of organisms, from Escherichia coli to Neanderthal and human genomes, introducing novel quadruplet-frequency histograms and 3D-diagrams with combined interstrand frequencies. These "landscapes" are mutually similar in all mammals, including extinct Neanderthals, and somewhat different in most of older species. In human chromosomes 1-12, and X, Y the "landscapes" are almost identical and slightly different in the remaining smaller and telocentric chromosomes. Quadruplet frequencies could provide a new robust tool for characterization and classification of genomes and their evolutionary trajectories.
Hyperbolic conservation laws in continuum physics
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...
Invariance analysis and conservation laws of the wave equation on Vaidya manifolds
Indian Academy of Sciences (India)
R Narain; A H Kara
2011-09-01
In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave equation, the symmetries and number of conservation laws, inter alia, are altered by the manifold on which the model wave rests. We ﬁnd Lie and Noether point symmetries of the corresponding wave equations and give some reductions. Some interesting physical conclusions relating to conservation laws such as energy, linear and angular momenta are also determined. We also present some interesting comparisons with the standard wave equations on a ﬂat geometry. Finally, we pursue the existence of higher-order variational symmetries of equations on nonﬂat manifolds.
CONSERVATION LAWS IN FINITE MICROCRACKING BRITTLE SOLIDS
Institute of Scientific and Technical Information of China (English)
Wang Defa; Chen Yiheng; Fukui Takuo
2005-01-01
This paper addresses the conservation laws in finite brittle solids with microcracks.The discussion is limited to the 2-D cases. First, after considering the combination of the PseudoTraction Method and the indirect Boundary Element Method, a versatile method for solving multicrack interacting problems in finite plane solids is proposed, by which the fracture parameters (SIF and path-independent integrals) can be calculated with a desirable accuracy. Second, with the aid of the method proposed, the roles the conservation laws play in the fracture analysis for finite microcracking solids are studied. It is concluded that the conservation laws do play important roles in not only the fracture analysis but also the analysis of damage and stability for the finite microcracking system. Finally, the physical interpretation of the M-integral is discussed further.An explicit relation between the M-integral and the crack face area, I.e., M = GS, has been discovered using the analytical method, which can shed some light on the Damage Mechanics issues from a different perspective.
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)
Exact solutions and conservation laws for a generalized improved Boussinesq equation
Motsepa, Tanki; Khalique, Chaudry Masood
2016-06-01
In this paper we study a nonlinear generalized improved Boussinesq equation, which describes nonlinear dispersive wave phenomena. Exact solutions are derived by using the Lie symmetry analysis and the simplest equation methods. Moreover, conservation laws are constructed by using the multiplier method.
An extension of the Noether theorem: Accompanying equations possessing conservation laws
Dorodnitsyn, V. A.; Ibragimov, N. H.
2014-02-01
It is shown that the Noether theorem can be extended for some equations associated (accompanying) with Euler-Lagrange equation. Each symmetry of Lagrangian yields a class of accompanying equations possessing conservation law (first integral). The generalization is done for canonical Hamiltonian equations as well.
A generalized Mei conserved quantity and Mei symmetry of Birkhoff system
Institute of Scientific and Technical Information of China (English)
Wang Peng; Fang Jian-Hui; Wang Xian-Ming
2009-01-01
This paper studies a new conserved quantity which can be called generalized Mei conserved quantity and directly deduced by Mei symmetry of Birkhoff system.The conditions under which the Mei symmetry can directly lead to generalized Mei conserved quantity and the form of generalized Mei conserved quantity are given.An example is given to illustrate the application of the results.
Entropy viscosity method for nonlinear conservation laws
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.
Institute of Scientific and Technical Information of China (English)
ZHANG Xiao-Ni; FANG Jian-Hui; PANG Ting; LIN Peng
2009-01-01
For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied.The criterion equation of the Noether symmetry for the system is got.The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained.Finally, an example is given to illustrate the application of the results.
Conservation laws in metric-affine gravitation theories: Superpotentials
Energy Technology Data Exchange (ETDEWEB)
Giachetta, G.; Giambo`, R.; Mangiarotti, L. [Camerino, Univ. (Italy). Dipt. di Matematica e Fisica
1997-08-01
By applying the machinery of the Lagrangian formalism in field theory, they study the conservation laws of a metric-affine gravitation theory in which the dynamical fields are the spin structures, the linear connections and the fermion fields on a 4-dimensional manifold. The system is assumed to be symmetric with respect to the group of all transformations of the spin bundle. The results obtained are the following. The currents associated with the infinitesimal vertical transformations of the symmetry group vanish identically. As a consequence, to every vector field on the world manifold there corresponds a well-defined current, namely the energy-momentum current. The superpotential term contained in this current is independent of the presence of fermion fields. The expression they get for the superpotential coincides with that found in the purely metric-affine context and generalized the well-known expression obtained by Komar.
Front tracking for hyperbolic conservation laws
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.
Front tracking for hyperbolic conservation laws
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 ...
Solutions and Conservation Laws of a (2+1-Dimensional Boussinesq Equation
Directory of Open Access Journals (Sweden)
Letlhogonolo Daddy Moleleki
2013-01-01
Full Text Available We study a nonlinear evolution partial differential equation, namely, the (2+1-dimensional Boussinesq equation. For the first time Lie symmetry method together with simplest equation method is used to find the exact solutions of the (2+1-dimensional Boussinesq equation. Furthermore, the new conservation theorem due to Ibragimov will be utilized to construct the conservation laws of the (2+1-dimensional Boussinesq equation.
A remark on symmetry of stochastic dynamical systems and their conserved quantities
Albeverio, Sergio A; Albeverio, Sergio; Fei, Shao Ming
1995-01-01
Symmetry properties of stochastic dynamical systems described by stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given by applying symmetry operators to known conserved quantities. Some detailed examples are presented.
Two Types of New Conserved Quantities and Mei Symmetry of Mechanical Systems in Phase Space
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, two types of new conserved quantities directly deduced by Mei symmetry in phase space are studied. The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities and the forms of the two types of new conserved quantities are given. An example is given to illustrate the application of the results.
Conservation Laws of Random Matrix Theory
Ercolani, Nicholas M
2012-01-01
This paper presents an overview of the derivation and significance of recently derived conservation laws for the matrix moments of Hermitean random matrices with dominant exponential weights that may be either even or odd. This is based on a detailed asymptotic analysis of the partition function for these unitary ensembles and their scaling limits. As a particular application we derive closed form expressions for the coefficients of the genus expansion for the associated free energy in a particular class of dominant even weights. These coefficients are generating functions for enumerating g-maps, related to graphical combinatorics on Riemann surfaces. This generalizes and resolves a 30+ year old conjecture in the physics literature related to quantum gravity.
A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A new type of conserved quantity, which is induced from the Mei symmetry of Lagrange systems, is studied.The conditions for that the new type of conserved quantity exists and the form of the new type of conserved quantity are obtained. An illustrated example is given. The Noether conserved quantity induced from the Mei symmetry of Lagrange systems is a special case of the new type of conserved quantity given in this paper.
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....
Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems
Institute of Scientific and Technical Information of China (English)
Xie Jia-Fang; Gang Tie-Qiang; Mei Feng-Xiang
2008-01-01
This paper studies the Hojman conserved quantity,a non-Noether conserved quantity,deduced by special weak Noether symmetry for Lagrange systems.Under special infinitesimal transformations in which the time is not variable,its criterion is given and a method of how to seek the Hojman conserved quantity is presented.A Hojman conserved quantity can be found by using the special weak Noether symmetry.
Institute of Scientific and Technical Information of China (English)
Zheng Shi-Wang; Tang Yi-Fa; Fu Jing-Li
2006-01-01
Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally, an example is given to illustrate these results.
Conservation Laws of Discrete Korteweg-de Vries Equation
Directory of Open Access Journals (Sweden)
Olexandr G. Rasin
2005-12-01
Full Text Available All three-point and five-point conservation laws for the discrete Korteweg-de Vries equations are found. These conservation laws satisfy a functional equation, which we solve by reducing it to a system of partial differential equations. Our method uses computer algebra intensively, because the determining functional equation is quite complicated.
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.
The incompatibility between local hidden variable theories and the fundamental conservation laws
Indian Academy of Sciences (India)
C S Unnikrishnan
2005-09-01
I discuss in detail the result that the Bell's inequalities derived in the context of local hidden variable theories for discrete quantized observables can be satisfied only if a fundamental conservation law is violated on the average. This result shows that such theories are physically nonviable, and makes the demarcating criteria of the Bell's inequalities redundant. I show that a unique correlation function can be derived from the validity of the conservation law alone and this coincides with the quantum mechanical correlation function. Thus, any theory with a different correlation function, like any local hidden variable theory, is incompatible with the fundamental conservation laws and space-time symmetries. The results are discussed in the context of two-particle singlet and triplet states, GHZ states, and two-particle double slit interferometry. Some observations on quantum entropy, entanglement, and nonlocality are also discussed.
Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
Golkar, Siavash
2014-01-01
We explore the consequences of conformal symmetry for the operator product expansions in nonrelativistic field theories. Similar to the relativistic case, the OPE coefficients of descendants are related to that of the primary. However, unlike relativistic CFTs the 3-point function of primaries is not completely specified by conformal symmetry. Here, we show that the 3-point function between operators with nonzero particle number, where (at least) one operator has the lowest dimension allowed by unitarity, is determined up to a numerical coefficient. We also look at the structure of the family tree of primaries with zero particle number and discuss the presence of conservation laws in this sector.
Benjamin–Bona–Mahony Equation with Variable Coefficients: Conservation Laws
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Ben Muatjetjeja
2014-12-01
Full Text Available This paper aims to construct conservation laws for a Benjamin–Bona–Mahony equation with variable coefficients, which is a third-order partial differential equation. This equation does not have a Lagrangian and so we transform it to a fourth-order partial differential equation, which has a Lagrangian. The Noether approach is then employed to construct the conservation laws. It so happens that the derived conserved quantities fail to satisfy the divergence criterion and so one needs to make adjustments to the derived conserved quantities in order to satisfy the divergence condition. The conservation laws are then expressed in the original variable. Finally, a conservation law is used to obtain exact solution of a special case of the Benjamin–Bona–Mahony equation.
Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation
Yaşar, Emrullah; San, Sait; Özkan, Yeşim Sağlam
2016-01-01
In this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.
Conservation laws in the 1 f7 /2 shell model of 48Cr
Neergârd, K.
2015-04-01
Conservation laws in the 1 f7 /2 shell model of 48Cr found in numeric studies by Escuderos, Zamick, and Bayman [arXiv:nucl-th/0506050 (2005)] and me [K. Neergård, Phys. Rev. C 90, 014318 (2014) 10.1103/PhysRevC.90.014318] are explained by symmetry under particle-hole conjugation and the structure of the irreps of the symplectic group Sp(4). A generalization is discussed.
Ibragimov, Nail H
2011-01-01
The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint. This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams.
Scientific computation of conservation laws in the calculus of variations and optimal control
2005-01-01
We present analytic computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noether’s theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding the symmetries and cor...
Automatic computation of conservation laws in the calculus of variations and optimal control
2006-01-01
Computer Application We present analytic computational tools that permit us to identify, in an automatic way, conservation laws in optimal control. The central result we use is the famous Noether's theorem, a classical theory developed by Emmy Noether in 1918, in the context of the calculus of variations and mathematical physics, and which was extended recently to the more general context of optimal control. We show how a Computer Algebra System can be very helpful in finding the symmetrie...
Global large carnivore conservation and international law
Trouwborst, A.
2015-01-01
International cooperation, including through international legal instruments, appears important for the conservation of large carnivores worldwide. This is due to, inter alia, the worrying conservation status and population trends of many large carnivore species; the importance of large carnivores f
Global large carnivore conservation and international law
Trouwborst, A.
2015-01-01
International cooperation, including through international legal instruments, appears important for the conservation of large carnivores worldwide. This is due to, inter alia, the worrying conservation status and population trends of many large carnivore species; the importance of large carnivores
Energy Technology Data Exchange (ETDEWEB)
Basini, Giuseppe; Capozziello, Salvatore; Longo, Giuseppe
2003-05-26
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.
An Unbroken Axial-Vector Current Conservation Law
Sharafiddinov, Rasulkhozha S.
2016-04-01
The mass, energy and momentum of the neutrino of a true flavor have an axial-vector nature. As a consequence, the left-handed truly neutral neutrino in an axial-vector field of emission can be converted into a right-handed one and vice versa. This predicts the unidenticality of masses, energies and momenta of neutrinos of the different components. Recognizing such a difference in masses, energies, momenta and accepting that the left-handed axial-vector neutrino and the right-handed antineutrino of true neutrality refer to long-lived C-odd leptons, and the right-handed truly neutral neutrino and the left-handed axial-vector antineutrino are of short-lived fermions of C-oddity, we would write a new CP-even Dirac equation taking into account the flavor symmetrical axial-vector mass, energy and momentum matrices. Their presence explains the spontaneous mirror symmetry violation, confirming that an axial-vector current conservation law has never violated. They reflect the availability of a mirror Minkowski space in which a neutrino is characterized by left as well as by right space-time coordinates. Therefore, it is not surprising that whatever the main purposes experiments about a quasielastic axial-vector mass say in favor of an axial-vector mirror Minkowski space-time.
Institute of Scientific and Technical Information of China (English)
XIE Yin-Li; YANG Xin-Fang; JIA Li-Qun
2011-01-01
Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied.The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given.Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained.Finally, an example is given to illustrate the application of the results.PACS numbers: 11.30.-j, 45.20.Jj, 02.20.Sv
Interference and the Law of Energy Conservation
Drosd, Robert; Minkin, Leonid; Shapovalov, Alexander S.
2014-01-01
Introductory physics textbooks consider interference to be a process of redistribution of energy from the wave sources in the surrounding space resulting in constructive and destructive interferences. As one can expect, the total energy flux is conserved. However, one case of apparent non-conservation energy attracts great attention. Imagine that…
Hyperbolic Conservation Laws and Related Analysis with Applications
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...
Stationary solutions for conservation laws with singular nonlocal sources
Coclite, Giuseppe Maria; Coclite, Mario Michele
The existence of an a.e. positive stationary solution with bounded variation in [0,1] for an integro-differential conservation law with source depending on a function singular in the origin is proved.
Extension of the Chern-Simons Theory: Conservation Laws, Lagrange Structures, and Stability
Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.
2017-03-01
We consider the class of higher derivative 3d vector field models with the wave operator being a polynomial of the Chern-Simons operator. For the nth order theory of this type, we provide a covariant procedure for constructing n-parameter family of conservation laws associated with spatiotemporal symmetries. This family includes the canonical energy that is unbounded from below, whereas others conservation laws from the family can be bounded from below for certain combinations of the Lagrangian parameters, even though higher derivatives are present in the Lagrangian. We prove that any conserved quantity bounded from below is related with invariance of the theory with respect to the time translations and ensures the stability of the model.
Extension of the Chern-Simons Theory: Conservation Laws, Lagrange Structures, and Stability
Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.
2017-03-01
We consider the class of higher derivative 3d vector field models with the wave operator being a polynomial of the Chern-Simons operator. For the nth order theory of this type, we provide a covariant procedure for constructing n-parameter family of conservation laws associated with spatiotemporal symmetries. This family includes the canonical energy that is unbounded from below, whereas others conservation laws from the family can be bounded from below for certain combinations of the Lagrangian parameters, even though higher derivatives are present in the Lagrangian. We prove that any conserved quantity bounded from below is related with invariance of the theory with respect to the time translations and ensures the stability of the model.
Analysis of self-similar solutions of multidimensional conservation laws
Energy Technology Data Exchange (ETDEWEB)
Keyfitz, Barbara
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.
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Li-Qun; Chen Xian-Wei
2006-01-01
This paper investigates the momentum-dependent symmetries for nonholonomic nonconservative Hamilton canonical systems. The definition and determining equations of the momentum-dependent symmetries are presented, based on the invariance of differential equations under infinitesimal transformations with respect to the generalized coordinates and generalized momentums. The structure equation and the non-Noether conserved quantities of the systems are obtained. The inverse issues associated with the momentum-dependent symmetries are discussed. Finally, an example is discussed to further illustrate the applications.
Metric theories of gravity perturbation and conservation laws
Petrov, Alexander N; Lompay, Robert R; Tekin, Bayram
2017-01-01
By focusing on the most popular pertubation methods this monograph aspires to give a unified overview and comparison of ways to construct conserved quantities and study symmetries in general relativity. The main emphasis lies on the field-theoretical formulation of pertubations, the canonical Noether approach and the Belinfante procedure of symmetrisation.
Conservation Laws in the Hierarchical Model
Beijeren, H. van; Gallavotti, G.; Knops, H.
1974-01-01
An exposition of the renormalization-group equations for the hierarchical model is given. Attention is drawn to some properties of the spin distribution functions which are conserved under the action of the renormalization group.
New conserved quantities of Noether-Mei symmetry of mechanical system in phase space
Institute of Scientific and Technical Information of China (English)
Fang Jian-Hui; Liu Yang-Kui; Zhang Xiao-Ni
2008-01-01
This paper studies two new types of conserved quantities deduced by Noether-Mei symmetry of mechanical system in phase space. The definition and criterion of Noether-Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether-Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether-Mei symmetry of mechanical system can be obtained.
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.
Conservation laws for energy and momentum in curved spaces
Institute of Scientific and Technical Information of China (English)
L(O)PEZ-BONILLA J.; MORALES J.; OVANDO G.
2007-01-01
In arbitrary Riemannian 4-spaces, continuity equations are constructed which could be interpreted as conservation laws for the energy and momentum of the gravitational field. Special attention is given to general relativity to obtain, of natural manner, the pseudotensors of Einstein, Landau-Lifshitz, M(o)ller, Goldberg and Stachel, and also the conservation equations of Komar, Trautman, DuPlessis and Moss.
Symmetries of boundary layer equations of power-law fluids of second grade
Institute of Scientific and Technical Information of China (English)
Mehmet Pakdemirli; Yi(g)it Aksoy; Muhammet Y(u)r(u)soy; Chaudry Masood Khalique
2008-01-01
A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incom-pressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classifica-tion with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.
Conservation laws of inviscid Burgers equation with nonlinear damping
Abdulwahhab, Muhammad Alim
2014-06-01
In this paper, the new conservation theorem presented in Ibragimov (2007) [14] is used to find conservation laws of the inviscid Burgers equation with nonlinear damping ut+g(u)ux+λh(u)=0. We show that this equation is both quasi self-adjoint and self-adjoint, and use these concepts to simplify conserved quantities for various choices of g(u) and h(u).
New Superpotential in Conservation Laws in General Relativity
Adamek, J
2016-01-01
This work refers to the new formula for the superpotential Uikl in conservation laws in general relativity satisfying the integral and differential conservation laws within the Schwarzschild metric. The new superpotential is composed of two terms. The first term is based on Mollers concept and its a function of the metric gik and its first derivative only. The second term is the antisymmetric tensor density of weight plus one and it consists of higher derivatives of the metric gik. Although the new superpotential consists of higher derivatives of the metric gik it might bring a new evaluation of the conservative quantities in general relativity
Mei Symmetry and New Conserved Quantity of Tzénoff Equations for Holonomic Systems
Institute of Scientific and Technical Information of China (English)
ZHENG Shi-Wang; XIE Jia-Fang; ZHANG Qing-Hua
2007-01-01
@@ A new conserved quantity is deduced from Mei symmetry of Tzénoff equations for holonomic systems. The expression of this new conserved quantity is given, and the determining equation to induce this new conserved quantity is presented. The results exhibit that this new method is easier to find more conserved quantities than the previously reported ones. Finally, application of this new result is presented by a practical example.
Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry
Institute of Scientific and Technical Information of China (English)
Luo Yi-Ping; Fu Jin-Li
2011-01-01
This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry. The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given. The conformal factor in the determining equations is found. The relationship between Birkhoff system's conformal invariance and second-class Mei symmetry are discussed. The necessary and sufficient conditions of conformal invariance, which are simultaneously of second-class symmetry, are given. And Birkhoff system's conformal invariance may lead to corresponding Mei conserved quantities, which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.
Institute of Scientific and Technical Information of China (English)
LUO Shao-Kai; JIA Li-Qun; CAI Jian-Le
2005-01-01
For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.
Conservation Laws in Higher-Order Nonlinear Optical Effects
Kim, J; Shin, H J; Kim, Jongbae
1999-01-01
Conservation laws of the nonlinear Schrödinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a general expression for infinitely many conserved currents and charges of the coupled higher-order nonlinear Schrödinger equation. The first few currents and charges are also presented explicitly. Due to the higher-order effects, conservation laws of the nonlinear Schrödinger equation are violated in general. The differences between the types of the conserved currents for the Hirota and the Sasa-Satsuma equations imply that the higher-order terms determine the inherent types of conserved quantities for each integrable cases of the higher-order nonlinear Schrödinger equation.
Institute of Scientific and Technical Information of China (English)
Lou Zhi-Mei
2007-01-01
In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.
Conservation laws for colliding branes with induced gravity
Pellen, Mathieu
2013-01-01
We derive conservation laws for collisions of self-gravitating $n$-branes (or $n$-dimensional shells) in an $(n+2)$ dimensional spacetime including induced gravity on the brane. Previous work has shown how geometrical identities in general relativity enforce conservation of energy-momentum at collisions. The inclusion of induced gravity terms introduces a gravitational self-energy on the brane which permits energy-momentum conservation of matter fields on the brane to be broken, so long as the total energy-momentum, including induced gravity terms, is conserved. We give simple examples with two branes (one ingoing and one outgoing) and three branes.
Many conserved quantities induced by Lie symmetries of a Lagrangian system
Energy Technology Data Exchange (ETDEWEB)
Nucci, M.C., E-mail: nucci@unipg.i [Dipartimento di Matematica e Informatica and INFN Sezione Perugia, Universita di Perugia, 06123 Perugia (Italy)
2011-03-14
Lie symmetries along with either Noether theorem or Jacobi Last Multiplier yield all the conserved quantities that one may seek and even more. We show that three new conserved quantities derived in Jian-Hui Fang, Ming-Jiang Zhang, Wei-Wei Zhang (2010) can be algorithmically obtained by these old methods. Even more than three.
Lie Symmetry and Non-Noether Conserved Quantity for Hamiltonian Systems
Institute of Scientific and Technical Information of China (English)
吴惠彬
2004-01-01
A non-Noether conserved quantity for the Hamiltonian system is studied. A particular infinitesimal transformation is given and the determining equations of Lie symmetry are established. An existence theorem of the non-Noether conserved quantity is obtained. An example is given to illustrate the application of the result.
Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Li-Qun; Xie Feng-Ping
2004-01-01
This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations,and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results.
Conservation laws for multidimensional systems and related linear algebra problems
Energy Technology Data Exchange (ETDEWEB)
Igonin, Sergei
2002-12-13
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{sup t}S and SA=-A{sup t}S for a quadratic matrix A and its transpose A{sup t}, which may be of independent interest.
Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws
Chen, Gui-Qiang; Zhang, Yongqian
2012-01-01
We establish an $L^1$-estimate to validate the weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws with arbitrary initial data of small bounded variation. This implies that the simpler geometric optics expansion function can be employed to study the properties of general entropy solutions to hyperbolic systems of conservation laws. Our analysis involves new techniques which rely on the structure of the approximate equations, besides the properties of the wave-front tracking algorithm and the standard semigroup estimates.
ON THE CENTRAL RELAXING SCHEMES I:SINGLE CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Hua-zhong Tang
2000-01-01
In this first paper we present a central relaxing scheme for scalar conservation laws, based on using the local relaxation approximation. Our scheme is obtained without using linear or nonlinear Riemann solvers. A cell entropy inequality is studied for the semidiscrete central relaxing scheme, and a second order MUSCL scheme is shown to be TVD in the zero relaxation limit. The next paper will extend the central relaxing scheme to multi-dimensional systems of conservation laws in curvilinear coordinates, including numerical experiments for 1D and 2D problems.
Integrating Factors and Conservation Laws for Relativistic Mechanical System
Institute of Scientific and Technical Information of China (English)
ZHANG Yi
2005-01-01
In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativisticmechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generaized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.
Quantum law of rare events for systems with bosonic symmetry.
Sokolovski, D
2013-03-15
In classical physics, the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, the unidirectional transfer of a population between the densely and sparsely populated states of a classical two-state system. We derive a quantum version of the law for a large number of noninteracting systems (particles) obeying Bose-Einstein statistics. The classical law is significantly modified by quantum interference, which allows, among other effects, for the counterflow of particles back into the densely populated state. The suggested observation of this classically forbidden counterflow effect can be achieved with modern laser-based techniques used for manipulating and trapping cold atoms.
Institute of Scientific and Technical Information of China (English)
Luo Shao-Kai
2007-01-01
For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of the theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables t, qs and (q)s. An example is given to illustrate the application of the results.
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…
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Nie Ning-Ming; Huang Jian-Fei; Jiménez Salvador; Tang Yi-Fa; Vázquez Luis; Zhao Wei-Jia
2009-01-01
This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems, which leave invariant the set of solutions of the corresponding difference scheme.This approach makes it possible to devise techniques for solving the Lagrange-Maxwell equations in differences which correspond to mechanico-electrical systems, by adapting existing differential equations. In particular, it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems. As an application, it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.
Space-time domain decomposition method for scalar conservation laws
Doucoure, S
2012-01-01
The Space-Time Integrated Least-Squares (STILS) method is considered to analyze a space-time domain decomposition algorithm for scalar conservation laws. Continuous and discrete convergence estimates are given. Next using a time-marching finite element formulation, the STILS solution and its domain decomposition form are numerically compared.
NONUNIQUENESS AND SINGULAR RADIAL SOLUTIONS OF SYSTEMS OF CONSERVATION LAWS
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Michael G. Hilgers
2012-01-01
The case of a radial initial state for a family of hyperbolic systems of conservation laws with several spatial dimensions is considered. It will be shown that the singularity at the origin introduces multiple solutions outside of the traditional admissible classes.
