Symmetries, conservation laws and least action
International Nuclear Information System (INIS)
Maher, P.J.
1982-01-01
This article is a non-technical account of some recent work on the connection between symmetries and conservation laws. This recent work-which uses the modern algebraic concept of naturality-yields a new interpretation of the variational, or least action, principle. (author)
Approximate spacetime symmetries and conservation laws
Energy Technology Data Exchange (ETDEWEB)
Harte, Abraham I [Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 (United States)], E-mail: harte@uchicago.edu
2008-10-21
A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincare and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is a generalized Komar integral that may be taken to define the linear and angular momenta of a spacetime volume as seen by a particular observer. This is evaluated explicitly for a gravitational plane wave spacetime.
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.
Nonlocal symmetries and nonlocal conservation laws of Maxwell's equations
International Nuclear Information System (INIS)
Anco, S.C.; Bluman, G.
1997-01-01
Nonlocal symmetries are obtained for Maxwell's equations in three space-time dimensions through the use of two potential systems involving scalar and vector potentials for the electromagnetic field. Corresponding nonlocal conservation laws are derived from these symmetries. The conservation laws yield nine functionally independent constants of motion which cannot be expressed in terms of the constants of motion arising from local conservation laws for space-time symmetries. These nine constants of motion represent additional conserved quantities for the electromagnetic field in three space endash time dimensions. copyright 1997 American Institute of Physics
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the ...
Kac-Moody-Virasoro Symmetries and Related Conservation Laws
International Nuclear Information System (INIS)
Lou, S. Y.; Jia, M.; Tang, X. Y.
2010-01-01
In this report, some important facts on the symmetries and conservation laws of high dimensional integrable systems are discussed. It is summarized that almost all the known (2+1)-dimensional integrable models possess the Kac-Moody-Virasoro (KMV) symmetry algebras. One knows that infinitely many partial differential equations may possess a same KMV symmetry algebra. It is found that the KMV symmetry groups can be explicitly obtained by using some direct methods. For some quite general variable coefficient nonlinear systems, their sufficient and necessary condition for the existence of the KMV symmetry algebra is they can be changed to the related known constant coefficient models. Finally, it is found that every one symmetry may be related to infinitely many conservation laws and then infinitely many models may possess a same set of infinitely many conservation laws.
Nonlinear MHD-equations: symmetries, solutions and conservation laws
International Nuclear Information System (INIS)
Samokhin, A.V.
1985-01-01
To investigate stability and nonlinear effects in a high-temperature plasma the system of two scalar nonlinear equations is considered. The algebra of classical symmetries of this system and a certain natural part of its conservation laws are described. It is shown that first, with symmetries one can derive invariant (self-similar) solutions, second, acting with symmetry on the known solution the latter can be included into parametric family
Symmetry Principles and Conservation Laws in Atomic and ...
Indian Academy of Sciences (India)
Symmetry Principles and Conservation Laws in. Atomic and Subatomic Physics – 2. P C Deshmukh .... dicated that parity conservation, though often assumed, had not been verified in weak interactions. Acting on ... The gauge bosons W§ have a charge of +1 and −1 unit, but the Z0 boson of the standard model is neutral.
The symmetries and conservation laws of some Gordon-type
Indian Academy of Sciences (India)
Conservation laws; Milne space-time; Gordon-type equations. Abstract. In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented ... Pramana – Journal of Physics | News.
Painleve analysis, conservation laws, and symmetry of perturbed nonlinear equations
International Nuclear Information System (INIS)
Basak, S.; Chowdhury, A.R.
1987-01-01
The authors consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generators. When the perturbed KdV equation is subjected to Painleve analysis a la Weiss, it is found that the resonance position changes compared to the unperturbed one. They prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter epsilon to be small. They determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation they determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painleve analysis does not produce a positive answer for the perturbed NLS equation. So here they have two contrasting examples of perturbed nonlinear equations: one passes the Painleve test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painleve test, though its Lax pair is found in another way
Symmetry and conservation laws in particle physics in the fifties
International Nuclear Information System (INIS)
Michel, L.
1989-01-01
This paper puzzles over why symmetry, so central to particle physics today, was so little attended to in the 1950s when the need for it was becoming profound, with the notion of parity violation and other break-downs in conservation laws, such as angular momentum and charge conjugation. Group theory, including Lie groups, would also have helped understanding of the particle physics discoveries of the 1950s such as strange particles, resonances, and associated production. They were adopted ten years too late by the physics community. (UK)
Analysis of the Symmetries and Conservation Laws of the Nonlinear Jaulent-Miodek Equation
Directory of Open Access Journals (Sweden)
Mehdi Nadjafikhah
2014-01-01
Full Text Available Lie symmetry method is performed for the nonlinear Jaulent-Miodek equation. We will find the symmetry group and optimal systems of Lie subalgebras. The Lie invariants associated with the symmetry generators as well as the corresponding similarity reduced equations are also pointed out. And conservation laws of the J-M equation are presented with two steps: firstly, finding multipliers for computation of conservation laws and, secondly, symbolic computation of conservation laws will be applied.
Scaling symmetries, conservation laws and action principles in one-dimensional gas dynamics
International Nuclear Information System (INIS)
Webb, G M; Zank, G P
2009-01-01
Scaling symmetries of the planar, one-dimensional gas dynamic equations with adiabatic index γ are used to obtain Lagrangian and Eulerian conservation laws associated with the symmetries. The known Eulerian symmetry operators for the scaling symmetries are converted to the Lagrangian form, in which the Eulerian spatial position of the fluid element is given in terms of the Lagrangian fluid labels. Conditions for a linear combination of the three scaling symmetries to be a divergence or variational symmetry of the action are established. The corresponding Lagrangian and Eulerian form of the conservation laws are determined by application of Noether's theorem. A nonlocal conservation law associated with the scaling symmetries is obtained by applying a nonlocal symmetry operator to the scaling symmetry-conserved vector. An action principle incorporating known conservation laws using Lagrangian constraints is developed. Noether's theorem for the constrained action principle gives the same formulas for the conserved vector as the classical Noether theorem, except that the Lie symmetry vector field now includes the effects of nonlocal potentials. Noether's theorem for the constrained action principle is used to obtain nonlocal conservation laws. The scaling symmetry conservation laws only apply for special forms of the entropy of the gas.
Symmetries and Conservation Laws in Classical and Quantum ...
Indian Academy of Sciences (India)
sriranga
and conservation principles in the Lagrangian and. Hamiltonian ... theory. V Balakrishnan – his research interests are statistical phys- ics, stochastic .... We can appreciate this difference in yet another way: ... principles and conservation laws.
Probing Fundamental Symmetries: Questioning the Very Basics of Conservation Laws
Mohanmurthy, Prajwal
2017-09-01
Is the Lorentz-CPT symmetry, a core component of the standard model, valid? To what extent are the CP and T symmetries broken in the strong sector? What are we doing about the existing strong-CP problem? Do neutrons oscillate (like neutral kaons) or break the (Baryon - Lepton) number conservation? In this presentation, we will go over some of the experiments probing fundamental symmetries trying to answer the above questions. I will, very briefly, introduce the CompEx & nEx experiments probing the Lorentz symmetry in the electromagnetic (EM) sector, the nEDM experiment probing CP and T symmetries in the strong sector, NStar experiment searching for neutron oscillations, MASS & BDX experiments searching for axion like particles & dark matter. We will then briefly touch upon the highlights of these experiments and focus on the path we are taking towards answering those questions while also connecting the dots [experiments] with CEU. PM would like to acknowledge support from SERI SNSF Grant 2015.0594.
Symmetries and conservation laws in non-Hermitian field theories
Alexandre, Jean; Millington, Peter; Seynaeve, Dries
2017-09-01
Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for P T -symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the P T -conjugate variables, allowing for an unambiguous definition of the equations of motion. After discussing the resulting constraints on the consistency of the variational procedure, we show that the invariance of a non-Hermitian Lagrangian under a continuous symmetry transformation does not imply the existence of a corresponding conserved current. Conserved currents exist, but these are associated with transformations under which the Lagrangian is not invariant and which reflect the well-known interpretation of P T -symmetric theories in terms of systems with gain and loss. A formal understanding of this unusual feature of non-Hermitian theories requires a careful treatment of Noether's theorem, and we give specific examples for illustration.
On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
International Nuclear Information System (INIS)
Marrero, Juan Carlos; Roman-Roy, Narciso; Salgado, Modesto; Vilarino, Silvia
2011-01-01
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating conservation laws to them by means of a suitable generalization of Noether's theorem.
Symmetry and conservation law structures of some anti-self-dual
Indian Academy of Sciences (India)
The ASD systems and manifolds have been studied via a number of approaches and their origins have been well documented. In this paper, we look at the symmetry structures, variational symmetries and related concepts around the associated conservation laws for a number of such manifolds.
International Nuclear Information System (INIS)
Wang Ling; Dong Zhongzhou; Liu Xiqiang
2008-01-01
By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation (ANNV). Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.
The symmetries and conservation laws of some Gordon-type ...
Indian Academy of Sciences (India)
Hq; 02.30.Jr; 02.30.Xx; 02.40.Ky. 1. Introduction. A vast amount of work has been published in the literature studying differential equations. (DEs) in terms of the Lie point symmetries admitted by them [1,2]. These symmetries play an important ...
On double reductions from symmetries and conservation laws for a damped Boussinesq equation
International Nuclear Information System (INIS)
Gandarias, M.L.; Rosa, M.
2016-01-01
In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. Some nontrivial conservation laws are derived by using the multipliers method. Taking into account the relationship between symmetries and conservation laws and applying the double reduction method, we obtain a direct reduction of order of the ordinary differential equations and in particular a kink solution.
Lie symmetry analysis and conservation laws for the time fractional fourth-order evolution equation
Directory of Open Access Journals (Sweden)
Wang Li
2017-06-01
Full Text Available In this paper, we study Lie symmetry analysis and conservation laws for the time fractional nonlinear fourth-order evolution equation. Using the method of Lie point symmetry, we provide the associated vector fields, and derive the similarity reductions of the equation, respectively. The method can be applied wisely and efficiently to get the reduced fractional ordinary differential equations based on the similarity reductions. Finally, by using the nonlinear self-adjointness method and Riemann-Liouville time-fractional derivative operator as well as Euler-Lagrange operator, the conservation laws of the equation are obtained.
International Nuclear Information System (INIS)
Zhao Gang-Ling; Chen Li-Qun; Fu Jing-Li; Hong Fang-Yu
2013-01-01
In this paper, Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated. Firstly, the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices. Secondly, for cases of the two lattices, based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates, we present the quasi-extremal equation, the discrete analogues of Noether identity, Noether theorems, and the Noether conservation laws of the systems. Thirdly, in cases of the two lattices, we study the Mei symmetry in which we give the discrete analogues of the criterion, the theorem, and the conservative laws of Mei symmetry for the systems. Finally, an example is discussed for the application of the results
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
symmetries are expressed in the form of generators. We have studied the ..... For λ = 0, Iβ=1 represents the total energy of the harmonic oscillator with Uβ=1 as the time .... Ind. J. Pure Appl. Phys. 43, 479 (2005); Classical and quantum me-.
Symmetry and conservation law structures of some anti-self-dual ...
Indian Academy of Sciences (India)
2016-09-28
Sep 28, 2016 ... (2016) 87: 64 c Indian Academy of Sciences. DOI 10.1007/s12043-016-1258-y. Symmetry and conservation law structures of some anti-self-dual (ASD) manifolds. J BASINGWA1, A H KARA1,∗, ASHFAQUE H BOKHARI2, R A MOUSA2 and F D ZAMAN2. 1School of Mathematics, University of the ...
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
Directory of Open Access Journals (Sweden)
Stephen C. Anco
2017-02-01
Full Text Available A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law through a well-known Fréchet derivative identity. Furthermore, the connection of this formula (and of Ibragimov’s theorem to the standard action of symmetries on conservation laws is explained, which accounts for a number of major drawbacks that have appeared in recent work using the formula to generate conservation laws. In particular, the formula can generate trivial conservation laws and does not always yield all non-trivial conservation laws unless the symmetry action on the set of these conservation laws is transitive. It is emphasized that all local conservation laws for any given system of differential equations can be found instead by a general method using adjoint-symmetries. This general method is a kind of adjoint version of the standard Lie method to find all local symmetries and is completely algorithmic. The relationship between this method, Noether’s theorem and the symmetry/adjoint-symmetry formula is discussed.
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.
Symmetries and conservation laws for generalized Hamiltonian systems
International Nuclear Information System (INIS)
Cantrijn, F.; Sarlet, W.
1981-01-01
A class of dynamical systems which locally correspond to a general first-order system of Euler-Lagrange equations is studied on a contact manifold. These systems, called self-adjoint, can be regarded as generalizations of (time-dependent) Hamiltonian systems. It is shown that each one-parameter family of symmetries of the underlying contact form defines a parameter-dependent constant of the motion and vice versa. Next, an extension of the classical concept of canonical transformations is introduced. One-parameter families of canonical transformations are studied and shown to be generated as solutions of a self-adjoint system. Some of the results are illustrated on the Emden equation. (author)
International Nuclear Information System (INIS)
Amitava Choudhuri; Subrata Ghosh; Talukdar, B.
2011-01-01
We identify two alternative Lagrangian representations for the damped harmonic oscillator characterised by a frictional coefficient γ. The first one is explicitly time independent while the second one involves time parameter explicitly. With separate attention to both Lagrangians we make use of the Noether theorem to compute the variational symmetries and conservation laws in order to study how association between them changes as one goes from one representation to the other. In the case of time independent representation squeezing symmetry leads to conservation of angular momentum for γ = 0, while for the time-dependent Lagrangian the same conserved quantity results from rotational invariance. The Lie algebra (g) of the symmetry vectors that leaves the action corresponding to the time-independent Lagrangian invariant is semi-simple. On the other hand, g is only a simple Lie algebra for the action characterised by the time-dependent Lagrangian. (authors)
Symmetries and conservation laws for a sixth-order Boussinesq equation
International Nuclear Information System (INIS)
Recio, E.; Gandarias, M.L.; Bruzón, M.S.
2016-01-01
This paper considers a generalization depending on an arbitrary function f(u) of a sixth-order Boussinesq equation which arises in shallow water waves theory. Interestingly, this equation admits a Hamiltonian formulation when written as a system. A classification of point symmetries and conservation laws in terms of the function f(u) is presented for both, the generalized Boussinesq equation and the equivalent Hamiltonian system.
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.
Directory of Open Access Journals (Sweden)
Emrullah Yaşar
Full Text Available In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI equation with Riemann–Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi–Kober sense. Furthermore, adapting the Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method. Keywords: Fractional Sawada–Kotera–Ito equation, Lie symmetry, Riemann–Liouville fractional derivative, Conservation laws, Exact solutions
Waves, conservation laws and symmetries of a third-order nonlinear ...
African Journals Online (AJOL)
order is under consideration. Important properties concerning advanced character such like conservation laws and the equation of continuity are given. Characteristic wave properties such like dispersion relations and both the group and phase ...
Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa
2018-06-01
In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.
Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru
2018-04-01
This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.
International Nuclear Information System (INIS)
Tretyak, V.I.; Gaida, R.P.
1980-01-01
Symmetry properties of the single-time relativistic Lagrangian of an N-particle-system corresponding to the many-time action of the Fokker-type, which are a function of derivatives of particle coordinates with respect to time up to infinite order, are investigated. The conditions for quasi-invariance for such a Lagrangian, with respect to a representation of an arbitrary group in infinite continuation of configuration space of the system, are discussed. Using these conditions a general expression for the Lagrangian, securing Poincare covariance of corresponding equations of motion, is found, and the conservation laws related to this covariance are formulated. In the case of tensor interaction, the expansion of conserved quantities in c -1 up to terms of the order c -4 is performed. (author)
Space, time and conservation laws
International Nuclear Information System (INIS)
Aronov, R.A.; Ugarov, V.A.
1978-01-01
The Neter theorem establishing correspondence between conservation laws and symmetry properties (space and time in particular) is considered. The theorem is based on one of the possible ways of finding equations of motion for a physical system. From a certain expression (action functional) equations of motion for a system can be obtained which do not contain new physical assertions in principal in comparison with the Newtonian laws. Neter suggested a way of deriving conservation laws by transforming space and time coordinates. Neter theorem consequences raise a number of problems: 1). Are conservation laws (energy, momentum) consequences of space and time symmetry properties. 2). Is it possible to obtain conservation laws in theory neglecting equations of motion. 3). What is of the primary importance: equations of motion, conservation laws or properties of space and time symmetry. It is shown that direct Neter theorem does not testify to stipulation of conservation laws by properties of space and time symmetry and symmetry properties of other non-space -time properties of material systems in objective reality. It says nothing of whether there is any subordination between symmetry properties and conservation laws
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
Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian
2018-05-01
We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.
International Nuclear Information System (INIS)
Ivanov, G.G.
1985-01-01
In the non linear delta-model conserved tensor currents connected with the isometrical, homothetic and affine motions in the space Vsup(N) of the chiral field values are constructed. New classes of the exact solutions are obtained in the SO(3) and SO(5) invariant delta-models using the connection between the groups of isometrical and homothetic motions in the space-time and isometrical motions in Vsup(N). Some methods of obtaining exact solutions in 4-dimensional delta-model with non trivial topological charge are considered
International Nuclear Information System (INIS)
Goldhaber, M.
1988-01-01
For quite a while it has been realized that some discrete quantum numbers are conserved in some interactions but not in others. The most conspicuous cases are parity P, charge conjugation C, and the product CP which are conserved in strong and electromagnetic interactions but not in weak interactions. The question arises whether for some of the other conserved quantities, which are conserved in strong, electromagnetic and weak interactions, there is an interaction intermediate in strength between weak and gravitational which violates these quantum numbers, e.g., baryon number B and lepton number L. The possibility exists that these conservation laws, if they are broken at all, are only broken by the gravitational force which would make the mass of an intermediate boson which induces the break-down equal to the Planck mass. (orig.)
The structure of additive conservation laws
International Nuclear Information System (INIS)
Helmut Reen
1979-01-01
All additive conserved quantities are listed for a system with short range central force interaction between the particles: a special case shows up in Boltzmann H-theorem and his derivation of the Maxwell velocity distribution. It is concluded that in classical mechanics of mass points there are no other additive conservation laws besides of energy, momentum, angular momentum and center of mass motion. A generator is considered of a symmetry transformation defined as integral over a conserved local current density where the latter, in general, needs not be covariant under translations
Symmetries and conserved quantities in geodesic motion
International Nuclear Information System (INIS)
Hojman, S.; Nunez, L.; Patino, A.; Rago, H.
1986-01-01
Recently obtained results linking several constants of motion to one (non-Noetherian) symmetry to the problem of geodesic motion in Riemannian space-times are applied. The construction of conserved quantities in geodesic motion as well as the deduction of geometrical statements about Riemannian space-times are achieved
Relativistic dynamics without conservation laws
Rothenstein, Bernhard; Popescu, Stefan
2006-01-01
We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The derivations are based on the principle of relativity and on its direct consequence, the addition law of relativistic velocities.
Conservation laws shape dissipation
Rao, Riccardo; Esposito, Massimiliano
2018-02-01
Starting from the most general formulation of stochastic thermodynamics—i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs—we define a procedure to identify the conservative and the minimal set of nonconservative contributions in the entropy production. The former is expressed as the difference between changes caused by time-dependent drivings and a generalized potential difference. The latter is a sum over the minimal set of flux-force contributions controlling the dissipative flows across the system. When the system is initially prepared at equilibrium (e.g. by turning off drivings and forces), a finite-time detailed fluctuation theorem holds for the different contributions. Our approach relies on identifying the complete set of conserved quantities and can be viewed as the extension of the theory of generalized Gibbs ensembles to nonequilibrium situations.
Lagrange and Noether analysis of polarization laws of conservation for electromagnetic field
International Nuclear Information System (INIS)
Krivskij, I.Yu.; Simulik, V.M.
1988-01-01
Both well-known Bessel-Hagen conservation laws and conservation laws of polarized character are derived for electromagnetic field in the Lagrange approach to electrodynamics in terms of intensities (without using the A μ potentials as variation variables). The laws mentioned are derived according to Noether theorem because symmetry to which such concervation laws correspond is lost during the transition from intensities to potentials. Based on Noether theorem (and its generalization for Naeik's symmetries) and Lagrange function scalar in relation to complete Poincare group in terms of intensity tensor, a convenient formula for calculating and values conserved for electromagnetic field is derived which sets up a physically adequate symmetry operator -conservation law correlation and thus links the presence of conservation laws of polarized character with symmetry properties of Maxwell equations. Adiabaticity of conservation laws of polarized character under the presence of interaction with currents and charges is indicated
Reductions and conservation laws for BBM and modified BBM equations
Directory of Open Access Journals (Sweden)
Khorshidi Maryam
2016-01-01
Full Text Available In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM and modified Benjamin-Bona-Mahony equations (MBBM to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry properties are given too.
International Nuclear Information System (INIS)
Ibragimov, N Kh; Avdonina, E D
2013-01-01
The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions. Bibliography: 23 titles
Magnetohydrodynamics and fluid dynamics action principles and conservation laws
Webb, Gary
2018-01-01
This text focuses on conservation laws in magnetohydrodynamics, gasdynamics and hydrodynamics. A grasp of new conservation laws is essential in fusion and space plasmas, as well as in geophysical fluid dynamics; they can be used to test numerical codes, or to reveal new aspects of the underlying physics, e.g., by identifying the time history of the fluid elements as an important key to understanding fluid vorticity or in investigating the stability of steady flows. The ten Galilean Lie point symmetries of the fundamental action discussed in this book give rise to the conservation of energy, momentum, angular momentum and center of mass conservation laws via Noether’s first theorem. The advected invariants are related to fluid relabeling symmetries – so-called diffeomorphisms associated with the Lagrangian map – and are obtained by applying the Euler-Poincare approach to Noether’s second theorem. The book discusses several variants of helicity including kinetic helicity, cross helicity, magnetic helici...
Local conservation laws for principle chiral fields (d=1)
International Nuclear Information System (INIS)
Cherednik, I.V.
1979-01-01
The Beklund transformation for chiral fields in the two-dimensional Minkovski space is found. As a result an infinite series of conservation laws for principle chiral Osub(n) fields (d=1) has been built. It is shown that these laws are local, the infinite series of global invariants which do not depend on xi, eta, and which is rather rapidly decrease along xi (or along eta) solutions being connected with these laws (xi, eta - coordinates of the light cone). It is noted that with the help of the construction proposed it is possible to obtain conservation laws of principle chiral G fields, including G in the suitable ortogonal groups. Symmetry permits to exchange xi and eta. The construction of conservation laws may be carried out without supposition that lambda has a multiplicity equal to 1, however the proof of the locality applied does not transfer on the laws obtained
International Nuclear Information System (INIS)
Bokhari A H; Zaman F D; Fakhar K; Kara A H
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. (general)
Decoupling Subtraction Conserving Full Gauge Symmetries : Particles and Fields
Noriyasu, OHTSUBO; Hideo, MIYATA; Department of Phycics, Kanazawa Technical College; Department of Information Science, Kanazawa Institute of Technolgy
1984-01-01
A new subtraction scheme (^^^) which realizes the decoupling and conserves the symmetries of full gauge group simultaneously, is proposed. One particle irreducible Green's functions subtracted by ^^^ reveal the effective low energy symmetries at -p^2≪M^2 and the full symmetries at -p^2≫M^2, where M denotes a heavy mass. Also discussed are conditions in order to carry out ^^^ under two-loop approximation.
Numerical solutions of conservation laws
International Nuclear Information System (INIS)
Shu, C.W.
1986-01-01
In the computation of conservation laws u/sub t/ + f(u)/sub x/ 0, TVD (total-variation-diminishing) schemes have been very successful. TVB (total-variation-bounded) schemes share most the advantages and may remove some of the disadvantages (e.g. local degeneracy of accuracy at critical points) TVD schemes. Included in this dissertation are a class of m-step Runge-Kutta type TVD schemes with CFL number equaling m; a procedure to obtain uniformly high order in space TVB schemes; a class of TVD high order time discretizations; a special boundary treatment which keeps the high order of the scheme up to the boundary and preserves the TVB properties in the nonlinear scalar and linear system cases; a discrete entropy inequality for a modified Lax-Wendroff scheme applied to Burgers' equation; and discusses about error propagation in large regions
Conservation Laws in Biochemical Reaction Networks
DEFF Research Database (Denmark)
Mahdi, Adam; Ferragut, Antoni; Valls, Claudia
2017-01-01
We study the existence of linear and nonlinear conservation laws in biochemical reaction networks with mass-action kinetics. It is straightforward to compute the linear conservation laws as they are related to the left null-space of the stoichiometry matrix. The nonlinear conservation laws...... are difficult to identify and have rarely been considered in the context of mass-action reaction networks. Here, using the Darboux theory of integrability, we provide necessary structural (i.e., parameterindependent) conditions on a reaction network to guarantee the existence of nonlinear conservation laws...
Asymptotic Conservation Laws in Classical Field Theory
International Nuclear Information System (INIS)
Anderson, I.M.; Torre, C.G.
1996-01-01
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. copyright 1996 The American Physical Society
A Kirchhoff-like conservation law in Regge calculus
International Nuclear Information System (INIS)
Gentle, Adrian P; Kheyfets, Arkady; McDonald, Jonathan R; Miller, Warner A
2009-01-01
Simplicial lattices provide an elegant framework for discrete spacetimes. The inherent orthogonality between a simplicial lattice and its circumcentric dual yields an austere representation of spacetime which provides a conceptually simple form of Einstein's geometric theory of gravitation. A sufficient understanding of simplicial spacetimes has been demonstrated in the literature for spacetimes devoid of all non-gravitational sources. However, this understanding has not been adequately extended to non-vacuum spacetime models. Consequently, a deep understanding of the diffeomorphic structure of the discrete theory is lacking. Conservation laws and symmetry properties are attractive starting points for coupling matter with the lattice. We present a simplicial form of the contracted Bianchi identity which is based on the E Cartan moment of rotation operator. This identity manifests itself in the conceptually simple form of a Kirchhoff-like conservation law. This conservation law enables one to extend Regge calculus to non-vacuum spacetimes and provides a deeper understanding of the simplicial diffeomorphism group.
Symmetry mappings concomitant to particle-number-conservation-baryon-number conservation
International Nuclear Information System (INIS)
Davis, W.R.
1977-01-01
Four theorem serve to demonstrate that matter fields in space-time admit certain timelike symmetry mappings concomitant to the familiar notion of particle number conservation, which can be more fundamentally accounted for by a type of projective invariance principle. These particular symmetry mappings include a family of symmetry properties that may be admitted by Riemannian space-times. In their strongest form, the results obtained provide some insight relating to the conservation of baryon number
On Newton's third law and its symmetry-breaking effects
International Nuclear Information System (INIS)
Pinheiro, Mario J
2011-01-01
The law of action-reaction, considered by Ernst Mach as the cornerstone of physics, is thoroughly used to derive the conservation laws of linear and angular momentum. However, the conflict between momentum conservation law and Newton's third law, on experimental and theoretical grounds, calls for more attention. We give a background survey of several questions raised by the action-reaction law and, in particular, the role of the physical vacuum is shown to provide an appropriate framework for clarifying the occurrence of possible violations of the action-reaction law. Then, in the framework of statistical mechanics, using a maximizing entropy procedure, we obtain an expression for the general linear momentum of a body particle. The new approach presented here shows that Newton's third law is not verified in systems out of equilibrium due to an additional entropic gradient term present in the particle's momentum.
A general qualitative theory of conservation laws, their violation and other spontaneous phenomena
International Nuclear Information System (INIS)
Tahir Shah, K.
1976-10-01
A general theory of conservation laws and other invariants for a physical system through equivalence relations are formulated. The conservation laws are classified according to the type of equivalence relation; group equivalence, homotopical equivalence and other types of equivalence relations giving respective kinds of conservation laws. The stability properties in the topological (and differentiable) sense are discussed using continuous deformations with respect to control parameters. The conservation laws due to the abelian symmetries are shown to be stable through application of well-known theorems
Conservation Law Enforcement Program Standardization
National Research Council Canada - National Science Library
Rogers, Stan
2004-01-01
The ultimate goal of standardization is to develop a safe and effective program that is recognized within the USAF, DoD, and by other Federal and state law enforcement agencies, and the general public...
Infinite sets of conservation laws for linear and nonlinear field equations
International Nuclear Information System (INIS)
Mickelsson, J.
1984-01-01
The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the 'coupling constant') the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant under the group of space-time symmetries. As an example, our method is applied to the Korteweg-de Vries equation and to the massless Thirring model. (orig.)
Reduced energy conservation law for magnetized plasma
International Nuclear Information System (INIS)
Sosenko, P.P.; Decyk, V.K.
1994-01-01
A global energy conservation law for a magnetized plasma is studied within the context of a quasiparticle description. A reduced energy conservation law is derived for low-frequency, as compared to the gyromagnetic frequency, plasma motions with regard to both non-uniform mean flows and fluctuations in the plasma. The mean value of plasma energy is calculated and sufficient stability conditions for non-equilibrium plasmas are derived. (orig.)
Kersten, P.H.M.
1988-01-01
By the introduction of nonlocal basonic and fermionic variables we construct a recursion symmetry of the super KdV equation, leading to a hierarchy of bosonic symmetries and one of fermionic symmetries. The hierarchies of bosonic and fermionic conservation laws arise in a natural way in the
Conservation laws and nuclear transport models
International Nuclear Information System (INIS)
Gale, C.; Das Gupta, S.
1990-01-01
We discuss the consequences of energy and angular momentum conservation for nucleon-nucleon scattering in a nuclear environment during high-energy heavy-ion collisions. We describe algorithms that ensure stricter enforcement of such conservation laws within popular microscopic models of intermediate-energy heavy-ion collisions. We find that the net effects on global observables are small
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
Conservation laws for certain time fractional nonlinear systems of partial differential equations
Singla, Komal; Gupta, R. K.
2017-12-01
In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.
Nonlinearity, Conservation Law and Shocks
Indian Academy of Sciences (India)
However, genuine nonlinearity is always present in an ideal gas. The conservation form of the equation (25) brings in shocks which cut off the growing part of the amplitUde as shown in. Figure 15. Acknowledgements. The author sincerely thanks the two referees whose valuable comments led to an improvement of the ...
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.)
Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space
International Nuclear Information System (INIS)
Fang Jianhui; Ding Ning; Wang Peng
2006-01-01
In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance.
Symmetries, conservation principles, and the phenomenology of meson exchange currents. Chapter 12
International Nuclear Information System (INIS)
Foldy, L.L.; Lock, J.A.
1979-01-01
The authors show that as an alternative to one-pion exchange S-matrix calculations, one may learn quite a bit concerning meson exchange electromagnetic and weak currents by the application of various symmetries and conservation laws. In particular, one may determine the most general form that the exchange currents may take in the static approximation by the application of invariance under spatial translations, rotations, and space inversion, the electric charge superselection principle. Lorentz invariance, vector current conservation, time reversal invariance, Hermiticity of the interaction Hamiltonian, and invariance under coordinate interchange. (Auth.)
Renormalization, averaging, conservation laws and AdS (in)stability
International Nuclear Information System (INIS)
Craps, Ben; Evnin, Oleg; Vanhoof, Joris
2015-01-01
We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.
Italian energy conservation laws: Implementation problems
International Nuclear Information System (INIS)
Anon.
1993-01-01
Italian energy conservation Law No. 9 was designed to reduce Italy's worrisome 82% dependency on foreign energy supplies by encouraging the development and use of renewable energy sources, fuel diversification and auto-production/cogeneration by private industry. Law No. 10 was intended to promote energy conservation initiatives especially with regard to the efficient use of energy for space heating in public buildings. Both of these legal incentives have encountered great difficulties in implementation due to the inability of the Government to provide the necessary timely and sufficient start-up funds, as well as, due to the excessive bureaucratism that was built into the administrative procedures
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.
The conservation laws for deformed classical models
International Nuclear Information System (INIS)
Klimek, M.
1994-01-01
The problem of deriving the conservation laws for deformed linear equations of motion is investigated. The conserved currents are obtained in explicit form and used in the construction of constants of motion. The equations for the set of non-interacting oscillators with arbitrary scale-time as well as the κ-Klein-Gordon equation are considered as an example of application of the method. (author) 9 refs
Infinite sets of conservation laws for linear and non-linear field equations
International Nuclear Information System (INIS)
Niederle, J.
1984-01-01
The work was motivated by a desire to understand group theoretically the existence of an infinite set of conservation laws for non-interacting fields and to carry over these conservation laws to the case of interacting fields. The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of its space-time symmetry group was established. It is shown that in the case of the Korteweg-de Vries (KdV) equation to each symmetry of the corresponding linear equation delta sub(o)uxxx=u sub() determined by an element of the enveloping algebra of the space translation algebra, there corresponds a symmetry of the full KdV equation
The tensorial conservation law in general relativity
International Nuclear Information System (INIS)
Zhao, M.G.
1984-01-01
A general tensorial conservation law is formulated by starting from the invariance of the gravitational Lagrangian density. Utilising this new formula, the author derives some reasonable results for the mass-energy distribution which are in accordance with the Newtonian formulae. (author)
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
Truncated Wigner dynamics and conservation laws
Drummond, Peter D.; Opanchuk, Bogdan
2017-10-01
Ultracold Bose gases can be used to experimentally test many-body theory predictions. Here we point out that both exact conservation laws and dynamical invariants exist in the topical case of the one-dimensional Bose gas, and these provide an important validation of methods. We show that the first four quantum conservation laws are exactly conserved in the approximate truncated Wigner approach to many-body quantum dynamics. Center-of-mass position variance is also exactly calculable. This is nearly exact in the truncated Wigner approximation, apart from small terms that vanish as N-3 /2 as N →∞ with fixed momentum cutoff. Examples of this are calculated in experimentally relevant, mesoscopic cases.
Massively parallel computation of conservation laws
Energy Technology Data Exchange (ETDEWEB)
Garbey, M [Univ. Claude Bernard, Villeurbanne (France); Levine, D [Argonne National Lab., IL (United States)
1990-01-01
The authors present a new method for computing solutions of conservation laws based on the use of cellular automata with the method of characteristics. The method exploits the high degree of parallelism available with cellular automata and retains important features of the method of characteristics. It yields high numerical accuracy and extends naturally to adaptive meshes and domain decomposition methods for perturbed conservation laws. They describe the method and its implementation for a Dirichlet problem with a single conservation law for the one-dimensional case. Numerical results for the one-dimensional law with the classical Burgers nonlinearity or the Buckley-Leverett equation show good numerical accuracy outside the neighborhood of the shocks. The error in the area of the shocks is of the order of the mesh size. The algorithm is well suited for execution on both massively parallel computers and vector machines. They present timing results for an Alliant FX/8, Connection Machine Model 2, and CRAY X-MP.
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.
Nonlinear Conservation Laws and Finite Volume Methods
Leveque, Randall J.
Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References
Discontinuous Galerkin Method for Hyperbolic Conservation Laws
Mousikou, Ioanna
2016-01-01
Hyperbolic conservation laws form a special class of partial differential equations. They describe phenomena that involve conserved quantities and their solutions show discontinuities which reflect the formation of shock waves. We consider one-dimensional systems of hyperbolic conservation laws and produce approximations using finite difference, finite volume and finite element methods. Due to stability issues of classical finite element methods for hyperbolic conservation laws, we study the discontinuous Galerkin method, which was recently introduced. The method involves completely discontinuous basis functions across each element and it can be considered as a combination of finite volume and finite element methods. We illustrate the implementation of discontinuous Galerkin method using Legendre polynomials, in case of scalar equations and in case of quasi-linear systems, and we review important theoretical results about stability and convergence of the method. The applications of finite volume and discontinuous Galerkin methods to linear and non-linear scalar equations, as well as to the system of elastodynamics, are exhibited.
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.
Conservation laws with coinciding smooth solutions but different conserved variables
Colombo, Rinaldo M.; Guerra, Graziano
2018-04-01
Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.
Post-Newtonian conservation laws in rigid quasilocal frames
International Nuclear Information System (INIS)
McGrath, Paul L; Chanona, Melanie; Epp, Richard J; Mann, Robert B; Koop, Michael J
2014-01-01
In recent work we constructed completely general conservation laws for energy (McGrath et al 2012 Class. Quantum Grav. 29 215012) and linear and angular momentum (Epp et al 2013 Class. Quantum Grav. 30 195019) of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level that these RQF conservation laws are superior to conservation laws based on the local stress–energy–momentum tensor of matter because (1) they do not rely on spacetime symmetries and (2) they properly account for both matter and gravitational effects. Moreover, they provide simple, exact, operational expressions for fluxes of gravitational energy and linear and angular momentum. In this paper we derive the form of these laws in a general first post-Newtonian (1PN) approximation, and then apply these approximate laws to the problem of gravitational tidal interactions. We obtain formulas for tidal heating and tidal torque that agree with the literature, but without resorting to the use of pseudotensors. We describe the physical mechanism of these tidal interactions not in the traditional terms of a Newtonian gravitational force, but in terms of a much simpler and universal mechanism that is an exact, quasilocal manifestation of the equivalence principle in general relativity. As concrete examples, we look at the tidal heating of Jupiter’s moon Io and angular momentum transfer in the Earth–Moon system that causes a gradual spin-down of the Earth and recession of the Moon. In both examples we find agreement with observation. (paper)
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...
Hall magnetohydrodynamics: Conservation laws and Lyapunov stability
International Nuclear Information System (INIS)
Holm, D.D.
1987-01-01
Hall electric fields produce circulating mass flow in confined ideal-fluid plasmas. The conservation laws, Hamiltonian structure, equilibrium state relations, and Lyapunov stability conditions are presented here for ideal Hall magnetohydrodynamics (HMHD) in two and three dimensions. The approach here is to use the remarkable array of nonlinear conservation laws for HMHD that follow from its Hamiltonian structure in order to construct explicit Lyapunov functionals for the HMHD equilibrium states. In this way, the Lyapunov stability analysis provides classes of HMHD equilibria that are stable and whose linearized initial-value problems are well posed (in the sense of possessing continuous dependence on initial conditions). Several examples are discussed in both two and three dimensions
International Nuclear Information System (INIS)
Fakhar, K.; Kara, A. H.