Time-varying Riemann solvers for conservation laws on networks
Garavello, Mauro; Piccoli, Benedetto
We consider a conservation law on a network and generic Riemann solvers at nodes depending on parameters, which can be seen as control functions. Assuming that the parameters have bounded variation as functions of time, we prove existence of solutions to Cauchy problems on the whole network.
Vanishing non-local regularization of a scalar conservation law
Directory of Open Access Journals (Sweden)
Jerome Droniou
2003-11-01
Full Text Available We prove that the solution to the regularization of a scalar conservation law by a fractional power of the Laplacian converges, as the regularization vanishes, to the entropy solution of the hyperbolic problem. We also give an error estimate when the initial condition has bounded variation.
Conservation laws, differential identities, and constraints of partial differential equations
Zharinov, V. V.
2015-11-01
We consider specific cohomological properties such as low-dimensional conservation laws and differential identities of systems of partial differential equations (PDEs). We show that such properties are inherent to complex systems such as evolution systems with constraints. The mathematical tools used here are the algebraic analysis of PDEs and cohomologies over differential algebras and modules.
Calorimeter energy calibration using the energy conservation law
Indian Academy of Sciences (India)
Vasily L Morgunov
2007-12-01
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 for the simple calorimeter energy sum.
Hyperbolic conservation laws and the compensated compactness method
Lu, Yunguang
2002-01-01
The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research papers. Offering the first comprehensive treatment, Hyperbolic Conservation Laws and the Compensated Compactness Method gathers together into a single volume the essential ideas and developments.The authors begin with the fundamental theorems, then consider the Cauchy problem of the scalar equation, build a framework for L8 estimates of viscosity solutions, and introduce the Invariant Region Theory. The study then turns to methods for symmetric systems of two equations and two equations with quadratic flux, and the extension of these methods to the Le Roux system. After examining the system of polytropic gas dynamics (g-law), the authors first study two special systems of one-dimensional Euler equations, then consider the general Euler equations for one-dimensional com...
Effects of collisions on conservation laws in gyrokinetic field theory
Sugama, H; Nunami, M
2015-01-01
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 pres...
Institute of Scientific and Technical Information of China (English)
XIA Li-Li; ZHAO Xian-Lin
2009-01-01
On the basis of the total time derivative along the trajectory, we study the generalized Mei conserved quantity of Mei symmetry for mechanico-electrical systems with nonholonomie controllable constraints. Firstly, the definition and criterion of Mei symmetry for mechanico-electrical systems with nonholonomic controllable constraints are presented. Secondly, a coordination function is introduced, and the conditions of existence of generalized Mei conserved quantity as well as the forms are proposed. Lastly, an example is given to illustrate the application of the results.
Gravitation, C, P and T symmetries and the Second Law
Chardin, G
2008-01-01
The intimate links between gravitation and the second law are summarized and two less known relations between gravity and thermodynamics are studied. Firstly, the information cost required to operate a Maxwell's demon on a curved spacetime is estimated using the Kolmogorov-Sinai entropy. More importantly, the charge and time (C and T) reversal properties of the Kerr-Newman solution in General relativity show that this solution, similarly to the Dirac equation, appears to represent both a particle and its antiparticle and suggests a definition of antimatter in general relativity. This definition leads to a parameter free explanation of the cosmological constant term observed in the supernovae data. The relation of this definition of antimatter with the coupled systems through opposite time arrows studied by Schulman is also emphasized.
Noether symmetries and conserved quantities for fractional Birkhoffian systems with time delay
Zhai, Xiang-Hua; Zhang, Yi
2016-07-01
The Noether symmetries and the conserved quantities for fractional Birkhoffian systems with time delay in terms of Riemann-Liouville fractional derivatives are proposed and studied. First, the fractional Pfaff-Birkhoff principle with time delay is proposed, and the fractional Birkhoff's equations with time delay are obtained. Second, based on the invariance of the fractional Pfaff action with time delay under a group of infinitesimal transformations, the Noether symmetric transformations and the Noether quasi-symmetric transformations of the system are defined, and the criteria of the Noether symmetries are established. Finally, the relationship between the symmetries and the conserved quantities are studied, and the Noether theorems for fractional Birkhoffian systems with time delay are established. Some examples are given to illustrate the application of the results.
Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics
Institute of Scientific and Technical Information of China (English)
Zhang Yi
2011-01-01
This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results.
Partial Conservation Law in a Schematic Single j Shell Model
Pereira, Wesley; Zamick, Larry; Escuderos, Alberto; Neergård, Kai
2016-01-01
We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a j shell. In our Hamiltonian the interaction matrix element of two nucleons with combined angular momentum J is linear in J for even J and constant for odd J. It turns out that in some stationary states the sum J_p + J_n of the angular momenta J_p and J_n of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of J_p + J_n. The systematics of their occurrence is described and explained.
Conservation laws and evolution of pure states into mixed states
Liu, Jun
1993-09-01
Using the formulation of Banks, Peskin and Susskind (BPS), evolution equations are constructed for the quantum mechanical density matrix ϱ with operators which do not commute with the hamiltonian. These equations evolve pure states into mixed states, preserve the normalization and positivity of ϱ, and most importantly, conserve energy. Thus, these examples show that the conservation laws do not necessarily forbid the evolution of pure states into mixed states, in contrast to the case of a quantum mechanical system with random sources studied specifically by BPS. It remains to generalize these quantum mechanical examples to the more interesting case of quantum field theory.
Conservation laws and LETKF with 2D Shallow Water Model
Zeng, Yuefei; Janjic, Tijana
2016-04-01
Numerous approaches have been proposed to maintain physical conservation laws in the numerical weather prediction models. However, to achieve a reliable prediction, adequate initial conditions are also necessary, which are produced by a data assimilation algorithm. If an ensemble Kalman filters (EnKF) is used for this purpose, it has been shown that it could yield unphysical analysis ensemble that for example violates principles of mass conservation and positivity preservation (e.g. Janjic et al 2014) . In this presentation, we discuss the selection of conservation criteria for the analysis step, and start with testing the conservation of mass, energy and enstrophy. The simple experiments deal with nonlinear shallow water equations and simulated observations that are assimilated with LETKF (Localized Ensemble Transform Kalman Filter, Hunt et al. 2007). The model is discretized in a specific way to conserve mass, angular momentum, energy and enstrophy. The effects of the data assimilation on the conserved quantities (of mass, energy and enstrophy) depend on observation covarage, localization radius, observed variable and observation operator. Having in mind that Arakawa (1966) and Arakawa and Lamb (1977) showed that the conservation of both kinetic energy and enstrophy by momentum advection schemes in the case of nondivergent flow prevents systematic and unrealistic energy cascade towards high wave numbers, a cause of excessive numerical noise and possible eventual nonlinear instability, we test the effects on prediction depending on the type of errors in the initial condition. The performance with respect to nonlinear energy cascade is assessed as well.
A conservation law formulation of nonlinear elasticity in general relativity
Gundlach, Carsten; Erickson, Stephanie J
2011-01-01
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The resulting equations are presented as an extension of the standard Valencia formalism for a perfect fluid, with additional terms in the stress-energy tensor, plus a set of kinematic conservation laws that evolve a configuration gradient. We prove that the equations can be made symmetric hyperbolic by suitable constraint additions, at least in a neighbourhood of the unsheared state. We discuss the Newtonian limit of our formalism and its relation to a second formalism also used in Newtonian elasticity. We validate our framework by numerically solving a set of Riemann problems in Minkowski spacetime, as well as Newtonian ones from the literature.
Numerical methods for Eulerian and Lagrangian conservation laws
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.
Hybrid Riemann Solvers for Large Systems of Conservation Laws
Schmidtmann, Birte; Torrilhon, Manuel
2016-01-01
In this paper we present a new family of approximate Riemann solvers for the numerical approximation of solutions of hyperbolic conservation laws. They are approximate, also referred to as incomplete, in the sense that the solvers avoid computing the characteristic decomposition of the flux Jacobian. Instead, they require only an estimate of the globally fastest wave speeds in both directions. Thus, this family of solvers is particularly efficient for large systems of conservation laws, i.e. with many different propagation speeds, and when no explicit expression for the eigensystem is available. Even though only fastest wave speeds are needed as input values, the new family of Riemann solvers reproduces all waves with less dissipation than HLL, which has the same prerequisites, requiring only one additional flux evaluation.
Asymptotic-induced numerical methods for conservation laws
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
The conservation status of eagles in South African law
JC Knobel
2013-01-01
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 econo...
Boundary Layer to a System of Viscous Hyperbolic Conservation Laws
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we investigate the large-time behavior of solutions to the initial-boundary value problem for nxn hyperbolic system of conservation laws with artificial viscosity in the half line (0, ∞). We first show that a boundary layer exists if the corresponding hyperbolic part contains at least one characteristic field with negative propagation speed. We further show that such boundary layer is nonlinearly stable under small initial perturbation. The proofs are given by an elementary energy method.
Chang, Sin-Chung; To, Wai-Ming
1991-01-01
A new numerical framework for solving conservation laws is being developed. It employs: (1) a nontraditional formulation of the conservation laws in which space and time are treated on the same footing, and (2) a nontraditional use of discrete variables such as numerical marching can be carried out by using a set of relations that represents both local and global flux conservation.
Gonoskov, Arkady
2016-01-01
We propose an algorithm for reducing the number of macro-particles in PIC simulations in such a way that an arbitrary number of conservation laws can be preserved exactly and all the distribution functions are not modified in any other way than due to the statistical noise.
Velocity-dependent symmetries and conserved quantities of the constrained dynamical systems
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Li-Qun; Yang Xiao-Dong
2004-01-01
In this paper, we have exterided the theorem of the velocity-dependent symmetries to nonholonomic dynamical systems. Based on the infinitesimal transformations with respect to the coordinates, we establish the determining equations and restrictive equation of the velocity-dependent system before the structure equation is obtained. The direct and the inverse issues of the velocity-dependent symmetries for the nonholonomic dynamical system is studied and the non-Noether type conserved quantity is found as the result. Finally, we give an example to illustrate the conclusion.
Spontaneous symmetry breaking in a non-conserving two-species driven model
Energy Technology Data Exchange (ETDEWEB)
Levine, E [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100 (Israel); Willmann, R D [Institut fuer Festkoerperforschung, Forschungszentrum Juelich, 52425 Juelich (Germany)
2004-03-12
A two-species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behaviour which includes spontaneous symmetry breaking and localized shocks. The phase diagram in several regions of parameter space is calculated within the mean-field approximation, and compared with Monte Carlo simulations. In the limit where fluctuations in the number of particles in the system are taken to be zero, an exact solution is obtained. We present and analyse a physical picture which serves to explain the different phases of the model.
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.
Energy Technology Data Exchange (ETDEWEB)
Polettini, Matteo, E-mail: matteo.polettini@uni.lu; Esposito, Massimiliano [Complex Systems and Statistical Mechanics, University of Luxembourg, Campus Limpertsberg, 162a avenue de la Faïencerie, L-1511 Luxembourg, G. D. Luxembourg (Luxembourg)
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{sup Y} between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats s{sup 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.
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.
Energy Technology Data Exchange (ETDEWEB)
Narain, R; Kara, A H, E-mail: Abdul.Kara@wits.ac.z [School of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg (South Africa)
2010-02-26
The construction of conserved vectors using Noether's theorem via a knowledge of a Lagrangian (or via the recently developed concept of partial Lagrangians) is well known. The formulas to determine these for higher order flows are somewhat cumbersome but peculiar and become more so as the order increases. We carry out these for a class of high-order partial differential equations from mathematical physics and then consider some specific ones with mixed derivatives. In the latter set of examples, our main focus is that the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives. Overall, we consider a large class of equations of interest and construct some new conservation laws.
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
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.
Institute of Scientific and Technical Information of China (English)
Xie Yin-Li; Jia Li-Qun; Luo Shao-Kai
2011-01-01
Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.
Spin geometry and conservation laws in the Kerr spacetime
Andersson, Lars; Blue, Pieter
2015-01-01
In this paper we will review some facts, both classical and recent, concerning the geometry and analysis of the Kerr and related black hole spacetimes. This includes the analysis of test fields on these spacetimes. Central to our analysis is the existence of a valence $(2,0)$ Killing spinor, which we use to construct symmetry operators and conserved currents as well as a new energy momentum tensor for the Maxwell test fields on a class of spacetimes containing the Kerr spacetime. We then outline how this new energy momentum tensor can be used to obtain decay estimated for Maxwell test fields. An important motivation for this work is the black hole stability problem, where fields with non-zero spin present interesting new challenges. The main tool in the analysis is the 2-spinor calculus, and for completeness we introduce its main features.
Conformal field theories with infinitely many conservation laws
Energy Technology Data Exchange (ETDEWEB)
Todorov, Ivan [Institut des Hautes Etudes Scientifiques F-91440, Bures-sur-Yvette (France)
2013-02-15
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th
Energy-momentum conservation and Lipkin's zilch
Lashkari-Ghouchan, H
2014-01-01
As Noether's theorem states any differentiable symmetry of the action of a physical system has a corresponding conservation law. Lipkin introduced the conservation laws of zilches. But the corresponding symmetries are yet to be determined. Here we find a method to determine those symmetries and by direct calculations express the zilch tensor's relation to current-density for $n$-dimensional Minkowski space-time. Also, we extend this method to calculate symmetries of conservation of energy-momentum.
DEFF Research Database (Denmark)
Hodgdon, Jennifer A.; Sethna, James P.
1993-01-01
We derive a general crack-propagation law for slow brittle cracking, in two and three dimensions, using discrete symmetries, gauge invariance, and gradient expansions. Our derivation provides explicit justification for the ‘‘principle of local symmetry,’’ which has been used extensively to describe...
Valset, K; Tafto, J
2011-06-01
We classify the point symmetries at the different points in the Brillouin zone for the 17 two-dimensional space groups and the symmetries of the Bloch waves for the 10 two-dimensional crystallographic point groups. Simple examples involving breakdown of Friedels law, Gjonnes-Moodie lines, and reflection and refraction at interfaces are presented.
Numerical resolution of conservation laws with OpenCL
Directory of Open Access Journals (Sweden)
Crestetto A.
2013-07-01
Full Text Available We present several numerical simulations of conservation laws on recent multicore processors, such as GPUs, using the OpenCL programming framework. Depending on the chosen numerical method, different implementation strategies have to be considered, for achieving the best performance. We explain how to program efficiently three methods: a finite volume approach on a structured grid, a high order Discontinuous Galerkin (DG method on an unstructured grid and a Particle-In-Cell (PIC method. The three methods are respectively applied to a two-fluid computation, a Maxwell simulation and a Vlasov-Maxwell simulation.
Conservation Laws in Quantum-Correlation-Function Dynamics
Directory of Open Access Journals (Sweden)
Wei Wang
2010-01-01
Full Text Available For a complete and lucid discussion of quantum correlation, we introduced two new first-order correlation tensors defined as linear combinations of the general coherence tensors of the quantized fields and derived the associated coherence potentials governing the propagation of quantum correlation. On the basis of these quantum optical coherence tensors, we further introduced new concepts of scalar, vector and tensor densities and presented some related properties, such as conservation laws and the wave-particle duality for quantum correlation, which provide new insights into photon statistics and quantum correlation.
Modified energy-momentum conservation laws and vacuum Cherenkov radiation
Carmona, J M; Romeo, B
2014-01-01
We present a general parametrization for the leading order terms in a momentum power expansion of a non-universal Lorentz-violating, but rotational invariant, kinematics and its implications for two-body decay thresholds. The considered framework includes not only modified dispersion relations for particles, but also modified energy-momentum conservation laws, something which goes beyond effective field theory. As a particular and relevant example, bounds on the departures from special relativistic kinematics from the non-observation of vacuum Cherenkov radiation are discussed and compared with those obtained within the effective field theory scenario.
MULTIDIMENSIONAL RELAXATION APPROXIMATIONS FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Mohammed Sea(l)d
2007-01-01
We construct and implement a non-oscillatory relaxation scheme for multidimensional hyperbolic systems of conservation laws. The method transforms the nonlinear hyperbolic system to a semilinear model with a relaxation source term and linear characteristics which can be solved numerically without using either Riemann solver or linear iterations.To discretize the relaxation system we consider a high-resolution reconstruction in space and a TVD Runge-Kutta time integration. Detailed formulation of the scheme is given for problems in three space dimensions and numerical experiments are implemented in both scalar and system cases to show the effectiveness of the method.
Dual number coefficient octonion algebra, field equations and conservation laws
Chanyal, B. C.; Chanyal, S. K.
2017-09-01
Starting with octonion algebra, we develop the dual number coefficient octonion (DNCO) algebra having sixteen components. DNCO forms of generalized potential, field and current equations are discussed in consistent manner. We have made an attempt to write the DNCO form of generalized Dirac-Maxwell's equations in presence of electric and magnetic charges (dyons). Accordingly, we demonstrate the work-energy theorem of classical mechanics reproducing the continuity equation for dyons in terms of DNCO algebra. Further, we discuss the DNCO form of linear momentum conservation law for dyons.
Dual number coefficient octonion algebra, field equations and conservation laws
Chanyal, B. C.; Chanyal, S. K.
2016-08-01
Starting with octonion algebra, we develop the dual number coefficient octonion (DNCO) algebra having sixteen components. DNCO forms of generalized potential, field and current equations are discussed in consistent manner. We have made an attempt to write the DNCO form of generalized Dirac-Maxwell's equations in presence of electric and magnetic charges (dyons). Accordingly, we demonstrate the work-energy theorem of classical mechanics reproducing the continuity equation for dyons in terms of DNCO algebra. Further, we discuss the DNCO form of linear momentum conservation law for dyons.
Conservation Laws and Stress-energy-momentum Tensors for Systems with Background Fields
Gratus, Jonathan; Tucker, Robin W
2012-01-01
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.
Conservation laws and evolution schemes in geodesic, hydrodynamic, and magnetohydrodynamic flows
Markakis, Charalampos; Uryū, Kōji; Gourgoulhon, Eric; Nicolas, Jean-Philippe; Andersson, Nils; Pouri, Athina; Witzany, Vojtěch
2017-09-01
Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. In this framework, Ertel's potential vorticity theorem for baroclinic fluids arises as a special case of a conservation law valid for any Hamiltonian system. Moreover, conserved circulation laws, such as those of Kelvin, Alfvén and Bekenstein-Oron, emerge simply as special cases of the Poincaré-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin's theorem to baroclinic (nonisentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space.
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.
Symmetries, Symmetry Breaking, Gauge Symmetries
Strocchi, Franco
2015-01-01
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field ...
Revisiting conserved currents in F(R) theory of gravity via Noether symmetry
Sk., Nayem; 10.1088/0256-307X/30/2/020401
2013-01-01
Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields F(R) \\propto R^{3/2} along with the conserved current \\frac{d}{dt}(a\\sqrt R) in Robertson-Walker metric and nothing else. Still some authors recently claimed to have obtained four conserved currents setting F(R) \\propto R^{3/2} a-priori, taking time translation along with a gauge term. We show that the first one of these does not satisfy the field equations and the second one is the Hamiltonian which is constrained to vanish in gravity and thus a part and parcel of the field equations. We also show that the other two conserved currents, which do not contain time translation are the same in disguise and identical to the one mentioned above. Thus the claim is wrong.
NEW CONSERVATION LAWS OF ENERGY AND C-D INEQUALITIES IN CONTINUA WITH MICROSTRUCTURE
Institute of Scientific and Technical Information of China (English)
戴天民
2001-01-01
Existing fundamental laws, balance equations and Clausius- Duhem inequalities in continua with microstructure are systematically restudied, and the incomplete formulations of conservation laws of energy and related C-D inequalities are pointed out. Some remarks on existing results are made, and new conservation laws of energy and related C-D inequalities are presented.
Lie Symmetries and Conserved Quantities for Super-Long Elastic Slender Rod
Institute of Scientific and Technical Information of China (English)
ZHAO Wei-Jia; WENG Yu-Quan; FU Jing-Li
2007-01-01
DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of infinitesimal transformation. Based on Kirchhoff's analogue, generalized Hamilton canonical equations are analysed. The infinitesimal transformations with respect to the radian coordinate, the generalized coordinate, and the quasimomentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.
A Taylor weak-statement algorithm for hyperbolic conservation laws
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.
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.
Conformal field theories with infinitely many conservation laws
Todorov, Ivan
2013-02-01
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Unitary positive energy representations of scalar bilocal fields," Commun. Math. Phys. 271, 223-246 (2007), 10.1007/s00220-006-0182-2; e-print arXiv:math-ph/0604069v3; B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Infinite dimensional Lie algebras in 4D conformal quantum field theory," J. Phys. A Math Theor. 41, 194002 (2008), 10.1088/1751-8113/41/19/194002; e-print arXiv:0711.0627v2 [hep-th
The origin of the energy-momentum conservation law
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.
NEW CONSERVATION LAWS OF ENERGY AND C-D INEQUALITIES IN CONTINUA WITHOUT MICROSTRUCTURE
Institute of Scientific and Technical Information of China (English)
戴天民
2001-01-01
Fundamental laws and balance equations as well as C-D inequalities in continuum mechanics are carefully restudied, incompleteness of existing balance laws of angular momentum and conservation laws of energy as well as C-D inequalities are pointed out, and finally new and more general conservation laws of energy and corresponding balance equations of energy as well as C-D inequalities in local and nonlocal asymmetric continua are presented.
Conservation Laws for a Generalized Coupled Korteweg-de Vries System
Directory of Open Access Journals (Sweden)
Daniel Mpho Nkwanazana
2013-01-01
Full Text Available We construct conservation laws for a generalized coupled KdV system, which is a third-order system of nonlinear partial differential equations. We employ Noether's approach to derive the conservation laws. Since the system does not have a Lagrangian, we make use of the transformation u=Ux, v=Vx and convert the system to a fourth-order system in U, V. This new system has a Lagrangian, and so the Noether approach can now be used to obtain conservation laws. Finally, the conservation laws are expressed in the u, v variables, and they constitute the conservation laws for the third-order generalized coupled KdV system. Some local and infinitely many nonlocal conserved quantities are found.
Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids
Energy Technology Data Exchange (ETDEWEB)
Burton, D.E.
1994-10-17
We consider the conservation properties of a staggered-grid Lagrange formulation of the hydrodynamics equations (SGH). Hydrodynamics algorithms are often formulated in a relatively ad hoc manner in which independent discretizations are proposed for mass, momentum, energy, and so forth. We show that, once discretizations for mass and momentum are stated, the remaining discretizations are very nearly uniquely determined, so there is very little latitude for variation. As has been known for some time, the kinetic energy discretization must follow directly from the momentum equation; and the internal energy must follow directly from the energy currents affecting the kinetic energy. A fundamental requirement (termed isentropicity) for numerical hydrodynamics algorithms is the ability to remain on an isentrope in the absence of heating or viscous forces and in the limit of small timesteps. We show that the requirements of energy conservation and isentropicity lead to the replacement of the usual volume calculation with a conservation integral. They further forbid the use of higher order functional representations for either velocity or stress within zones or control volumes, forcing the use of a constant stress element and a constant velocity control volume. This, in turn, causes the point and zone coordinates to formally disappear from the Cartesian formulation. The form of the work equations and the requirement for dissipation by viscous forces strongly limits the possible algebraic forms for artificial viscosity. The momentum equation and a center-of-mass definition lead directly to an angular momentum conservation law that is satisfied by the system. With a few straightforward substitutions, the Cartesian formulation can be converted to a multidimensional curvilinear one. The formulation in 2D symmetric geometry preserves rotational symmetry.
He, Yan; Guo, Hao
2016-07-01
Respecting the conservation laws of momentum and energy in a many body theory is very important for understanding the transport phenomena. The previous conserving approximation requires that the self-energy of a single particle could be written as a functional derivative of a full dressed Green's function. This condition can not be satisfied in the G0 G t-matrix or pair fluctuation theory which emphasizes the fermion pairing with a stronger than the Bardeen-Cooper-Schrieffer (BCS) attraction. In the previous work [1], we have shown that when the temperature is above the superfluid transition temperature Tc, the G0 G t-matrix theory can be put into a form that satisfies the stress tensor Ward identity (WI) or local form of conservation laws by introducing a new type of vertex correction. In this paper, we will extend the above conservation approximation to the superfluid phase in the BCS mean field level. To establish the stress tensor WI, we have to include the fluctuation of the order parameter or the contribution from the Goldstone mode. The result will be useful for understanding the transport properties such as the behavior of the viscosity of Fermionic gases in the superfluid phases.
Blomberg, A.B.; De Gier, A.A.J.; Robbe, J.
2009-01-01
An important question concerning the protection of designated areas in Dutch environmental law is the extent to which area protection plays a part in other fields of Dutch law. The question of integrating the protection of nature reserves as regulated in the Dutch Nature Conservation Act 1998, which
A conservation law model for bidensity suspensions on an incline
Wong, Jeffrey T.; Bertozzi, Andrea L.
2016-09-01
We study bidensity suspensions of a viscous fluid on an incline. The particles migrate within the fluid due to a combination of gravity-induced settling and shear induced migration. We propose an extension of a recent model (Murisic et al., 2013) for monodisperse suspensions to two species of particles, resulting in a hyperbolic system of three conservation laws for the height and particle concentrations. We analyze the Riemann problem and show that the system exhibits three-shock solutions representing distinct fronts of particles and liquid traveling at different speeds as well as singular shock solutions for sufficiently large concentrations, for which the mechanism is essentially the same as the single-species case. We also consider initial conditions describing a fixed volume of fluid, where solutions are rarefaction-shock pairs, and present a comparison to recent experimental results. The long-time behavior of solutions is identified for settled mono- and bidisperse suspensions and some leading-order asymptotics are derived in the single-species case for moderate concentrations.
A nonlinear discrete integrable coupling system and its infinite conservation laws
Institute of Scientific and Technical Information of China (English)
Yu Fa-Jun
2012-01-01
We construct a nonlinear integrable coupling of discrete soliton hierarchy,and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy.As an explicit application of the method proposed in the paper,the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.
TWO-DIMENSIONAL RIEMANN PROBLEMS:FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS
Institute of Scientific and Technical Information of China (English)
Li Jiequan; Sheng Wancheng; Zhang Tong; Zheng Yuxi
2009-01-01
In this paper we survey the authors' and related work on two-dimensional Rie-mann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections: 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.
Illustrations of the Relativistic Conservation Law for the Center of Energy
Boyer, T H
2005-01-01
The relativistic conservation law involving the center of energy is reviewed and illustrated using simple examples from classical electromagnetic theory. It is emphasized that this conservation law is parallel to the conservation laws for energy, linear momentum, and energy, in arising from the generators of the Poincare group for electromagnetic theory; yet this relativistic law reflecting the continuous flow of energy goes virtually unmentioned in the text books. The illustrations here present situations both where external forces are present and are absent. The cases of a parallel plate capacitor, a flattened slip-joint solenoid, and two interacting charges are included.
Institute of Scientific and Technical Information of China (English)
Wang Xiao-Xiao; Han Yue-Lin; Zhang Mei-Ling; Jia Li-Qun
2013-01-01
Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.
Frank, J.E.
2006-01-01
In this note we show that multisymplectic Runge-Kutta box schemes, of which the Gauss-Legendre methods are the most important, preserve a discrete conservation law of wave action. The result follows by loop integration over an ensemble of flow realizations, and the local energy-momentum conservation
DNS of turbulent Couette flow with transpiration - spectra and symmetry induced scaling laws
Hoyas, Sergio; Kraheberger, Stefanie; Oberlack, Martin
2016-11-01
We present DNS results of turbulent plane Couette flow with constant wall-normal transpiration for Reynolds numbers of Reτ = 250 , 500 , 1000 and several transpiration Reynolds numbers Retr =V0 /Uw . To obtain the DNS data, a pseudo-spectral code, which originally was developed at UP Madrid, see (Hoyas and Jiménez 2006), is used for the simulations. Due to the lack of experimental and DNS data, the convergence of every simulation has been validated using the total shear stress equation and the relation between the friction velocities at the lower and upper wall. Examining the spectra we found that the large and wide structures, which appear in pure Couette flow, see (Avsarkisov et al. 2014), are destroyed as soon as transpiration velocity is different from zero. This and the presence of anomalous spectra near the blowing wall indicates the strong influence of suction on the whole flow, which was observed in (Antonia et al. 1988) as well. As classical scaling laws are not valid due to transpiration, new scaling laws of the mean velocity are derived using Lie symmetry methods. Additionally, suction creates a comparably larger uτ which, in turn, causes a flat and long region in the indicator function for the largest transpiration rate. SH was partially funded by ENE2015-71333-R. SK was funded by DFG under Grant No. OB96/39-1. Computer resources have been provided by LRZ Munich under Grant pr92la.
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.
High-Order Space-Time Methods for Conservation Laws
Huynh, H. T.
2013-01-01
Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown
Noether theorem for {mu}-symmetries
Energy Technology Data Exchange (ETDEWEB)
Cicogna, Giampaolo [Dipartimento di Fisica, Universita di Pisa and INFN, Sezione di Pisa, Largo B Pontecorvo 3, 50127 Pisa (Italy); Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, via Saldini 50, 20133 Milano (Italy)
2007-09-28
We give a version of Noether theorem adapted to the framework of {mu}-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of {lambda}-symmetries, and connects {mu}-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this '{mu}-conservation law' actually reduces to a standard one; we also note a relation between {mu}-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under {mu}-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting, {mu}-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.
A General Approach to the Construction of Conservation Laws for Birkhoffian Systems in Event Space
Institute of Scientific and Technical Information of China (English)
ZHANG Yi
2008-01-01
For a Birkhoman system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.
Indian Academy of Sciences (India)
Chaudry Masood Khalique
2013-03-01
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 and soliton solutions. Subsequently, the conservation laws are derived for the underlying equations.
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
de la Rosa, R.; Gandarias, M. L.; Bruzón, M. S.
2016-11-01
In this paper we study the generalized variable-coefficient Gardner equations of the form ut + A(t) unux + C(t) u2nux + B(t) uxxx + Q(t) u = 0 . This class broadens out many other equations previously considered: Johnpillai and Khalique (2010), Molati and Ramollo (2012) and Vaneeva et al. (2015). The use of the equivalence group of this class allows us to perform an exhaustive study and a simple and clear formulation of the results. Some conservation laws are derived for the nonlinearly self-adjoint equations by using a general theorem on conservation laws. We also construct conservation laws by applying the multipliers method.
Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity
Directory of Open Access Journals (Sweden)
Sergey I. Senashov
2012-10-01
Full Text Available For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for quasilinear system and the problem for conservation laws system permits to construct the characteristic lines in domains, where Jacobian of hodograph transformations is equal to zero. Moreover, the conservation laws give all solutions of the linearized system. Some examples from the gas dynamics and theory of plasticity are considered.
Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids
Indian Academy of Sciences (India)
Yan Jiang; Bo Tian; Pan Wang; Kun Su
2014-07-01
In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.
Translationally invariant conservation laws of local Lindblad equations
Energy Technology Data Exchange (ETDEWEB)
Žnidarič, Marko [Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana (Slovenia); Benenti, Giuliano; Casati, Giulio [CNISM and Center for Nonlinear and Complex Systems, Università degli Studi dell' Insubria, Via Valleggio 11, 22100 Como (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano (Italy)
2014-02-15
We study the conditions under which one can conserve local translationally invariant operators by local translationally invariant Lindblad equations in one-dimensional rings of spin-1/2 particles. We prove that for any 1-local operator (e.g., particle density) there exist Lindblad dissipators that conserve that operator, while on the other hand we prove that among 2-local operators (e.g., energy density) only trivial ones of the Ising type can be conserved, while all the other cannot be conserved, neither locally nor globally, by any 2- or 3-local translationally invariant Lindblad equation. Our statements hold for rings of any finite length larger than some minimal length determined by the locality of Lindblad equation. These results show in particular that conservation of energy density in interacting systems is fundamentally more difficult than conservation of 1-local quantities.
Self-adjointness and conservation laws of a generalized Burgers equation
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.se, E-mail: torrisi@dmi.unict.it, E-mail: tracina@dmi.unict.it [Dipartimento di Matematica e Informatica, University of Catania, Catania (Italy)
2011-04-08
A (2 + 1)-dimensional generalized Burgers equation is considered. Having written this equation as a system of two dependent variables, we show that it is quasi self-adjoint and find a nontrivial additional conservation law.
Gravitational radiation of angular—momentum from general covariant conservation law
Institute of Scientific and Technical Information of China (English)
冯世祥; 宗红石
1996-01-01
The quadrupole angular-momentum radiation of gravity is obtained from the recently obtained covariant conservation law of angular-momentum.The result agrees with that derived from the Landau-Lifshitz energy-momentum pseudo-tensor.
Institute of Scientific and Technical Information of China (English)
Wang Xiao-Xiao; Sun Xian-Ting; Zhang Mei-Ling; Han Yue-Lin; Jia Li-Qun
2012-01-01
The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results.
Institute of Scientific and Technical Information of China (English)
Wang Xiao-Xiao; Sun Xian-Ting; Zhang Mei-Ling; Xie Yin-Li; Jia Li-Qun
2011-01-01
The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied.The differential equations of motion of the Nielsen equation for the system,the definition and the criterion of Lie symmetry,and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained.An example is given to illustrate the application of the results.
Araújo, Manoel P.; Carvalho, Silvânia A.; De Leo, Stefano
2014-09-01
A detailed analysis of the propagation of laser Gaussian beams at critical angles shows under which conditions it is possible to maximize the breaking of symmetry in the angular distribution and for which values of the laser wavelength and beam waist it is possible to find an analytic formula for the maximal angular deviation from the optical path predicted by the Snell law. For beam propagation through N dielectric blocks and for a maximal breaking of symmetry, a closed expression for the Goos-Hänchen shift is obtained. The multiple-peak phenomenon clearly represents additional evidence of the breaking of symmetry in the angular distribution of optical beams. Finally, the laser wavelength and beam-waist conditions to produce focal effects in the outgoing beam are also briefly discussed.
Inviscid Limit for Scalar Viscous Conservation Laws in Presence of Strong Shocks and Boundary Layers
Institute of Scientific and Technical Information of China (English)
MA Shixiang
2012-01-01
In this paper,we study the inviscid limit problem for the scalar viscous conservation laws on half plane.We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition,then there exist solutions to the viscous conservation laws which converge to the inviscid solution away from the shock discontinuity and the boundary at a rate of ε1 as the viscosity ε tends to zero.
Conservation laws and a new expansion method for sixth order Boussinesq equation
Yokuş, Asıf; Kaya, Doǧan
2015-09-01
In this study, we analyze the conservation laws of a sixth order Boussinesq equation by using variational derivative. We get sixth order Boussinesq equation's traveling wave solutions with (1/G) -expansion method which we constitute newly by being inspired with (G/G) -expansion method which is suggested in [1]. We investigate conservation laws of the analytical solutions which we obtained by the new constructed method. The analytical solution's conductions which we get according to new expansion method are given graphically.
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.
Mishra, Siddhartha
2011-01-01
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating conservation laws do not take into account this fact and converge to solutions that are not necessarily physically relevant. We design numerical schemes that incorporate explicit information about the underlying viscosity mechanism and approximate the physically relevant solution. Numerical experiments illustrating the robust performance of these schemes are presented.
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.
Observation of Conservations Laws in Diffusion Limited Aggregation
Mineev-Weinstein, M B; Mineev-Weinstein, Mark B.; Mainieri, Ronnie
1994-01-01
We repeat the numerical experiments for diffusion limited aggregation (DLA) and show that there is a potentially infinite set of conserved quantities for the long time asymptotics. We connect these observations with the exact integrability of the continuum limit of the DLA (quasi-static Stefan problem). The conserved quantities of the Stefan problem (harmonic moments) when discretized are our conserved quantities. These numerical experiments show that the exact integrability of the Stefan problem may be continued beyond the formation of cusps in the moving boundary.
The symmetry and simplicity of the laws of physics and the Higgs boson
Maldacena, Juan
2014-01-01
We describe the theoretical ideas, developed between the 1950s-1970s, which led to the prediction of the Higgs boson, the particle that was discovered in 2012. The forces of nature are based on symmetry principles. We explain the nature of these symmetries through an economic analogy. We also discuss the Higgs mechanism, which is necessary to avoid some of the naive consequences of these symmetries, and to explain various features of elementary particles.
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Directory of Open Access Journals (Sweden)
Antonio Enea Romano
2016-04-01
We then consider an example in which cw=cs, where δPnad=δPc,nad=0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense is not always enough to ensure the conservation of Rc or ζ.
Conservation Laws and Soliton Solutions for Generalized Seventh Order KdV Equation
Institute of Scientific and Technical Information of China (English)
YAO Ruo-Xia; XU Gui-Qiong; LI Zhi-Bin
2004-01-01
With the assistance of the symbolic computation system Maple,rich higher order polynomial-type conservation laws and a sixth order t/x-dependent conservation law are constructed for a generalized seventh order nonlinear evolution equation by using a direct algebraic method.From the compatibility conditions that guaranteeing the existence of conserved densities,an integrable unnamed seventh order KdV-type equation is found.By introducing some nonlinear transformations,the one-,two-,and three-solition solutions as well as the solitary wave solutions are obtained.
Myong, R. S.; Park, J. H.
2012-11-01
The constitutive laws, which describe the material's inherent properties, play a special role in the study of materials such as gases. In this study, the validity of non-classical constitutive laws in rarefied and micro gases is first considered. In particular, non-Navier and non-Fourier laws in algebraic forms identified in the velocity shear gas flows are investigated using DSMC. In addition, a new method based on the conservation laws is applied to the Couette flow and shock structure problems for the verification study of the DSMC. It is shown that, in flow problems involving with the wall boundary condition, the pressure among various properties is the most critical quantity in the verification and validation study of rarefied and micro gases. Such observation may imply the need of further theoretical and experimental investigation on the whole pressure and temperature flowfields beyond a reduced quantity such as the mass flow rate in the Poiseuille gas flows.
Kepler方程的Noether-Lie对称性与守恒量%Noether-Lie Symmetry and Conserved Quantities of the Kepler Equation
Institute of Scientific and Technical Information of China (English)
殷保祥; 刘晓巍; 李元成; 徐超; 宋子龙
2012-01-01
The Noether-Lie symmetry and conserved quantities of the Kepler equation are studied. The Kepler equation, we obtain the Noether symmetry and the Lie symmetry for the equation and the conserved quantities deduced from them, then the definition and criterion for Noether-Lie symmetry of the Kepler equation are derived. Lastly,the Noether conserved quantity and the Hojman conserved quantity are deduced from the Noether-Lie symmetry.%研究Kepler方程的对称性与守恒量。给出Kepler方程的Noether-Lie对称性的定义和判据,以及由Noether-Lie对称性导出Noether守恒量和Hojman守恒量。
Institute of Scientific and Technical Information of China (English)
刘晓巍; 李元成
2011-01-01
The Noether-Lie symmetry and conserved quantities of the Rosenberg problem are studied. From the study of the Rosenberg problem,the Noether symmetry and the Lie symmetry for the equation are obtained, thereby the conserved quantities are deduced. Then the definition and the criterion for Noether-Lie symmetry of the Rosenberg problem are derived. Finally,the Noether conserved quantity and the Hojman conserved quantity are deduced from the Noether-Lie symmetry%研究Rosenberg问题的对称性与守恒量．给出Rosenberg问题的Noether-Lie对称性的定义和判据，以及由Noether-Lie对称性导出Noether守恒量和Hojman守恒量．
CONSERVATION LAW AND APPLICATION OF J- INTEGRAL IN MULTI-MATERIALS
Institute of Scientific and Technical Information of China (English)
王利民; 陈浩然; 徐世烺
2001-01-01
The conservation law of J-integral in two-media with a crack paralleling to the interface of the two media was firstly proved by analytical and numerical finite element method. Then a schedule model was established that an interface crack is inserted in four media. According to the J-integral conservation law on multi-media, the energy release ratio of I-type crack was considered to be conservation when the middle medium layers are very thin. And the conservation law was also convinced by numerical method. By means of the dimension analysis on the model, the asymptotic results and formula calculating the energy release ratio and complex stress intensity factor are presented.
the conservation status of eagles in south african law
African Journals Online (AJOL)
10332324
expressions of human admiration of eagles include the deifying of eagles in ancient .... Eagles breed in Europe and Asia, while the Ayres's Hawk-Eagle breeds in .... Conflicts between national and provincial legislation are dealt with in s 146. .... 3.1.4 The Convention on the Conservation of Migratory Species of Wild Animals.
Nonlocal Conservation Laws Derived from an Explicit Equivalence Principle
Vera, R A
1997-01-01
According to this principle (EEP), in order that the local physical laws cannot change, after changes of velocity and potentials of a measuring system, the relativistic changes of any particle and any stationary radiation (like those used to measure it) must occur in identical proportion. Thus particles and stationary radiations must have the same general physical properties. In principle more exact and better defined physical laws for particles and their gravitational (G) fields can be derived from properties of particle models made up of radiation in stationary states after using fixed reference frames that don't change in the same way as the objects. Effectively, the new laws derived in this way do correspond with relativistic quantum mechanics and with all of the G tests. The main difference with current gravity is the linearity fixed by the EEP, i.e., the G field itself has not a real field energy to exchange with the bodies and it is not a secondary source of field. G work liberates energy confined in t...
Directory of Open Access Journals (Sweden)
Hongjun Cheng
2013-01-01
Full Text Available This paper is devoted to the study of a nonsymmetric Keyfitz-Kranzer system of conservation laws with the generalized and modified Chaplygin gas pressure law, which may admit delta shock waves, a topic of interest. Firstly, we solve the Riemann problems with piecewise constant data having a single discontinuity. For the generalized Chaplygin gas pressure law, the solution consists of three different structures: R+J, S+J, and δ. Existence and uniqueness of delta shock solution are established under the generalized Rankine-Hugoniot relation and entropy condition. For the modified Chaplygin gas pressure law, the structures of solution are R+J and S+J. Secondly, we discuss the limits of Riemann solutions for the modified Chaplygin gas pressure law as the pressure law tends to the generalized Chaplygin gas one. In particular, for some cases, the solution S+J tends to a delta shock wave, and it is different from the delta shock wave for the generalized Chaplygin gas pressure law with the same initial data. Thirdly, we simulate the Riemann solutions and examine the formation process of delta shock wave by employing the Nessyahu-Tadmor scheme. The numerical results are coincident with the theoretical analysis.
Law of Conservation of the Capital-Output Ratio*
Samuelson, Paul A.
1970-01-01
Just as simple harmonic motion, definable by a variational condition, δ [unk] (½ ẋ2 - ½ x2) dt = 0, has motions which must conserve the sum of kinetic and potential energies, ½ ẋ2 + ½x2 ≅ constant, so in a neoclassical von Neumann economy, where all output is saved to provide capital formation for the system's growth, it will be true that there exists a conservation law—namely the constancy along any intertemporally-efficient motion of the capital-output ratio ΣPtjKtj/ΣPtjKt j. This is derived as an „energy” integral of a time-free integrand1 in an optimal-control problem of variational type. PMID:16591882
Numerical solution of conservation laws on moving grids
Khakimzyanov, Gayaz; Mitsotakis, Dimitrios; Shokina, Nina
2015-01-01
In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension. The underlying finite volume scheme is conservative and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with high solution gradients or any other special features. No interpolation procedure is employed, thus an unnecessary solution smearing is avoided. Thus, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves.
Soft Black Hole Absorption Rates as Conservation Laws
Avery, Steven G
2016-01-01
The absorption rate of low-energy, or soft, electromagnetic radiation by spherically symmetric black holes in arbitrary dimensions is shown to be fixed by conservation of energy and large gauge transformations. We interpret this result as the explicit realization of the Hawking-Perry-Strominger Ward identity for large gauge transformations in the background of a non-evaporating black hole. Along the way we rederive and extend previous analytic results regarding the absorption rate for the minimal scalar and the photon.
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
Chen, Han
2016-01-01
Many control applications can be formulated as optimization constrained by conservation laws. Such optimization can be efficiently solved by gradient-based methods, where the gradient is obtained through the adjoint method. Traditionally, the adjoint method has not been able to be implemented in "gray-box" conservation law simulations. In gray-box simulations, the analytical and numerical form of the conservation law is unknown, but the space-time solution of relevant flow quantities is available. Without the adjoint gradient, optimization can be challenging for problems with many control variables. However, much information about the gray-box simulation is contained in its space-time solution, which motivates us to estimate the adjoint gradient by leveraging the space-time solution. This article considers a type of gray-box simulations where the flux function is partially unknown. A method is introduced to estimate the adjoint gradient at a cost independent of the number of control variables. The method firs...
A New Energy Conservation Law for Time-Harmonic Electromagnetic Fields and Its Applications
Geyi, Wen
2016-01-01
We report a new energy conservation law for time-harmonic electromagnetic fields, which is valid for an arbitrary medium. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy conservation law gives an equation for the sum of stored electric and magnetic field energies and the imaginary part involves an equation related to the difference between the dissipated electric and magnetic energies. Universally applicable expressions for both the electric and magnetic field energies have been obtained and demonstrated to be valuable in characterizing the energy storage and transport properties in complex media. For a lossless isotropic and homogeneous medium, the new energy conservation law implies that the stored electromagnetic field energy of a radiating system enclosed by a surface is equal to the total field energy inside the surface subtracted by the energy flowing out of the surface.
Asymptotic Behaviors of the Solutions to Scalar Viscous Conservation Laws on Bounded Interval
Institute of Scientific and Technical Information of China (English)
Quansen Jiu; Tao Pan
2003-01-01
This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value problem for scalar viscous conservations laws ut + f(u)x = uxx on [0, 1], with the boundary condition u(0, t) =u_,u(1,t) = u+ and the initial data u(x, 0) = u0(x), where u_ ≠ u+ and f is a given function satisfying f″ (u) ＞ 0 for u under consideration. By means of energy estimates method and under some more regular conditions on the initial data, both the global existence and the asymptotic behavior are obtained. When u_ ＜ u+, which corresponds to rarefaction waves in inviscid conservation laws, no smallness conditions are needed. While for u_ ＞ u+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shock waves, which means that |u_ - u+| is small. Moreover, exponential decay rates are both given.
Cauchy problem for multiscale conservation laws: Application to structured cell populations
Shang, Peipei
2010-01-01
In this paper, we study a vector conservation law that models the growth and selection of ovarian follicles. During each ovarian cycle, only a definite number of follicles ovulate, while the others undergo a degeneration process called atresia. This work is motivated by a multiscale mathematical model starting on the cellular scale, where ovulation or atresia result from a hormonally controlled selection process. A two-dimensional conservation law describes the age and maturity structuration of the follicular cell populations. The densities intersect through a coupled hyperbolic system between different follicles and cell phases, which results in a vector conservation law and coupling boundary conditions. The maturity velocity functions possess both a local and nonlocal character. We prove the existence and uniqueness of the weak solution to the Cauchy problem with bounded initial and boundary data.
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Romano, Antonio Enea; Sasaki, Misao
2015-01-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid $\\delta P_{nad}$, another is for a general matter field $\\delta P_{c,nad}$, and the last one is valid only on superhorizon scales. The first two definitions coincide if $c_s^2=c_w^2$ where $c_s$ is the propagation speed of the perturbation, while $c_w^2=\\dot P/\\dot\\rho$. Assuming the adiabaticity in the general sense, $\\delta P_{c,nad}=0$, we derive a relation between the lapse function in the comoving slicing $A_c$ and $\\delta P_{nad}$ valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as $c_s\
Conservation laws for classical particles in anti-de Sitter-Beltrami space
Angsachon, T.; Manida, S. N.; Tchaikovskii, M. E.
2013-07-01
The behavior of free classical pointlike particles is governed by conservation laws in the anti-de Sitter space. We present the general form of these laws and their realization in the Beltrami coordinates. In these coordinates, we can pass to the nonrelativistic limit resulting in physics in the R space. We construct the initial covariant distribution function for an ideal gas uniformly filling the entire R space.
Statistical conservation law in two- and three-dimensional turbulent flows
Frishman, Anna; Boffetta, Guido; De Lillo, Filippo; Liberzon, Alex
2015-03-01
Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in Falkovich et al. [Phys. Rev. Lett. 110, 214502 (2013), 10.1103/PhysRevLett.110.214502] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a d -dimensional flow the distance R (t ) between two neutrally buoyant particles, raised to the power -d and averaged over velocity realizations, remains at all times equal to the initial, fixed, separation raised to the same power. In this work we present evidence from direct numerical simulations of two- and three-dimensional turbulence for this conservation. In both cases the conservation is lost when particles exit the linear flow regime. In two dimensions we show that, as an extension of the conservation law, an Evans-Cohen-Morriss or Gallavotti-Cohen type fluctuation relation exists. We also analyze data from a 3D laboratory experiment [Liberzon et al., Physica D 241, 208 (2012), 10.1016/j.physd.2011.07.008], finding that although it probes small scales they are not in the smooth regime. Thus instead of , we look for a similar, power-law-in-separation conservation law. We show that the existence of an initially slowly varying function of this form can be predicted but that it does not turn into a conservation law. We suggest that the conservation of , demonstrated here, can be used as a check of isotropy, incompressibility, and flow dimensionality in numerical and laboratory experiments that focus on small scales.
Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equation
Institute of Scientific and Technical Information of China (English)
Chen Xiang-Wei; Liu Cui-Mei; Li Yan-Min
2006-01-01
Based on the invariance of differential equations under infinitesimal transformations,Lie symmetry,laws of conservations,perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented.The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed.The conditions for existence of the exact invariants and adiabatic invariants are proved,and their forms are also given.In addition,an example is presented to illustrate these results.
Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions
Directory of Open Access Journals (Sweden)
Andrew N. Guarendi
2013-01-01
Full Text Available We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. Parallel scaling analysis and grid-independent results including contours and isosurfaces of density and velocity and magnetic field vectors are shown in this study, confirming the ability of these types of solvers to approximate the solutions of hyperbolic equations efficiently and accurately.
Petrov, Alexander N
2013-01-01
A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian covariantized Noether identities are carried out. Identically conserved currents with corresponding superpotentials are united into a family. Such a generalized formalism of the covariantized identities gives a natural basis for constructing conserved quantities for perturbations. A new family of conserved currents and correspondent superpotentials for perturbations on arbitrary curved backgrounds in metric theories is suggested. The conserved quantities are both of pure canonical Noether and of Belinfante corrected types. To test the results each of the superpotentials of the family is applied to calculate the mass of the Schwarzschild-anti-de Sitter black hole in the Einstein-Gauss-Bonnet gravity. Using all the superpotentials of the family gives the standard accepted ma...
Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation
Directory of Open Access Journals (Sweden)
Khadijo Rashid Adem
2014-01-01
Full Text Available We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the (G'/G-expansion method.
Error Analysis of Explicit Partitioned Runge–Kutta Schemes for Conservation Laws
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.
Conservation Laws and Energy Budget in a Static Universe
Heymann, Yuri
2016-10-01
The universe is characterized by large concentrations of energy contained in small, dense areas such as galaxies, which radiate energy towards the surrounding space. However, no current theory balances the loss of energy of galaxies, a requirement for a conservative universe. This study is an investigation of the physics nature might use to maintain the energy differential between its dense parts and the vacuum. We propose time contraction as a principle to maintain this energy differential. Time contraction has the following effects: photons lose energy, while masses gain potential energy and lose kinetic energy. From the virial theorem, which applies to a system of bodies, we find that the net energy resulting from the gain in potential energy and the loss in kinetic energy remains unchanged, meaning that the orbitals of stars in galaxies remain unaffected by time contraction. However, each object in a galaxy has an internal potential energy leading to a surplus of energy within the object. This internal energy surplus should balance with the energy radiated at the level of a galaxy. We illustrate this principle with a calculation of the energy balance of the Milky Way.