2011-01-01
A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties (through the Lie point symmetry generators) and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ‘multipliers’ associated with the conservation laws with a stronger emphasis on the ‘higher-order’ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers. (general)
Infinitely many conservation laws for the discrete KdV equation
International Nuclear Information System (INIS)
Rasin, Alexander G; Schiff, Jeremy
2009-01-01
Rasin and Hydon (2007 J. Phys. A: Math. Theor. 40 12763-73) suggested a way to construct an infinite number of conservation laws for the discrete KdV equation (dKdV), by repeated application of a certain symmetry to a known conservation law. It was not decided, however, whether the resulting conservation laws were distinct and nontrivial. In this paper we obtain the following results: (1) we give an alternative method to construct an infinite number of conservation laws using a discrete version of the Gardner transformation. (2) We give a direct proof that the conservation laws obtained by the method of Rasin and Hydon are indeed distinct and nontrivial. (3) We consider a continuum limit in which the dKdV equation becomes a first-order eikonal equation. In this limit the two sets of conservation laws become the same, and are evidently distinct and nontrivial. This proves the nontriviality of the conservation laws constructed by the Gardner method, and gives an alternative proof of the nontriviality of the conservation laws constructed by the method of Rasin and Hydon
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)
Conservation laws for a system of two point masses in general relativity
International Nuclear Information System (INIS)
Damour, Thibaut; Deruelle, Nathalie
1981-01-01
We study the symmetries of the generalized lagrangian of two point masses, in the post-post newtonian approximation of General Relativity. We deduce, via Noether's theorem, conservation laws for energy, linear and angular momentum, as well as a generalisation of the center-of-mass theorem [fr
Conservation laws in the SLsub(2,C) gauge theory of gravitation
International Nuclear Information System (INIS)
Nissani, N.
1983-01-01
A one-parameter family of new Lagrangian densities for the SLsub(2,C) gauge theory of gravitation is proposed. The relation between the laws of conservation and the SLsub(2,C) symmetry of general relativity through the Noether theorem is investigated
International Nuclear Information System (INIS)
Zheng Shi-Wang; Wang Jian-Bo; Chen Xiang-Wei; Xie Jia-Fang
2012-01-01
Operational systems of spacecraft are general variable mass mechanics systems, and their symmetries and conserved quantities imply profound physical rules of the space system. We study the Mei symmetry of Tzénoff equations for a variable mass nonholonomic system and the new conserved quantities derived. The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented. This result has some theoretical values in further research of conservation laws obeyed by the variable mass system. (general)
Compensatory Measures in European Nature Conservation Law
Directory of Open Access Journals (Sweden)
Geert Van Hoorick
2014-05-01
Full Text Available The Birds and Habitats Directives are the cornerstones of EU nature conservation law, aiming at the conservation of the Natura 2000 network, a network of protected sites under these directives, and the protection of species. The protection regime for these sites and species is not absolute: Member States may, under certain conditions, allow plans or projects that can have an adverse impact on nature. In this case compensatory measures can play an important role in safeguarding the Natura 2000 network and ensuring the survival of the protected species.This contribution analyses whether taking compensatory measures is always obligatory, and discusses the aim and the characteristics of compensatory measures, in relation to other kinds of measures such as mitigation measures, usual nature conservation measures, and former nature development measures, and to the assessment of the adverse impact caused by the plan or project and of the alternative solutions. The questions will be discussed in light of the contents of the legislation, the guidance and practice by the European Commission, (legal doctrine and case law, mainly of the Court of Justice of the European Union.
Lie-Mei symmetry and conserved quantities of the Rosenberg problem
International Nuclear Information System (INIS)
Liu Xiao-Wei; Li Yuan-Cheng
2011-01-01
The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry. (general)
Lie-Mei symmetry and conserved quantities of the Rosenberg problem
Liu, Xiao-Wei; Li, Yuan-Cheng
2011-07-01
The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry.
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.
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.
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan
2011-01-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
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 ...
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.
Unimodular Einstein-Cartan gravity: Dynamics and conservation laws
Bonder, Yuri; Corral, Cristóbal
2018-04-01
Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the most general matter Lagrangian allowed by the symmetries is considered, dynamical restrictions arise on their functional dependence. The field equations are obtained and the conservation laws associated with the symmetries are derived. It is found that, analogous to torsion-free unimodular gravity, the field equation for the vierbein is traceless; nevertheless, torsion is algebraically related to the spin density as in standard Einstein-Cartan theory. The particular example of massless Dirac spinors is studied, and comparisons with standard Einstein-Cartan theory are shown.
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 Conservation Principles and Kepler's Laws of Planetary Motion
Motz, Lloyd
1975-01-01
Derives Kepler's three laws of planetary motion algebraically from conservation principles without introducing Newton's law of force explicitly. This procedure can be presented to students who have had no more than high school algebra. (Author)
Layer-Mean Quantities, Local Conservation Laws, and Vorticity
International Nuclear Information System (INIS)
Camassa, R.; Levermore, C.D.
1997-01-01
We derive local conservation laws for layer-mean quantities in two general settings. When applied to Euler flows, the first of these settings yields well-known local conservation laws for quantities averaged between material surfaces. The second, however, leads to new local conservation laws for quantities involving the vorticity that are averaged between arbitrary surfaces. These produce the crucial vorticity conservation laws in shallow water models that admit nonhydrostatic and noncolumnar motion. Moreover, they seem to lie outside the Hamiltonian paradigm of fluid dynamics. The formalism generalizes to skew-symmetric matrix fields; applications to electromagnetism are suggested. copyright 1997 The American Physical Society
Conformal invariance and conserved quantities of Appell systems under second-class Mei symmetry
International Nuclear Information System (INIS)
Yi-Ping, Luo; Jing-Li, Fu
2010-01-01
In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system's conformal invariance and Mei symmetry are discussed. And Appell system's conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result. (general)
Variational approaches to conservation laws for a nonlinear ...
African Journals Online (AJOL)
The conservation laws of a nonlinear evolution equation of time dependent variable coefficients of damping and dispersion is studied. The equation under consideration is not derivable from a variational principle which means that one cannot appeal to the Noether theorem to determine the conservation laws. We utilize the ...
Conservation laws and covariant equations of motion for spinning particles
Obukhov, Yuri N.; Puetzfeld, Dirk
2015-01-01
We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of motion for test bodies with minimal and nonminimal coupling.
Quasilocal conservation laws in the quantum Hirota model
International Nuclear Information System (INIS)
Zadnik, Lenart; Prosen, Tomaž
2017-01-01
The extensivity of the quantum Hirota model’s conservation laws on a 1 + 1 dimensional lattice is considered. This model can be interpreted in terms of an integrable many-body quantum Floquet dynamics. We establish the procedure to generate a continuous family of quasilocal conservation laws from the conserved operators proposed by Faddeev and Volkov. The Hilbert–Schmidt kernel which allows the calculation of inner products of these new conservation laws is explicitly computed. This result has potential applications in quantum quench and transport problems in integrable quantum field theories. (paper)
A Kinematic Conservation Law in Free Surface Flow
Gavrilyuk , Sergey; Kalisch , Henrik; Khorsand , Zahra
2015-01-01
The Green-Naghdi system is used to model highly nonlinear weakly dispersive waves propagating at the surface of a shallow layer of a perfect fluid. The system has three associated conservation laws which describe the conservation of mass, momentum, and energy due to the surface wave motion. In addition, the system features a fourth conservation law which is the main focus of this note. It will be shown how this fourth conservation law can be interpreted in terms of a concrete kinematic quanti...
Solutions and conservation laws of Benjamin–Bona–Mahony ...
Indian Academy of Sciences (India)
obtained with power-law and dual power-law nonlinearities. The Lie group analysis as ... The notion of conservation laws plays an important role in the solution process of differential ... For the theory and applications of Lie group analysis the ...
International Nuclear Information System (INIS)
Basini, Giuseppe; Capozziello, Salvatore; Longo, Giuseppe
2003-01-01
We propose a new approach in which several paradoxes and shortcomings of modern physics can be solved because conservation laws are always conserved. Directly due to the fact that conservation laws can never be violated, the symmetry of the theory leads to the very general consequence that backward and forward time evolution are both allowed. The generalization of the approach to five dimensions, each one with real physical meaning, leads to the derivation of particle masses as a result of a process of embedding
Intrinsic symmetry of the scaling laws and generalized relations for critical indices
International Nuclear Information System (INIS)
Plechko, V.N.
1982-01-01
It is shown that the scating taws for criticat induces can be expressed as a consequence of a simple symmetry principle. Heuristic relations for critical induces of generalizing scaling laws for the case of arbitrary order parameters are presented, which manifestiy have a symmetric form and include the standard scalling laws as a particular case
Violations of conservation laws in viscous liquid dynamics
DEFF Research Database (Denmark)
Dyre, Jeppe
2007-01-01
The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring equipment over the long times needed to study the dynamics. Moreover,......, although particle number conservation applies strictly for any liquid, the solidity of viscous liquids implies that even this conservation law is apparently violated in coarse-grained descriptions of density fluctuations.......The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring equipment over the long times needed to study the dynamics. Moreover...
Symmetries and Conservation Laws in Classical and Quantum ...
Indian Academy of Sciences (India)
(classical) field theory is quite elementary, in principle. In Part 1, we ... progression from elementary considerations to a com- prehensive ...... Pearson Education, Singapore, 2002. [5]. E J Saletan and ... Indian Institute of Technology. Madras ...
Symmetry Principles and Conservation Laws in Atomic and ...
Indian Academy of Sciences (India)
a relationship between position, velocity, and accelera- tion. .... tion, namely that the position q and velocity. : q specify ... statement of the `principle of extremum action'. The necessary .... of Pauli{Runge{Lenz vector which is the quantum ana-.
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…
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.
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...
The Fourier law in a momentum-conserving chain
Giardinà, C.; Kurchan, J.
2005-01-01
We introduce a family of models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases the Fourier law is verified in one dimension.
Direct Construction of Conservation Laws from Field Equations
International Nuclear Information System (INIS)
Anco, S.C.; Bluman, G.
1997-01-01
This Letter presents an algorithm to obtain all local conservation laws for any system of field equations. The algorithm uses a formula which directly generates the conservation laws and does not depend on the system having a Lagrangian formulation, in contrast to Noether close-quote s theorem which requires a Lagrangian. Several examples are considered including dissipative systems inherently having no Lagrangian. copyright 1997 The American Physical Society
Analysis of self-similar solutions of multidimensional conservation laws
Energy Technology Data Exchange (ETDEWEB)
Keyfitz, Barbara Lee [The Ohio State Univ., Columbus, OH (United States)
2014-02-15
This project focused on analysis of multidimensional conservation laws, specifically on extensions to the study of self-siminar solutions, a project initiated by the PI. In addition, progress was made on an approach to studying conservation laws of very low regularity; in this research, the context was a novel problem in chromatography. Two graduate students in mathematics were supported during the grant period, and have almost completed their thesis research.
Conservation law of plants' energy value dependence of plants ...
African Journals Online (AJOL)
The plants differences in biochemical composition are analyzed, and the conservation law of energy value in plants is obtained. The link between the need for the nutrients and the plants biochemical composition is examined, Liebig's law is specified. Keywords: plant's biochemical composition, biochemistry, energy value in ...
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 Partially Conservative Variable Mass Systems via d'Alembert's Principle
International Nuclear Information System (INIS)
Ahmed, Aftab; Ahmed, Naseer; Khan, Qudrat
2008-01-01
Conservation laws for partially conservative variable mass dynamical systems under symmetric infinitesimal transformations are determined. A generalization of Lagrange-d'Alembert's principle for a variable mass system in terms of asynchronous virtual variation is presented. The generalized Killing equations are obtained such that their solution yields the transformations and the associated conservation laws. An example illustrative of the theory is furnished at the end as well. (the physics of elementary particles and fields)
Power-law and runaway growth in conserved aggregation systems
International Nuclear Information System (INIS)
Yamamoto, Hiroshi; Ohtsuki, Toshiya; Fujihara, Akihiro; Tanimoto, Satoshi
2006-01-01
The z-transform technique is used to analyze the Smoluchowski coagulation equation for conserved aggregation systems. A universal power law with the exponent -5/2 appears when a total 'mass' has a certain critical value. Below the threshold, ordinary scaling relations hold and the system exhibits a behavior like usual critical phenomena. Above the threshold, in contrast, the excess amount of mass coagulates into a runaway member, and remaining members follow the power law. Here the runaway growth coexists with the power law. It is argued that these behaviors are observed universally in conserved aggregation processes
Probing the design of grand unification through conservation laws
International Nuclear Information System (INIS)
Pati, J.C.
1981-01-01
The purpose of this talk is to note a few special consequences of gauging ''maximal'' quark-lepton symmetries such as SO(16), which is the maximal symmetry for a single family of fermions. Within these symmetries, violations for B, L and F are spontaneous rather than explicit. Furthermore these symmetries as a rule permit intermediate mass scales approx.(10 3 -10 6 GeV) and (10 8 -10 11 GeV) filling the so-called grand plateau between 10 2 and 10 15 GeV. It has been shown in earlier papers that within these symmetries proton may decay via four alternative models: i.e. proton→one or three leptons or antileptons plus mesons; some of which can coexist. It is now observed that even n-n-bar oscillations can coexist with (B-L) conserving proton-decays of the type p→e + π 0 etc. without posing any conflict with the cosmological generation of baryon-excess; both these processes can possess measurable strengths so as to be amenable to forthcoming searches. Search for alternative decay modes of proton and n-n-bar oscillations, even as processes in second and third generation experiments, would provide valuable information on the question of intermediate mass-scales and thereby on the design of grand unification
A Note on Weak Solutions of Conservation Laws and Energy/Entropy Conservation
Gwiazda, Piotr; Michálek, Martin; Świerczewska-Gwiazda, Agnieszka
2018-03-01
A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such cases most often related to the second law of thermodynamics. This observation easily generalizes to any symmetrizable system of conservation laws; they are endowed with nontrivial companion conservation laws, which are immediately satisfied by classical solutions. Not surprisingly, weak solutions may fail to satisfy companion laws, which are then often relaxed from equality to inequality and overtake the role of physical admissibility conditions for weak solutions. We want to answer the question: what is a critical regularity of weak solutions to a general system of conservation laws to satisfy an associated companion law as an equality? An archetypal example of such a result was derived for the incompressible Euler system in the context of Onsager's conjecture in the early nineties. This general result can serve as a simple criterion to numerous systems of mathematical physics to prescribe the regularity of solutions needed for an appropriate companion law to be satisfied.
Conservation laws for multidimensional systems and related linear algebra problems
International Nuclear Information System (INIS)
Igonin, Sergei
2002-01-01
We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for the existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A t S and SA=-A t S for a quadratic matrix A and its transpose A t , which may be of independent interest
Symmetry of Hamiltonian and conserved quantity for a system of generalized classical mechanics
International Nuclear Information System (INIS)
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. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Area law microstate entropy from criticality and spherical symmetry
Dvali, Gia
2018-05-01
It is often assumed that the area law of microstate entropy and the holography are intrinsic properties exclusively of the gravitational systems, such as black holes. We construct a nongravitational model that exhibits an entropy that scales as area of a sphere of one dimension less. It is represented by a nonrelativistic bosonic field living on a d -dimensional sphere of radius R and experiencing an angular-momentum-dependent attractive interaction. We show that the system possesses a quantum critical point with the emergent gapless modes. Their number is equal to the area of a d -1 -dimensional sphere of the same radius R . These gapless modes create an exponentially large number of degenerate microstates with the corresponding microstate entropy given by the area of the same d -1 -dimensional sphere. Thanks to a double-scaling limit, the counting of the entropy and of the number of the gapless modes is made exact. The phenomenon takes place for arbitrary number of dimensions and can be viewed as a version of holography.
Convergence of spectral methods for nonlinear conservation laws. Final report
International Nuclear Information System (INIS)
Tadmor, E.
1987-08-01
The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows
Invariance analysis and conservation laws of the wave equation on ...
Indian Academy of Sciences (India)
in [7], the more interesting case being the latter since these lead to conservation laws via ... obtained and, hence, more conservation laws are classified. .... −2r2 sin θurt − 2r sin θut + 2r sin θ. (. 1 −. 2t r. ) ur + 2t sin θur. +r2 sin θ. (. 1 −. 2t r. ) urr + cos θuθ + sin θuθθ = 0,. (15) and then ¯X2 = u∂u + t∂t + r∂r leads to dt t. = dr.
Wu, S. Q.; Cai, X.
2000-01-01
Four classical laws of black hole thermodynamics are extended from exterior (event) horizon to interior (Cauchy) horizon. Especially, the first law of classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to those in quantum form. Then five quantum conservation laws on the KNBH evaporation effect are derived in virtue of thermodynamical equilibrium conditions. As a by-product, Bekenstein-Hawking's relation $ S=A/4 $ is exactly recovered.
International Nuclear Information System (INIS)
Wu, S.Q.; Cai, X.
2000-01-01
Four classical laws of black-hole thermodynamics are extended from exterior (event) horizon to interior (Cauchy) horizon. Especially, the first law of classical thermodynamics for Kerr-Newman black hole (KNBH) is generalized to those in quantum form. Then five quantum conservation laws on the KNBH evaporation effect are derived in virtue of thermodynamical equilibrium conditions. As a by-product, Bekenstein-Haw king's relation S=A/4 is exactly recovered
Infinite set of conservation laws for relativistic string
International Nuclear Information System (INIS)
Isaev, A.P.
1981-01-01
The solution of the Cauchy problem has been found. An infinite class of conserving values Jsub(α) for a free closed relativistic string has been constructed. Jsub(α) values characterize three-parametric generating functions of conservation laws. It is shown using particular examples that it is necessary to order subintegral expressions of quantum values Jsub(α) and do not disturb a property of commutativity with a hamiltonian to attach sense to these values [ru
Notes on the Mass Definition with Covariant Conservation Law
Fujimura, Jun
1990-01-01
Mass definition based on the conservation law of some physical quantities is investigated, adopting the 2nd rank tensor in four space world as the conserving quantity. It is shown that the scalar function appeared as coefficients in the general expression of this tensor quantity should be independent on s, s being the line element of the world line, under the postulate that the trajectories of free particle must be geodesic lines of the world. Discussions are made on this constant factor whic...
Enforcing conservation laws in nonequilibrium cluster perturbation theory
Gramsch, Christian; Potthoff, Michael
2017-05-01
Using the recently introduced time-local formulation of the nonequilibrium cluster perturbation theory (CPT), we construct a generalization of the approach such that macroscopic conservation laws are respected. This is achieved by exploiting the freedom for the choice of the starting point of the all-order perturbation theory in the intercluster hopping. The proposed conserving CPT is a self-consistent propagation scheme which respects the conservation of energy, particle number, and spin, which treats short-range correlations exactly up to the linear scale of the cluster, and which represents a mean-field-like approach on length scales beyond the cluster size. Using Green's functions, conservation laws are formulated as local constraints on the local spin-dependent particle and the doublon density. We consider them as conditional equations to self-consistently fix the time-dependent intracluster one-particle parameters. Thanks to the intrinsic causality of the CPT, this can be set up as a step-by-step time propagation scheme with a computational effort scaling linearly with the maximum propagation time and exponentially in the cluster size. As a proof of concept, we consider the dynamics of the two-dimensional, particle-hole-symmetric Hubbard model following a weak interaction quench by simply employing two-site clusters only. Conservation laws are satisfied by construction. We demonstrate that enforcing them has strong impact on the dynamics. While the doublon density is strongly oscillating within plain CPT, a monotonic relaxation is observed within the conserving CPT.