Conservation laws, vertex corrections, and screening in Raman spectroscopy
Maiti, Saurabh; Chubukov, Andrey V.; Hirschfeld, P. J.
2017-07-01
We present a microscopic theory for the Raman response of a clean multiband superconductor, with emphasis on the effects of vertex corrections and long-range Coulomb interaction. The measured Raman intensity, R (Ω ) , is proportional to the imaginary part of the fully renormalized particle-hole correlator with Raman form factors γ (k ⃗) . In a BCS superconductor, a bare Raman bubble is nonzero for any γ (k ⃗) and diverges at Ω =2 Δmax , where Δmax is the largest gap along the Fermi surface. However, for γ (k ⃗) = constant, the full R (Ω ) is expected to vanish due to particle number conservation. It was sometimes stated that this vanishing is due to the singular screening by long-range Coulomb interaction. In our general approach, we show diagrammatically that this vanishing actually holds due to vertex corrections from the same short-range interaction that gives rise to superconductivity. We further argue that long-range Coulomb interaction does not affect the Raman signal for any γ (k ⃗) . We argue that vertex corrections eliminate the divergence at 2 Δmax . We also argue that vertex corrections give rise to sharp peaks in R (Ω ) at Ω <2 Δmin (the minimum gap along the Fermi surface), when Ω coincides with the frequency of one of the collective modes in a superconductor, e.g., Leggett and Bardasis-Schrieffer modes in the particle-particle channel, and an excitonic mode in the particle-hole channel.
Power-law distribution functions derived from maximum entropy and a symmetry relationship
Peterson, G J
2011-01-01
Power-law distributions are common, particularly in social physics. Here, we explore whether power-laws might arise as a consequence of a general variational principle for stochastic processes. We describe communities of 'social particles', where the cost of adding a particle to the community is shared equally between the particle joining the cluster and the particles that are already members of the cluster. Power-law probability distributions of community sizes arise as a natural consequence of the maximization of entropy, subject to this 'equal cost sharing' rule. We also explore a generalization in which there is unequal sharing of the costs of joining a community. Distributions change smoothly from exponential to power-law as a function of a sharing-inequality quantity. This work gives an interpretation of power-law distributions in terms of shared costs.
Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws
Directory of Open Access Journals (Sweden)
Wladimir Neves
2005-11-01
Full Text Available In this paper we answer some open questions concerning totally degenerate systems of conservation laws. We study the augmented Born-Infeld system, which is the Born-Infeld model augmented by two additional conservations laws. This system is a nice example of totally degenerate system of conservation laws and, global smooth solutions are conjectured to exist when the initial-data is smooth. We show that this conjecture is false, for the more natural and general condition of initial-data. In fact, first we show that does not exist global smooth solution for any 2X2 totally degenerated system of conservation laws, which the characteristics speeds do not have singular points. Moreover, we sharpen the conjecture in Majda [20]. Under the same hypothesis of initial-data, we show that the Riemann Problem is not well-posed, which follows for weak solutions of the Cauchy Problem. In the end, we prove some results on the direction of well-posedness for the less physically initial-data.
Conservation Laws and Lax Pair of the Variable Coefficient KdV Equation
Institute of Scientific and Technical Information of China (English)
ZHANG Da-Jun
2007-01-01
By a transformation between a Painlevé integrable variable coefficient KdV equation and the standard KdV equation, we derive the Lax pair and infinitely many conservation laws of the variable coefficient KdV equation from the counterparts of the KdV equation.
From conservation laws to port-Hamiltonian representations of distributed-parameter systems
Maschke, B.M.; Schaft, van der A.J.; Piztek, P.
2005-01-01
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 Dira
Wanlu, Somchai; Singseewo, Adisak; Suksringarm, Paitool
2015-01-01
This research aimed to develop knowledge and awareness about environmental laws and participation in environmental conservation of probationers in MahaSarakham Province, Thailand. This study was divided into 3 stages. Stage 1: was the development of a training manual and construction of training evaluation instruments which consisted of a…
Conservation laws of the generalized nonlocal nonlinear Schr(o)dinger equation
Institute of Scientific and Technical Information of China (English)
Ouyang Shi-Gen; Quo Qi; Wu Li-Jun; Lan Sheng
2007-01-01
The derivations of several conservation laws of the generalized nonlocal nonlinear Schr(o)dinger equation are presented. These invariants are the number of particles, the momentum, the angular momentum and the Hamiltonian in the quantum mechanical analogy. The Lagrangian is also presented.
Wanlu, Somchai; Singseewo, Adisak; Suksringarm, Paitool
2015-01-01
This research aimed to develop knowledge and awareness about environmental laws and participation in environmental conservation of probationers in MahaSarakham Province, Thailand. This study was divided into 3 stages. Stage 1: was the development of a training manual and construction of training evaluation instruments which consisted of a…
Adding an energy-like conservation law to the leapfrog integrator
Maggs, A C
2013-01-01
The leapfrog integrator is widely used because of its excellent stability in molecular dynamics simulation. This is recognized as being due to the existence of a discrete variational structure of the equations. We introduce a modified leapfrog method which includes an additional energy-like conservation law by embedding a molecular dynamics simulation within a larger dynamical system.
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.
Conservation laws for two (2 + 1)-dimensional differential-difference systems
Energy Technology Data Exchange (ETDEWEB)
Yu Guofu [Institute of Computational Mathematics and Scientific Engineering Computing, AMSS, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080 (China) and Graduate School of the Chinese Academy of Sciences, Beijing (China)]. E-mail: gfyu@lsec.cc.ac.cn; Tam, H.-W. [Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China)]. E-mail: tam@comp.hkbu.edu.hk
2006-10-15
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.
Lax pairs and conservation laws for two differential-difference systems
Energy Technology Data Exchange (ETDEWEB)
Li Chunxia E-mail: lichx@lsec.cc.ac.cn
2003-11-01
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.
Solutions to a hyperbolic system of conservation laws on two boundaries
Institute of Scientific and Technical Information of China (English)
JIA Zhi; YAO Ai-di
2009-01-01
This paper studies the interaction of elementary waves including delta-shock waves on two boundaries for a hyperbolic system of conservation laws. The solutions of the initial-boundary value problem for the system are constructively obtained. In the problem the initial-boundary data are in piecewise constant states.
ON A CELL ENTROPY INEQUALITY OF THE RELAXING SCHEMES FOR SCALAR CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Hua-zhong Tang; Hua-mo Wu
2000-01-01
In this paper we study a cell entropy inequality for a class of the local relaxation approximation -The Relaxing Schemes for scalar conservation laws presented by Jin and Xin in [1], which implies convergence for the one-dimensional scalar case.
Energy Technology Data Exchange (ETDEWEB)
Dzhioev, Alan [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980 (Russian Federation)]. E-mail: dzhioev@thsun1.jinr.ru; Wambach, J. [Institut fuer Kernphysik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany); Gesellschaft fuer Schwerionenforschung, D-64291 Darmstadt (Germany)]. E-mail: wambach@physik.tu-darmstadt.de; Vdovin, A. [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980 (Russian Federation)]. E-mail: vdovin@thsun1.jinr.ru; Aouissat, Z. [Institut fuer Kernphysik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)
2005-02-21
Symmetry conserving 1/N expansion method combined with the Holstein-Primakoff mapping for bosonic systems is applied to the quantum anharmonic O(N+1) oscillator model which imitates essential features of the quantum-field linear sigma model. The Holstein-Primakoff mapping earlier extended to incorporate both single- and double-boson images is used. In the leading and next-to-leading order the existence of N-Goldstone modes and the validity of the Ward identity are proved. For matrix elements of the pion-pion interaction we show the equivalence of the results obtained via a diagrammatic technique and the extended Holstein-Primakoff mapping.
Flux-vector splitting algorithm for chain-rule conservation-law form
Energy Technology Data Exchange (ETDEWEB)
Shih, T.I.-P.; Nguyen, H.L.; Willis, E.A.; Steinthorsson, E.; Li, Z. (Carnegie Mellon University, Pittsburgh, PA (United States) NASA, Lewis Research Center, Cleveland, OH (United States))
1991-07-01
A flux-vector splitting algorithm with Newton-Raphson iteration was developed for the 'full compressible' Navier-Stokes equations cast in chain-rule conservation-law form. The algorithm is intended for problems with deforming spatial domains and for problems whose governing equations cannot be cast in strong conservation-law form. The usefulness of the algorithm for such problems was demonstrated by applying it to analyze the unsteady, two- and three-dimensional flows inside one combustion chamber of a Wankel engine under nonfiring conditions. Solutions were obtained to examine the algorithm in terms of conservation error, robustness, and ability to handle complex flows on time-dependent grid systems. 16 refs.
Integrating Factors and Conservation Laws of Generalized Birkhoff System Dynamics in Event Space
Institute of Scientific and Technical Information of China (English)
ZHANG Yi
2009-01-01
In this paper, the conservation laws or generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.
Energy Technology Data Exchange (ETDEWEB)
Sarlet, W, E-mail: Willy.Sarlet@ugent.b [Department of Mathematics, Ghent University, Krijgslaan 281, B-9000 Ghent (Belgium); Department of Mathematics and Statistics, La Trobe University, Bundoora, Victoria 3086 (Australia)
2010-11-12
In a recent paper (R Narain and A H Kara 2010 J. Phys. A: Math. Theor. 43 085205), the authors claim to be applying Noether's theorem to higher-order partial differential equations and state that in a large class of examples 'the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives' (citation from their abstract). It turns out that what this obscure sentence is meant to say is that the vector whose divergence must be zero (according to Noether's theorem), turns out to have non-zero divergence and subsequently must be modified to obtain a true conservation law. Clearly this cannot be right: we explain in detail the main source of the error. (comment)
2013-11-22
... From the Federal Register Online via the Government Publishing Office NATIONAL SCIENCE FOUNDATION Notice of Permit Applications Received Under the Antarctic Conservation Act of 1978 (Public Law 95-541... Conservation Act of 1978, Public Law 95-541. SUMMARY: The National Science Foundation (NSF) is required...
Applications of hidden symmetries to black hole physics
Energy Technology Data Exchange (ETDEWEB)
Frolov, Valeri, E-mail: vfrolov@ualberta.ca [Institute of Theoretical Physics, Department of Physics University of Alberta, Edmonton, Alberta, T6G 2G7 (Canada)
2011-02-01
This work is a brief review of applications of hidden symmetries to black hole physics. Symmetry is one of the most important concepts of the science. In physics and mathematics the symmetry allows one to simplify a problem, and often to make it solvable. According to the Noether theorem symmetries are responsible for conservation laws. Besides evident (explicit) spacetime symmetries, responsible for conservation of energy, momentum, and angular momentum of a system, there also exist what is called hidden symmetries, which are connected with higher order in momentum integrals of motion. A remarkable fact is that black holes in four and higher dimensions always possess a set ('tower') of explicit and hidden symmetries which make the equations of motion of particles and light completely integrable. The paper gives a general review of the recently obtained results. The main focus is on understanding why at all black holes have something (symmetry) to hide.
Applications of hidden symmetries to black hole physics
Frolov, Valeri
2010-01-01
This work is a brief review of applications of hidden symmetries to black hole physics. Symmetry is one of the most important concepts of the science. In physics and mathematics the symmetry allows one to simplify a problem, and often to make it solvable. According to the Noether theorem symmetries are responsible for conservation laws. Besides evident (explicit) spacetime symmetries, responsible for conservation of energy, momentum, and angular momentum of a system, there also exist what is called hidden symmetries, which are connected with higher order in momentum integrals of motion. A remarkable fact is that black holes in four and higher dimensions always possess a set (`tower') of explicit and hidden symmetries which make the equations of motion of particles and light completely integrable. The paper gives a general review of the recently obtained results. The main focus is on understanding why at all black holes have something (symmetry) to hide.
Natural R parity conservation with horizontal symmetries a four generation model
Berezhiani, Z G; Berezhiani, Zurab; Nardi, Enrico
1995-01-01
The absence of R parity violating operators can be naturally ensured in the presence of a SU(N)_H\\ (N=4,6...) horizontal gauge symmetry, independently of the vertical gauge group. We study an extension of the supersymmetric standard model with four families and gauged SU(4)_H. Beyond preserving R parity, the model gives rise to the realistic fermion mass matrices which naturally ensure the heaviness of the fourth family fermions b',t',\\tau',\
General vorticity conservation
Gümral, H
1998-01-01
The motion of an incompressible fluid in Lagrangian coordinates involves infinitely many symmetries generated by the left Lie algebra of group of volume preserving diffeomorphisms of the three dimensional domain occupied by the fluid. Utilizing a 1+3-dimensional Hamiltonian setting an explicit realization of this symmetry algebra and the related Lagrangian and Eulerian conservation laws are constructed recursively. Their Lie algebraic structures are inherited from the same construction. The laws of general vorticity and helicity conservations are formulated globally in terms of invariant differential forms of the velocity field.
Applying Upwind Godunov Methods to Calculate Two—Phase Mixture Conservation Laws
Zeidan, D.
2010-09-01
This paper continues a previous work (ICNAAM 2009; AIP Conference Proceedings, 1168, 601-604) on solving a hyperbolic conservative model for compressible gas—solid mixture flow using upwind Godunov methods. The numerical resolution of the model from Godunov first—order upwind and MUSCL—Hancock methods are reported. Both methods are based on the HLL Riemann solver in the framework of finite volume techniques. Calculation results are presented for a series of one—dimensional test problems. The results show that upwind Godunov methods are accurate and robust enough for two—phase mixture conservation laws.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
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.
Flores, J C
2016-03-01
This work applies the competitive exclusion principle and the concept of potential competitors as simple axiomatic tools to generalized situations in ecology. These tools enable apparent competition and its dual counterpart to be explicitly evaluated in poorly understood ecological systems. Within this set-theory framework we explore theoretical symmetries and invariances, De Morgan's laws, frozen evolutionary diversity and virtual processes. In particular, we find that the exclusion principle compromises the geometrical growth of the number of species. By theoretical extending this principle, we can describe interspecific depredation in the dual case. This study also briefly considers the debated situation of intraspecific competition. The ecological consequences of our findings are discussed; particularly, the use of our framework to reinterpret coupled mathematical differential equations describing certain ecological processes.
On the application of subcell resolution to conservation laws with stiff source terms
Chang, Shih-Hung
1989-01-01
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.
Unified theory to describe and engineer conservation laws in light-matter interactions
Fernandez-Corbaton, Ivan; Rockstuhl, Carsten
2017-05-01
The effects of the electromagnetic field on material systems are governed by joint light-matter conservation laws. An increasing number of these balance equations are currently being considered both theoretically and with an eye to their practical applicability. We present a unified theory to treat conservation laws in light-matter interactions. It can be used to describe and engineer the transfer of any measurable property from the electromagnetic field to any object. The theory allows one to explicitly characterize and separately compute the transfer due to asymmetry of the object and the transfer due to field absorption by the object. It also allows one to compute the upper bound of the transfer rate of any given property to any given object, together with the corresponding most efficient illumination which achieves the bound. Due to its algebraic nature, the approach is inherently suited for computer implementation.
A unified theory to describe and engineer conservation laws in light-matter interactions
Fernandez-Corbaton, Ivan
2016-01-01
The effects of the electromagnetic field on material systems are governed by joint light-matter conservation laws. An increasing number of these balance equations are currently being considered both theoretically and with an eye to their practical applicability. We present a unified theory to treat conservation laws in light-matter interactions. It can be used to describe and engineer the transfer of any measurable property from the electromagnetic field to any object. The theory allows to explicitly characterize and separately compute the transfer due to asymmetry of the object and the transfer due to field absorption by the object. It also allows to compute the upper bound of the transfer rate of any given property to any given object, together with the corresponding most efficient illumination which achieves the bound. Due to its algebraic nature, the approach is inherently suited for computer implementation.
Recursion relations for graviton scattering amplitudes from Bose symmetry and bonus scaling laws
McGady, David A.; Rodina, Laurentiu
2015-05-01
Modern on-shell S -matrix methods may dramatically improve our understanding of perturbative quantum gravity, but current foundations of on-shell techniques for general relativity still rely on off-shell Feynman diagram analysis. Here, we complete the fully on-shell proof of Schuster and Toro J. High Energy Phys. 06 (2009) 079] that the recursion relations of Britto, Cachazo, Feng, and Witten (BCFW) apply to relativity tree amplitudes. We do so by showing that the surprising requirement of "bonus" z-2 scaling under a BCFW shift directly follows from Bose symmetry. Moreover, we show that amplitudes in generic theories subjected to BCFW deformations of identical particles necessarily scale as zeven. When applied to the color ordered expansions of Yang-Mills, this directly implies the improved behavior under nonadjacent gluon shifts. Using the same analysis, three-dimensional gravity amplitudes scale as z-4, compared to the z-1 behavior for conformal Chern-Simons matter theory.
Yang-Mills gauge fields conserving symmetry algebra of Dirac equation in homogeneous space
Breev, A I
2014-01-01
We consider the Dirac equation with external Yang-Mills gauge field in a homogeneous space with invariant metric. The Yang-Mills fields for which the motion group of the space serves as symmetry group of the Dirac equation are found by comparison of the Dirac equation with a invariant matrix differential operator of the first order. General constructions are illustrated by the example of de Sitter space. The basis of eigenfunctions and corresponding spectrum are obtained for the Dirac equation in the space $\\mathbb{R}^2 \\times \\mathbb{S}^2$ in the framework of the noncommutative integration method.
Liao, Fei; Ye, Zhengyin
2015-12-01
Despite significant progress in recent computational techniques, the accurate numerical simulations, such as direct-numerical simulation and large-eddy simulation, are still challenging. For accurate calculations, the high-order finite difference method (FDM) is usually adopted with coordinate transformation from body-fitted grid to Cartesian grid. But this transformation might lead to failure in freestream preservation with the geometric conservation law (GCL) violated, particularly in high-order computations. GCL identities, including surface conservation law (SCL) and volume conservation law (VCL), are very important in discretization of high-order FDM. To satisfy GCL, various efforts have been made. An early and successful approach was developed by Thomas and Lombard [6] who used the conservative form of metrics to cancel out metric terms to further satisfy SCL. Visbal and Gaitonde [7] adopted this conservative form of metrics for SCL identities and satisfied VCL identity through invoking VCL equation to acquire the derivative of Jacobian in computation on moving and deforming grids with central compact schemes derived by Lele [5]. Later, using the metric technique from Visbal and Gaitonde [7], Nonomura et al. [8] investigated the freestream and vortex preservation properties of high-order WENO and WCNS on stationary curvilinear grids. A conservative metric method (CMM) was further developed by Deng et al. [9] with stationary grids, and detailed discussion about the innermost difference operator of CMM was shown with proof and corresponding numerical test cases. Noticing that metrics of CMM is asymmetrical without coordinate-invariant property, Deng et al. proposed a symmetrical CMM (SCMM) [12] by using the symmetric forms of metrics derived by Vinokur and Yee [10] to further eliminate asymmetric metric errors with stationary grids considered only. The research from Abe et al. [11] presented new asymmetric and symmetric conservative forms of time metrics and
Non-polynomial ENO and WENO finite volume methods for hyperbolic conservation laws
Guo, Jingyang; Jung, Jae-Hun
2016-01-01
The essentially non-oscillatory (ENO) method is an efficient high order numerical method for solving hyperbolic conservation laws designed to reduce the Gibbs oscillations, if existent, by adaptively choosing the local stencil for the interpolation. The original ENO method is constructed based on the polynomial interpolation and the overall rate of convergence provided by the method is uniquely determined by the total number of interpolation points involved for the approximation. In this pape...
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.
A chain rule formula in BV and applications to conservation laws
Crasta, Graziano
2010-01-01
In this paper we prove a new chain rule formula for the distributional derivative of the composite function $v(x)=B(x,u(x))$, where $u:]a,b[\\to\\R^d$ has bounded variation, $B(x,\\cdot)$ is continuously differentiable and $B(\\cdot,u)$ has bounded variation. We propose an application of this formula in order to deal in an intrinsic way with the discontinuous flux appearing in conservation laws in one space variable.
Entropy Viscosity Method for High-Order Approximations of Conservation Laws
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.
CONVERGENCE OF AN EXPLICIT UPWIND FINITE ELEMENT METHOD TO MULTI-DIMENSIONAL CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Jin-chao Xu; Lung-an Ying
2001-01-01
An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality.To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the Lp strong convergence of this scheme is proved.
On the Convergence of Space-Time Discontinuous Galerkin Schemes for Scalar Conservation Laws
May, Georg
2016-01-01
We prove convergence of a class of space-time discontinuous Galerkin schemes for scalar hyperbolic conservation laws. Convergence to the unique entropy solution is shown for all orders of polynomial approximation, provided strictly monotone flux functions and a suitable shock-capturing operator are used. The main improvement, compared to previously published results of similar scope, is that no streamline-diffusion stabilization is used. This is the way discontinuous Galerkin schemes were originally proposed, and are most often used in practice.
On the Cauchy problem of a 2 times 2 system of nonstrictly hyperbolic conservation laws
Energy Technology Data Exchange (ETDEWEB)
Kan, P.T.
1989-01-01
Global existence for a 2 {times} 2 system of nonstrictly hyperbolic conservation law is established for data of arbitrary bounded variation. This result is obtained by proving a convergence theorem for the method of artificial viscosity applied to this system of conservation law. For this purpose, the method of compensated compactness and an analysis of the entropy functions are used. This system under consideration is a special case of a canonical class of 2 {times} 2 systems of conservation laws with quadratic flux functions possessing an isolated umbilic point (point of coinciding wave speeds where strict hyperbolicity fails) at the origin of the state space. These systems arise as model equations to equations used in oil reservoir simulations. Their wave curves and Riemann problem solutions are known to exhibit complexities not seen in any strictly hyperbolic systems. In this thesis, besides establishing global existence for a special system in the canonical class, general properties of a subclass are also investigated. The geometry of rarefaction wave curves are analytically studied and Riemann invariants are constructed. An L{sup {infinity}} bound (independent of the viscosity) for the solutions of the corresponding viscous systems are obtained. Also studied is the monotonicity properties of the wave speeds in the Riemann invariant plane.
Robust numerical methods for conservation laws using a biased averaging procedure
Choi, Hwajeong
In this thesis, we introduce a new biased averaging procedure (BAP) and use it in developing high resolution schemes for conservation laws. Systems of conservation laws arise in variety of physical problems, such as the Euler equation of compressible flows, magnetohydrodynamics, multicomponent flows, the blast waves and the flow of glaciers. Many modern shock capturing schemes are based on solution reconstructions by high order polynomial interpolations, and time evolution by the solutions of Riemann problems. Due to the existence of discontinuities in the solution, the interpolating polynomial has to be carefully constructed to avoid possible oscillations near discontinuities. The BAP is a more general and simpler way to approximate higher order derivatives of given data without introducing oscillations, compared to limiters and the essentially non-oscillatory interpolations. For the solution of a system of conservation laws, we present a finite volume method which employs a flux splitting and uses componentwise reconstruction of the upwind fluxes. A high order piecewise polynomial constructed by using BAP is used to approximate the component of upwind fluxes. This scheme does not require characteristic decomposition nor Riemann solver, offering easy implementation and a relatively small computational cost. More importantly, the BAP is naturally extended for unstructured grids and it will be demonstrated through a cell-centered finite volume method, along with adaptive mesh refinement. A number of numerical experiments from various applications demonstrates the robustness and the accuracy of this approach, and show the potential of this approach for other practical applications.
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...
Nonlocal Symmetries and Exact Solutions for PIB Equation
Xin, Xiang-Peng; Miao, Qian; Chen, Yong
2012-09-01
In this paper, the symmetry group of the (2+1)-dimensional Painlevé integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.
Nonlocal Symmetries and Exact Solutions for PIB Equation
Institute of Scientific and Technical Information of China (English)
辛祥鹏; 苗倩; 陈勇
2012-01-01
In this paper, the symmetry group of the is studied by means of the classical symmetry method （2＋l）-dimensionM Painlevd integrable Burgers （PIB） equations Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.
Continuous point symmetries in Group Field Theories
Kegeles, Alexander
2016-01-01
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equation of motion, from a geometric perspective. We then focus on Group Field Theory (GFT) models of quantum gravity. We provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them, and apply it to several GFT models of interest to current research.
A statistical conservation law in two and three dimensional turbulent flows
Frishman, Anna; De Lillo, Filippo; Liberzon, Alex
2015-01-01
Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in [Falkovich et al., Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a d-dimensional flow the distance $R(t)$ between two neutrally buoyant particles, raised to the power $-d$ and averaged over velocity realizations, remains at all times equal to the initial, fixed, separation raised to the same power. In this work we present evidence from direct numerical simulations of two and three dimensional turbulence for this conservation. In both cases the conservation is lost when particles exit the linear flow regime. In 2D we show that, as an extension of the conservation law, a Evans-Cohen-Morriss/Gallavotti-Cohen type fluctuation relation exists. We also analyse data from a 3D laboratory experiment [Liberzon et al., Physica D 241, 208 (2...
Pacific Northwest Electric Power Planning and Conservation Act, with Index (Public Law 96-501).
Energy Technology Data Exchange (ETDEWEB)
1991-12-01
The Pacific Northwest Electric Power Planning and Conservation Act was enacted by the Senate and House of Representatives of the United States of America. It was enacted to assist the electrical consumers of the Pacific Northwest through use of the Federal columbia River Power System to achieve cost-effective energy conservation, to encourage the development of renewable energy resources, to establish a representative regional power planning process, to assure the region of an efficient and adequate power supply, and for other purposes. Contents of the Act are: short title and table of contents; purposes; definitions; regional planning and participation; sale of power; conservation and resource acquisition; rates; amendments to existing law; administrative provisions; savings provisions; effective date; and severability.
Nonlocal symmetry generators and explicit solutions of some partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Qin Maochang [School of Science, Chongqing Technology and Business University, Chongqing 400067 (China)
2007-04-27
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.