International Nuclear Information System (INIS)
Zhang Mei-Ling; Wang Xiao-Xiao; Xie Yin-Li; Jia Li-Qun; Sun Xian-Ting
2011-01-01
Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results. (general)
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…
Cayley number and conservation laws for elementary particles
International Nuclear Information System (INIS)
Vollendorf, F.
1975-01-01
It is shown that the five conservation laws of charge, hyper-charge, barion number and the two lepton numbers lead to the construction of a commutative non-associative 24 dimensional linear algebra. Each element of the algebra is an ordered set of three Cayley numbers. (orig.) [de
Gravitation SL(2,C) gauge theory and conservation laws
Carmeli, Moshe; Nissani, Noah
1990-01-01
This monograph gives a comprehensive presentation of the SL(2,C) Gauge Theory of Gravitation along with some recent developments in the problem of Conservation Laws in General Relativity. Emphasis is put on quadratic Lagrangians which yield the Einstein field equations, as compared with Hilbert's original linear Langrangian, thus gravitation follows the other Gauge Fields all of which are derived from nonlinear Lagrangians.
Helicity and other conservation laws in perfect fluid motion
Serre, Denis
2018-03-01
In this review paper, we discuss helicity from a geometrical point of view and see how it applies to the motion of a perfect fluid. We discuss its relation with the Hamiltonian structure, and then its extension to arbitrary space dimensions. We also comment about the existence of additional conservation laws for the Euler equation, and its unlikely integrability in Liouville's sense.
Energy conservation law for randomly fluctuating electromagnetic fields
International Nuclear Information System (INIS)
Gbur, G.; Wolf, E.; James, D.
1999-01-01
An energy conservation law is derived for electromagnetic fields generated by any random, statistically stationary, source distribution. It is shown to provide insight into the phenomenon of correlation-induced spectral changes. The results are illustrated by an example. copyright 1999 The American Physical Society
Calorimeter energy calibration using the energy conservation law
Indian Academy of Sciences (India)
A new calorimeter energy calibration method was developed for the proposed ILC detectors. The method uses the center-of-mass energy of the accelerator as the reference. It has been shown that using the energy conservation law it is possible to make ECAL and HCAL cross calibration to reach a good energy resolution ...
2×2 systems of conservation laws with L data
Bianchini, Stefano; Colombo, Rinaldo M.; Monti, Francesca
Consider a hyperbolic system of conservation laws with genuinely nonlinear characteristic fields. We extend the classical Glimm-Lax (1970) result [13, Theorem 5.1] proving the existence of solutions for L initial datum, relaxing the assumptions taken therein on the geometry of the shock-rarefaction curves.
ADM pseudotensors, conserved quantities and covariant conservation laws in general relativity
International Nuclear Information System (INIS)
Fatibene, L.; Ferraris, M.; Francaviglia, M.; Lusanna, L.
2012-01-01
The ADM formalism is reviewed and techniques for decomposing generic components of metric, connection and curvature are obtained. These techniques will turn out to be enough to decompose not only Einstein equations but also covariant conservation laws. Then a number of independent sets of hypotheses that are sufficient (though not necessary) to obtain standard ADM quantities (and Hamiltonian) from covariant conservation laws are considered. This determines explicitly the range in which standard techniques are equivalent to covariant conserved quantities. The Schwarzschild metric in different coordinates is then considered, showing how the standard ADM quantities fail dramatically in non-Cartesian coordinates or even worse when asymptotically flatness is not manifest; while, in view of their covariance, covariant conservation laws give the correct result in all cases. - Highlights: ► In the paper ADM conserved quantities for GR are obtained from augmented conservation laws. ► Boundary conditions for this to be possible are considered and compared with the literature. ► Some different forms of Schwarzschild solutions are considered as simple examples of different boundary conditions.
Conservation laws in the quantum mechanics of closed systems
International Nuclear Information System (INIS)
Hartle, J.B.; Laflamme, R.; Marolf, D.
1995-01-01
We investigate conservation laws in the quantum mechanics of closed systems and begin by reviewing an argument that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian. However, we also show that decoherence limits the alternatives that can be included in sets of histories that assess the conservation of these quantities. In the case of charge and energy, these limitations would be severe were these quantities not coupled to a gauge field. However, for the realistic cases of electric charge coupled to the electromagnetic field and mass coupled to spacetime curvature, we show that when alternative values of charge and mass decohere they always decohere exactly and are exactly conserved. Further, while decohering histories that describe possible changes in time of the total charge and mass are also subject to the limitations mentioned above, we show that these do not, in fact, restrict physical alternatives and are therefore not really limitations at all
International Nuclear Information System (INIS)
Fu Jing-Li; He Yu-Fang; Hong Fang-Yu; Song Duan; Fu Hao
2013-01-01
In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz—Ladik—Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz—Ladik—Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz—Ladik—Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz—Ladik—Lattice method is verified. (general)
Contractive relaxation systems and interacting particles for scalar conservation laws
International Nuclear Information System (INIS)
Katsoulakis, M.A.; Tzavaras, A.E.
1996-01-01
We consider a class of semi linear hyperbolic systems with relaxation that are contractive in the L 1 -norm and admit invariant regions. We show that, as the relaxation parameter ξ goes to zero, their solutions converge to a weak solution of the scalar multidimensional conversation law that satisfies the Kruzhkov conditions. In the case of one space dimension, we propose certain interacting particle systems, whose mesoscopic limit is the systems with relaxation and their macroscopic dynamics is described by entropy solutions of a scalar conservation law. (author)
Energy Technology Data Exchange (ETDEWEB)
Donchev, Veliko, E-mail: velikod@ie.bas.bg [Laboratory “Physical Problems of Electron and Ion Technologies,” Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko shosse, 1784 Sofia (Bulgaria)
2014-03-15
We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.
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...
Averaged multivalued solutions and time discretization for conservation laws
International Nuclear Information System (INIS)
Brenier, Y.
1985-01-01
It is noted that the correct shock solutions can be approximated by averaging in some sense the multivalued solution given by the method of characteristics for the nonlinear scalar conservation law (NSCL). A time discretization for the NSCL equation based on this principle is considered. An equivalent analytical formulation is shown to lead quite easily to a convergence result, and a third formulation is introduced which can be generalized for the systems of conservation laws. Various numerical schemes are constructed from the proposed time discretization. The first family of schemes is obtained by using a spatial grid and projecting the results of the time discretization. Many known schemes are then recognized (mainly schemes by Osher, Roe, and LeVeque). A second way to discretize leads to a particle scheme without space grid, which is very efficient (at least in the scalar case). Finally, a close relationship between the proposed method and the Boltzmann type schemes is established. 14 references
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.
Propagation of multidimensional nonlinear waves and kinematical conservation laws
Prasad, Phoolan
2017-01-01
This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1–4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved sho...
Physical conservation laws and the β-decay of nuclei
International Nuclear Information System (INIS)
Bagge, E.
1975-04-01
The law of conservation of energy is extended to the region of the Dirac states of negative energy. When particles are produced or disappear, energy changes occur in the negative energy region which can be seen in the positive energy region. The law of conservation of energy then says that the total change in energy is equal to naught. The same is valid for translations and angular momentum. The way in which completely occupied states change energy and momentum is not shown. The β-decay of the neutron is considered as pair production in which an electron is emitted and a positron is bonded to the neutron. Neutrinos are not produced. The latest results on neutrino experiments on accelerators are not discussed. (BJ/LH) [de
On 'conflict of conservation laws in cyclotron radiation'
International Nuclear Information System (INIS)
White, S.M.; Parle, A.J.
1985-01-01
The authors reconsider the apparent conflict of conservation laws in cyclotron radiation, and show that earlier workers in this field did not correctly include the effects of radiation reaction in their calculations. When a 'recoil' term, calculated using relativistic quantum theory, is included in the angular momentum of the particle the conflict disappears. It is found that the guiding centre of the particle drifts outwards during cyclotron radiation. (author)
Determination of constants of factorized pairing force from conservation laws
International Nuclear Information System (INIS)
Voronkov, Yu.P.; Mikhajlov, V.M.
1975-01-01
The constants of a factorized interaction in the particle-particle channel are evaluated on the basis of average field parameters and Cooper pairing. The relations between the constants of multipole particle-particle forces are derived for the spherical nuclei. The constants of the quadrupole pairing are obtained for deformed nuclei from the angular momentum conservation law. The calculated constants are compared with empiricalones
Different realizations of Cooper-Frye sampling with conservation laws
Schwarz, C.; Oliinychenko, D.; Pang, L.-G.; Ryu, S.; Petersen, H.
2018-01-01
Approaches based on viscous hydrodynamics for the hot and dense stage and hadronic transport for the final dilute rescattering stage are successfully applied to the dynamic description of heavy ion reactions at high beam energies. One crucial step in such hybrid approaches is the so-called particlization, which is the transition between the hydrodynamic description and the microscopic degrees of freedom. For this purpose, individual particles are sampled on the Cooper-Frye hypersurface. In this work, four different realizations of the sampling algorithms are compared, with three of them incorporating the global conservation laws of quantum numbers in each event. The algorithms are compared within two types of scenarios: a simple ‘box’ hypersurface consisting of only one static cell and a typical particlization hypersurface for Au+Au collisions at \\sqrt{{s}{NN}}=200 {GeV}. For all algorithms the mean multiplicities (or particle spectra) remain unaffected by global conservation laws in the case of large volumes. In contrast, the fluctuations of the particle numbers are affected considerably. The fluctuations of the newly developed SPREW algorithm based on the exponential weight, and the recently suggested SER algorithm based on ensemble rejection, are smaller than those without conservation laws and agree with the expectation from the canonical ensemble. The previously applied mode sampling algorithm produces dramatically larger fluctuations than expected in the corresponding microcanonical ensemble, and therefore should be avoided in fluctuation studies. This study might be of interest for the investigation of particle fluctuations and correlations, e.g. the suggested signatures for a phase transition or a critical endpoint, in hybrid approaches that are affected by global conservation laws.
Construction of elasto-plastic boundaries using conservation laws
Senashov, S.; Filyushina, E.; Gomonova, O.
2015-01-01
The solution of elasto-plastic problems is one of the most complicated and actual problems of solid mechanics. Traditionally, these problems are solved by the methods of complex analysis, calculus of variations or semi-inverse methods. Unfortunately, all these methods can be applied to a limited number of problems only. In this paper, a technique of conservation laws is used. This technique allows constructing analytical formulas to determine the elasto-plastic boundary for a wide class of pr...
An exactly conservative particle method for one dimensional scalar conservation laws
International Nuclear Information System (INIS)
Farjoun, Yossi; Seibold, Benjamin
2009-01-01
A particle scheme for scalar conservation laws in one space dimension is presented. Particles representing the solution are moved according to their characteristic velocities. Particle interaction is resolved locally, satisfying exact conservation of area. Shocks stay sharp and propagate at correct speeds, while rarefaction waves are created where appropriate. The method is variation diminishing, entropy decreasing, exactly conservative, and has no numerical dissipation away from shocks. Solutions, including the location of shocks, are approximated with second order accuracy. Source terms can be included. The method is compared to CLAWPACK in various examples, and found to yield a comparable or better accuracy for similar resolutions.
Finite difference techniques for nonlinear hyperbolic conservation laws
International Nuclear Information System (INIS)
Sanders, R.
1985-01-01
The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references
International Nuclear Information System (INIS)
Polettini, Matteo; Esposito, Massimiliano
2014-01-01
In this paper and Paper II, we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks “in a box”, whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated with nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation a + b = s Y between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats s Y . We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction, and of thermodynamic constraints for network reconstruction
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.
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.
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
Crystalline Symmetry-Protected Majorana Mode in Number-Conserving Dirac Semimetal Nanowires
Zhang, Rui-Xing; Liu, Chao-Xing
2018-04-01
One of the cornerstones for topological quantum computations is the Majorana zero mode, which has been intensively searched in fractional quantum Hall systems and topological superconductors. Several recent works suggest that such an exotic mode can also exist in a one-dimensional (1D) interacting double-wire setup even without long-range superconductivity. A notable instability in these proposals comes from interchannel single-particle tunneling that spoils the topological ground state degeneracy. Here we show that a 1D Dirac semimetal (DSM) nanowire is an ideal number-conserving platform to realize such Majorana physics. By inserting magnetic flux, a DSM nanowire is driven into a 1D crystalline-symmetry-protected semimetallic phase. Interaction enables the emergence of boundary Majorana zero modes, which is robust as a result of crystalline symmetry protection. We also explore several experimental consequences of Majorana signals.
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.
International Nuclear Information System (INIS)
Jia Liqun; Cui Jinchao; Zhang Yaoyu; Luo Shaokai
2009-01-01
Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results. (general)
Multi-component WKI equations and their conservation laws
Energy Technology Data Exchange (ETDEWEB)
Qu Changzheng [Department of Mathematics, Northwest University, Xi' an 710069 (China) and Center for Nonlinear Studies, Northwest University, Xi' an 710069 (China)]. E-mail: qu_changzheng@hotmail.com; Yao Ruoxia [Department of Computer Sciences, East China Normal University, Shanghai 200062 (China); Department of Computer Sciences, Weinan Teacher' s College, Weinan 715500 (China); Liu Ruochen [Department of Mathematics, Northwest University, Xi' an 710069 (China)
2004-10-25
In this Letter, a two-component WKI equation is obtained by using the fact that when curvature and torsion of a space curve satisfy the vector modified KdV equation, a graph of the curve satisfies the two-component WKI equation, which is a natural generalization to the WKI equation. It is shown that the two-component WKI equation can be solved in terms of the extended WKI scheme, and it admits an infinite number of conservation laws. In the same vein, a n-component generalization to the WKI equation is proposed.
Conformal conservation laws for second-order scalar fields
International Nuclear Information System (INIS)
Blakeskee, J.S.; Logan, J.D.
1976-01-01
It is considered an action integral over space-time whose Lagrangian depends upon a scalar field an upon derivatives of the field function up to second order. From invariance identities obtained by the authors in an earlier work it is shown how a new proof of Noether's theorem for this second-order problem follows in the multiple integral case. Finally, conservation laws are written down in the case that the given action integral be invariant under the fifteen-parameter special conformal group
Conservation laws and mass distribution in the planet formation process
International Nuclear Information System (INIS)
Farinella, P.; Paolicchi, P.
1977-01-01
Within the framework of the nebular theory of the origin of the solar system, conservation laws are applied to the condensation of a ring-shaped cloud of orbiting particles. The final configuration is assumed to be a point-like planet in a circular orbit around the Sun. On this ground, it is possible to relate the masses of the planets with the interplanetary distances. This relation is confirmed satisfactorily by the observed masses and orbital radii of several planets and satellites of the solar system. (Auth.)
Systems of conservation laws with third-order Hamiltonian structures
Ferapontov, Evgeny V.; Pavlov, Maxim V.; Vitolo, Raffaele F.
2018-02-01
We investigate n-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in P^{n+2} satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space W of dimension n+2 , classify n-tuples of skew-symmetric 2-forms A^{α } \\in Λ ^2(W) such that φ _{β γ }A^{β }\\wedge A^{γ }=0, for some non-degenerate symmetric φ.
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.
High-resolution finite-difference algorithms for conservation laws
International Nuclear Information System (INIS)
Towers, J.D.
1987-01-01
A new class of Total Variation Decreasing (TVD) schemes for 2-dimensional scalar conservation laws is constructed using either flux-limited or slope-limited numerical fluxes. The schemes are proven to have formal second-order accuracy in regions where neither u/sub x/ nor y/sub y/ vanishes. A new class of high-resolution large-time-step TVD schemes is constructed by adding flux-limited correction terms to the first-order accurate large-time-step version of the Engquist-Osher scheme. The use of the transport-collapse operator in place of the exact solution operator for the construction of difference schemes is studied. The production of spurious extrema by difference schemes is studied. A simple condition guaranteeing the nonproduction of spurious extrema is derived. A sufficient class of entropy inequalities for a conservation law with a flux having a single inflection point is presented. Finite-difference schemes satisfying a discrete version of each entropy inequality are only first-order accurate
Local conservation law and dark radiation in cosmological braneworld
International Nuclear Information System (INIS)
Minamitsuji, Masato; Sasaki, Misao
2004-01-01
In the context of the Randall-Sundrum (RS) single-brane scenario, we discuss the bulk geometry and dynamics of a cosmological brane in terms of the local energy conservation law which exists for the bulk that allows slicing with a maximally symmetric three-space. This conservation law enables us to define a local mass in the bulk. We show that there is a unique generalization of the dark radiation on the brane, which is given by the local mass. We find there also exists a conserved current associated with the Weyl tensor, and the corresponding local charge, which we call the Weyl charge, is given by the sum of the local mass and a certain linear combination of the components of the bulk energy-momentum tensor. This expression of the Weyl charge relates the local mass to the projected Weyl tensor, E μν , which plays a central role in the geometrical formalism of the RS braneworld. On the brane, in particular, this gives a decomposition of the projected Weyl tensor into the local mass and the bulk energy-momentum tensor. Then, as an application of these results, we consider a null dust model for the bulk energy-momentum tensor and discuss the black hole formation in the bulk. We investigate the causal structure by identifying the locus of the apparent horizon and clarify possible brane trajectories in the bulk. We find that the brane stays always outside the black hole as long as it is expanding. We also find an upper bound on the value of the Hubble parameter in terms of the matter energy density on the brane, irrespective of the energy flux emitted from the brane
Residual distribution for general time-dependent conservation laws
International Nuclear Information System (INIS)
Ricchiuto, Mario; Csik, Arpad; Deconinck, Herman
2005-01-01
We consider the second-order accurate numerical solution of general time-dependent hyperbolic conservation laws over unstructured grids in the framework of the Residual Distribution method. In order to achieve full conservation of the linear, monotone and first-order space-time schemes of (Csik et al., 2003) and (Abgrall et al., 2000), we extend the conservative residual distribution (CRD) formulation of (Csik et al., 2002) to prismatic space-time elements. We then study the design of second-order accurate and monotone schemes via the nonlinear mapping of the local residuals of linear monotone schemes. We derive sufficient and necessary conditions for the well-posedness of the mapping. We prove that the schemes obtained with the CRD formulation satisfy these conditions by construction. Thus the nonlinear schemes proposed in this paper are always well defined. The performance of the linear and nonlinear schemes are evaluated on a series of test problems involving the solution of the Euler equations and of a two-phase flow model. We consider the resolution of strong shocks and complex interacting flow structures. The results demonstrate the robustness, accuracy and non-oscillatory character of the proposed schemes. d schemes
International Nuclear Information System (INIS)
Ting, Pang; Jian-Hui, Fang; Ming-Jiang, Zhang; Peng, Lin; Kai, Lu
2009-01-01
This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system's results. (general)
International Nuclear Information System (INIS)
Hojman, Sergio A.
1996-01-01
The purpose of these lectures is to present some of the ways in which non-Noetherian symmetries are used in contemporary mathematical physics. These include, among others, obtaining conservation laws for dynamical systems, solving non-linear problems, getting alternative Lagrangians for systems of differential equations and constructing symplectic structures and Hamiltonians for dynamical systems starting from scratch
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.
Global conservation laws and femtoscopy of small systems
International Nuclear Information System (INIS)
Chajecki, Zbigniew; Lisa, Mike
2008-01-01
It is increasingly important to understand, in detail, two-pion correlations measured in p+p and d+A collisions. In particular, one wishes to understand the femtoscopic correlations to compare to similar measurements in heavy-ion collisions. However, in the low-multiplicity final states of these systems, global conservation laws generate significant N-body correlations that project onto the two-pion space in nontrivial ways and complicate the femtoscopic analysis. We discuss a formalism to calculate and account for these correlations in collisions dominated by a single particle species (e.g., pions). We also discuss effects on two-particle correlations between nonidentical particles, the understanding of which may be important in the study of femtoscopic space-time asymmetries
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.
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.
The laws of conservation of physics and the β-decay of atomic nuclei
International Nuclear Information System (INIS)
Bagge, E.R.
1976-01-01
The laws of conservation of energy, the momentum of translation and the angular momentum of a system form a closed unit according to Noether's theorem. A generalisation of these laws taking into account the states of negative energies must therefore comprise all laws of conservation. A new interpretation of the β-decay without neutrinos should thus take the law of conservation of energy at the β-continuum for the world and anti-world as motivation to demand corresponding laws of conservation for the linear momentum and the spin and it will be shown that this new interpretation of the laws of conservation exactly suffices to interpret all characteristic phenomena of β-decay in a manner free of contradiction. (orig.) [de
Conservation laws and geometry of perturbed coset models
Bakas, Ioannis
1994-01-01
We present a Lagrangian description of the $SU(2)/U(1)$ coset model perturbed by its first thermal operator. This is the simplest perturbation that changes sign under Krammers--Wannier duality. The resulting theory, which is a 2--component generalization of the sine--Gordon model, is then taken in Minkowski space. For negative values of the coupling constant $g$, it is classically equivalent to the $O(4)$ non--linear $\\s$--model reduced in a certain frame. For $g > 0$, it describes the relativistic motion of vortices in a constant external field. Viewing the classical equations of motion as a zero curvature condition, we obtain recursive relations for the infinitely many conservation laws by the abelianization method of gauge connections. The higher spin currents are constructed entirely using an off--critical generalization of the $W_{\\infty}$ generators. We give a geometric interpretation to the corresponding charges in terms of embeddings. Applications to the chirally invariant $U(2)$ Gross--Neveu model ar...
On the structure of the new electromagnetic conservation laws
International Nuclear Information System (INIS)
Edgar, S Brian
2004-01-01
New electromagnetic conservation laws have recently been proposed: in the absence of electromagnetic currents, the trace of the Chevreton superenergy tensor, H ab is divergence free in four-dimensional (a) Einstein spacetimes for test fields, and (b) Einstein-Maxwell spacetimes. Subsequently it has been pointed out, in analogy with flat spaces, that for Ricci-flat spacetimes the trace of the Chevreton superenergy tensor H ab can be rearranged in the form of a generalized wave operator □ L acting on the energy-momentum tensor T ab of the test fields, i.e., H ab □ L T ab /2. In this letter we show, for Einstein-Maxwell spacetimes in the full nonlinear theory, that, although, the trace of the Chevreton superenergy tensor H ab can again be rearranged in the form of a generalized wave operator □ G acting on the electromagnetic energy-momentum tensor, in this case the result is also crucially dependent on Einstein's equations; hence we argue that the divergence-free property of the tensor H ab = □ G T ab /2 has significant independent content beyond that of the divergence-free property of T ab . (letter to the editor)
Investigating and improving introductory physics students’ understanding of symmetry and Gauss’s law
Li, Jing; Singh, Chandralekha
2018-01-01
We discuss an investigation of student difficulties with symmetry and Gauss’s law and how the research on students’ difficulties was used as a guide to develop a tutorial related to these topics to help students in the calculus-based introductory physics courses learn these concepts. During the development of the tutorial, we interviewed students individually at various stages of development and administered written tests in the free-response and multiple-choice formats on these concepts to learn about common student difficulties. We also obtained feedback from physics instructors who teach introductory physics courses regularly in which these concepts were covered. The students in several ‘equivalent’ sections worked on the tutorial after traditional lecture-based instruction. We discuss the performance of students on the written pre-test (administered after lecture-based instruction in relevant concepts) and post-test given after students worked on the tutorial. We find that on the pre-test, all sections of the course performed comparably regardless of the instructor. Also, on average, student performance on the post-test after working on the tutorial is significantly better than on the pre-test after lecture-based instruction. We also compare the post-test performance of introductory students in sections of the course in which the tutorial was used versus not used and find that sections in which students engaged with the tutorial outperformed those in which students did not engage with it.
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.
Approximate Noether symmetries and collineations for regular perturbative Lagrangians
Paliathanasis, Andronikos; Jamal, Sameerah
2018-01-01
Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.
Conservation laws in quantum mechanics on a Riemannian manifold
International Nuclear Information System (INIS)
Chepilko, N.M.
1992-01-01
In Refs. 1-5 the quantum dynamics of a particle on a Riemannian manifold V n is considered. The advantage of Ref. 5, in comparison with Refs. 1-4, is the fact that in it the differential-geometric character of the theory and the covariant definition (via the known Lagrangian of the particle) of the algebra of quantum-mechanical operators on V n are mutually consistent. However, in Ref. 5 the procedure for calculating the expectation values of operators from the known wave function of the particle is not discussed. In the authors view, this question is problematical and requires special study. The essence of the problem is that integration on a Riemannian manifold V n , unlike that of a Euclidean manifold R n , is uniquely defined only for scalars. For this reason, the calculation of the expectation value of, e.g., the operator of the momentum or angular momentum of a particle on V n is not defined in the usual sense. However, this circumstance was not taken into account by the authors of Refs. 1-4, in which quantum mechanics on a Riemannian manifold V n was studied. In this paper the author considers the conservation laws and a procedure for calculating observable quantities in the classical mechanics (Sec. 2) and quantum mechanics (Sec. 3) of a particle on V n . It is found that a key role here is played by the Killing vectors of the Riemannian manifold V n . It is shown that the proposed approach to the problem satisfies the correspondence principle for both the classical and the quantum mechanics of a particle on a Euclidean manifold R n
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
Solutions and conservation laws of Benjamin–Bona–Mahony
Indian Academy of Sciences (India)
In this paper, exact solutions of Benjamin–Bona–Mahony–Peregrine equation are obtained with power-law and dual power-law nonlinearities. The Lie group analysis as well as the simplest equation method are used to carry out the integration of these equations. The solutions obtained are cnoidal waves, periodic solutions ...
Numerical viscosity of entropy stable schemes for systems of conservation laws. Final Report
International Nuclear Information System (INIS)
Tadmor, E.
1985-11-01
Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones
Generalized symmetries and conserved quantities of the Lotka-Volterra model
Baumann, G.; Freyberger, M.
1991-07-01
We examine the generalized symmetries of the Lotka-Volterra model to find the parameter values at which one time-dependent integral of motion exists. In this case the integral can be read off from the symmetries themselves. We also demonstrate the connection to a Hamiltonian structure of the Lotka-Volterra model.
On 'conflict of conservation laws in cyclotron radiation'
International Nuclear Information System (INIS)
DasGupta, P.
1984-01-01
It is shown that conservation of energy, linear momentum and angular momentum are all compatible with each other in the case of an electron undergoing cyclotron emission in a uniform and constant magnetic field. The flaw in the argument of previous workers claiming the incompatibility of the conservation principles is also pointed out. (author)
Classically and quantum stable emergent universe from conservation laws
Energy Technology Data Exchange (ETDEWEB)
Campo, Sergio del; Herrera, Ramón [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2950, Casilla 4059, Valparaíso (Chile); Guendelman, Eduardo I. [Physics Department, Ben Gurion University of the Negev, Beer Sheva 84105 (Israel); Labraña, Pedro, E-mail: guendel@bgu.ac.il, E-mail: ramon.herrera@ucv.cl, E-mail: plabrana@ubiobio.cl [Departamento de Física, Universidad del Bío Bío and Grupo de Cosmología y Gravitación-UBB, Avenida Collao 1202, Casilla 5-C, Concepción (Chile)
2016-08-01
It has been recently pointed out by Mithani-Vilenkin [1-4] that certain emergent universe scenarios which are classically stable are nevertheless unstable semiclassically to collapse. Here, we show that there is a class of emergent universes derived from scale invariant two measures theories with spontaneous symmetry breaking (s.s.b) of the scale invariance, which can have both classical stability and do not suffer the instability pointed out by Mithani-Vilenkin towards collapse. We find that this stability is due to the presence of a symmetry in the 'emergent phase', which together with the non linearities of the theory, does not allow that the FLRW scale factor to be smaller that a certain minimum value a {sub 0} in a certain protected region.
International Nuclear Information System (INIS)
Webb, G M; Zank, G P
2007-01-01
We explore the role of the Lagrangian map for Lie symmetries in magnetohydrodynamics (MHD) and gas dynamics. By converting the Eulerian Lie point symmetries of the Galilei group to Lagrange label space, in which the Eulerian position coordinate x is regarded as a function of the Lagrange fluid labels x 0 and time t, one finds that there is an infinite class of symmetries in Lagrange label space that map onto each Eulerian Lie point symmetry of the Galilei group. The allowed transformation of the Lagrangian fluid labels x 0 corresponds to a fluid relabelling symmetry, including the case where there is no change in the fluid labels. We also consider a class of three, well-known, scaling symmetries for a gas with a constant adiabatic index γ. These symmetries map onto a modified form of the fluid relabelling symmetry determining equations, with non-zero source terms. We determine under which conditions these symmetries are variational or divergence symmetries of the action, and determine the corresponding Lagrangian and Eulerian conservation laws by use of Noether's theorem. These conservation laws depend on the initial entropy, density and magnetic field of the fluid. We derive the conservation law corresponding to the projective symmetry in gas dynamics, for the case γ = (n + 2)/n, where n is the number of Cartesian space coordinates, and the corresponding result for two-dimensional (2D) MHD, for the case γ = 2. Lie algebraic structures in Lagrange label space corresponding to the symmetries are investigated. The Lie algebraic symmetry relations between the fluid relabelling symmetries in Lagrange label space, and their commutators with a linear combination of the three symmetries with a constant adiabatic index are delineated
Lehoucq, R B; Sears, Mark P
2011-09-01
The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics.
The Conservation Status of Eagles in South African Law | Knobel ...
African Journals Online (AJOL)
... and succumb); habitat loss; mortality induced by dangerous structures; and disturbance. ... prey species that are not Critically Endangered, Endangered, or Vulnerable, ... Better application of the existing laws could be achieved by improving ...
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.
Tendril perversion-a physical implication of the topological conservation law
International Nuclear Information System (INIS)
Pieranski, Piotr; Baranska, Justyna; Skjeltorp, Arne
2004-01-01
Tendril perversion-a phenomenon ruled by the topological conservation law-is presented. A contemporary, quantitative analysis of the phenomenon is confronted with its qualitative, intuitive analysis carried out by Charles Darwin. The linking number, twist and writhe are defined. The topological conservation law is introduced. The Gauss formula for calculating the linking number and the Calugareanu formula for calculating writhe are derived and discussed using physical arguments
Tendril perversion-a physical implication of the topological conservation law
Energy Technology Data Exchange (ETDEWEB)
Pieranski, Piotr [Laboratory of Computational Physics and Semiconductors, Poznan University of Technology, Nieszawska 13A, 60 965 Poznan (Poland); Baranska, Justyna [Laboratory of Computational Physics and Semiconductors, Poznan University of Technology, Nieszawska 13A, 60 965 Poznan (Poland); Skjeltorp, Arne [Institute for Energy Technology, Kjeller (Norway)
2004-09-10
Tendril perversion-a phenomenon ruled by the topological conservation law-is presented. A contemporary, quantitative analysis of the phenomenon is confronted with its qualitative, intuitive analysis carried out by Charles Darwin. The linking number, twist and writhe are defined. The topological conservation law is introduced. The Gauss formula for calculating the linking number and the Calugareanu formula for calculating writhe are derived and discussed using physical arguments.
Bianchi-Baecklund transformations, conservation laws, and linearization of various field theories
International Nuclear Information System (INIS)
Chau Wang, L.L.
1980-01-01
The discussion includes: the Sine-Gordon equation, parametric Bianchi-Baecklund transformations and the derivation of local conservation laws; chiral fields, parametric Bianchi-Baecklund transformations, local and non-local conservation laws, and linearization; super chiral fields, a parallel development similar to the chiral field; and self-dual Yang-Mills fields in 4-dimensional Euclidean space; loop-cpace chiral equations, parallel development but with subtlety
the conservation status of eagles in south african law
African Journals Online (AJOL)
10332324
The conservation threats to eagles in South Africa may be classified into two broad ..... 3.1.6 The Convention on Persistent Organic Pollutants (2001) (the ...... South Africa has highly advanced biodiversity legislation in place, but merely having.
Nearly auto-parallel maps and conservation laws on curved spaces
International Nuclear Information System (INIS)
Vacaru, S.
1994-01-01
The theory of nearly auto-parallel maps (na-maps, generalization of conformal transforms) of Einstein-Cartan spaces is formulated. The transformation laws of geometrical objects and gravitational and matter field equations under superpositions of na-maps are considered. A special attention is paid to the very important problem of definition of conservation laws for gravitational fields. (Author)
EL-Kalaawy, O. H.
2018-02-01
We consider the nonlinear propagation of non-planar (cylindrical and spherical) ion-acoustic (IA) envelope solitary waves in an unmagnetized plasma consisting of electron-positron-ion-dust plasma with two-electron temperature distributions in the context of the non-extensive statistics. The basic set of fluid equations is reduced to the modified nonlinear Schrödinger (MNLS) equation in cylindrical and spherical geometry by using the reductive perturbation method (RPM). It is found that the nature of the modulational instabilities would be significantly modified due to the effects of the non-extensive and other plasma parameters as well as cylindrical and spherical geometry. Conservation laws of the MNLS equation are obtained by Lie symmetry and multiplier method. A new exact solution (envelope bright soliton) is obtained by the extended homogeneous balance method. Finally, we study the results of this article.
Simple connection between conservation laws in the Korteweg--de Vriesand sine-Gordon systems
International Nuclear Information System (INIS)
Chodos, A.
1980-01-01
An infinite sequence of conserved quantities follows from the Lax representation in both the Korteweg--de Vries and sine-Gordon systems. We show that these two sequences are related by a simple substitution. In an appendix, two different methods of deriving conservation laws from the Lax representation are presented
On a quantum version of conservation laws for derivative nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Sen, S.; Chowdhury, A.R.
1988-01-01
The authors derived the quantum mechanical versions of infinite number of conservation laws associated with Derivative Nonlinear Schrodinger equation with the help of a methodology used in string theory. The renormalised version of the conserved quantities are obtained with explicit forms of the counter terms
Conservation laws for steady flow and solitons in a multifluid plasma revisited
International Nuclear Information System (INIS)
Mace, R. L.; McKenzie, J. F.; Webb, G. M.
2007-01-01
The conservation laws used in constructing the governing equations for planar solitons in multifluid plasmas are revisited. In particular, the concept of generalized vorticity facilitates the derivation of some general ''Bernoulli theorems,'' which reduce, in specific instances, to conservation laws previously deduced by other means. These theorems clarify the underlying physical principles that give rise to the conserved quantities. As an example of the usefulness of the techniques, even for relatively simple flows and progressive waves, the equations governing stationary nonlinear whistler waves propagating parallel to an ambient magnetic field are derived using generalized vorticity concepts
International Nuclear Information System (INIS)
Nordbrock, U.; Kienzler, R.
2007-01-01
Conservation laws are a recognized tool in physical and engineering sciences. The classical procedure to construct conservation laws is to apply Noether's Theorem. It requires the existence of a Lagrange-function for the system under consideration. Two unknown sets of functions have to be found. A broader class of such laws is obtainable, if Noether's Theorem is used together with the Bessel-Hagen extension, raising the number of sets of unknown functions to three. By using the recently developed Neutral-Action Method, the same conservation laws can be obtained by calculating only one unknown set of functions. Moreover the Neutral Action Method can also be applied in the absence of a Lagrangian, since only the governing differential equations are required for this procedure. In the paper, an application of this method to the Schroedinger equation is presented. (authors)
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao
2016-04-01
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 δPnad, another is for a general matter field δPc,nad, and the last one is valid only on superhorizon scales. The first two definitions coincide if cs2 = cw2 where cs is the propagation speed of the perturbation, while cw2 = P ˙ / ρ ˙ . Assuming the adiabaticity in the general sense, δPc,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δPnad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs ≠cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δPnad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. 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.
Scaling and scale invariance of conservation laws in Reynolds transport theorem framework
Haltas, Ismail; Ulusoy, Suleyman
2015-07-01
Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.
Soft black hole absorption rates as conservation laws
International Nuclear Information System (INIS)
Avery, Steven G.; Schwab, Burkhard UniversityW.
2017-01-01
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.
Soft black hole absorption rates as conservation laws
Energy Technology Data Exchange (ETDEWEB)
Avery, Steven G. [Brown University, Department of Physics,182 Hope St, Providence, RI, 02912 (United States); Michigan State University, Department of Physics and Astronomy,East Lansing, MI, 48824 (United States); Schwab, Burkhard UniversityW. [Harvard University, Center for Mathematical Science and Applications,1 Oxford St, Cambridge, MA, 02138 (United States)
2017-04-10
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.
Applications of hidden symmetries to black hole physics
International Nuclear Information System (INIS)
Frolov, Valeri
2011-01-01
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.
Identifying all moiety conservation laws in genome-scale metabolic networks.
De Martino, Andrea; De Martino, Daniele; Mulet, Roberto; Pagnani, Andrea
2014-01-01
The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.
Identifying all moiety conservation laws in genome-scale metabolic networks.
Directory of Open Access Journals (Sweden)
Andrea De Martino
Full Text Available The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.
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
Multiplicity fluctuations in a hadron gas with exact conservation laws
International Nuclear Information System (INIS)
Becattini, Francesco; Keraenen, Antti; Ferroni, Lorenzo; Gabbriellini, Tommaso
2005-01-01
The study of fluctuations of particle multiplicities in relativistic heavy-ion reactions has drawn much attention in recent years, because they have been proposed as a probe for underlying dynamics and possible formation of quark-gluon plasma. Thus it is of uttermost importance to describe the baseline of statistical fluctuations in the hadron gas phase in a correct way. We performed a comprehensive study of multiplicity distributions in the full ideal hadron-resonance gas in different ensembles, namely grand canonical, canonical, and microcanonical, by using two different methods: Asymptotic expansions and full Monte Carlo simulations. The method based on asymptotic expansion allows a quick numerical calculation of dispersions in the hadron gas with three conserved charges at the primary hadron level, while the Monte Carlo simulation is suitable for studying the effect of resonance decays. Even though mean multiplicities converge to the same values, major differences in fluctuations for these ensembles persist in the thermodynamic limit, as pointed out in recent studies. We observe that this difference is ultimately related to the nonadditivity of the variances in the ensembles with exact conservation of extensive quantities
Symmetry and symmetry breaking
International Nuclear Information System (INIS)
Balian, R.; Lambert, D.; Brack, A.; Lachieze-Rey, M.; Emery, E.; Cohen-Tannoudji, G.; Sacquin, Y.