Quasilocal conservation laws in XXZ spin-1/2 chains: Open, periodic and twisted boundary conditions
Directory of Open Access Journals (Sweden)
Tomaž Prosen
2014-09-01
Full Text Available A continuous family of quasilocal exact conservation laws is constructed in the anisotropic Heisenberg (XXZ spin-1/2 chain for periodic (or twisted boundary conditions and for a set of commensurate anisotropies densely covering the entire easy plane interaction regime. All local conserved operators follow from the standard (Hermitian transfer operator in fundamental representation (with auxiliary spin s=1/2, and are all even with respect to a spin flip operation. However, the quasilocal family is generated by differentiation of a non-Hermitian highest weight transfer operator with respect to a complex auxiliary spin representation parameter s and includes also operators of odd parity. For a finite chain with open boundaries the time derivatives of quasilocal operators are not strictly vanishing but result in operators localized near the boundaries of the chain. We show that a simple modification of the non-Hermitian transfer operator results in exactly conserved, but still quasilocal operators for periodic or generally twisted boundary conditions. As an application, we demonstrate that implementing the new exactly conserved operator family for estimating the high-temperature spin Drude weight results, in the thermodynamic limit, in exactly the same lower bound as for almost conserved family and open boundaries. Under the assumption that the bound is saturating (suggested by agreement with previous thermodynamic Bethe ansatz calculations we propose a simple explicit construction of infinite time averages of local operators such as the spin current.
Energy Technology Data Exchange (ETDEWEB)
Borja, R I; White, J A
2010-02-19
We develop conservation laws for coupled hydro-mechanical processes in unsaturated porous media using three-phase continuum mixture theory. From the first law of thermodynamics, we identify energy-conjugate variables for constitutive modeling at macroscopic scale. Energy conjugate expressions identified relate a certain measure of effective stress to the deformation of the solid matrix, the degree of saturation to the matrix suction, the pressure in each constituent phase to the corresponding intrinsic volume change of this phase, and the seepage forces to the corresponding pressure gradients. We then develop strong and weak forms of boundary-value problems relevant for 3D finite element modeling of coupled hydro-mechanical processes in unsaturated porous media. The paper highlights a 3D numerical example illustrating the advances in the solution of large-scale coupled finite element systems, as well as the challenges in developing more predictive tools satisfying the basic conservation laws and the observed constitutive responses for unsaturated porous materials.
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.
Wang, Huimin
2017-01-01
In this paper, a new lattice Boltzmann model for the Korteweg-de Vries (KdV) equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher- order moments of equilibrium distribution functions are obtained. In order to make the scheme obey the three conservation laws of the KdV equation, two equilibrium distribution functions are used and a correlation between the first conservation law and the second conservation law is constructed. In numerical examples, the numerical results of the KdV equation obtained by this scheme are compared with those results obtained by the previous lattice Boltzmann model. Numerical experiments demonstrate this scheme can be used to reduce the truncation error of the lattice Boltzmann scheme and preserve the three conservation laws.
Institute of Scientific and Technical Information of China (English)
CHEN Xiang-Jun; HOU Li-Jie; LAM Wa Kun
2005-01-01
@@ Conservation laws for the derivative nonlinear Schr(o)dinger equation with non-vanishing boundary conditions are derived, based on the recently developed inverse scattering transform using the affine parameter technique.
Vondráček, M.; Cornils, L.; Minár, J.; Warmuth, J.; Michiardi, M.; Piamonteze, C.; Barreto, L.; Miwa, J. A.; Bianchi, M.; Hofmann, Ph.; Zhou, L.; Kamlapure, A.; Khajetoorians, A. A.; Wiesendanger, R.; Mi, J.-L.; Iversen, B.-B.; Mankovsky, S.; Borek, St.; Ebert, H.; Schüler, M.; Wehling, T.; Wiebe, J.; Honolka, J.
2016-10-01
We report on the quenching of single Ni adatom moments on Te-terminated Bi2Te2Se and Bi2Te3 topological insulator surfaces. The effect is noted as a missing x-ray magnetic circular dichroism for resonant L3 ,2 transitions into partially filled Ni 3 d states of theory-derived occupancy nd=9.2 . On the basis of a comparative study of Ni and Fe using scanning tunneling microscopy and ab initio calculations, we are able to relate the element specific moment formation to a local Stoner criterion. Our theory shows that while Fe adatoms form large spin moments of ms=2.54 μB with out-of-plane anisotropy due to a sufficiently large density of states at the Fermi energy, Ni remains well below an effective Stoner threshold for local moment formation. With the Fermi level remaining in the bulk band gap after adatom deposition, nonmagnetic Ni and preferentially out-of-plane oriented magnetic Fe with similar structural properties on Bi2Te2Se surfaces constitute a perfect platform to study the off-on effects of time-reversal symmetry breaking on topological surface states.
New fermion mass textures from anomalous U(1) symmetries with baryon and lepton number conservation
Energy Technology Data Exchange (ETDEWEB)
Leontaris, G.K.; Rizos, J
2000-02-14
In this paper we present solutions to the fermion mass hierarchy problem in the context of the minimal supersymmetric standard theory augmented by an anomalous family dependent U(1){sub X} symmetry. The latter is spontaneously broken by non-zero vevs of a pair of singlet fields whose magnitude is determined through the D- and F-flatness conditions of the superpotential. We derive the general solutions to the anomaly cancellation conditions and show that they allow numerous choices for the U(1){sub X} fermion charges which give several fermion mass textures in agreement with the observed fermion mass hierarchy and mixing. Solutions with U(1){sub X} fermion charge assignments are found which forbid or substantially suppress the dangerous baryon and lepton number violating operators and the lepton-Higgs mixing coupling while a Higgs mixing mass parameter ({mu}-term) can be fixed at the electroweak level. We give a general classification of the fermion mass textures with respect to the sum of the doublet-Higgs U(1){sub X} charges and show that suppression of dimension-five operators naturally occurs for various charge assignments. We work out cases which retain a quartic term providing the left-handed neutrinos with Majorana masses in the absence of right-handed neutrino components and consistent with the experimental bounds. Although there exist solutions which naturally combine all the above features with rather natural U(1){sub X} charges, the suppression of the {mu}-term occurs for particular assignments.
THE CONSERVATION LAW OF NONHOLONOMIC SYSTEM OF SECOND-ORDER NON-CHETAVE'S TYPE IN EVENT SPACE
Institute of Scientific and Technical Information of China (English)
方建会
2002-01-01
The conservation law of nonholonomic system of second-order non-Chatae's type in event space is studied. The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's principle under infinitesimal transformation is given by introducing Jourdain's generators in event space. Then the conservation law of the system in event space is obtained under certain conditions. Finally a calculating example is given.
Directory of Open Access Journals (Sweden)
Jela Susic
2007-08-01
Full Text Available From a Hopf equation we develop a recently introduced technique, the weak asymptotic method, for describing the shock wave formation and the interaction processes. Then, this technique is applied to a system of conservation laws arising from pressureless gas dynamics. As an example, we study the shock wave formation process in a two-dimensional scalar conservation laws arising in oil reservoir problems.
Institute of Scientific and Technical Information of China (English)
顾书龙
2011-01-01
The research on the Noether symmetry and its conserved quantity for dynamics system is a relatively new direction of development in modern mathematical physics, and can be applied to quantum mechanics, mechanics of space flight and some fields in modern engineering science. In this paper, the Noether symmetry and the Noether conserved quantities of the H6non-Heiles system were studied. The determining equations of Noether symmetry for the system had been got. The Noether symmetry definition and criterion of Henon-Heiles system were given. A theorem asserting that the Noether symmetry for the system leads to the several conserved quantity was presented.%动力学系统的Noether对称性与守恒量研究一直是近代数学物理的一个重要的新发展方向,多应用于量子力学、空间飞行力学及现代工程力学领域.研究Hénon-Heiles系统动力学方程在群无限小变换下的Noether对称性,得到其确定方程,给出其Norther对称性的定义与判据,并由其Noether对称性直接导出几个Noether守恒量.
An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis
Bey, Kim S.
1994-01-01
This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.
Numerical methods for systems of conservation laws of mixed type using flux splitting
Shu, Chi-Wang
1990-01-01
The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.
Zhang, Yufeng; Zhang, Xiangzhi; Wang, Yan; Liu, Jiangen
2017-01-01
With the help of R-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula by R-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.
On existence of weak solutions to a Cauchy problem for one class of conservation laws
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P. I. Kogut
2015-02-01
Full Text Available We discuss the existence of weak solutions to the Cauchy problem for one classof hyperbolic conservation laws that models a highly re-entrant production system.The output of the factory is described as a function of the work in progress and theposition of the so-called push-pull point (PPP where we separate the beginning ofthe factory employing a push policy from the end of the factory, which uses a pullpolicy. The main question we discuss in this paper is about the optimal choice ofthe input in-ux, push and pull constituents, and the position of PPP.
Convergence of a continuous BGK model for initial boundary-value problems for conservation laws
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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.
Scaling Approach to the Growth Equation with a Generalized Conservation Law
Institute of Scientific and Technical Information of China (English)
唐刚; 张丽萍; 吴玉喜; 夏辉; 郝大鹏; 陈华
2003-01-01
The Flory-type scaling approach proposed by Hentschel and Family [Phys.Rev.Lett.66(1991)1982] is generalized to the analysis of the growth equation with a generalized conservation law,which contains the KardarParisi-Zhang,Sun-Guo-Grant,and molecular-beam epitaxy growth equations as special cases and allows for a unified investigation of growth equations.The scaling exponents obtained here can be in agreement well with the corresponding results derived by the dynamic renormalization group theory and the previous scaling analyses.
Constructing conservation laws for fractional-order integro-differential equations
Lukashchuk, S. Yu.
2015-08-01
In a class of functions depending on linear integro-differential fractional-order variables, we prove an analogue of the fundamental operator identity relating the infinitesimal operator of a point transformation group, the Euler-Lagrange differential operator, and Noether operators. Using this identity, we prove fractional-differential analogues of the Noether theorem and its generalizations applicable to equations with fractional-order integrals and derivatives of various types that are Euler-Lagrange equations. In explicit form, we give fractional-differential generalizations of Noether operators that gives an efficient way to construct conservation laws, which we illustrate with three examples.
Delle Monache, M. L.; Goatin, P.
2014-12-01
We consider a strongly coupled PDE-ODE system that describes the influence of a slow and large vehicle on road traffic. The model consists of a scalar conservation law accounting for the main traffic evolution, while the trajectory of the slower vehicle is given by an ODE depending on the downstream traffic density. The moving constraint is expressed by an inequality on the flux, which models the bottleneck created in the road by the presence of the slower vehicle. We prove the existence of solutions to the Cauchy problem for initial data of bounded variation.
Institute of Scientific and Technical Information of China (English)
LI Xin-Yue; ZHAO Qiu-Lan
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 rationed type. Further, we construct infinite conservation laws about the positive hierarchy.
Hybrid entropy stable HLL-type Riemann solvers for hyperbolic conservation laws
Schmidtmann, Birte; Winters, Andrew R.
2017-02-01
It is known that HLL-type schemes are more dissipative than schemes based on characteristic decompositions. However, HLL-type methods offer greater flexibility to large systems of hyperbolic conservation laws because the eigenstructure of the flux Jacobian is not needed. We demonstrate in the present work that several HLL-type Riemann solvers are provably entropy stable. Further, we provide convex combinations of standard dissipation terms to create hybrid HLL-type methods that have less dissipation while retaining entropy stability. The decrease in dissipation is demonstrated for the ideal MHD equations with a numerical example.
L^1 stability of conservation laws for a traffic flow model
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Tong Li
2001-02-01
Full Text Available We establish the $L^1$ well-posedness theory for a system of nonlinear hyperbolic conservation laws with relaxation arising in traffic flows. In particular, we obtain the continuous dependence of the solution on its initial data in $L^1$ topology. We construct a functional for two solutions which is equivalent to the $L^1$ distance between the solutions. We prove that the functional decreases in time which yields the $L^1$ well-posedness of the Cauchy problem. We thus obtain the $L^1$-convergence to and the uniqueness of the zero relaxation limit.
The Noether Theorems Invariance and Conservation Laws in the 20th Century
Kosmann-Schwarzbach, Yvette
2011-01-01
In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems. But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the vario
A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint
Barth, Timothy
2004-01-01
This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.
Xia, Ya-Rong; Xin, Xiang-Peng; Zhang, Shun-Li
2017-01-01
This paper mainly discusses the (2+1)-dimensional modified dispersive water-wave (MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlevé analysis and consistent tanh-function expansion (CTE) method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved. Supported by National Natural Science Foundation of China under Grant Nos. 11371293, 11505090, the Natural Science Foundation of Shaanxi Province under Grant No. 2014JM2-1009, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009 and the Science and Technology Innovation Foundation of Xi’an under Grant No. CYX1531WL41
Institute of Scientific and Technical Information of China (English)
许斌; 刘希强
2011-01-01
In this paper, infinitesimal generator and group invariant solutions to Landau- Lifshitz equation via the classical Lie group method have been obtained, at the same time corresponding Lie algebra and the relations between new solutions and olds have been found. At the same time, we also give the conservation laws of Landau-Lifshitz equation by symmetries and the adjoint equations.%利用经典李群方法得到了Landau—Lifshitz方程不变群的无穷小生成元，验证其对换位运算构成一个七维的李代数，得到了对应的群不变解，建立了Landau—Lifshitz新解和旧解之间的关系．同时利用对称和共轭方程组求得了Landau—Lifshitz方程的守恒律．
Optimal results on TV bounds for scalar conservation laws with discontinuous flux
Ghoshal, Shyam Sundar
2015-02-01
This paper is concerned with the total variation of the solution of scalar conservation law with discontinuous flux in one space dimension. One of the main unsettled questions concerning conservation law with discontinuous flux was the boundedness of the total variation of the solution near interface. In [1], it has been shown by a counter-example at T = 1, that the total variation of the solution blows up near interface, but in that example the solution become of bounded variation after time T > 1. So the natural question is what happens to the BV-ness of the solution for large time. Here we give a complete picture of the bounded variation of the solution for all time. For a uniform convex flux with only L∞ data, we obtain a natural smoothing effect in BV for all time t >T0. Also we give a counter-example (even for a BV data) to show that the assumptions which have been made are optimal.
A Space-time Smooth Artificial Viscosity Method For Nonlinear Conservation Laws
Reisner, Jon; Shkoller, Steve
2012-01-01
We introduce the $C$-method, a simple scheme for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities. In particular, we focus our attention on the compressible Euler equations which form a 3x3 system in one space dimension. The novel feature of our approach involves the coupling of a linear scalar reaction diffusion equation to our system of conservation laws, whose solution $C(x,t)$ is the coefficient to an additional (and artificial) term added to the flux, which determines both the location and strength of the added viscosity. Near shock discontinuities, $C(x,t)$ is large and localized, and transitions smoothly in space-time to zero away from the shock. This simple approach has two fundamental features: (1) our regularization is at the continuum level--i.e., the level of he partial differential equations (PDE)-- so that any higher-order numerical discretization scheme can be employed, and ...
Rašin, Andrija
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Test of Von Baer's law of the conservation of early development.
Poe, Steven
2006-11-01
One of the oldest and most pervasive ideas in comparative embryology is the perceived evolutionary conservation of early ontogeny relative to late ontogeny. Karl Von Baer first noted the similarity of early ontogeny across taxa, and Ernst Haeckel and Charles Darwin gave evolutionary interpretation to this phenomenon. In spite of a resurgence of interest in comparative embryology and the development of mechanistic explanations for Von Baer's law, the pattern itself has been largely untested. Here, I use statistical phylogenetic approaches to show that Von Baer's law is an unnecessarily complex explanation of the patterns of ontogenetic timing in several clades of vertebrates. Von Baer's law suggests a positive correlation between ontogenetic time and amount of evolutionary change. I compare ranked position in ontogeny to frequency of evolutionary change in rank for developmental events and find that these measures are not correlated, thus failing to support Von Baer's model. An alternative model that postulates that small changes in ontogenetic rank are evolutionarily easier than large changes is tentatively supported.
Chen, Tianheng; Shu, Chi-Wang
2017-09-01
It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy cell entropy inequalities for the square entropy for both scalar conservation laws (Jiang and Shu (1994) [39]) and symmetric hyperbolic systems (Hou and Liu (2007) [36]), in any space dimension and for any triangulations. However, this property holds only for the square entropy and the integrations in the DG methods must be exact. It is significantly more difficult to design DG methods to satisfy entropy inequalities for a non-square convex entropy, and/or when the integration is approximated by a numerical quadrature. In this paper, we develop a unified framework for designing high order DG methods which will satisfy entropy inequalities for any given single convex entropy, through suitable numerical quadrature which is specific to this given entropy. Our framework applies from one-dimensional scalar cases all the way to multi-dimensional systems of conservation laws. For the one-dimensional case, our numerical quadrature is based on the methodology established in Carpenter et al. (2014) [5] and Gassner (2013) [19]. The main ingredients are summation-by-parts (SBP) operators derived from Legendre Gauss-Lobatto quadrature, the entropy conservative flux within elements, and the entropy stable flux at element interfaces. We then generalize the scheme to two-dimensional triangular meshes by constructing SBP operators on triangles based on a special quadrature rule. A local discontinuous Galerkin (LDG) type treatment is also incorporated to achieve the generalization to convection-diffusion equations. Extensive numerical experiments are performed to validate the accuracy and shock capturing efficacy of these entropy stable DG methods.
Energy Conservation Law in Industrial Architecture: An Approach through Geometric Algebra
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Juan C. Bravo
2016-09-01
Full Text Available Since 1892, the electrical engineering scientific community has been seeking a power theory for interpreting the power flow within electric networks under non-sinusoidal conditions. Although many power theories have been proposed regarding non-sinusoidal operation, an adequate solution is yet to be found. Using the framework based on complex algebra in non-sinusoidal circuit analysis (frequency domain, the verification of the energy conservation law is only possible in sinusoidal situations. In this case, reactive energy turns out to be proportional to the energy difference between the average electric and magnetic energies stored in the loads and its cancellation is mathematically trivial. However, in industrial architecture, apparent power definition of electric loads (non-sinusoidal conditions is inconsistent with the energy conservation law. Up until now, in the classical complex algebra approach, this goal is only valid in the case of purely resistive loads. Thus, in this paper, a new circuit analysis approach using geometric algebra is used to develop the most general proof of energy conservation in industrial building loads. In terms of geometric objects, this powerful tool calculates the voltage, current, and apparent power in electrical systems in non-sinusoidal, linear/nonlinear situations. In contrast to the traditional method developed by Steinmetz, the suggested powerful tool extends the concept of phasor to multivector-phasors and is performed in a new Generalized Complex Geometric Algebra structure (CGn, where Gn is the Clifford algebra in n-dimensional real space and C is the complex vector space. To conclude, a numerical example illustrates the clear advantages of the approach suggested in this paper.
Ermakov's Superintegrable Toy and Nonlocal Symmetries
Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.
2005-11-01
We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Ermakov's Superintegrable Toy and Nonlocal Symmetries
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P.G.L. Leach
2005-11-01
Full Text Available We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R. The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Energy Technology Data Exchange (ETDEWEB)
Ketteler, G.; Kippels, K. (Fachhochschule fuer Oeffentliche Verwaltung Nordrhein-Westfalen, Gelsenkirchen (Germany, F.R.))
1988-01-01
In section I 'Basic principles' the following topics are considered: Constitutional-legal aspects of environmental protection, e.g. nuclear hazards and the remaining risk; European environmental law; international environmental law; administrative law, private law and criminal law relating to the environment; basic principles of environmental law, the instruments of public environmental law. Section II 'Special areas of law' is concerned with the law on water and waste, prevention of air pollution, nature conservation and care of the countryside. Legal decisions and literature up to June 1988 have been taken into consideration. (orig./RST).
Singular solutions of a fully nonlinear 2x2 system of conservation laws
Kalisch, Henrik
2011-01-01
Existence and admissibility of $\\delta$-shock type solution is discussed for the following nonconvex strictly hyperbolic system arising in studues of plasmas: \\pa_t u + \\pa_x \\big(\\Sfrac{u^2+v^2}{2} \\big) &=0 \\pa_t v +\\pa_x(v(u-1))&=0. The system is fully nonlinear, i.e. it is nonlinear with respect to both variables. The latter system does not admit the classical Lax-admissible solution to certain Riemann problems. By introducing complex valued corrections in the framework of the weak asymptotic method, we show that an overcompressive $\\delta$-shock type solution resolves such Riemann problems. By letting the approximation parameter to zero, the corrections become real valued and we obtain a $\\delta$-type solution concept. In the frame of that concept, we can show that every $2\\times 2$ system of conservation laws admits $\\delta$-type solution.
Conservation Laws and Bounds on the Efficiency of Wind-Wave Growth
Chafin, Clifford
2014-01-01
We examine two means by which wind can impart energy to waves: sheltering and deposition of material upwards from windward surface shear. The shear driven deposition is shown to be the more efficient process. Lengthening of waves to match the wind speed is shown to be very inefficient and consume a large fraction of the energy imparted by the wind. The surface shear provides a low energy sink that absorbs most of the momentum from the wind. These produce bounds on the efficiency of wave growth. The results here are computed in a model independent and perturbation free fashion by a careful consideration of conservation laws. By combining these effects we can place bounds on the rates waves can grow in a given fetch and the relative amount of shear flow versus the, relatively small, Stokes drift that must arise.
Conservation Laws and Web-Solutions for the Benney--Luke Equation
Ablowitz, Mark
2012-01-01
A long wave multi-dimensional approximation of shallow water waves is the bi-directional Benney-Luke equation. It yields the well-known Kadomtsev-Petviashvili equation in a quasi one-directional limit. A direct perturbation method is developed; it uses the underlying conservation laws to determine the slow evolution of parameters of two space dimensional, non-decaying web-type solutions to the Benney-Luke equation. New numerical simulations, based on windowing methods which are effective for non-decaying data, are presented. These simulations support the analytical results and elucidate the relationship between the Kadomtsev-Petviashvilli and the Benney-Luke equations and are also used to obtain amplitude information regarding particular web solutions. Additional dissipative perturbations to the Benney-Luke equation are also studied.
Lp stability for entropy solutions of scalar conservation laws with strict convex flux
Adimurthi; Ghoshal, Shyam Sundar; Veerappa Gowda, G. D.
Here we consider the scalar convex conservation laws in one space dimension with strictly convex flux which is in C1. Existence, uniqueness and L1 contractivity were proved by Kružkov [14]. Using the relative entropy method, Leger showed that for a uniformly convex flux and for the shock wave solutions, the L2 norm of a perturbed solution relative to the shock wave is bounded by the L2 norm of the initial perturbation. Here we generalize the result to Lp norm for all 1⩽p<∞. Also we show that for the non-shock wave solution, Lp norm of the perturbed solution relative to the modified N-wave is bounded by the Lp norm of the initial perturbation for all 1⩽p<∞.
Conserved Charges and First Law of Thermodynamics for Kerr-de Sitter Black Holes
Hajian, Kamal
2016-01-01
Recently, a general formulation for calculating conserved charges for (black hole) solutions to generally covariant gravitational theories, in any dimensions and with arbitrary asymptotic behaviors has been introduced. Equipped with this method, which can be dubbed as "solution phase space method," we calculate mass and angular momentum for the Kerr-dS black hole. Then, for any choice of horizons, associated entropy and the first law of thermodynamics are derived. Interestingly, according to insensitivity of the analysis to the chosen cosmological constant, the analysis unifies the thermodynamics of rotating stationary black holes in 4 (and other) dimensions with either AdS, flat or dS asymptotics. We extend the analysis to include electric charge, i.e. to the Kerr-Newman-dS black hole.
Borsche, Raul
2014-01-01
In this paper we propose a model for a sewer network coupled to surface flow and investigate it numerically. In particular, we present a new model for the manholes in storm sewer systems. It is derived using the balance of the total energy in the complete network. The resulting system of equations contains, aside from hyperbolic conservation laws for the sewer network and algebraic relations for the coupling conditions, a system of ODEs governing the flow in the manholes. The manholes provide natural points for the interaction of the sewer system and the run off on the urban surface modelled by shallow water equations. Finally, a numerical method for the coupled system is presented. In several numerical tests we study the influence of the manhole model on the sewer system and the coupling with 2D surface flow.
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)
Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws
Kang, Moon-Jin; Vasseur, Alexis F.
2016-10-01
We study the contraction properties (up to shift) for admissible Rankine-Hugoniot discontinuities of {n× n} systems of conservation laws endowed with a convex entropy. We first generalize the criterion developed in (Serre and Vasseur, J l'Ecole Polytech 1, 2014), using the spatially inhomogeneous pseudo-distance introduced in (Vasseur, Contemp Math AMS, 2013). Our generalized criterion guarantees the contraction property for extremal shocks of a large class of systems, including the Euler system. Moreover, we introduce necessary conditions for contraction, specifically targeted for intermediate shocks. As an application, we show that intermediate shocks of the two-dimensional isentropic magnetohydrodynamics do not verify any of our contraction properties. We also investigate the contraction properties, for contact discontinuities of the Euler system, for a certain range of contraction weights. None of the results involve any smallness condition on the initial perturbation or on the size of the shock.
Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric
Holzegel, Gustav
2016-01-01
We derive an energy conservation law for the system of gravitational perturbations on the Schwarzschild spacetime expressed in a double null gauge. The resulting identity involves only first derivatives of the metric perturbation. Exploiting the gauge invariance up to boundary terms of the fluxes that appear, we are able to establish positivity of the flux on any outgoing null hypersurface to the future of the initial data. This allows us to bound the total energy flux through any such hypersurface, including the event horizon, in terms of initial data. We similarly bound the total energy radiated to null infinity. Our estimates provide a direct approach to a weak form of stability, thereby complementing the proof of the full linear stability of the Schwarzschild solution recently obtained in [M. Dafermos, G. Holzegel and I. Rodnianski \\emph{The linear stability of the Schwarzschild solution to gravitational perturbations}, arXiv:1601.06467].
Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric
Holzegel, Gustav
2016-10-01
We derive an energy conservation law for the system of gravitational perturbations on the Schwarzschild spacetime expressed in a double null gauge. The resulting identity involves only first derivatives of the metric perturbation. Exploiting the gauge invariance up to boundary terms of the fluxes that appear, we are able to establish positivity of the flux on any outgoing null hypersurface to the future of the initial data. This allows us to bound the total energy flux through any such hypersurface, including the event horizon, in terms of initial data. We similarly bound the total energy radiated to null infinity. Our estimates provide a direct approach to a weak form of stability, thereby complementing the proof of the full linear stability of the Schwarzschild solution recently obtained in Dafermos et al (2016 The linear stability of the Schwarzschild solution to gravitational perturbations arXiv:1601.06467).
Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws
El, G A; Shearer, M
2015-01-01
We compare the structure of solutions of Riemann problems for a conservation law with nonconvex (specifically, cubic) flux, regularized by two different mechanisms: 1) dispersion (in the modified Korteweg--de Vries (mKdV) equation); and 2) a combination of diffusion and dispersion (in the mKdV-Burgers equation). In the first case, the possible dynamics involve two qualitatively different types of expanding dispersive shock waves (DSWs), rarefaction waves (RWs) and kinks (smooth fronts). In the second case, in addition to RWs, there are travelling wave solutions approximating both classical (Lax) and nonclassical (undercompressive) shock waves. Despite the singular nature of the zero-diffusion limit and rather differing analytical approaches employed in the descriptions of dispersive and diffusive-dispersive regularization, the resulting comparison of the two cases reveals a number of striking parallels. In particular the mKdV kink solution is identified as an undercompressive DSW. Other prominent features, su...
Verma, Prabal Singh
2015-01-01
The dimensionally split reconstruction method as described by Kurganov et al.\\cite{kurganov-2000} is revisited for better understanding and a simple fourth order scheme is introduced to solve 3D hyperbolic conservation laws following dimension by dimension approach. Fourth order central weighted essentially non-oscillatory (CWENO) reconstruction methods have already been proposed to study multidimensional problems \\cite{lpr4,cs12}. In this paper, it is demonstrated that a simple 1D fourth order CWENO reconstruction method by Levy et al.\\cite{lpr7} provides fourth order accuracy for 3D hyperbolic nonlinear problems when combined with the semi-discrete scheme by Kurganov et al.\\cite{kurganov-2000} and fourth order Runge-Kutta method for time integration.
Fuhry, Martin; Krivodonova, Lilia
2016-01-01
We present a novel implementation of the modal discontinuous Galerkin (DG) method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDIA's Compute Unified Device Architecture (CUDA). Both flexible and highly accurate, DG methods accommodate parallel architectures well as their discontinuous nature produces element-local approximations. High performance scientific computing suits GPUs well, as these powerful, massively parallel, cost-effective devices have recently included support for double-precision floating point numbers. Computed examples for Euler equations over unstructured triangle meshes demonstrate the effectiveness of our implementation on an NVIDIA GTX 580 device. Profiling of our method reveals performance comparable to an existing nodal DG-GPU implementation for linear problems.
The finite volume local evolution Galerkin method for solving the hyperbolic conservation laws
Sun, Yutao; Ren, Yu-Xin
2009-07-01
This paper presents a finite volume local evolution Galerkin (FVLEG) scheme for solving the hyperbolic conservation laws. The FVLEG scheme is the simplification of the finite volume evolution Galerkin method (FVEG). In FVEG, a necessary step is to compute the dependent variables at cell interfaces at tn + τ (0 FVEG. The FVLEG scheme greatly simplifies the evaluation of the numerical fluxes. It is also well suited with the semi-discrete finite volume method, making the flux evaluation being decoupled with the reconstruction procedure while maintaining the genuine multi-dimensional nature of the FVEG methods. The derivation of the FVLEG scheme is presented in detail. The performance of the proposed scheme is studied by solving several test cases. It is shown that FVLEG scheme can obtain very satisfactory numerical results in terms of accuracy and resolution.
Angular momentum conservation law in light-front quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Chiu, Kelly Yu-Ju; Brodsky, Stanley J.; /SLAC /Stanford U.
2017-03-01
We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that j 3 , the z -component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j 3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.
Directory of Open Access Journals (Sweden)
Long Wei
2014-01-01
Full Text Available In a recent paper (Zhang (2013, the author claims that he has proposed two rules to modify Ibragimov’s theorem on conservation laws to “ensure the theorem can be applied to nonlinear evolution equations with any mixed derivatives.” In this letter, we analysis the paper. Indeed, the so-called “modification rules” are needless and the theorem of Ibragimov can be applied to construct conservation laws directly for nonlinear equations with any mixed derivatives as long as the formal Lagrangian is rewritten in symmetric form. Moreover, the conservation laws obtained by the so-called “modification rules” in the paper under discussion are equivalent to the one obtained by Ibragimov’s theorem.
Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations
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.
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=g dt+{-D∇ϕ dt+√{2D} dB(t)}, with ∇ṡg=0 and {⋯} respectively representing phase-volume preserving dynamics and stochastic damping. The zeroth law implies stationary distribution u(x)=e. We find an orthogonality ∇ϕṡg=0 as a hallmark of the system. Stochastic thermodynamics based on time reversal (t,ϕ,g)→(-t,ϕ,-g) is formulated: entropy production ep#(t)=-dF(t)/dt; generalized “heat” hd#(t)=-dU(t)/dt, U(t)=∫ϕ(x)u(x,t) dx being “internal energy”, and “free energy” F(t)=U(t)+∫u(x,t)ln u(x,t) dx never increases. Entropy follows {dS}/{dt}=ep#-hd#. 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.
Directory of Open Access Journals (Sweden)
Lenart Zadnik
2016-01-01
Full Text Available We construct quasilocal conserved charges in the gapless (|Δ|≤1 regime of the Heisenberg XXZ spin-1/2 chain, using semicyclic irreducible representations of Uq(sl2. These representations are characterized by a periodic action of ladder operators, which act as generators of the aforementioned algebra. Unlike previously constructed conserved charges, the new ones do not preserve magnetization, i.e. they do not possess the U(1 symmetry of the Hamiltonian. The possibility of application in relaxation dynamics resulting from U(1-breaking quantum quenches is discussed.
Directory of Open Access Journals (Sweden)
Wei-Cheng Wang
2002-06-01
Full Text Available We study the asymptotic equivalence of the Jin-Xin relaxation model and its formal limit for genuinely nonlinear $2imes 2$ conservation laws. The initial data is allowed to have jump discontinuities corresponding to centered rarefaction waves, which includes Riemann data connected by rarefaction curves. We show that, as long as the initial data is a small perturbation of a constant state, the solution for the relaxation system exists globally in time and converges, in the zero relaxation limit, to the solution of the corresponding conservation law uniformly except for an initial layer.
Yu, Pengfei; Wang, Hailong; Chen, Jianyong; Shen, Shengping
2017-07-01
In this study, the conservation laws οf dissipative mechanical-diffusion-electrochemical reaction system are systematically obtained based on Noether's theorem. According to linear, irreversible thermodynamics, dissipative phenomena can be described by an irreversible force and an irreversible flow. Additionally, the Lagrange function, L and the generalized Hamilton least-action principle are proposed to be used to obtain the conservation integrals. A group of these integrals, including the J-, M-, and L-integrals, can be then obtained using the classical Noether approach for dissipative processes. The relation between the J-integral and the energy release rate is illustrated. The path-independence of the J-integral is then proven. The J-integral, derived based on Noether's theorem, is a line integral, contrary to the propositions of existing published works that describe it both as a line and an area integral. Herein, we prove that the outcomes are identical, and identify the physical meaning of the area integral, a concept that was not explained previously. To show that the J-integral can dominate the distribution of the corresponding field quantities, an example of a partial, stress-diffusion coupling process is disscussed.
Wright, Christopher K
2010-07-01
Although habitat networks show promise for conservation planning at regional scales, their spatiotemporal dynamics have not been well studied, especially in climate-sensitive landscapes. Here I use satellite remote sensing to compile wetland habitat networks from the Prairie Pothole Region (PPR) of North America. An ensemble of networks assembled across a hydrologic gradient from deluge to drought and a range of representative dispersal distances exhibits power-law scaling of important topological parameters. Prairie wetland networks are "meso-worlds" with mean topological distance increasing faster with network size than small-world networks, but slower than a regular lattice (or "large world"). This scaling implies rapid dispersal through wetland networks without some of the risks associated with "small worlds" (e.g., extremely rapid propagation of disease or disturbance). Retrospective analysis of wetland networks establishes a climatic envelope for landscape connectivity in the PPR, where I show that a changing climate might severely impact metapopulation viability and restrict long-distance dispersal and range shifts. More generally, this study demonstrates an efficient approach to conservation planning at a level of abstraction addressing key drivers of the global biodiversity crisis: habitat fragmentation and climatic change.
Generating wind fields that honour point observations and physical conservation laws
Schlabing, Dirk; Bárdossy, András
2015-04-01
Wind exhibits a strong spatial and temporal variability. In the application of lake modelling, these features are important for simulating water flows and stratification correctly, as mean and variance of wind speed determine the input of momentum into the lake. This makes a mere interpolation of point measurements an unsuitable method for producing model input. Additionally to concrete point measurements, more subtle aspects of wind fields are to be reproduced. It follows from the fact that wind vectors represent moving air that a wind field has to be divergency-free in order to be mass-conservative. Further, a temporal sequence of wind fields has to comply with the Navier-Stokes equation in order to conserve momentum. All these constraints can be met by representing the conditioned wind field as a linear combination of unconditioned, normally distributed random fields that individually possess the same spatial covariance structuref as observed wind fields. The aim of having the same covariance structure in the conditioned wind field is formulated as an optimization problem with respect to the weights used in the linear combination. With the help of Quadratic Programming (QP) and exploiting the convexity of the problem, feasible solutions can easily be found. In this QP problem, observations become linear constraints. Conservation laws can be incorporated by introducing control volumes in a similar fashion as they are used in fluid mechanics. Budgets of flows through these control volumes become integral conditions in the QP problem. The applicability of the approach will be shown using an artificial example and real-world data measured on shore and on a moving boat on Lake Constance.
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
Haas, Fernando
2016-11-01
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced.
Anomalous Fourier's Law and Long Range Correlations in a 1D Non-momentum Conserving Mechanical Model
Gerschenfeld, A.; Derrida, B.; Lebowitz, J. L.
2010-12-01
We study by means of numerical simulations the velocity reversal model, a one-dimensional mechanical model of heat transport introduced in 1985 by Ianiro and Lebowitz. Our numerical results indicate that this model, which does not conserve momentum, exhibits nevertheless an anomalous Fourier's law similar to the ones previously observed in momentum-conserving models. This disagrees with what can be expected by solving the Boltzmann equation (BE) for this system. The pair correlation velocity field also looks very different from the correlations usually seen in diffusive systems, and shares some similarity with those of momentum-conserving heat transport models.
Directory of Open Access Journals (Sweden)
Hongwei Yang
2014-01-01
Full Text Available In the paper, by using multiple-scale method, the Benjamin-Ono-Burgers-MKdV (BO-B-MKdV equation is obtained which governs algebraic Rossby solitary waves in stratified fluids. This equation is first derived for Rossby waves. By analysis and calculation, some conservation laws are derived from the BO-B-MKdV equation without dissipation. The results show that the mass, momentum, energy, and velocity of the center of gravity of algebraic Rossby waves are conserved and the presence of a small dissipation destroys these conservations.
An assessment of semi-discrete central schemes for hyperbolic conservation laws.
Energy Technology Data Exchange (ETDEWEB)
Christon, Mark Allen; Robinson, Allen Conrad; Ketcheson, David Isaac
2003-09-01
High-resolution finite volume methods for solving systems of conservation laws have been widely embraced in research areas ranging from astrophysics to geophysics and aero-thermodynamics. These methods are typically at least second-order accurate in space and time, deliver non-oscillatory solutions in the presence of near discontinuities, e.g., shocks, and introduce minimal dispersive and diffusive effects. High-resolution methods promise to provide greatly enhanced solution methods for Sandia's mainstream shock hydrodynamics and compressible flow applications, and they admit the possibility of a generalized framework for treating multi-physics problems such as the coupled hydrodynamics, electro-magnetics and radiative transport found in Z pinch physics. In this work, we describe initial efforts to develop a generalized 'black-box' conservation law framework based on modern high-resolution methods and implemented in an object-oriented software framework. The framework is based on the solution of systems of general non-linear hyperbolic conservation laws using Godunov-type central schemes. In our initial efforts, we have focused on central or central-upwind schemes that can be implemented with only a knowledge of the physical flux function and the minimal/maximal eigenvalues of the Jacobian of the flux functions, i.e., they do not rely on extensive Riemann decompositions. Initial experimentation with high-resolution central schemes suggests that contact discontinuities with the concomitant linearly degenerate eigenvalues of the flux Jacobian do not pose algorithmic difficulties. However, central schemes can produce significant smearing of contact discontinuities and excessive dissipation for rotational flows. Comparisons between 'black-box' central schemes and the piecewise parabolic method (PPM), which relies heavily on a Riemann decomposition, shows that roughly equivalent accuracy can be achieved for the same computational cost with both
Energy Technology Data Exchange (ETDEWEB)
Qian, Hong, E-mail: hqian@u.washington.edu
2014-01-31
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{sup ss}(x)=e{sup −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{sub p}{sup #}(t)=−dF(t)/dt; generalized “heat” h{sub d}{sup #}(t)=−dU(t)/dt, U(t)=∫{sub R{sup n}}ϕ(x)u(x,t)dx being “internal energy”, and “free energy” F(t)=U(t)+∫{sub R{sup n}}u(x,t)lnu(x,t)dx never increases. Entropy follows (dS)/(dt) =e{sub p}{sup #}−h{sub d}{sup #}. 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.
Group classification and conservation laws of the generalized Klein-Gordon-Fock equation
Muatjetjeja, B.
2016-08-01
In the present paper, we perform Lie and Noether symmetries of the generalized Klein-Gordon-Fock equation. It is shown that the principal Lie algebra, which is one-dimensional, has several possible extensions. It is further shown that several cases arise for which Noether symmetries exist. Exact solutions for some cases are also obtained from the invariant solutions of the investigated equation.
Some exact anisotropic solutions via Noether symmetry in f(R) gravity
Energy Technology Data Exchange (ETDEWEB)
Sharif, M., E-mail: msharif.math@pu.edu.pk; Nawazish, I., E-mail: iqranawazish07@gmail.com [University of the Punjab, Department of Mathematics (Pakistan)
2015-01-15
We attempt to find exact solutions of the Bianchi I model in f(R) gravity using the Noether symmetry approach. For this purpose, we take a perfect fluid and formulate conserved quantities for the power-law f(R) model. We discuss some cosmological parameters for the resulting solution which are responsible for expanding behavior of the universe. We also explore Noether gauge symmetry and the corresponding conserved quantity. It is concluded that symmetry generators as well as conserved quantities exist in all cases and the behavior of cosmological parameters shows consistency with recent observational data.
Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui; YAN Xiang-Hong; LI Hong; CHEN Pei-Sheng
2004-01-01
The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.
Products of Distributions, Conservation Laws and the Propagation of δ'-Shock Waves
Institute of Scientific and Technical Information of China (English)
Carlos Orlando R.SARRICO
2012-01-01
This paper contains a study of propagation of singular travelling waves u(x,t)for conservation laws ut + [φ(u)]x =Ψ(u),where φ,Ψ are entire functions taking real values on the real axis.Conditions for the propagation of wave profiles β + mδ and β + mδ' are presented (β is a real continuous function,m ≠ 0 is a real number and δ' is the derivative of the Dirac measure δ).These results are obtained with a consistent concept of solution based on our theory of distributional products.Burgers equation ut + (u2/2)x =0,the diffusionless Burgers-Fischer equation ut + a(u2/2)x =ru(1 - u/k) with a,r,k being positive numbers,Leveque and Yee equation ut + ux =μu(1 - u)(u - 1/2) with μ ≠ 0,and some other examples are studied within such a setting.A "tool box" survey of the distributional products is also included for the sake of completeness.
Chang, Shih-Hung
1991-01-01
Two approaches are used to extend the essentially non-oscillatory (ENO) schemes to treat conservation laws with stiff source terms. One approach is the application of the Strang time-splitting method. Here the basic ENO scheme and the Harten modification using subcell resolution (SR), ENO/SR scheme, are extended this way. The other approach is a direct method and a modification of the ENO/SR. Here the technique of ENO reconstruction with subcell resolution is used to locate the discontinuity within a cell and the time evolution is then accomplished by solving the differential equation along characteristics locally and advancing in the characteristic direction. This scheme is denoted ENO/SRCD (subcell resolution - characteristic direction). All the schemes are tested on the equation of LeVeque and Yee (NASA-TM-100075, 1988) modeling reacting flow problems. Numerical results show that these schemes handle this intriguing model problem very well, especially with ENO/SRCD which produces perfect resolution at the discontinuity.
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.
Efficient robust control of first order scalar conservation laws using semi-analytical solutions
Li, Yanning
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.
A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws
Zhu, Jun; Qiu, Jianxian
2016-08-01
In this paper a new simple fifth order weighted essentially non-oscillatory (WENO) scheme is presented in the finite difference framework for solving the hyperbolic conservation laws. The new WENO scheme is a convex combination of a fourth degree polynomial with two linear polynomials in a traditional WENO fashion. This new fifth order WENO scheme uses the same five-point information as the classical fifth order WENO scheme [14,20], could get less absolute truncation errors in L1 and L∞ norms, and obtain the same accuracy order in smooth region containing complicated numerical solution structures simultaneously escaping nonphysical oscillations adjacent strong shocks or contact discontinuities. The associated linear weights are artificially set to be any random positive numbers with the only requirement that their sum equals one. New nonlinear weights are proposed for the purpose of sustaining the optimal fifth order accuracy. The new WENO scheme has advantages over the classical WENO scheme [14,20] in its simplicity and easy extension to higher dimensions. Some benchmark numerical tests are performed to illustrate the capability of this new fifth order WENO scheme.
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.
A Few Discrete Lattice Systems and Their Hamiltonian Structures, Conservation Laws
Guo, Xiu-Rong; Zhang, Yu-Feng; Zhang, Xiang-Zhi; Yue, Rong
2017-04-01
With the help of three shift operators and r-matrix theory, a few discrete lattice systems are obtained which can be reduced to the well-known Toda lattice equation with a constraint whose Hamiltonian structures are generated by Poisson tensors of some induced Lie-Poisson bracket. The recursion operators of these lattice systems are constructed starting from Lax representations. Finally, reducing the given shift operators to get a simpler one and its expanding shift operators, we produce a lattice system with three vector fields whose recursion operator is given. Furthermore, we reduce the lattice system with three vector fields to get a lattice system whose Lax pair and conservation laws are obtained, respectively. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province Hosted by China University of Mining and Technology (2014), the the Key Discipline Construction by China University of Mining and Technology under Grant No. XZD201602, the Shandong Provincial Natural Science Foundation, China under Grant Nos. ZR2016AM31, ZR2016AQ19, ZR2015EM042, the Development of Science and Technology Plan Projects of TaiAn City under Grant No. 2015NS1048, National Social Science Foundation of China under Grant No. 13BJY026, and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58
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.
A Hybrid Riemann Solver for Large Hyperbolic Systems of Conservation Laws
Schmidtmann, Birte
2016-01-01
We are interested in the numerical solution of large systems of hyperbolic conservation laws or systems in which the characteristic decomposition is expensive to compute. Solving such equations using finite volumes or Discontinuous Galerkin requires a numerical flux function which solves local Riemann problems at cell interfaces. There are various methods to express the numerical flux function. On the one end, there is the robust but very diffusive Lax-Friedrichs solver; on the other end the upwind Godunov solver which respects all resulting waves. The drawback of the latter method is the costly computation of the eigensystem. This work presents a family of simple first order Riemann solvers, named HLLX$\\omega$, which avoid solving the eigensystem. The new method reproduces all waves of the system with less dissipation than other solvers with similar input and effort, such as HLL and FORCE. The family of Riemann solvers can be seen as an extension or generalization of the methods introduced by Degond et al. \\...
2014-01-01
A generalization of the usual gauge symmetry leads to fourth-order gauge field equations, which imply a new constant force independent of distances. The force associated with the new $U_1$ gauge symmetry is repulsive among baryons. Such a constant force based on baryon charge conservation gives a field-theoretic understanding of the accelerated cosmic-expansion in the observable portion of the universe dominated by baryon galaxies. In consistent with all conservation laws and known forces, a ...
Institute of Scientific and Technical Information of China (English)
ZHANG Chun-Yi; LI Juan; MENG Xiang-Hua; XU Tao; GAO Yi-Tian
2008-01-01
@@ Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries(KdV)equation,we prove that the variable-coefficient KdV equation under the Painlevé test condition also possesses the formal conservation laws.
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.
Cozma, M D
2014-01-01
The charged pion multiplicity ratio in intermediate energy central heavy-ion collisions has been proposed as a suitable observable to constrain the high density dependence of the isovector part of the equation of state, with contradicting results. Using an upgraded version of the T\\"ubingen QMD transport model, which allows the conservation of energy at a local or global level by accounting for the potential energy of hadrons in two-body collisions and leading thus to particle production threshold shifts, we demonstrate that compatible constraints for the symmetry energy stiffness can be extracted from pion multiplicity and elliptic flow observables. Nevertheless, pion multiplicities are proven to be highly sensitive to the yet unknown isovector part of the in-medium $\\Delta$(1232) potential which hinders presently the extraction of meaningful information on the high density dependence of the symmetry energy. A solution to this problem together with the inclusion of contributions presently neglected, such as ...
Symmetries and singularities of the Szekeres system
Energy Technology Data Exchange (ETDEWEB)
Paliathanasis, Andronikos, E-mail: anpaliat@phys.uoa.gr [Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia (Chile); Institute of Systems Science, Durban University of Technology, POB 1334, Durban 4000 (South Africa); Leach, P.G.L., E-mail: leach.peter@ucy.ac.cy [Department of Mathematics and Institute of Systems Science, Research and Postgraduate Support, Durban University of Technology, POB 1334, Durban 4000 (South Africa); School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa)
2017-04-18
Highlights: • Lagrangian formalism of the Szekeres system. • Symmetries and conservation laws for the silent universe. • Comparison of stability analysis of special solutions with the Laurent expansion provided by the singularity analysis. - Abstract: The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits a Lagrangian and the conservation laws that we find can be derived by the application of Noether's theorem. The stability for the special solutions of the Szekeres system is studied and it is related with the Left or Right Painlevé Series which describes the expansions.
Miller, G A
2003-01-01
Two new experiments have detected charge-symmetry breaking, the mechanism responsible for protons and neutrons having different masses. Symmetry is a crucial concept in the theories that describe the subatomic world because it has an intimate connection with the laws of conservation. The theory of the strong interaction between quarks - quantum chromodynamics - is approximately invariant under what is called charge symmetry. In other words, if we swap an up quark for a down quark, then the strong interaction will look almost the same. This symmetry is related to the concept of sup i sospin sup , and is not the same as charge conjugation (in which a particle is replaced by its antiparticle). Charge symmetry is broken by the competition between two different effects. The first is the small difference in mass between up and down quarks, which is about 200 times less than the mass of the proton. The second is their different electric charges. The up quark has a charge of +2/3 in units of the proton charge, while ...
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.
Non-Noetherian symmetries for oscillators in classical mechanics and in field theory
Hojman, Sergio A.; Delajara, Jamie; Pena, Leda
1995-01-01
Infinitely many new conservation laws both for free fields as well as for test fields evolving on a given gravitational background are presented. The conserved currents are constructed using the field theoretical counterpart of a recently discovered non-Noetherian symmetry which gives rise to a new way of solving the classical small oscillations problem. Several examples are discussed.
Institute of Scientific and Technical Information of China (English)
张毅; 陈甦
2005-01-01
The effects of non-conservative forces and nonholonomic constraints on Noether symmetries and conserved quantities of a Hamilton system are studied. When non-conservative forces or nonholonomic constraints are exerted on a Hamilton system,the Noether symmetries and the conserved quantities of the system may vary. It can be seen that some Noether symmetries disappear, some new Noether symmetries emerge, and under certain conditions some Noether symmetries will still remain. In this paper, the conditions under which the Noether symmetries and the conserved quantities of the system will remain are respectively obtained, and two examples are given to illustrate the application of the results.%研究非保守力和非完整约束对Hamilton系统的Noether对称性的影响.Hamilton系统受到非保守力或非完整约束作用时,系统的Noether对称性和守恒量都会发生变化.原有的一些Noether对称性消失了,一些新的Noether对称性产生了,在一定条件下,一些Noether对称性仍保持不变.文中分别给出了系统的Noether对称性以及守恒量保持不变的条件,并举例说明结果的应用.
Directional Diffusion Regulator (DDR) for some numerical solvers of hyperbolic conservation laws
Jaisankar, S.; Sheshadri, T. S.
2013-01-01
A computational tool called "Directional Diffusion Regulator (DDR)" is proposed to bring forth real multidimensional physics into the upwind discretization in some numerical schemes of hyperbolic conservation laws. The direction based regulator when used with dimension splitting solvers, is set to moderate the excess multidimensional diffusion and hence cause genuine multidimensional upwinding like effect. The basic idea of this regulator driven method is to retain a full upwind scheme across local discontinuities, with the upwind bias decreasing smoothly to a minimum in the farthest direction. The discontinuous solutions are quantified as gradients and the regulator parameter across a typical finite volume interface or a finite difference interpolation point is formulated based on fractional local maximum gradient in any of the weak solution flow variables (say density, pressure, temperature, Mach number or even wave velocity etc.). DDR is applied to both the non-convective as well as whole unsplit dissipative flux terms of some numerical schemes, mainly of Local Lax-Friedrichs, to solve some benchmark problems describing inviscid compressible flow, shallow water dynamics and magneto-hydrodynamics. The first order solutions consistently improved depending on the extent of grid non-alignment to discontinuities, with the major influence due to regulation of non-convective diffusion. The application is also experimented on schemes such as Roe, Jameson-Schmidt-Turkel and some second order accurate methods. The consistent improvement in accuracy either at moderate or marked levels, for a variety of problems and with increasing grid size, reasonably indicate a scope for DDR as a regular tool to impart genuine multidimensional upwinding effect in a simpler framework.