1999-01-01
The symmetry concept is a powerful tool for our understanding of the world. It allows a reduction of the volume of information needed to apprehend a subject thoroughly. Moreover this concept does not belong to a particular field, it is involved in the exact sciences but also in artistic matters. Living beings are characterized by a particular asymmetry: the chiral asymmetry. Although this asymmetry is visible in whole organisms, it seems it comes from some molecules that life always produce in one chirality. The weak interaction presents also the chiral asymmetry. The mass of particles comes from the breaking of a fundamental symmetry and the void could be defined as the medium showing as many symmetries as possible. The texts put together in this book show to a great extent how symmetry goes far beyond purely geometrical considerations. Different aspects of symmetry ideas are considered in the following fields: the states of matter, mathematics, biology, the laws of Nature, quantum physics, the universe, and the art of music. (A.C.)
Barker, Blake; Jung, Soyeun; Zumbrun, Kevin
2018-03-01
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability in conservation laws and (ii) use these conditions to find families of periodic solutions bifurcating from uniform states, numerically continuing these families into the large-amplitude regime. For the examples studied, numerical stability analysis suggests that stable periodic waves can emerge either from supercritical Turing bifurcations or, via secondary bifurcation as amplitude is increased, from subcritical Turing bifurcations. This answers in the affirmative a question of Oh-Zumbrun whether stable periodic solutions of conservation laws can occur. Determination of a full small-amplitude stability diagram - specifically, determination of rigorous Eckhaus-type stability conditions - remains an interesting open problem.
Conservation law for distributed entanglement of formation and quantum discord
International Nuclear Information System (INIS)
Fanchini, Felipe F.; Cornelio, Marcio F.; Oliveira, Marcos C. de; Caldeira, Amir O.
2011-01-01
We present a direct relation, based upon a monogamic principle, between entanglement of formation (EOF) and quantum discord (QD), showing how they are distributed in an arbitrary tripartite pure system. By extending it to a paradigmatic situation of a bipartite system coupled to an environment, we demonstrate that the EOF and the QD obey conservation relation. By means of this relation we show that in the deterministic quantum computer with one pure qubit the protocol has the ability to rearrange the EOF and the QD, which implies that quantum computation can be understood on a different basis as a coherent dynamics where quantum correlations are distributed between the qubits of the computer. Furthermore, for a tripartite mixed state we show that the balance between distributed EOF and QD results in a stronger version of the strong subadditivity of entropy.
Conservation Laws for Gyrokinetic Equations for Large Perturbations and Flows
Dimits, Andris
2017-10-01
Gyrokinetic theory has proved to be very useful for the understanding of magnetized plasmas, both to simplify analytical treatments and as a basis for efficient numerical simulations. Gyrokinetic theories were previously developed in two extended orderings that are applicable to large fluctuations and flows as may arise in the tokamak edge and scrapeoff layer. In the present work, we cast the resulting equations in a field-theoretical variational form, and derive, up to second order in the respective orderings, the associated global and local energy and (linear and toroidal) momentum conservation relations that result from Noether's theorem. The consequences of these for the various possible choices of numerical discretization used in gyrokinetic simulations are considered. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and supported by the U.S. DOE, OFES.
International Nuclear Information System (INIS)
Havas, P.
1978-01-01
The various classical or quantum mechanical equations describing a system of N particles with central two-body interactions are invariant under the 10 transformations of the Galilei group, and for interaction potential inversely proportional to the squares of the particle separations also under two further transformations. From the invariance of the corresponding classical and quantum mechanical variation principles under this 12-parameter conformal extension of the Galilei group, the 'Jacobi-Schroedinger group', the 12 well-known conservation laws of Newtonian dynamics as well as 12 local conservation laws implied by the Schroedinger equation are obtained via Noether's theorem. Under appropriate conditions on the wave functions, these local laws yield 12 global conservation laws which are analogous to the Newtonian ones. The Hamiltonian-Jacobi equation implies a classical equation differing from the Schroedinger equation only by a potential-like term involving the Van Vleck determinant, from which 12 local balance equations and the corresponding global equations are obtained, which under certain conditions reduce the true conservation laws. (Auth.)
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.
On the checking of electric charge conservation law and the pauli principle
International Nuclear Information System (INIS)
Okun', L.B.
1989-01-01
This is a short critical review of the attempts to check the accuracy with which are carried out in experiment the electric charge conservation law and the Pauli principle. The absence of the inwardly noncontradictory phenomenological theory is emphasized, which could describe the charge conservation and/or the Pauli principle violation. Under charge nonconservation longitudinal photons are of a principal importance. New suggestions concerning the principle Puli checking are discussed
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; Ketcheson, David I.; Savostianov, Igor
2014-01-01
An error analysis is presented for explicit partitioned Runge–Kutta methods and multirate methods applied to conservation laws. The interfaces, across which different methods or time steps are used, lead to order reduction of the schemes. Along with cell-based decompositions, also flux-based decompositions are studied. In the latter case mass conservation is guaranteed, but it will be seen that the accuracy may deteriorate.
Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles
2011-01-01
Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.
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.
Conservation laws of wave action and potential enstrophy for Rossby waves in a stratified atmosphere
Straus, D. M.
1983-01-01
The evolution of wave energy, enstrophy, and wave motion for atmospheric Rossby waves in a variable mean flow are discussed from a theoretical and pedagogic standpoint. In the absence of mean flow gradients, the wave energy density satisfies a local conservation law, with the appropriate flow velocity being the group velocity. In the presence of mean flow variations, wave energy is not conserved, but wave action is, provided the mean flow is independent of longitude. Wave enstrophy is conserved for arbitrary variations of the mean flow. Connections with Eliassen-Palm flux are also discussed.
Natural R parity conservation with horizontal symmetries: A four generation model
International Nuclear Information System (INIS)
Berezhiani, Z.; Nardi, E.
1995-01-01
In most supersymmetric models the stability of the proton is ensured by invoking R parity. A necessary ingredient to enforce R parity is the possibility of distinguishing the lepton superfields from the Higgs ones. This is generally achieved either by assuming different charges under some matter parity, or by assigning the superfields to different representations of a unified gauge group. We want to put forward the idea that the replica of the fermion generations, which constitute an intrinsic difference between the fermions and the Higgs superfields, can give a clue to understanding R parity as an accidental symmetry. More ambitiously, we suggest a possible relation between proton stability and the actual number of fermion generations. We carry out our investigation in the framework of non-Abelian horizontal gauge symmetries. We identify SU(4) H as the only acceptable horizontal gauge group which can naturally ensure the absence of R-parity-violating operators, without conflicting with other theoretical and phenomenological constraints. We analyze a version of the supersymmetric standard model equipped with a gauged horizontal SU(4) H , in which R parity is accidental. The model predicts four families of fermions, it allows for the dynamical generation of a realistic hierarchy of fermion masses without any ad hoc choice of small Yukawa couplings; it ensures in a natural way the heaviness of all the fourth family fermions (including the neutrino), and it predicts a lower limit for the τ-neutrino mass of a few eV. The scale of the breaking of the horizontal symmetry can be constrained rather precisely in a narrow window around ∼10 11 GeV. Some interesting astrophysical and cosmological implications of the model are addressed as well
International Nuclear Information System (INIS)
Sheftel', M.B.
1997-01-01
The basics of modern group analysis of different equations are presented. The group analysis produces in a natural way the variables, which are most suitable for a problem of question, and also the associated differential-geometric structures, such as pseudo Riemann geometry, connections, Hamiltonian and Lagrangian formalism
Waves, conservation laws and symmetries of a third-order nonlinear ...
African Journals Online (AJOL)
user
We observe that a linear part of the wave vector is overlaid. .... Eq.(1) admits the three-dimensional Lie algebra L of its classical ...... He did his diploma thesis titled 'Systematic in the physics of elementary particles focusing the quarkonium ...
Conservation laws arising in the study of forward-forward Mean-Field Games
Gomes, Diogo A.; Nurbekyan, Levon; Sedjro, Marc
2017-01-01
We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models.
Conservation laws in disordered electron systems: Thermodynamic limit and configurational averaging
Czech Academy of Sciences Publication Activity Database
Janiš, Václav; Kolorenč, Jindřich
2004-01-01
Roč. 241, č. 9 (2004), s. 2032-2042 ISSN 0370-1972 R&D Projects: GA ČR GA202/04/1055 Institutional research plan: CEZ:AV0Z1010914 Keywords : conservation laws * noninteracting disordered electrons * diffusion pole Subject RIV: BE - Theoretical Physics Impact factor: 0.982, year: 2004
From conservation laws to port-Hamiltonian representations of distributed-parameter systems
Maschke, B.M.; van der Schaft, Arjan; Piztek, P.
Abstract: In this paper it is shown how the port-Hamiltonian formulation of distributed-parameter systems is closely related to the general thermodynamic framework of systems of conservation laws and closure equations. The situation turns out to be similar to the lumped-parameter case where the
Conservation laws and self-consistent sources for a super-CKdV equation hierarchy
International Nuclear Information System (INIS)
Li Li
2011-01-01
From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy.
On the coupling of systems of hyperbolic conservation laws with ordinary differential equations
International Nuclear Information System (INIS)
Borsche, Raul; Colombo, Rinaldo M; Garavello, Mauro
2010-01-01
Motivated by applications to the piston problem, to a manhole model, to blood flow and to supply chain dynamics, this paper deals with a system of conservation laws coupled with a system of ordinary differential equations. The former is defined on a domain with boundary and the coupling is provided by the boundary condition. For each of the examples considered, numerical integrations are provided
Generalized internal long wave equations: construction, hamiltonian structure and conservation laws
International Nuclear Information System (INIS)
Lebedev, D.R.
1982-01-01
Some aspects of the theory of the internal long-wave equations (ILW) are considered. A general class of the ILW type equations is constructed by means of the Zakharov-Shabat ''dressing'' method. Hamiltonian structure and infinite numbers of conservation laws are introduced. The considered equations are shown to be Hamiltonian in the so-called second Hamiltonian structu
1/N perturbation theory and quantum conservation laws for supersymmetrical chiral field. 2
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Krivoshchekov, V.K.; Medvedev, P.B.; Gosudarstvennyj Komitet Standartov Soveta Ministrov SSSR, Moscow; Gosudarstvennyj Komitet po Ispol'zovaniyu Atomnoj Ehnergii SSSR, Moscow. Inst. Teoreticheskoj i Ehksperimental'noj Fiziki)
1980-01-01
The renormalizability of the supersymmetric chiral model (supersymmetric nonlinear σ-model) is proved in the framework of the 1/N perturbation theory expansion proposed in the previous paper. The renormalizability proof is essentially based on the quantum supersymmetric chirality condition. The supersymmetric formulation of equations of motion is given. The first non-trivial quantum conservation laws are derived
Sensitivity analysis of 1−d steady forced scalar conservation laws
Czech Academy of Sciences Publication Activity Database
Ersoy, M.; Feireisl, Eduard; Zuazua, E.
2013-01-01
Roč. 254, č. 9 (2013), s. 3817-3834 ISSN 0022-0396 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : sensitivity * scalar conservation law * control Subject RIV: BA - General Mathematics Impact factor: 1.570, year: 2013 http://www.sciencedirect.com/science/article/pii/S0022039613000892#
Interactions of Delta Shock Waves for Zero-Pressure Gas Dynamics with Energy Conservation Law
Wei Cai; Yanyan Zhang
2016-01-01
We study the interactions of delta shock waves and vacuum states for the system of conservation laws of mass, momentum, and energy in zero-pressure gas dynamics. The Riemann problems with initial data of three piecewise constant states are solved case by case, and four different configurations of Riemann solutions are constructed. Furthermore, the numerical simulations completely coinciding with theoretical analysis are shown.
Exact solutions for a discrete unidimensional Boltzmann model satisfying all conservation laws
International Nuclear Information System (INIS)
Cornille, H.
1989-01-01
We consider a four-velocity discrete and unidimensional Boltzmann model. The mass, momentum and energy conservation laws being satisfied we can define a temperature. We report the exact positive solutions which have been found: periodic in the space and propagating or not when the time is growing, shock waves similarity solutions and (1 + 1)-dimensional solutions [fr
Lax pairs and conservation laws for two differential-difference systems
International Nuclear Information System (INIS)
Li Chunxia
2003-01-01
A coupled extended Lotka-Volterra lattice and a special Toda lattice are derived from the existing bilinear equations. Starting from the corresponding bilinear Baecklund transformation, Lax pairs for these two differential-difference systems are obtained. Furthermore, an infinite number of conservation laws for the differential-difference equations are deduced from the Lax pairs in a systematic way
Conservation laws for two (2 + 1)-dimensional differential-difference systems
International Nuclear Information System (INIS)
Yu Guofu; Tam, H.-W.
2006-01-01
Two integrable differential-difference equations are considered. One is derived from the discrete BKP equation and the other is a symmetric (2 + 1)-dimensional Lotka-Volterra equation. An infinite number of conservation laws for the two differential-difference equations are deduced
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 arising in the study of forward-forward Mean-Field Games
Gomes, Diogo A.
2017-04-24
We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models.
Du, Xia-Xia; Tian, Bo; Chai, Jun; Sun, Yan; Yuan, Yu-Qiang
2017-11-01
In this paper, we investigate a (3+1)-dimensional modified Zakharov-Kuznetsov equation, which describes the nonlinear plasma-acoustic waves in a multicomponent magnetised plasma. With the aid of the Hirota method and symbolic computation, bilinear forms and one-, two- and three-soliton solutions are derived. The characteristics and interaction of the solitons are discussed graphically. We present the effects on the soliton's amplitude by the nonlinear coefficients which are related to the ratio of the positive-ion mass to negative-ion mass, number densities, initial densities of the lower- and higher-temperature electrons and ratio of the lower temperature to the higher temperature for electrons, as well as by the dispersion coefficient, which is related to the ratio of the positive-ion mass to the negative-ion mass and number densities. Moreover, using the Lie symmetry group theory, we derive the Lie point symmetry generators and the corresponding symmetry reductions, through which certain analytic solutions are obtained via the power series expansion method and the (G'/G) expansion method. We demonstrate that such an equation is strictly self-adjoint, and the conservation laws associated with the Lie point symmetry generators are derived.
Nonlocal symmetry generators and explicit solutions of some partial differential equations
International Nuclear Information System (INIS)
Qin Maochang
2007-01-01
The nonlocal symmetry of a partial differential equation is studied in this paper. The partial differential equation written as a conservation law can be transformed into an equivalent system by introducing a suitable potential. The nonlocal symmetry group generators of original partial differential equations can be obtained through their equivalent system. Further, new explicit solutions can be constructed from the newly obtained symmetry generators. The Burgers equation is chosen as an example; many new valuable explicit solutions and nonlocal symmetry generators are presented
International Nuclear Information System (INIS)
Alexander, P.
1993-01-01
A hydromagnetic equation system for the interplanetary collisionless solar wind is used to derive a set of conservation laws for that medium. It is found that every equation of the original system, including the closure relation, is related to one conservation law. The set that has been derived does not only include the traditional laws, but also a new one for the magnetic moment of the electrons. The conservation set is then used to obtain the space constants for the solar coronal expansion. The new law yields a constant that has not been predicted by other models
Seniority-conserving forces and USp(2j+1) partial dynamical symmetry
International Nuclear Information System (INIS)
Rosensteel, G.; Rowe, D.J.
2003-01-01
A quasispin tensor decomposition of the two-nucleon interaction determines the most general seniority-conserving rotationally invariant two-body interaction in a j shell. Such interactions define solvable and partially solvable shell model Hamiltonians for which the unitary symplectic algebra USp(2j+1) provides a complete set of quantum numbers for a subset of states. The matrix elements of seniority-conserving interactions are deduced from the matrix elements of USp(2j+1) operators. A new and powerful numerical technique is presented for computing irreps of the USp(2j+1) algebra. Applications are reported for the low-energy spectra of N=50 and N=126 isotones. The effects of including seniority nonconserving interactions are investigated
Background Killing vectors and conservation laws in Rosen's bimetric theories of gravitation
International Nuclear Information System (INIS)
Israelit, M.
1979-01-01
The problem of global energy, linear momentum, and angular momentum in Rosen's bimetric theories of gravitation is considered from the point of view of motions of the background space-time. It turns out that by means of background Killing vectors global mechanical integrals for matter and field can be defined in a correct manner. For the flat-background bimetric theory conditions are obtained which have been imposed on the algebraic structure of the matter tensor Tsub(μ)sup(ν) in order to get global mechanical conservation laws. For bimetric gravitation theories based on a cosmological (nonflat) background the set of Killing vectors is found. For these theories the obtained restrictions on the algebraic structure of Tsub(μ)sup(ν) lead to global generation laws (instead of conservation laws in the flat-background theory) for mechanical quantities. In particular cases the generation effect vanishes and then conservation laws exist. By means of the method developed in this paper, Rosen's homogeneous isotropic universe in the framework of the cosmological-background bimetric theory with k = 1 is considered. It turns out that such a universe does not generate globally, but will generate locally. The global energy of this universe is found to be zero. (author)
Kleinstein, G. G.; Gunzburger, M. D.
1976-01-01
An integral conservation law for wave numbers is considered. In order to test the validity of the proposed conservation law, a complete solution for the reflection and transmission of an acoustic wave impinging normally on a material interface moving at a constant speed is derived. The agreement between the frequency condition thus deduced from the dynamic equations of motion and the frequency condition derived from the jump condition associated with the integral equation supports the proposed law as a true conservation law. Additional comparisons such as amplitude discontinuities and Snells' law in a moving media further confirm the stated proposition. Results are stated concerning frequency and wave number relations across a shock front as predicted by the proposed conservation law.
New fermion mass textures from anomalous U(1) symmetries with baryon and lepton number conservation
Leontaris, George K
2000-01-01
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)_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)_X fermion charges which give several fermion mass textures in agreement with the observed fermion mass hierarchy and mixing. Solutions with U(1)_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 classification of the fermion mass textures with respect to the sum of the doublet-higgs U(1)_X-charges and show that suppression of dimension-five operators naturally occurs for vario...
On conserved densities and asymptotic behaviour for the potential Kadomtsev-Petviashvili equation
International Nuclear Information System (INIS)
Rosenhaus, V
2006-01-01
We study local conservation laws with non-vanishing conserved densities and corresponding boundary conditions for the potential Kadomtsev-Petviashvili equation. We analyse an infinite symmetry group of the equation, and generate a finite number of conserved densities corresponding to infinite symmetries through appropriate boundary conditions
On 2X2 systems of conservation laws with fluxes that are entropies
Directory of Open Access Journals (Sweden)
Michael Junk
2003-03-01
Full Text Available In this article, we study systems of conservation laws with two dependent and two independent variables which have the property that the fluxes are entropies. Several characterizations of such flux functions are presented. It turns out, that the corresponding systems automatically possess a large class of additional entropies, they are closely related to a kinetic equation, and, in the case of strict hyperbolicity, they can be decoupled into two independent Burgers' equations. The isentropic Euler equations with zero or cubic pressure laws are the most prominent examples of such systems, but other examples are also presented.
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.
Rarefaction and shock waves for multi-dimensional hyperbolic conservation laws
International Nuclear Information System (INIS)
Dening, Li
1991-01-01
In this paper, the author wants to show the local existence of a solution of combination of shock and rarefaction waves for the multi-dimensional hyperbolic system of conservation laws. The typical example he has in mind is the Euler equations for compressible fluid. More generally, he studies the hyperbolic system of conservation laws ∂ t F 0 (u) + Σ j=1 n ∂ x j F j (u)=0 where u=(u 1 ....,u m ) and F j (u), j=0,...,n are m-dimensional vector-valued functions. He'll impose some conditions in the following on the systems (1.2). All these conditions are satisfied by the Euler equations
International Nuclear Information System (INIS)
Zhao Dun; Zhang Yujuan; Lou Weiwei; Luo Honggang
2011-01-01
By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLS systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.
On the application of subcell resolution to conservation laws with stiff source terms
International Nuclear Information System (INIS)
Chang, S.
1989-11-01
LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented
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 conservation law, entropy principle and quantization of fractal dimensions in hadron interactions
Czech Academy of Sciences Publication Activity Database
Zborovský, Imrich
2018-01-01
Roč. 33, č. 10 (2018), č. článku 1850057. ISSN 0217-751X R&D Projects: GA MŠk(CZ) LG15052 Institutional support: RVO:61389005 Keywords : Hadron interactions * self-similarity * fractality * conservation laws * quanta Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.597, year: 2016
LETTER TO THE EDITOR: Bicomplexes and conservation laws in non-Abelian Toda models
Gueuvoghlanian, E. P.
2001-08-01
A bicomplex structure is associated with the Leznov-Saveliev equation of integrable models. The linear problem associated with the zero-curvature condition is derived in terms of the bicomplex linear equation. The explicit example of a non-Abelian conformal affine Toda model is discussed in detail and its conservation laws are derived from the zero-curvature representation of its equation of motion.
Stationarity-conservation laws for fractional differential equations with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
Klimek, Malgorzata [Institute of Mathematics and Computer Science, Technical University of Czestochowa, Czestochowa (Poland)
2002-08-09
In this paper, we study linear fractional differential equations with variable coefficients. It is shown that, by assuming some conditions for the coefficients, the stationarity-conservation laws can be derived. The area where these are valid is restricted by the asymptotic properties of solutions of the respective equation. Applications of the proposed procedure include the fractional Fokker-Planck equation in (1+1)- and (d+1)-dimensional space and the fractional Klein-Kramers equation. (author)
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.
Stationarity-conservation laws for fractional differential equations with variable coefficients
International Nuclear Information System (INIS)
Klimek, Malgorzata
2002-01-01
In this paper, we study linear fractional differential equations with variable coefficients. It is shown that, by assuming some conditions for the coefficients, the stationarity-conservation laws can be derived. The area where these are valid is restricted by the asymptotic properties of solutions of the respective equation. Applications of the proposed procedure include the fractional Fokker-Planck equation in (1+1)- and (d+1)-dimensional space and the fractional Klein-Kramers equation. (author)
Higher conservation laws for ten-dimensional supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Abdalla, E.; Forger, M.; Freiburg Univ.; Jacques, M.
1988-01-01
It is shown that ten-dimensional supersymmetric Yang-Mills theories are integrable systems, in the (weak) sense of admitting a (superspace) Lax representation for their equations of motion. This is achieved by means of an explicit proof that the equations of motion are not only a consequence of but in fact fully equivalent to the superspace constraint F αβ =0. Moreover, a procedure for deriving infinite series of non-local conservation laws is outlined. (orig.)
Entropy Viscosity Method for High-Order Approximations of Conservation Laws
Guermond, J. L.; Pasquetti, R.
2010-01-01
A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.
International Nuclear Information System (INIS)
Anykeyev, V.B.; Zhigunov, V.P.; Spiridonov, A.A.
1981-01-01
Special choice of parameters for minimization is offered in the problem of improving estimates for particle momenta in the vertex of the event with the use of 4-momentum conservation law. This choice permits to use any unconditional minimization method instead of that of Lagrange multipliers. The above method is used when analysing the data on the K - +p→n + anti k 0 +π 0 reaction [ru
Wave, particle-family duality and the conservation of discrete symmetries in strong interaction
International Nuclear Information System (INIS)
van der Spuy, E.
1984-01-01
This paper starts from a nonlinear fermion field equation of motion with a strongly coupled self-interaction. Nonperturbative quark solutions of the equation of motion are constructed in terms of a Reggeized infinite component free spinor field. Such a field carries a family of strongly interacting unstable compounds lying on a Regge locus in the analytically continued quark spin. Such a quark field is naturally confined and also possesses the property of asymptotic freedom. Furthermore, the particular field self-regularizes the interactions and naturally breaks the chiral invariance of the equation of motion. We show why and how the existence of such a strongly coupled solution and its particle-family, wave duality forces a change in the field equation of motion such that it conserves C,P,T, although its individual interaction terms are of V-A and thus C,P nonconserving type
Wave, particle-family duality and the conservation of discrete symmetries in strong interaction
International Nuclear Information System (INIS)
Van der Spuy, E.
1984-01-01
This paper starts from a nonlinear fermion field equation of motion with a strongly coupled selfinteraction. Nonperturbative quark solutions of the equation of motion are constructed in terms of a Reggeized infinite component free spinor field. Such a field carries a family of strongly interacting unstable compounds lying on a Regge locus in the analytically continued quark spin. Such a quark field is naturally confined and also possesses the property of asymptotic freedom. Furthermore the particular field selfregularizes the interactions and naturally breaks the chiral invariance of the equation of motion. We show why and how the existence of such a strongly coupled solution and its particle-family, wave duality forces a change in the field equation of motion such that it conserves C, P, T although its individual interaction terms are of V - A and thus C, P nonconserving type
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...
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.
International Nuclear Information System (INIS)
Chaichian, M.; Montonen, C.; Perez Rojas, H.
1991-01-01
The completely different conservation properties of charges associated to unbroken and broken symmetries are discussed. The impossibility of establishing a conservation law for nondegenerate Hilbert space representations in the broken case leads to a reciprocal of Coleman's theorem. The quantum statistical implication is that these charges cannot be introduced as conserved operators in the density matrix. (orig.)
Van Hooydonk, G
2000-11-01
Following recent work in search for a universal function (Van Hooydonk, Eur. J. Inorg. Chem., (1999), 1617), we test four symmetric +/- a(n)Rn potentials for reproducing molecular potential energy curves (PECs). Classical gauge symmetry for 1/R-potentials results in generic left right asymmetric PECs. A pair of symmetric perturbed Coulomb potentials is quantitatively in accordance with observed PECs. For a bond, a four-particle system, charge inversion (a parity effect, atom chirality) is the key to explain this shape generically. A parity adapted Hamiltonian reduces from ten to two terms and to a soluble Bohr-like formula, a Kratzer (1 - Re/R)2 potential. The result is similar to the combined action of spin and wave function symmetry upon the Hamiltonian in Heitler-London theory. Analytical perturbed Coulomb functions varying with (1 - Re/R) scale attractive and repulsive branches of PECs for 13 bonds H2, HF, LiH, KH, AuH, Li2, LiF, KLi, NaCs, Rb2, RbCs, Cs2 and I2 in a single straight line. The 400 turning points for 13 bonds are reproduced with a deviation of 0.007 A at both branches. For 230 points at the repulsive side, the deviation is 0.003 A. The perturbed electrostatic Coulomb law is a universal molecular function. Ab initio zero molecular parameter functions give PECs of acceptable quality, just using atomic ionisation energies. The function can be used as a model potential for inverting levels and gives a first principle's comparison of short- and long-range interactions, important for the study of cold atoms. Wave-packet dynamics, femto-chemistry applied to the crossing of covalent and ionic curves, can provide evidence for this theory. We anticipate this scale/shape invariant scheme applies to smaller scales in nuclear and high-energy particle physics. For larger gravitational scales (Newton 1/R potentials), problems with super-unification are discussed. Reactions between hydrogen and antihydrogen, feasible in the near future, will probably produce
Quasilocal conservation laws in XXZ spin-1/2 chains: Open, periodic and twisted boundary conditions
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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.
Variational principles and symmetries on fibered multisymplectic manifolds
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Gaset Jordi
2016-12-01
Full Text Available The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (premulti-symplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws, symmetries, Cartan (Noether symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous mechanics.
Unsplit schemes for hyperbolic conservation laws with source terms in one space dimension
International Nuclear Information System (INIS)
Papalexandris, M.V.; Leonard, A.; Dimotakis, P.E.
1997-01-01
The present work is concerned with an application of the theory of characteristics to conservation laws with source terms in one space dimension, such as the Euler equations for reacting flows. Space-time paths are introduced on which the flow/chemistry equations decouple to a characteristic set of ODE's for the corresponding homogeneous laws, thus allowing the introduction of functions analogous to the Riemann invariants in classical theory. The geometry of these paths depends on the spatial gradients of the solution. This particular decomposition can be used in the design of efficient unsplit algorithms for the numerical integration of the equations. As a first step, these ideas are implemented for the case of a scalar conservation law with a nonlinear source term. The resulting algorithm belongs to the class of MUSCL-type, shock-capturing schemes. Its accuracy and robustness are checked through a series of tests. The stiffness of the source term is also studied. Then, the algorithm is generalized for a system of hyperbolic equations, namely the Euler equations for reacting flows. A numerical study of unstable detonations is performed. 57 refs
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.
Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains
Przedborski, Michelle; Anco, Stephen C.
2017-09-01
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.
Test of post-newtonian conservation laws in the binary system PSR 1913+16
International Nuclear Information System (INIS)
Will, C.M.
1976-01-01
Observations that set upper limits on secular changes in the pulsar period and orbital period in the binary system PSR 1913+16 may provide a test of post-Newtonian conservation laws. According to some metric theories of gravitation, the center of mass of a binary system may be accelerated in the direction of the periastron of the orbit because of a violation of post-Newtonian momentum conservation. In the binary system PSR 1913+16, this effect could produce secular changes in both pulsar and orbital periods (changing overall Doppler shift) as large as two parts in 10 6 per year. The size of the effect is proportional to the sine of the angle of periastron, to the difference in the masses of the components of the binary system, and to the combination of parametrized post-Newtonian parameters α 3 +zeta 2 -zeta/subw/. This combination is zero in any theory that predicts conserved total momentum for isolated systems (including general relativity and Brans-Dicke theory). Although solar-system experiments constrain α 3 and zeta/subw/ to be small, no decent direct limit has been placed on zeta 2 . Other possible sources of secular period changes in PSR 1913+16 are discussed and compared with this effect. It is also shown that a breakdown in the equality of active and passive gravitational masses (violation of ''Newton's third law'') leads only to periodic, unobservable orbital effects in a system like PSR 1913+16
International Nuclear Information System (INIS)
Wang, L.C.
1980-01-01
Baecklund Transformations (BT) and the derivation of local conservation laws are first reviewed in the classic case of the Sine-Gordon equation. The BT, conservation laws (local and nonlocal), and the inverse-scattering formulation are discussed for the chiral and the self-dual Yang-Mills fields. Their possible applications to the loop formulation for the Yang-Mills fields are mentioned. 55 references, 1 figure
International Nuclear Information System (INIS)
Kita, Takafumi
2009-01-01
Quantum-field-theoretic descriptions of interacting condensed bosons have suffered from the lack of self-consistent approximation schemes satisfying Goldstone's theorem and dynamical conservation laws simultaneously. We present a procedure to construct such approximations systematically by using either an exact relation for the interaction energy or the Hugenholtz-Pines relation to express the thermodynamic potential in a Luttinger-Ward form. Inspection of the self-consistent perturbation expansion up to the third order with respect to the interaction shows that the two relations yield a unique identical result at each order, reproducing the conserving-gapless mean-field theory [T. Kita, J. Phys. Soc. Jpn. 74, 1891 (2005)] as the lowest-order approximation. The uniqueness implies that the series becomes exact when infinite terms are retained. We also derive useful expressions for the entropy and superfluid density in terms of Green's function and a set of real-time dynamical equations to describe thermalization of the condensate.
Equations of motion and conservation laws in a theory of stably stratified turbulence
Energy Technology Data Exchange (ETDEWEB)
L' vov, Victor S; Rudenko, Oleksii [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)], E-mail: oleksii.rudenko@weizmann.ac.il
2008-12-15
This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider non-isothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of state including both non-ideal gases as well as liquids. The proposed approach is based on a suggested general definition of potential temperature. Special attention is paid to the energy conservation principle: the proposed approximation exactly preserves the total mechanical energy by approximate equations of motion. It is emphasized explicitly the importance for any turbulent boundary layer model to respect the conservation laws.
A second-order iterative implicit-explicit hybrid scheme for hyperbolic systems of conservation laws
International Nuclear Information System (INIS)
Dai, Wenlong; Woodward, P.R.
1996-01-01
An iterative implicit-explicit hybrid scheme is proposed for hyperbolic systems of conservation laws. Each wave in a system may be implicitly, or explicitly, or partially implicitly and partially explicitly treated depending on its associated Courant number in each numerical cell, and the scheme is able to smoothly switch between implicit and explicit calculations. The scheme is of Godunov-type in both explicit and implicit regimes, is in a strict conservation form, and is accurate to second-order in both space and time for all Courant numbers. The computer code for the scheme is easy to vectorize. Multicolors proposed in this paper may reduce the number of iterations required to reach a converged solution by several orders for a large time step. The feature of the scheme is shown through numerical examples. 38 refs., 12 figs
Discrete conservation laws and the convergence of long time simulations of the mkdv equation
Gorria, C.; Alejo, M. A.; Vega, L.
2013-02-01
Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.
ON HAMILTONIAN FORMULATIONS AND CONSERVATION LAWS FOR PLATE THEORIES OF VEKUA-AMOSOV TYPE
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Sergey I. Zhavoronok
2017-12-01
Full Text Available Some variants of the generalized Hamiltonian formulation of the plate theory of I. N. Vekua – A. A. Amosov type are presented. The infinite dimensional formulation with one evolution variable, or an “instantaneous” formalism, as well as the de Donder – Weyl one are considered, and their application to the numerical simulation of shell and plate dynamics is briefly discussed. The main conservation laws are formulated for the general plate theory of Nth order, and the possible motion integrals are introduced
International Nuclear Information System (INIS)
Li Xinyue; Zhao Qiulan
2009-01-01
Two hierarchies of nonlinear integrable positive and negative lattice equations are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws about the positive hierarchy.
Group theoretical construction of two-dimensional models with infinite sets of conservation laws
International Nuclear Information System (INIS)
D'Auria, R.; Regge, T.; Sciuto, S.
1980-01-01
We explicitly construct some classes of field theoretical 2-dimensional models associated with symmetric spaces G/H according to a general scheme proposed in an earlier paper. We treat the SO(n + 1)/SO(n) and SU(n + 1)/U(n) case, giving their relationship with the O(n) sigma-models and the CP(n) models. Moreover, we present a new class of models associated to the SU(n)/SO(n) case. All these models are shown to possess an infinite set of local conservation laws. (orig.)
Local conservation laws and the structure of the many-body localized states.
Serbyn, Maksym; Papić, Z; Abanin, Dmitry A
2013-09-20
We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its nonequilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.
Fast sweeping methods for hyperbolic systems of conservation laws at steady state II
Engquist, Björn; Froese, Brittany D.; Tsai, Yen-Hsi Richard
2015-04-01
The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency.
Conservation laws and radiation in the scale covariant theory of gravitation
International Nuclear Information System (INIS)
Beesham, A.
1988-01-01
The conservation laws for mass, energy, and momentum are derived in the scale covariant theory of gravitation. The entropy problem which exists in the standard Friedmann-Lemaitre-Robertson-Walker models can be solved in the present context. Since the weak and strong energy conditions may be violated, a big bang singularity may be avoided, in contrast to general relativity. Since beta is shown to be constant during the radiation-dominated era, the difficulties in the theory associated with nucleosynthesis are avoided. 10 references
Convergence of a continuous BGK model for initial boundary-value problems for conservation laws
Directory of Open Access Journals (Sweden)
Driss Seghir
2001-11-01
Full Text Available We consider a scalar conservation law in the quarter plane. This equation is approximated in a continuous kinetic Bhatnagar-Gross-Krook (BGK model. The convergence of the model towards the unique entropy solution is established in the space of functions of bounded variation, using kinetic entropy inequalities, without special restriction on the flux nor on the equilibrium problem's data. As an application, we establish the hydrodynamic limit for a $2imes2$ relaxation system with general data. Also we construct a new family of convergent continuous BGK models with simple maxwellians different from the $chi$ models.
Basic conservation laws in the electromagnetic theory of cyclotron radiation: further analysis
International Nuclear Information System (INIS)
Lieu, R.; Leahy, D.A.
1984-01-01
The conflict of basic conservation laws in cyclotron radiation is considered in more general terms, taking into account relativistic effects of the electron. Also investigated are the effects due to the most important approximation in cyclotron theory, viz the omission of radiation back reaction. The conclusions are (i) the disagreement is of a magnitude considerably larger than any errors introduced by the approximation; (ii) the 'degree of conflict' attains its maximum in relativistic velocities, when the energy loss to radiation can approach the total energy of the electron. (author)
Conservation laws for voter-like models on random directed networks
International Nuclear Information System (INIS)
Ángeles Serrano, M; Klemm, Konstantin; Vazquez, Federico; Eguíluz, Víctor M; San Miguel, Maxi
2009-01-01
We study the voter model, under node and link update, and the related invasion process on a single strongly connected component of a directed network. We implement an analytical treatment in the thermodynamic limit using the heterogeneous mean-field assumption. From the dynamical rules at the microscopic level, we find the equations for the evolution of the relative densities of nodes in a given state on heterogeneous networks with arbitrary degree distribution and degree–degree correlations. We prove that conserved quantities as weighted linear superpositions of spin states exist for all three processes and, for uncorrelated directed networks, we derive their specific expressions. We also discuss the time evolution of the relative densities that decay exponentially to a homogeneous stationary value given by the conserved quantity. The conservation laws obtained in the thermodynamic limit for a system that does not order in that limit determine the probabilities of reaching the absorbing state for a finite system. The contribution of each degree class to the conserved quantity is determined by a local property. Depending on the dynamics, the highest contribution is associated with influential nodes reaching a large number of outgoing neighbors, not too influenceable ones with a low number of incoming connections, or both at the same time
On the structure on non-local conservation laws in the two-dimensional non-linear sigma-model
International Nuclear Information System (INIS)
Zamolodchikov, Al.B.
1978-01-01
The non-local conserved charges are supposed to satisfy a special multiplicative law in the space of asymptotic states of the non-linear sigma-model. This supposition leads to factorization equations for two-particle scattering matrix elements and determines to some extent the action of these charges in the asymptotic space. Their conservation turns out to be consistent with the factorized S-matrix of the non-linear sigma-model. It is shown also that the factorized sine-Gordon S-matrix is consistent with a similar family of conservation laws
International Nuclear Information System (INIS)
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. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced. (paper)
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.