Energy Technology Data Exchange (ETDEWEB)
1976-08-01
Construction is under way on a new University of Minnesota Law School Building, whose distinctive features include a stepped design on its southern elevation and an earth-covered roof to promote energy conservation. The design is described with emphasis on the library facilities. Energy conservation was a major design factor. The portion of the earth-covered roof will be 15 inches thick planted with low ground-cover vegetation. Overall ..mu.. value of the building envelope will be 0.11. (MCW)
Systematic Derivation of Noether Point Symmetries in Special Relativistic Field Theories
Haas, Fernando
2016-01-01
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined.
Directory of Open Access Journals (Sweden)
Victor Nikolaevich Pervushin
2015-01-01
Full Text Available The aim of the investigation is to show a role of principles of symmetry of the initial data in formation of the consistent physical theory in a context of the newest advances in cosmology and physics of elementary particles.Methods. Methodological problems of modernity are considered on the basis of the retrospective analysis of physical theories, history of theology, comparison and generalisation of knowledge, the facts and positions from scientific, philosophical and religious spheres.Results and scientific novelty. The problems of consistency and completeness of scientific knowledge and convergence of the maintenance of religious texts and the observant scientific data in the physics and cosmology are discussed by the example of modern cosmologic models of the description of the Universe. It is proved that such convergence is claimed and actual not only concerning classification of physical processes in the Universe, including its origin from vacuum, but also in area of ontology and at forming of logics of scientific researches.Former and newest scientific achievements in the physics and cosmology are reinterpreted in a context of Hilbert geometrodynamics, added with a choice of relative standards of lengths and principles measurement of conformal symmetry.Practical significance. The author sees the further prospect of development of the scientific theory in a priority of conformal symmetry of a totality of any initial research data. So, in accordance with conformal symmetry, elementary objects of space-time are twistors that mathematically equivalent to cubits or to quantum generalisations of bits – information units. The general theory of knowledge eventually conducts to the fundamental theory of the information which, probably, will accept the name of quantum informodynamics, by analogy with quantum chromodynamics.
Optical chirality in gyrotropic media: symmetry approach
Proskurin, Igor; Ovchinnikov, Alexander S.; Nosov, Pavel; Kishine, Jun-ichiro
2017-06-01
We discuss optical chirality in different types of gyrotropic media. Our analysis is based on the formalism of nongeometric symmetries of Maxwell’s equations in vacuum generalized to material media with given constituent relations. This approach enables us to directly derive conservation laws related to nongeometric symmetries. For isotropic chiral media, we demonstrate that like a free electromagnetic field, both duality and helicity generators belong to the basis set of nongeometric symmetries that guarantees the conservation of optical chirality. In gyrotropic crystals, which exhibit natural optical activity, the situation is quite different from the case of isotropic media. For light propagating along a certain crystallographic direction, there arises two distinct cases: (1) the duality is broken but the helicity is preserved, or (2) only the duality symmetry survives. We show that the existence of one of these symmetries (duality or helicity) is enough to define optical chirality. In addition, we present examples of low-symmetry media, where optical chirality cannot be defined.
Bliokh, K Yu; Bliokh, Yu P
2007-06-01
We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov-Imbert transverse shifts of the centers of gravity of the reflected and refracted beams are calculated. Our results differ in the general case from those derived previously by other authors. In particular, they obey general conservation law for the beams' total angular momentum but do not obey one-particle conservation laws for individual photons, which have been proposed by [Onoda Phys. Rev. Lett. 93, 083901 (2004)]. We ascertain that these circumstances relate to the artificial model accepted in the literature for the polarized beam; this model does not fit to real beams. The present paper resolves the recent controversy and confirms the results of our previous paper [Bliokh Phys. Rev. Lett. 96, 073903 (2006)]. In addition, a diffraction effect of angular transverse shifts of the reflected and refracted beams is described.
Blachère, F.; Turpault, R.
2016-06-01
The objective of this work is to design explicit finite volumes schemes for specific systems of conservations laws with stiff source terms, which degenerate into diffusion equations. We propose a general framework to design an asymptotic preserving scheme, that is stable and consistent under a classical hyperbolic CFL condition in both hyperbolic and diffusive regime, for any two-dimensional unstructured mesh. Moreover, the scheme developed also preserves the set of admissible states, which is mandatory to keep physical solutions in stiff configurations. This construction is achieved by using a non-linear scheme as a target scheme for the diffusive equation, which gives the form of the global scheme for the complete system of conservation laws. Numerical results are provided to validate the scheme in both regimes.
Institute of Scientific and Technical Information of China (English)
杨小舟
2005-01-01
@@ 1 Introduction and Main Results For Riemann problem in n(n ≥ 3) dimensional(n-D) conservation laws, dimension of equations can beonly reduced one dimension by applying self-similar approach, so transformed equations are at least two dimensional (2D) equations which are also very hard although some pioneer works have been done in References [1-3]. Additionally as generalization of Riemann data, n-D Riemann data are set as constant states in different octants under self-silimar transformation,so many complicated cases of wave interacton will happen. So except some symmetric situations that can be reduced to one dimensional cases, there are rare theoretical results for n-D conservation laws.
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.
Singh, Manjit; Gupta, R. K.
2016-08-01
Based on binary Bell polynomial approach, the bilinear equation and B a ¨cklund transformations for (3+1)-dimensional Jimbo-Miwa equation are obtained. By virtue of Cole-Hopf transformation, Lax system is constructed by direct linearization of coupled system of binary Bell polynomials. Furthermore, infinite conservation laws are obtained from two field condition in quick and natural way. Finally, a test function of extended three wave method is used to construct multisoliton solutions via bilinear equation.
The origin of order in random matrices with symmetries
Johnson, Calvin W
2012-01-01
From Noether's theorem we know symmetries lead to conservation laws. What is left to nature is the ordering of conserved quantities; for example, the quantum numbers of the ground state. In physical systems the ground state is generally associated with `low' quantum numbers and symmetric, low-dimensional irreps, but there is no \\textit{a priori} reason to expect this. By constructing random matrices with nontrivial point-group symmetries, I find the ground state is always dominated by extremal low-dimensional irreps. Going further, I suggest this explains the dominance of J=0 g.s. even for random two-body interactions.
Power Law Behavior of the Zero Bias Tunneling Conductance: the New Evidence for d-Wave Symmetry
Institute of Scientific and Technical Information of China (English)
LI Shao-Xiong; TAO Hong-Jie; XUAN Yi; ZHAO Bai-Ru; ZHAO Zhong-Xian
2000-01-01
We report temperature-dependent behavior of the zero bias tunneling conductance (ZBTC), derived from tun neling spectroscopies on as-grown Bi2Sr2CaCu2O8+5 (Bi2212) single crystals taken with evaporated Zn and Pb planar junctions. At Tc the measured ZBTC shows a kink which gives an in situ measure of the superconducting transition temperature (Tc). Below Tc, the T2 dependence of the ZBTC has been observed repeatedly as a new evidence of the d-wave symmetry in Bi2212.
Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi
2017-05-01
This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.
Directory of Open Access Journals (Sweden)
Hendrik Schoukens
2014-05-01
Full Text Available For years, the predicament of many of the European protected habitats and species in the Flemish Region, as in many other Member States, passed relatively unnoticed. The lack of proper rules and clear implementation rules fuelled the impression amongst project developers and planning authorities that the impacts of project developments on biodiversity did not really warrant closer assessment. However, in the past ten years, strict national case law has significantly altered this view. Faced with tighter judicial scrutiny, the Habitats and Birds Directives were seen as an important obstacle to project development. Hence mitigation and compensation have now come up as novel approaches to better align spatial aspirations with the conservation of nature. In reality, mitigation was often used as a cover-up for projects that would not fit the strict requirements enshrined in the derogatory clauses. Interestingly, the Belgian Council of State showed itself quite cautious in reasserting the lax view of some planning authorities on mitigation and compensation. In reviewing the legality of several new approaches to mitigation and compensation, the Belgian Council of State, which was initially very cautious in quashing decisions that would actually jeopardise major infrastructure developments, has rendered some compelling rulings on the specific application of mitigation and compensatory measures in a spatial planning context. By letting the objectives of EU nature conservation law prevail in the face of economic interests, the recent case law of the Belgian Council of State can be seen as a remarkable example of judicial environmental activism.
Relabeling symmetry in relativistic fluids and plasmas
Kawazura, Yohei; Fukumoto, Yasuhide
2014-01-01
The conservation of the recently formulated relativistic canonical helicity [Yoshida Z, Kawazura Y, and Yokoyama T 2014 J. Math. Phys. 55 043101] is derived from Noether's theorem by constructing an action principle on the relativistic Lagrangian coordinates (we obtain general cross helicities that include the helicity of the canonical vorticity). The conservation law is, then, explained by the relabeling symmetry pertinent to the Lagrangian label of fluid elements. Upon Eulerianizing the Noether current, the purely spatial volume integral on the Lagrangian coordinates is mapped to a space-time mixed three-dimensional integral on the four-dimensional Eulerian coordinates. The relativistic conservation law in the Eulerian coordinates is no longer represented by any divergence-free current; hence, it is not adequate to regard the relativistic helicity (represented by the Eulerian variables) as a Noether charge, and this stands the reason why the "conventional helicity" is no longer a constant of motion. We have...
Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System
Institute of Scientific and Technical Information of China (English)
FANGJian-Hui
2003-01-01
The Mei symmetry and the Lie symmetry of a rotational relativistic variable mass system are studied. The definitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system are given. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.
Noether Symmetry Analysis of the Dynamic Euler-Bernoulli Beam Equation
Johnpillai, A. G.; Mahomed, K. S.; Harley, C.; Mahomed, F. M.
2016-05-01
We study the fourth-order dynamic Euler-Bernoulli beam equation from the Noether symmetry viewpoint. This was earlier considered for the Lie symmetry classification. We obtain the Noether symmetry classification of the equation with respect to the applied load, which is a function of the dependent variable of the underlying equation. We find that the principal Noether symmetry algebra is two-dimensional when the load function is arbitrary and extends for linear and power law cases. For all cases, for each of the Noether symmetries associated with the usual Lagrangian, we construct conservation laws for the equation via the Noether theorem. We also provide a basis of conservation laws by using the adjoint algebra. The Noether symmetries pick out the special value of the power law, which is -7. We consider the Noether symmetry reduction for this special case, which gives rise to a first integral that is used for our numerical code. For this, we then find numerical solutions using an in-built function in MATLAB called bvp4c, which is a boundary value solver for differential equations that are depicted in five figures. The physical solutions obtained are for the deflection of the beam with an increase in displacement. These are given in four figures and discussed.
Directory of Open Access Journals (Sweden)
Johann C Knobel
2014-12-01
Full Text Available This contribution reflects on the contributory role of environmental law and policy in the successful conservation interventions on behalf of the rare Spanish Imperial Eagle (Aquila Adalberti, with the aim of gaining insights that may be more universally applicable, including in jurisdictions such as South Africa. An overview of applicable international, European and Spanish laws and policies is given, and the role played by these instruments is considered together with successes attained with diverse conservation goals in respect of the Spanish Imperial Eagle. The exceptionally comprehensive character of the legal protection of the Spanish Imperial Eagle is highlighted, in conjunction with some extra-legal factors that have contributed to successful outcomes. While quantification of the role of the law in the conservation of a species remains elusive, it is probably safe to conclude that environmental law and policy have played a vital and central role in the improvement of the conservation status of the Spanish Imperial Eagle. It is submitted that the conservation interventions on behalf of the Spanish Imperial Eagle show that concerted legal and other conservation interventions can effectively halt and reverse the decline of an endangered species. However, such interventions are onerous and expensive and ideally, effective conservation measures should be in place before populations have declined to a critical level. Birds of prey face similar threats in South Africa and Spain, and a number of South African raptor species will soon be classified as endangered. While South African biodiversity laws and policy are similar to the European and Spanish laws in general import and methodology, the South African laws and policy are more restricted in scope, less detailed and less prescriptive. When comparing the use of Spanish and South African legislation in the conservation of birds of prey, sight must not be lost of the varying conservation needs
Zahr, M. J.; Persson, P.-O.
2016-12-01
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high-order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsulates the domain deformation and parametrization, resulting in an Arbitrary Lagrangian-Eulerian form of the governing equations. A high-order discontinuous Galerkin method is used to discretize the transformed equation in space and a high-order diagonally implicit Runge-Kutta scheme is used for the temporal discretization. Quantities of interest that take the form of space-time integrals are discretized in a solver-consistent manner. The corresponding fully discrete adjoint method is used to compute exact gradients of quantities of interest along the manifold of solutions of the fully discrete conservation law. These quantities of interest and their gradients are used in the context of gradient-based PDE-constrained optimization. The adjoint method is used to solve two optimal shape and control problems governed by the isentropic, compressible Navier-Stokes equations. The first optimization problem seeks the energetically optimal trajectory of a 2D airfoil given a required initial and final spatial position. The optimization solver, driven by gradients computed via the adjoint method, reduced the total energy required to complete the specified mission nearly an order of magnitude. The second optimization problem seeks the energetically optimal flapping motion and time-morphed geometry of a 2D airfoil given an equality constraint on the x-directed impulse generated on the airfoil. The optimization solver satisfied the impulse constraint to greater than 8 digits of accuracy and reduced the required energy between a factor of 2 and 10, depending on the value of the impulse constraint, as compared to the nominal configuration.
Directory of Open Access Journals (Sweden)
M.D. Cozma
2016-02-01
Full Text Available The charged pion multiplicity ratio in intermediate energy central heavy-ion collisions has been proposed as a suitable observable to constrain the high density dependence of the isovector part of the equation of state. A comparison of various transport model predictions with existing experimental data has led, however, to contradictory results. Using an upgraded version of the Tübingen QMD transport model, which allows the conservation of energy at a local or global level by accounting for the potential energy of hadrons in two-body collisions and leading thus to particle production threshold shifts, we demonstrate that compatible constraints for the symmetry energy stiffness can be extracted from pion multiplicity and elliptic flow observables. However, pion multiplicities and ratios are proven to be highly sensitive to the yet unknown isovector part of the in-medium Δ(1232 potential which hinders, at present, the extraction of meaningful information on the high density dependence of the symmetry energy. A solution to this problem together with the inclusion of contributions presently neglected, such as in-medium pion potentials and retardation effects, are needed for a final verdict on this topic.
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.
Nikulov, A V
2009-01-01
Superconducting loop interrupted by one or three Josephson junctions is considered in many publications as a possible quantum bit, flux qubit, which can be used for creation of quantum computer. But the assumption on superposition of two macroscopically distinct quantum states of superconducting loop contradict to the fundamental law of angular momentum conservation and the universally recognized quantum formalism. Numerous publications devoted to the flux qubit testify to an inadequate interpretation by many authors of paradoxical nature of superposition principle and the subject of quantum description.
Coron, Jean-Michel; Ervedoza, Sylvain; Ghoshal, Shyam Sundar; Glass, Olivier; Perrollaz, Vincent
2017-01-01
In this article, we investigate the BV stability of 2 × 2 hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions. More precisely, we derive sufficient conditions guaranteeing the exponential stability of the system under consideration for entropy solutions in BV. Our proof is based on a front tracking algorithm used to construct approximate piecewise constants solutions whose BV norms are controlled through a Lyapunov functional. This Lyapunov functional is inspired by the one proposed in J. Glimm's seminal work [16], modified with some suitable weights in the spirit of the previous works [9,10].
Institute of Scientific and Technical Information of China (English)
Zhigang WANG; Yachun LI
2012-01-01
The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where ris the size of artificial viscosity.
D'Apice, Ciro; Kogut, Peter I.
2017-07-01
We discuss the optimal control problem stated as the minimization in the L2-sense of the mismatch between the actual out-flux and a demand forecast for a hyperbolic conservation law that models a highly re-entrant production system. The output of the factory is described as a function of the work in progress and the position of the so-called push-pull point (PPP) where we separate the beginning of the factory employing a push policy from the end of the factory, which uses a pull policy.
McCann, Stewart J H
2011-01-01
The present study was conducted to determine whether individual-level correlates of sexual prejudice (i.e., conservatism-liberalism, religious fundamentalism, educational levels, urbanism, income, and living in the South) are predictive at the state level of laws restricting homosexual behaviors and desires. Criterion 1 was a multifaceted index of state laws concerning gay men and lesbians; Criterion 2 was an index of state laws regarding same-sex partnerships. Multiple regression strategies showed that state conservatism-liberalism, as determined from the responses of 141,798 individuals aggregated at the state level (Erikson, Wright, & McIver, 1993), was the prime state-level predictor of both criteria. For Criterion 1, only Southern state status accounted for additional variance (4.2%) above the 54.8% already accounted for by conservatism-liberalism. For Criterion 2, no other variables accounted for variance beyond the 44.6% accounted for by state conservatism-liberalism.
Noether symmetries of discrete mechanico-electrical systems
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Ben-Yong; Xie Feng-Ping
2008-01-01
This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems.Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.
Rossani, A.
2016-11-01
If electrons (e) and holes (h) in metals or semiconductors are heated to the temperatures Te and Th greater than the lattice temperature Tp, the electron-phonon interaction causes energy relaxation. In the nonuniform case, a momentum relaxation occurs as well. In view of such an application, a new model based on an asymptotic procedure for solving the kinetic equations of carriers and phonons is proposed, with generation-recombination of electrons and holes, which gives naturally the displaced Maxwellian at the leading order. After that, balance equations for the electron number, hole number, energy densities, and momentum densities are constructed, which constitute now a system of eight equations for the chemical potentials (carriers), the temperatures (carriers and phonons), and the drift velocities (carriers and phonons). In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered.
Chang, Sin-Chung; To, Wai-Ming
1992-01-01
A new numerical method for solving conservation laws is being developed. It differs substantially from the well established methods, i.e., finite difference, finite volume, finite element, and spectral methods, in both concept and methodology. It is much simpler than a typical high resolution method. No flux limiter or any technique related to characteristics is involved. No artificial viscosity or smoothing is introduced, and no moving mesh is used. Yet this method is capable of generating highly accurate shock tube solutions. The slight numerical overshoot and/or oscillations generated can be removed if a simple averaging formula initially used is replaced by a weighted formula. This modification has little effect on other parts of the solution. Because of its simplicity, generalization of this new method for multi-dimensional problems is straightforward.
Equilibrium gas flow computations. II - An analysis of numerical formulations of conservation laws
Vinokur, Marcel; Liu, Yen
1988-01-01
Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, equilibrium gas laws. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer flux-vector splittings, and Roe's approximate Riemann solver are presented for three-dimensional, time-varying grids. The approximations inherent in previous generalizations are discussed.
Higher derivative extensions of 3d Chern-Simons models: conservation laws and stability
Energy Technology Data Exchange (ETDEWEB)
Kaparulin, D.S.; Karataeva, I.Yu.; Lyakhovich, S.L. [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)
2015-11-15
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.)
Taking about the Derivation Method on Law of Conservation of Momentum%浅谈动量守恒定律的导出方式
Institute of Scientific and Technical Information of China (English)
张悦; 冯杰
2016-01-01
The law of conservation of momentum is com mon in the nature of law and has a broad application field , applies not only to macroscopic movement of the object ,also apply to the micro field . In current textbooks of most , however ,are all derived from Newton′s second law and the law of Newton′s third law of conservation of momentum ,it can make people ignore other export momentum conservation .This paper tries to expound several different ways of export of conservation of momentum ,strengthen the awareness of the law of conservation of momentum and the application .%动量守恒定律是自然界中最普遍的定律并有着广泛的应用领域，不仅适用于宏观物体的运动，同样适用于微观领域。不过，在目前的大多数教材中，都是由牛顿第二定律和牛顿第三定律导出动量守恒定律的，那么就会让人们忽略动量守恒定律的其他导出方式。试图阐述动量守恒的几种不同导出方式，强化对动量守恒定律的认识和应用。
Universal Symmetry of Complexity and Its Manifestations at Different Levels of World Dynamics
Kirilyuk, A P
2004-01-01
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived, universal definitions of randomness, probability, chaoticity, complexity, fractality, self-organisation, and other properties, extending their axiomatic introduction in the conventional, dynamically single-valued (unitary) theory (physics/9806002, physics/0211071). Any real system emergence, structure, and behaviour can be expressed now by the universal law of conservation, or symmetry, of complexity that unifies extended versions of any (correct) symmetry, law, or "principle". Both the observed world structure and its unreduced dynamics result from that universal, unique symmetry, instead of formal imposition of separated, broken and simplified symmetries upon the existing, postulated structures in the unitary world "model". Whereas any unitary "symmetry" is regular and therefore ...
On the Form of Local Conservation Laws for some Relativistic Field Theories in $1+1$ Dimensions
Höhler, E G B
1994-01-01
We investigate the possible form of local translation invariant conservation laws associated with the relativistic field equations \\partial\\bar\\partial\\phi_i=-v_i(\\bphi) for a multicomponent field \\bphi. Under the assumptions that (i)~the v_i's can be expressed as linear combinations of partial derivatives \\partial w_j/\\partial\\phi_k of a set of functions w_j(\\bphi), (ii)~the space of functions spanned by the w_j's is closed under partial derivations, and (iii)~the fields \\bphi take values in a simply connected space, the local conservation laws can either be transformed to the form \\partial{\\bar{\\cal P}}=\\bar\\partial\\sum_j w_j {\\cal Q}_j (where \\bar{\\cal P} and {\\cal Q}_j are homogeneous polynomials in the variables \\bar\\partial\\phi_i, \\bar\\partial^2\\phi_i,\\ldots), or to the parity transformed version of this expression \\partial\\equiv(\\partial_ t+\\partial_x)/ \\sqrt{2}\\rightleftharpoons\\bar\\partial \\equiv (\\partial_t-\\partial_ x)/\\sqrt{2}.
Evaluation of the Learning Process of Students Reinventing the General Law of Energy Conservation
Logman, Paul; Kaper, Wolter; Ellermeijer, Ton
2015-01-01
To investigate the relationship between context and concept we have constructed a conceptual learning path in which students reinvent the concept of energy conservation and embedded this path in two authentic practices. A comparison of the expected learning outcome with actual student output for the most important steps in the learning path gives…
Some remarks on the definition of classical energy and its conservation laws
Arminjon, Mayeul
2015-01-01
In classical non-relativistic theories, there is an exact local conservation equation for the energy, having the form of the continuity equation for mass conservation, and this equation occurs from the power equation. We illustrate this by the example of Newtonian gravity for self-gravitating elastic bodies. In classical special-relativistic theories, there is also an exact local conservation equation for the energy, though it comes from the definition of the energy-momentum tensor. We then study that definition in a general spacetime: Hilbert's variational definition is briefly reviewed, with emphasis on the boundary conditions. We recall the difference between the local equation verified by Hilbert's tensor T in a curved spacetime and the true local conservation equations discussed before. We ask if the addition of a total divergence may change T and find that the usual formula giving T is not generally valid when the matter Lagrangian depends on the derivatives of the metric. We end with a result proving u...
Conservation of energy and momentum in nonrelativistic plasmas
Energy Technology Data Exchange (ETDEWEB)
Sugama, H.; Watanabe, T.-H. [National Institute for Fusion Science, Toki 509-5292 (Japan); Graduate University for Advanced Studies, Toki 509-5292 (Japan); Nunami, M. [National Institute for Fusion Science, Toki 509-5292 (Japan)
2013-02-15
Conservation laws of energy and momentum for nonrelativistic plasmas are derived from applying Noether's theorem to the action integral for the Vlasov-Poisson-Ampere 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-Ampere system.
On the Hojman conservation quantities in Cosmology
Paliathanasis, A.; Leach, P. G. L.; Capozziello, S.
2016-04-01
We discuss the application of the Hojman's Symmetry Approach for the determination of conservation laws in Cosmology, which has been recently applied by various authors in different cosmological models. We show that Hojman's method for regular Hamiltonian systems, where the Hamiltonian function is one of the involved equations of the system, is equivalent to the application of Noether's Theorem for generalized transformations. That means that for minimally-coupled scalar field cosmology or other modified theories which are conformally related with scalar-field cosmology, like f (R) gravity, the application of Hojman's method provide us with the same results with that of Noether's Theorem. Moreover we study the special Ansatz. ϕ (t) = ϕ (a (t)) , which has been introduced for a minimally-coupled scalar field, and we study the Lie and Noether point symmetries for the reduced equation. We show that under this Ansatz, the unknown function of the model cannot be constrained by the requirement of the existence of a conservation law and that the Hojman conservation quantity which arises for the reduced equation is nothing more than the functional form of Noetherian conservation laws for the free particle. On the other hand, for f (T) teleparallel gravity, it is not the existence of Hojman's conservation laws which provide us with the special function form of f (T) functions, but the requirement that the reduced second-order differential equation admits a Jacobi Last multiplier, while the new conservation law is nothing else that the Hamiltonian function of the reduced equation.
Lompay, Robert R
2013-01-01
Arbitrary diffeomorphically invariant metric-torsion theories of gravity are considered. It is assumed that Lagrangians of such theories contain derivatives of field variables (tensor densities of arbitrary ranks and weights) up to a second order only. The generalized Klein-Noether methods for constructing manifestly covariant identities and conserved quantities are developed. Manifestly covariant expressions are constructed without including auxiliary structures like a background metric. In the Riemann-Cartan space, the following \\emph{manifestly generally covariant results} are presented: (a) The complete generalized system of differential identities (the Klein-Noether identities) is obtained. (b) The generalized currents of three types depending on an arbitrary vector field displacements are constructed: they are the canonical Noether current, symmetrized Belinfante current and identically conserved Hilbert-Bergmann current. In particular, it is stated that the symmetrized Belinfante current does not depen...
Higher moments of multiplicity fluctuations in a hadron-resonance gas with exact conservation laws
Fu, Jing-Hua
2016-01-01
Higher moments of multiplicity fluctuations of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the canonical ensemble. The conservation of three charges, baryon number, electric charge, and strangeness, is enforced in the large volume limit. Moments up to the forth order of various particles are calculated at SPS, RHIC and LHC energies. The asymptotic fluctuations within a simplified model with only one conserved charge in the canonical ensemble are discussed where simple analytical expressions for moments of multiplicity distribution can be obtained. Moments products of net-proton, net-kaon, and net-charge distributions in Au + Au collisions at RHIC energies are calculated and compared to the experimental measurements. The pseudo-rapidity coverage dependence of net-charge fluctuation is discussed.
Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui
2003-01-01
The Mei symmetry and the Lie symmetry of a rotational relativistic variable masssystem are studied. Thedefinitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system aregiven. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Meisymmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.
Continuous dependence estimate for conservation laws with Lévy noise
Biswas, Imran H.; Koley, Ujjwal; Majee, Ananta K.
2015-11-01
We are concerned with multidimensional stochastic balance laws driven by Lévy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the nonlinearities of the entropy solutions under the assumption that Lévy noise only depends on the solution. This result is used to show the error estimate for the stochastic vanishing viscosity method. In addition, we establish fractional BV estimate for vanishing viscosity approximations in case the noise coefficient depends on both the solution and spatial variable.
Similarity and symmetry methods applications in elasticity and mechanics of materials
Mladenov, Ivaïlo
2014-01-01
The principle aim of the book is to present a self-contained, modern account of similarity and symmetry methods, which are important mathematical tools for both physicists, engineers and applied mathematicians. The idea is to provide a balanced presentation of the mathematical techniques and applications of symmetry methods in mathematics, physics and engineering. That is why it includes recent developments and many examples in finding systematically conservation laws, local and nonlocal symmetries for ordinary and partial differential equations. The role of continuous symmetries in classical and quantum field theories is exposed at a technical level accessible even for non specialists. The importance of symmetries in continuum mechanics and mechanics of materials is highlighted through recent developments, such as the construction of constitutive models for various materials combining Lie symmetries with experimental data. As a whole this book is a unique collection of contributions from experts in the field...
Institute of Scientific and Technical Information of China (English)
郑世旺; 王建波; 陈向炜; 李彦敏; 解加芳
2012-01-01
航天器运行系统大都属于变质量力学系统,变质量力学系统的对称性和守恒量隐含着航天系统更深刻的物理规律.本文首先导出了变质量非完整力学系统的Tzénoff方程,然后研究了变质量非完整力学系统Tzénoff方程的Lie对称性及其所导出的守恒量,给出了这种守恒量的函数表达式和导出这种守恒量的判据方程.该研究结果对进一步探究变质量系统所遵循的守恒规律具有一定的理论价值.%The operational system of the spacecraft is general a variable mass one,of which the symmetry and the conserved quantity imply physical rules of the space system.In this paper,Tzénoff equations of the variable mass nonholonomic system are derived,from which the Lie symmetries of Tzénoff equations for the variable mass nonholonomic system and conserved quantities are derived and are researched.The function expressions of conserved quantities and the criterion equations which deduce these conserved quantities are presented.This result has some theoretical value for further research of the conservation laws obeyed by the variable mass system.
Directory of Open Access Journals (Sweden)
Robin Margaret Warner
2014-05-01
Full Text Available As global shipping intensifies and technological advances provide more opportunities to access the resources of the high seas and the deep seabed beyond national jurisdiction (ABNJ, the catalogue of threats to the marine environment and its biodiversity increase commensurately. Beyond these threats, new and emerging uses of ABNJ including more intrusive marine scientific research, bio-prospecting, deep seabed mining and environmental modification activities to mitigate the effects of climate change have the potential to harm the highly interconnected and sensitive ecosystems of the open ocean and the deep seabed if not sustainably managed now and into the future. Modern conservation norms such as environmental impact assessment, marine protected areas, marine spatial planning and development mechanisms such as technology transfer and capacity building are under developed in the legal and institutional framework for ABNJ. This article examines key normative features of the legal and institutional framework for ABNJ and their applicability to conservation of marine biodiversity, gaps and disconnects in that framework and ongoing global initiatives to develop more effective governance structures. It discusses some of the options being considered in the UN Ad Hoc Informal Open-ended Working Group to study issues related to the conservation and sustainable use of marine biodiversity in areas beyond national jurisdiction (BBNJ Working Group to evolve the legal and institutional framework for conservation and sustainable use of marine biodiversity in ABNJ and their current and future relevance for the law of the sea. It concludes that the discussions in the BBNJ Working Group and related initiatives in the Convention on Biological Diversity (CBD and at regional level have demonstrated that a more integrated legal and institutional structure is needed to address growing threats to marine biodiversity in ABNJ.
Sugama, H.; Nunami, M.; Nakata, M.; Watanabe, T.-H.
2017-02-01
A novel gyrokinetic formulation is presented by including collisional effects into the Lagrangian variational principle to yield the governing equations for background and turbulent electromagnetic fields and gyrocenter distribution functions, which can simultaneously describe classical, neoclassical, and turbulent transport processes in toroidal plasmas with large toroidal flows on the order of the ion thermal velocity. Noether's theorem modified for collisional systems and the collision operator given in terms of Poisson brackets are applied to derivation of the particle, energy, and toroidal momentum balance equations in the conservative forms, which are desirable properties for long-time global transport simulation.
Bulíček, Miroslav; Gwiazda, Piotr; Świerczewska-Gwiazda, Agnieszka
2017-01-01
We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelty of the paper is the introduction of a kinetic formulation for the considered problem. To handle the discontinuities we work in the framework of re-parametrization of the flux and the source functions, which was previously used for Kružkov entropy solutions. Within this approach we obtain a fairly complete picture: existence of entropy measure valued solutions, entropy weak solutions and their equivalence to the kinetic solution. The results of existence and uniqueness follow under the assumption of Hölder continuity at zero of the flux. The source term, what is another novelty for the studies on problems with discontinuous flux, is only assumed to be one-side Lipschitz, not necessarily monotone function.
Auluck, S K H
2014-01-01
Experimental data compiled over five decades of dense plasma focus research is consistent with the snowplow model of sheath propagation, based on the hypothetical balance between magnetic pressure driving the plasma into neutral gas ahead and wind pressure resisting its motion. The resulting sheath velocity, or the numerically proportional drive parameter, is known to be approximately constant for devices optimized for neutron production over 8 decades of capacitor bank energy. This paper shows that the validity of the snowplow hypothesis, with some correction, as well as the non-dependence of sheath velocity on device parameters, have their roots in local conservation laws for mass, momentum and energy coupled with the ionization stability condition. Both upper and lower bounds on sheath velocity are shown to be related to material constants of the working gas and independent of the device geometry and capacitor bank impedance.
Auluck, S. K. H.
2014-09-01
Experimental data compiled over five decades of dense plasma focus research are consistent with the snowplow model of sheath propagation, based on the hypothetical balance between magnetic pressure driving the plasma into neutral gas ahead and "wind pressure" resisting its motion. The resulting sheath velocity, or the numerically proportional "drive parameter," is known to be approximately constant for devices optimized for neutron production over 8 decades of capacitor bank energy. This paper shows that the validity of the snowplow hypothesis, with some correction, as well as the non-dependence of sheath velocity on device parameters, have their roots in local conservation laws for mass, momentum, and energy coupled with the ionization stability condition. Both upper and lower bounds on sheath velocity are shown to be related to material constants of the working gas and independent of the device geometry and capacitor bank impedance.
Albeverio, S; Shelkovich, V M
2011-01-01
We introduce integral identities to define delta-shock wave type solutions for the multidimensional zero-pressure gas dynamics Using these integral identities, the Rankine-Hugoniot conditions for delta-shocks are obtained. We derive the balance laws describing mass, momentum, and energy transport from the area outside the delta-shock wave front onto this front. These processes are going on in such a way that the total mass, momentum, and energy are conserved and at the same time mass and energy of the moving delta-shock wave front are increasing quantities. In addition, the total kinetic energy transfers into the total internal energy. The process of propagation of delta-shock waves is also described. These results can be used in modeling of mediums which can be treated as a {pressureless continuum} (dusty gases, two-phase flows with solid particles or droplets, granular gases).
Polettini, Matteo
2014-01-01
In this and a companion paper 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 to nonvanishing affinities, whose symmet...
Directory of Open Access Journals (Sweden)
Nixon Sifuna
2006-06-01
Full Text Available Under Kenyan law, the provisioning for eminent domain is in the Constitution, as well as in legislation. Exercising these powers, the State may compulsorily acquire private lands, provided the acquisition is for a public good and compensation is given. Generally, eminent domain is a fairly contentious legal issue: the law on the one part guarantees the sanctity of private property and, on the other, allows the government to expropriate such property even against the will of the landowner. With regard to land, the State has a legal obligation to respect and protect privately owned lands, and a corresponding moral obligation to ensure that land is available to sustain other forms of life as well. While Kenya's wildlife estate is slightly less than eight per cent of the total land area, it is fast shrinking due to an increasing human population and human activities. As such, the wildlife sector has a bleak future unless the trend is reversed. One way of doing this is by using the powers of eminent domain to acquire private lands for purposes of creating and expanding the wildlife protected areas and their support zones. However, for this manner of acquisition to be desirable and advisable, it has to be fair, humane, democratic and honest. This is to ensure that conservation does not violate the rights of people or undermine livelihoods. Incidentally, the process of eminent domain in Kenya is bereft of these attributes and tends to be draconian and militaristic. The paper critically examines the potential of using eminent domain for acquiring lands for protected area conservation and makes recommendations for reforms.
Powell, B J
2015-01-01
There is longstanding fundamental interest in 6-fold coordinated $d^6$ ($t_{2g}^6$) transition metal complexes such as [Ru(bpy)$_3$]$^{2+}$ and Ir(ppy)$_3$, particularly their phosphorescence. This interest has increased with the growing realisation that many of these complexes have potential uses in applications including photovoltaics, imaging, sensing, and light-emitting diodes. In order to design new complexes with properties tailored for specific applications a detailed understanding of the low-energy excited states, particularly the lowest energy triplet state, $T_1$, is required. Here we describe a model of pseudo-octahedral complexes based on a pseudo-angular momentum representation and show that the predictions of this model are in excellent agreement with experiment - even when the deviations from octahedral symmetry are large. This model gives a natural explanation of zero-field splitting of $T_1$ and of the relative radiative rates of the three sublevels in terms of the conservation of time-revers...
Solutions in the large for some nonlinear hyperbolic conservation laws of gas dynamics
Temple, J. B.
1980-03-01
The constraints under which a gas at a certain state will evolve can be given by three partial differential equations which express the conservation of mass, momentum, and energy. A particular energy function was discovered for which there is a global weak solution for bounded measurable data having finite total variation. This energy function models an ideal gas, and is given by the formula e = - lambda eta V + (S/R). The following general existence theorem is also obtained: let e sub epsilon (v,S) be any smooth one parameter family of energy functions such that at epsilon = 0 the energy is given by e (v,S) = - lambda eta V + (S/R). It is proven that there exists a constant C independent of epsilon, such that, if the total variation of the inertial data C, then there exists a global weak solution to the equations. An existence theorem for polytropic gases was also obtained.
Ismail, Farzad; Chizari, Hossain
2017-02-01
This paper presents preliminary developments of entropy-stable residual distribution methods for scalar problems. Controlling entropy generation is achieved by formulating an entropy conserved signals distribution coupled with an entropy-stable signals distribution. Numerical results of the entropy-stable residual distribution methods are accurate and comparable with the classic residual distribution methods for steady-state problems. High order accurate extensions for the new method on steady-state problems are also demonstrated. Moreover, the new method preserves second order accuracy on unsteady problems using an explicit time integration scheme. The idea of the multi-dimensional entropy-stable residual distribution method is generic enough to be extended to the system of hyperbolic equations, which will be presented in the sequel of this paper.
Directory of Open Access Journals (Sweden)
Gooch Pernille
2009-01-01
Full Text Available The Van (forest Gujjars, surviving as forest pastoralists in the central part of the Indian Himalaya, are a people who, due to their nomadic lifestyle, have since colonial rule found themselves at the margin of Indian society. This paper will look at the relationship between the Van Gujjars and their forest base in a historical perspective from colonial rule to ′conservation of nature′ and the ′rights of forest dwellers′ and further discuss how changing codes and rules of power affect the society-citizen-nature / forest relationship for the community. We will look back into history and see how a system of strict control and regulation of Van Gujjars as nomadic pastoralists without a fixed address, initiated during colonial time, was continued by the national state of India after independence. We will further discuss how a history of unequal treatment and marginalisation of Van Gujjar pastoralists has continued into the present. What is manifest here is ′the forest′ as a contested space: a site of power struggles, where forest dwellers are threatened with displacement in order to provide space, first for modern forestry and revenue producing land, and later for conservation of nature. The paper further looks at the latest developments where the Van Gujjars now have obtained domicile rights such as voters′ rights and have been linked with Government services for education and health. It finishes by discussing the new possibilities and hopes for the community provided by the The Scheduled Tribes and Other Traditional Forest Dwellers (Recognition of Forest Rights Act.
Unified symmetry of Vacco dynamical systems
Institute of Scientific and Technical Information of China (English)
Li Yuan-Cheng; Jing Hong-Xing; Xia Li-Li; Wang Jing; Hou Qi-Bao
2007-01-01
Based on the total time derivative along the trajectory of the time, we study the unified symmetry of Vacco dynamical systems. The definition and the criterion of the unified symmetry for the system are given. Three kinds of conserved quantities, i.e. the Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity, are deduced from the unified symmetry. An example is presented to illustrate the results.
Orbital Motions and the Conservation-Law/Preferred-Frame α_3 Parameter
Iorio, Lorenzo
2014-09-01
We analytically calculate some orbital effects induced by the Lorentz-invariance/ momentum-conservation parameterized post-Newtonian (PPN) parameter α_3 in a gravitationally bound binary system made of a primary orbited by a test particle. We neither restrict ourselves to any particular orbital configuration nor to specific orientations of the primary's spin axis ψ. We use our results to put preliminary upper bounds on α_3 in the weak-field regime by using the latest data from Solar System's planetary dynamics. By linearly combining the supplementary perihelion precessions Δw of the Earth, Mars and Saturn, determined by astronomers with the Ephemerides of Planets and the Moon (EPM) 2011 ephemerides for the general relativistic values of the PPN parameters β = γ = 1, we infer |α_3| ;5 6 × 10^-10. Our result is about three orders of magnitude better than the previous weak-field constraints existing in the literature and of the same order of magnitude of the constraint expected from the future BepiColombo mission to Mercury. It is, by construction, independent of the other preferred-frame PPN parameters α1, α2, both preliminarily constrained down to a ≈ 10^-6 level. Future analyses should be performed by explicitly including α3 and a selection of other PPN parameters in the models fitted by the astronomers to the observations and estimating them in dedicated covariance analyses.
Alternating minimal energy approach to ODEs and conservation laws in tensor product formats
Dolgov, Sergey V
2014-01-01
We propose an algorithm for solution of high-dimensional evolutionary equations (ODEs and discretized time-dependent PDEs) in tensor product formats. The solution must admit an approximation in a low-rank separation of variables framework, and the right-hand side of the ODE (for example, a matrix) must be computable in the same low-rank format at a given time point. The time derivative is discretized via the Chebyshev spectral scheme, and the solution is sought simultaneously for all time points from the global space-time linear system. To compute the solution adaptively in the tensor format, we employ the Alternating Minimal Energy algorithm, the DMRG-flavored alternating iterative technique. Besides, we address the problem of maintaining system invariants inside the approximate tensor product scheme. We show how the conservation of a linear function, defined by a vector given in the low-rank format, or the second norm of the solution may be accurately and elegantly incorporated into the tensor product metho...
Global canonical symmetry in a quantum system
Institute of Scientific and Technical Information of China (English)
李子平
1996-01-01
Based on the phase-space path integral for a system with a regular or singular Lagrangian the generalized canonical Ward identities under the global symmetry transformation in extended phase space are deduced respectively, thus the relations among Green functions can be found. The connection between canonical symmetries and conservation laws at the quantum level is established. It is pointed out that this connection in classical theories, in general, is no longer always preserved in quantum theories. The advantage of our formulation is that we do not need to carry out the integration over the canonical momenta in phase-space generating functional as usually performed. A precise discussion of quantization for a nonlinear sigma model with Hopf and Chern-Simons terms is reexamined. The property of fractional spin at quantum level has been clarified.
A relativistic symmetry in nuclei
Energy Technology Data Exchange (ETDEWEB)
Ginocchio, J N [MS B283, Theoretical Division, Los Alamos National Laboratory Los Alamos, New Mexico 87545 (Mexico)
2007-11-15
We review some of the empirical and theoretical evidence supporting pseudospin symmetry in nuclei as a relativistic symmetry. We review the case that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry in nuclei. We discuss the implications of pseudospin symmetry for magnetic dipole transitions and Gamow-Teller transitions between states in pseudospin doublets. We explore a more fundamental rationale for pseudospin symmetry in terms of quantum chromodynamics (QCD), the basic theory of the strong interactions. We show that pseudospin symmetry in nuclei implies spin symmetry for an anti-nucleon in a nuclear environment. We also discuss the future and what role pseudospin symmetry may be expected to play in an effective field theory of nucleons.
Hsu, Jong-Ping
2014-02-01
A generalization of the usual gauge symmetry leads to fourth-order gauge field equations, which imply a new constant force independent of distances. The force associated with the new U1 gauge symmetry is repulsive among baryons. Such a constant force based on baryon charge conservation gives a field-theoretic understanding of the accelerated cosmic expansion in the observable portion of the universe dominated by baryon galaxies. In consistent with all conservation laws and known forces, a simple rotating "dumbbell model" of the universe is briefly discussed.
Hsu, Jong-Ping
2014-01-01
A generalization of the usual gauge symmetry leads to fourth-order gauge field equations, which imply a new constant force independent of distances. The force associated with the new $U_1$ gauge symmetry is repulsive among baryons. Such a constant force based on baryon charge conservation gives a field-theoretic understanding of the accelerated cosmic-expansion in the observable portion of the universe dominated by baryon galaxies. In consistent with all conservation laws and known forces, a simple rotating `dumbbell model' of the universe is briefly discussed.
Wilczek, Frank
2004-01-01
Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world (8 pages) Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence for these bold ideas is indirect. But soon the theory will undergo a critical test depending on whether the quanta of this symmetry-breaking field, the so-called Higgs particles, are produced at the Large Hadron Collider (due to begin operation in 2007).
New Symmetries for a Model of Fast Diffusion
Institute of Scientific and Technical Information of China (English)
QIN Mao-Chang; XU Xue-Jun; MEI Feng-Xiang
2004-01-01
@@ The new symmetries for a mathematical model of fast diffusion are determined. A new system method is given to search for new symmetries of differential equations written in a conserved form, several new symmetry generators and exact solutions are presented.
Physical Theories with Average Symmetry
Alamino, Roberto C.
2013-01-01
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violat...
Symmetries in fundamental physics
Sundermeyer, Kurt
2014-01-01
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P.Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also underst...
Symmetries in fundamental physics
Sundermeyer, Kurt
2014-01-01
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also unders...
Directory of Open Access Journals (Sweden)
Gülden Gün
2013-01-01
Full Text Available We analyze Noether and -symmetries of the path equation describing the minimum drag work. First, the partial Lagrangian for the governing equation is constructed, and then the determining equations are obtained based on the partial Lagrangian approach. For specific altitude functions, Noether symmetry classification is carried out and the first integrals, conservation laws and group invariant solutions are obtained and classified. Then, secondly, by using the mathematical relationship with Lie point symmetries we investigate -symmetry properties and the corresponding reduction forms, integrating factors, and first integrals for specific altitude functions of the governing equation. Furthermore, we apply the Jacobi last multiplier method as a different approach to determine the new forms of -symmetries. Finally, we compare the results obtained from different classifications.
Yee, H. C.; Shinn, Judy L.
1987-01-01
Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogeneous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the source terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.
Institute of Scientific and Technical Information of China (English)
Hong Xia; LIU Tao PAN
2007-01-01
This paper is concerned with an initial boundary value problem for strictly convex conser-vation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial valuemethod to the weak entropy solution of the initial boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial boundary value problem includesthe following new interaction type: an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L1-error estimate for viscous methods to this initial boundary value problem by using the matching travelling wave solutions method. If the inviscid solution includes the interaction that an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the invis-cidsolution is bounded by O (1/2)in1-norm; otherwise, as in the initial value problem, the L1-error bound is O ( | ln ε | ).
Institute of Scientific and Technical Information of China (English)
K. H. KARLSEN; J. D. TOWERS
2004-01-01
The authors give the first convergence proof for the Lax-Friedrichs finite difference scheme for non-convex genuinely nonlinear scalar conservation laws of the form ut+ f(k(x, t), u)x = 0,where the coefficient k(x, t) is allowed to be discontinuous along curves in the (x, t)plane. In contrast to most of the existing literature on problems with discontinuous coefficients, here the convergence proof is not based on the singular mapping approach,but rather on the div-curl lemma (but not the Young measure) and a Lax type entropy estimate that is robust with respect to the regularity of k(x, t). Following [14],the authors propose a definition of entropy solution that extends the classical Kruzkov definition to the situation where k(x, t) is piecewise Lipschitz continuous in the (x, t)plane, and prove the stability (uniqueness) of such entropy solutions, provided that the flux function satisfies a so-called crossing condition, and that strong traces of the solution exist along the curves where k(x, t) is discontinuous. It is shown that a convergent subsequence of approximations produced by the Lax-Friedrichs scheme converges to such an entropy solution, implying that the entire computed sequence converges.
Vides, Jeaniffer; Nkonga, Boniface; Audit, Edouard
2015-01-01
We derive a simple method to numerically approximate the solution of the two-dimensional Riemann problem for gas dynamics, using the literal extension of the well-known HLL formalism as its basis. Essentially, any strategy attempting to extend the three-state HLL Riemann solver to multiple space dimensions will by some means involve a piecewise constant approximation of the complex two-dimensional interaction of waves, and our numerical scheme is not the exception. In order to determine closed form expressions for the involved fluxes, we rely on the equivalence between the consistency condition and the use of Rankine-Hugoniot conditions that hold across the outermost waves. The proposed scheme is carefully designed to simplify its eventual numerical implementation and its advantages are analytically attested. In addition, we show that the proposed solver can be applied to obtain the edge-centered electric fields needed in the constrained transport technique for the ideal magnetohydrodynamic (MHD) equations. We present several numerical results for hydrodynamics and magnetohydrodynamics that display the scheme's accuracy and its ability to be applied to various systems of conservation laws.
Directory of Open Access Journals (Sweden)
Jingjing Peng
2015-11-01
Full Text Available Albedo characterizes the radiometric interface of land surfaces, especially vegetation, and the atmosphere. Albedo is a critical input to many models, such as crop growth models, hydrological models and climate models. For the extensive attention to crop monitoring, a physical albedo model for crops is developed based on the law of energy conservation and spectral invariants, which is derived from a prior forest albedo model. The model inputs have been efficiently and physically parameterized, including the dependency of albedo on the solar zenith/azimuth angle, the fraction of diffuse skylight in the incident radiance, the canopy structure, the leaf reflectance/transmittance and the soil reflectance characteristics. Both the anisotropy of soil reflectance and the clumping effect of crop leaves at the canopy scale are considered, which contribute to the improvement of the model accuracy. The comparison between the model results and Monte Carlo simulation results indicates that the canopy albedo has high accuracy with an RMSE < 0.005. The validation using ground measurements has also demonstrated the reliability of the model and that it can reflect the interaction mechanism between radiation and the canopy-soil system.
Institute of Scientific and Technical Information of China (English)
Hua-zhong Tang; Gerald Warnecke
2006-01-01
This paper presents a class of high resolution local time step schemes for nonlinear hyperbolic conservation laws and the closely related convection-diffusion equations, by projecting the solution increments of the underlying partial differential equations (PDE)at each local time step. The main advantages are that they are of good consistency, and it is convenient to implement them. The schemes are L∞ stable, satisfy a cell entropy inequality, and may be extended to the initial boundary value problem of general unsteady PDEs with higher-order spatial derivatives. The high resolution schemes are given by combining the reconstruction technique with a second order TVD Runge-Kutta scheme or a Lax-Wendroff type method, respectively.The schemes are used to solve a linear convection-diffusion equation, the nonlinear inviscid Burgers' equation, the one- and two-dimensional compressible Euler equations, and the two-dimensional incompressible Navier-Stokes equations. The numerical results show that the schemes are of higher-order accuracy, and efficient in saving computational cost,especially, for the case of combining the present schemes with the adaptive mesh method [15]. The correct locations of the slow moving or stronger discontinuities are also obtained,although the schemes are slightly nonconservative.
Noether-Mei Symmetry of Mechanical System in Phase Space
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui; WANG Peng; DING Ning
2006-01-01
In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a Noether-Mei symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the Mei conserved quantity deduced from the Noether-Mei symmetry of the system are obtained. Finally, two examples are given to illustrate the application of the results.
Nucci, M. C.
2016-09-01
We review some of our recent work devoted to the problem of quantization with preservation of Noether symmetries, finding hidden linearity in superintegrable systems, and showing that nonlocal symmetries are in fact local. In particular, we derive the Schrödinger equation for the isochronous Calogero goldfish model using its relation to Darwin equation. We prove the linearity of a classical superintegrable system on a plane of nonconstant curvature. We find the Lie point symmetries that correspond to the nonlocal symmetries (also reinterpreted as λ-symmetries) of the Riccati chain.
Physical Theories with Average Symmetry
Alamino, Roberto C
2013-01-01
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violations of physical symmetries, as for instance Lorentz invariance in some quantum gravity theories, is briefly commented.