Kooijman; Kooi; Hallam
1999-04-07
Rules for energy uptake, and subsequent utilization, form the basis of population dynamics and, therefore, explain the dynamics of the ecosystem structure in terms of changes in standing crops and size distributions of individuals. Mass fluxes are concomitant with energy flows and delineate functional aspects of ecosystems by defining the roles of individuals and populations. The assumption of homeostasis of body components, and an assumption about the general structure of energy budgets, imply that mass fluxes can be written as weighted sums of three organizing energy fluxes with the weight coefficients determined by the conservation law of mass. These energy fluxes are assimilation, maintenance and growth, and provide a theoretical underpinning of the widely applied empirical method of indirect calorimetry, which relates dissipating heat linearly to three mass fluxes: carbon dioxide production, oxygen consumption and N-waste production. A generic approach to the stoichiometry of population energetics from the perspective of the individual organism is proposed and illustrated for heterotrophic organisms. This approach indicates that mass transformations can be identified by accounting for maintenance requirements and overhead costs for the various metabolic processes at the population level. The theoretical background for coupling the dynamics of the structure of communities to nutrient cycles, including the water balance, as well as explicit expressions for the dissipating heat at the population level are obtained based on the conservation law of energy. Specifications of the general theory employ the Dynamic Energy Budget model for individuals. Copyright 1999 Academic Press.
International Nuclear Information System (INIS)
Zhu, Zuo-nong; Tam, Hon-Wah; Ding, Qing
2003-01-01
In this Letter, by means of considering matrix form of a new Schroedinger discrete spectral operator equation, and constructing opportune time evolution equations, and using discrete zero curvature representation, two discrete integrable lattice hierarchies proposed by Boiti et al. [J. Phys. A: Math. Gen. 36 (2003) 139] are re-derived. From the matrix Lax representations, we demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes by means of formulae. Thus their integrability is further confirmed. Specially we obtain the infinitely many conservation laws for a new discrete version of the KdV equation. A connection between the conservation laws of the discrete KdV equation and the ones of the KdV equation is discussed by two examples
Unified Symmetry of Hamilton Systems
International Nuclear Information System (INIS)
Xu Xuejun; Qin Maochang; Mei Fengxiang
2005-01-01
The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. An example is finally given to illustrate the application of the results.
International Nuclear Information System (INIS)
Tadmor, E.
1988-07-01
A convergence theory for semi-discrete approximations to nonlinear systems of conservation laws is developed. It is shown, by a series of scalar counter-examples, that consistency with the conservation law alone does not guarantee convergence. Instead, a notion of consistency which takes into account both the conservation law and its augmenting entropy condition is introduced. In this context it is concluded that consistency and L(infinity)-stability guarantee for a relevant class of admissible entropy functions, that their entropy production rate belongs to a compact subset of H(loc)sup -1 (x,t). One can now use compensated compactness arguments in order to turn this conclusion into a convergence proof. The current state of the art for these arguments includes the scalar and a wide class of 2 x 2 systems of conservation laws. The general framework of the vanishing viscosity method is studied as an effective way to meet the consistency and L(infinity)-stability requirements. How this method is utilized to enforce consistency and stability for scalar conservation laws is shown. In this context we prove, under the appropriate assumptions, the convergence of finite difference approximations (e.g., the high resolution TVD and UNO methods), finite element approximations (e.g., the Streamline-Diffusion methods) and spectral and pseudospectral approximations (e.g., the Spectral Viscosity methods)
Electric-magnetic duality as a secondary symmetry
International Nuclear Information System (INIS)
Brandt, R.A.; Young, K.
1980-01-01
In both the abelian and non-abelian classical point magnetic monopole theories, electric current conservation is a consequence of gauge invariance, but, since there is no magnetic gauge group, magnetic current conservation is not a Noether-type conservation law. In the abelian models, the equations of motion (but not the lagrangian) are invariant to the duality rotations in electric-magnetic charge space, but this is not the case in the non-abelian models. In an attempt to understand these and related points, we introduce a generalization of Noether's theorem. Consider a physical system described by a set of variables THETA and characterized by a lagrangian density L(THETA). A transormation law THETA → G THETA which leaves L invariant leads to a conserved current Jsub(μ)(THETA). We then call G a primary symmetry. A second transformation law THETA → D THETA which leaves the equations of motion, but not L, invariant then leads to another conserved current Jsub(μ)(D THETA). We then call D a secondary symmetra. Our main point is that Jsub(μ) (D THETA) may be conserved even if the equations of motion are not invariant under D. All that is required is that the change of the equations of motion under D is perpendicular (in the field space) to the change of the fields under G. Then we call D an incomplete secondary symmetry. We show that in both the abelian and non-abelian monopole theories, duality is an incomplete secondary symmetry whose associated conservation law is magnetic current conservation. Thus it is the interpretation of duality as a secondary symmetry which explains magnetic current conservation and which generalizes from the abelian theories to the non-abelian ones. This suggests that magnetic current conservation may remain valid in quantum field theory. (orig.)
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.
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 ...
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)
Higher order Godunov methods for general systems of hyperbolic conservation laws
International Nuclear Information System (INIS)
Bell, J.B.; Colella, P.; Trangenstein, J.A.
1989-01-01
We describe an extension of higher order Godunov methods to general systems of hyperbolic conservation laws. This extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields. The method constructs an approximation of the Riemann problem from local wave information. A generalization of the Engquist--Osher flux for systems is then used to compute a numerical flux based on this approximation. This numerical flux replaces the Godunov numerical flux in the algorithm, thereby eliminating the need for a global Riemann problem solution. The additional modifications to the Godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail. The method is applied to some simple model problems for which the glocal analytic structure is known. The method is also applied to the black-oil model for multiphase flow in petroleum reservoirs. copyright 1989 Academic Press, Inc
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.
International Nuclear Information System (INIS)
Werner, K.D.
1990-01-01
In this paper we introduce briefly the Geometrical Shock Correction (GSC) method and consider various fields of applications, with special emphasis on two-phase flow problems in porous media. Some test problems are taken from this field. GSC is a very efficient numerical method for constructing the entropy solution of the Cauchy problem of scalar hyperboli conservation laws (with source term) in one space dimension and in specific two-dimensional cases. The novelty consists in constructing the solution at an arbitrary fixed time t=T>0 in one time step, based on transporting the initial values along characteristics and, if shocks appear, on a correction of the multivalued relation by a geometrical averaging technique. (orig.) With 7 figs [de
Divergence-Measure Fields, Sets of Finite Perimeter, and Conservation Laws
Chen, Gui-Qiang; Torres, Monica
2005-02-01
Divergence-measure fields in L∞ over sets of finite perimeter are analyzed. A notion of normal traces over boundaries of sets of finite perimeter is introduced, and the Gauss-Green formula over sets of finite perimeter is established for divergence-measure fields in L∞. The normal trace introduced here over a class of surfaces of finite perimeter is shown to be the weak-star limit of the normal traces introduced in Chen & Frid [6] over the Lipschitz deformation surfaces, which implies their consistency. As a corollary, an extension theorem of divergence-measure fields in L∞ over sets of finite perimeter is also established. Then we apply the theory to the initial-boundary value problem of nonlinear hyperbolic conservation laws over sets of finite perimeter.
International Nuclear Information System (INIS)
Botchorishvili, Ramaz; Pironneau, Olivier
2003-01-01
We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 5000 2 grid points
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
International Nuclear Information System (INIS)
Qian, Hong
2014-01-01
We propose a mathematical formulation of the zeroth law of thermodynamics and develop a stochastic dynamical theory, with a consistent irreversible thermodynamics, for systems possessing sustained conservative stationary current in phase space while in equilibrium with a heat bath. The theory generalizes underdamped mechanical equilibrium: dx=gdt+{−D∇ϕdt+√(2D)dB(t)}, with ∇⋅g=0 and {⋯} respectively representing phase-volume preserving dynamics and stochastic damping. The zeroth law implies stationary distribution u ss (x)=e −ϕ(x) . We find an orthogonality ∇ϕ⋅g=0 as a hallmark of the system. Stochastic thermodynamics based on time reversal (t,ϕ,g)→(−t,ϕ,−g) is formulated: entropy production e p # (t)=−dF(t)/dt; generalized “heat” h d # (t)=−dU(t)/dt, U(t)=∫ R n ϕ(x)u(x,t)dx being “internal energy”, and “free energy” F(t)=U(t)+∫ R n u(x,t)lnu(x,t)dx never increases. Entropy follows (dS)/(dt) =e p # −h d # . Our formulation is shown to be consistent with an earlier theory of P. Ao. Its contradistinctions to other theories, potential-flux decomposition, stochastic Hamiltonian system with even and odd variables, Klein–Kramers equation, Freidlin–Wentzell's theory, and GENERIC, are discussed.
Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact ...
African Journals Online (AJOL)
Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact solutions and conservation laws. ... In this paper we study the combined sinh-cosh-Gordon equation, which arises in mathematical physics and has a wide range of scientific applications that range from chemical reactions to water surface gravity waves.
A note on the interplay between symmetries, reduction and ...
Indian Academy of Sciences (India)
A note on the interplay between symmetries, reduction and conservation laws of Stokes' ﬁrst problem for third-grade rotating ﬂuids ... Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia; Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi ...
International Nuclear Information System (INIS)
Shelkovich, V M
2008-01-01
This is a survey of some results and problems connected with the theory of generalized solutions of quasi-linear conservation law systems which can admit delta-shaped singularities. They are the so-called δ-shock wave type solutions and the recently introduced δ (n) -shock wave type solutions, n=1,2,..., which cannot be included in the classical Lax-Glimm theory. The case of δ- and δ'-shock waves is analyzed in detail. A specific analytical technique is developed to deal with such solutions. In order to define them, some special integral identities are introduced which extend the concept of weak solution, and the Rankine-Hugoniot conditions are derived. Solutions of Cauchy problems are constructed for some typical systems of conservation laws. Also investigated are multidimensional systems of conservation laws (in particular, zero-pressure gas dynamics systems) which admit δ-shock wave type solutions. A geometric aspect of such solutions is considered: they are connected with transport and concentration processes, and the balance laws of transport of 'volume' and 'area' to δ- and δ'-shock fronts are derived for them. For a 'zero-pressure gas dynamics' system these laws are the mass and momentum transport laws. An algebraic aspect of these solutions is also considered: flux-functions are constructed for them which, being non-linear, are nevertheless uniquely defined Schwartz distributions. Thus, a singular solution of the Cauchy problem generates algebraic relations between its components (distributions).
International Nuclear Information System (INIS)
Bender, B.; Sparwasser, R.
1988-01-01
Environmental law is discussed exhaustively in this book. Legal and scientific fundamentals are taken into account, a systematic orientation is given, and hints for further information are presented. The book covers general environmental law, plan approval procedures, protection against nuisances, atomic law and radiation protection law, water protection law, waste management law, laws on chemical substances, conservation law. (HSCH) [de
Energy Technology Data Exchange (ETDEWEB)
Grinstein, Benjamín [Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (United States); Murphy, Christopher W. [Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa 56126 (Italy); Uttayarat, Patipan [Department of Physics, Srinakharinwirot University, Wattana, Bangkok 10110 (Thailand)
2016-06-13
We compute all of the one-loop corrections that are enhanced, O(λ{sub i}λ{sub j}/16π{sup 2}), in the limit s≫|λ{sub i}|v{sup 2}≫M{sub W}{sup 2}, s≫m{sub 12}{sup 2} to all the 2→2 longitudinal vector boson and Higgs boson scattering amplitudes in the CP-conserving two-Higgs doublet model with a softly broken ℤ{sub 2} symmetry. In the two simplified scenarios we study, the typical bound we find is |λ{sub i}(s)|⪅4.
Holography without translational symmetry
Vegh, David
2013-01-01
We propose massive gravity as a holographic framework for describing a class of strongly interacting quantum field theories with broken translational symmetry. Bulk gravitons are assumed to have a Lorentz-breaking mass term as a substitute for spatial inhomogeneities. This breaks momentum-conservation in the boundary field theory. At finite chemical potential, the gravity duals are charged black holes in asymptotically anti-de Sitter spacetime. The conductivity in these systems generally exhibits a Drude peak that approaches a delta function in the massless gravity limit. Furthermore, the optical conductivity shows an emergent scaling law: $|\\sigma(\\omega)| \\approx {A \\over \\omega^{\\alpha}} + B$. This result is consistent with that found earlier by Horowitz, Santos, and Tong who introduced an explicit inhomogeneous lattice into the system.
International Nuclear Information System (INIS)
Souriau, J.M.
1984-01-01
The sky uniformity can be noticed in studying the repartition of objects far enough. The sky isotropy description uses space rotations. The group theory elements will allow to give a meaning at the same time precise and general to the word a ''symmetry''. Universe models are reviewed, which must have both of the following qualities: - conformity with the physic known laws; - rigorous symmetry following one of the permitted groups. Each of the models foresees that universe evolution obeys an evolution equation. Expansion and big-bang theory are recalled. Is universe an open or closed space. Universe is also electrically neutral. That leads to a work hypothesis: the existing matter is not given data of universe but it appeared by evolution from nothing. Problem of matter and antimatter is then raised up together with its place in universe [fr
International Nuclear Information System (INIS)
Gañán-Calvo, A M; Rebollo-Muñoz, N; Montanero, J M
2013-01-01
We aim to establish the scaling laws for both the minimum rate of flow attainable in the steady cone–jet mode of electrospray, and the size of the resulting droplets in that limit. Use is made of a small body of literature on Taylor cone–jets reporting precise measurements of the transported electric current and droplet size as a function of the liquid properties and flow rate. The projection of the data onto an appropriate non-dimensional parameter space maps a region bounded by the minimum rate of flow attainable in the steady state. To explain these experimental results, we propose a theoretical model based on the generalized concept of physical symmetry, stemming from the system time invariance (steadiness). A group of symmetries rising at the cone-to-jet geometrical transition determines the scaling for the minimum flow rate and related variables. If the flow rate is decreased below that minimum value, those symmetries break down, which leads to dripping. We find that the system exhibits two instability mechanisms depending on the nature of the forces arising against the flow: one dominated by viscosity and the other by the liquid polarity. In the former case, full charge relaxation is guaranteed down to the minimum flow rate, while in the latter the instability condition becomes equivalent to the symmetry breakdown by charge relaxation or separation. When cone–jets are formed without artificially imposing a flow rate, a microjet is issued quasi-steadily. The flow rate naturally ejected this way coincides with the minimum flow rate studied here. This natural flow rate determines the minimum droplet size that can be steadily produced by any electrohydrodynamic means for a given set of liquid properties. (paper)
Gañán-Calvo, A. M.; Rebollo-Muñoz, N.; Montanero, J. M.
2013-03-01
We aim to establish the scaling laws for both the minimum rate of flow attainable in the steady cone-jet mode of electrospray, and the size of the resulting droplets in that limit. Use is made of a small body of literature on Taylor cone-jets reporting precise measurements of the transported electric current and droplet size as a function of the liquid properties and flow rate. The projection of the data onto an appropriate non-dimensional parameter space maps a region bounded by the minimum rate of flow attainable in the steady state. To explain these experimental results, we propose a theoretical model based on the generalized concept of physical symmetry, stemming from the system time invariance (steadiness). A group of symmetries rising at the cone-to-jet geometrical transition determines the scaling for the minimum flow rate and related variables. If the flow rate is decreased below that minimum value, those symmetries break down, which leads to dripping. We find that the system exhibits two instability mechanisms depending on the nature of the forces arising against the flow: one dominated by viscosity and the other by the liquid polarity. In the former case, full charge relaxation is guaranteed down to the minimum flow rate, while in the latter the instability condition becomes equivalent to the symmetry breakdown by charge relaxation or separation. When cone-jets are formed without artificially imposing a flow rate, a microjet is issued quasi-steadily. The flow rate naturally ejected this way coincides with the minimum flow rate studied here. This natural flow rate determines the minimum droplet size that can be steadily produced by any electrohydrodynamic means for a given set of liquid properties.
Gandiwa, E.; Zisadza-Gandiwa, P.; Mango, L.; Jakarasi, J.
2014-01-01
Globally, pressure from the illegal harvesting of wildlife is a recurrent issue for protected area management. In order to ensure the effective conservation of wildlife resources, law enforcement has been identified as one of the most important components of protected area management. Our study
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.
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
Borges, Rafael; Carmona, Monique; Costa, Bruno; Don, Wai Sun
2008-03-01
In this article we develop an improved version of the classical fifth-order weighted essentially non-oscillatory finite difference scheme of [G.S. Jiang, C.W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202-228] (WENO-JS) for hyperbolic conservation laws. Through the novel use of a linear combination of the low order smoothness indicators already present in the framework of WENO-JS, a new smoothness indicator of higher order is devised and new non-oscillatory weights are built, providing a new WENO scheme (WENO-Z) with less dissipation and higher resolution than the classical WENO. This new scheme generates solutions that are sharp as the ones of the mapped WENO scheme (WENO-M) of Henrick et al. [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542-567], however with a 25% reduction in CPU costs, since no mapping is necessary. We also provide a detailed analysis of the convergence of the WENO-Z scheme at critical points of smooth solutions and show that the solution enhancements of WENO-Z and WENO-M at problems with shocks comes from their ability to assign substantially larger weights to discontinuous stencils than the WENO-JS scheme, not from their superior order of convergence at critical points. Numerical solutions of the linear advection of discontinuous functions and nonlinear hyperbolic conservation laws as the one dimensional Euler equations with Riemann initial value problems, the Mach 3 shock-density wave interaction and the blastwave problems are compared with the ones generated by the WENO-JS and WENO-M schemes. The good performance of the WENO-Z scheme is also demonstrated in the simulation of two dimensional problems as the shock-vortex interaction and a Mach 4.46 Richtmyer-Meshkov Instability (RMI) modeled via the two dimensional Euler equations.
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
IAS Admin
At the Heart of Quantum Field Theory! Aritra Kr. ... principle of symmetry was not held as something very fundamental ... principle of local symmetry: the laws of physics are invariant un- .... Next, we would show that different coefficients of a state ...
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.
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.
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.
Li, Yanning; Canepa, Edward S.; Claudel, Christian
2014-01-01
This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.
Li, Yanning; Canepa, Edward S.; Claudel, Christian G.
2013-01-01
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.
Efficient robust control of first order scalar conservation laws using semi-analytical solutions
Li, Yanning; Canepa, Edward S.; Claudel, Christian G.
2014-01-01
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using initial density control and boundary flow control, as a Linear Program. We then show that this framework can be extended to arbitrary control problems involving the control of subsets of the initial and boundary conditions. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP/MILP. Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality.
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.
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.
Quantum conserved charges in N=1 and N=2 supersymmetric sine-Gordon theories
International Nuclear Information System (INIS)
Kobayashi, Ken-ichiro; Uematsu, Tsuneo; Yu Yangzheng
1993-01-01
We investigate quantum conservation laws in the N=1 and N=2 supersymmetric sine-Gordon theories. We study conserved charges at the quantum level based on perturbation theory formulated in superspace. It will turn out that there exist extra conserved charges of the vertex operator type at the quantum level and they generate a quantum group symmetry in supersymmetric sine-Gordon systems. We also discuss the implication of the quantum group symmetry on the S-matrix structure. (orig.)
The nucleon- nucleon interaction and symmetries
International Nuclear Information System (INIS)
Van Oers, W.T.H.
1992-11-01
With the advent of the possibility to study nucleon-nucleon scattering at medium energies, its extension to investigate fundamental symmetries was recognized early on. It was precisely the introduction of rotational invariance, parity conservation, time reversal invariance, and isotopic spin conversation that led to the description of the N - N scattering matrix in terms of five complex amplitudes: one set of five for proton-proton scattering and one set of five for neutron-proton scattering, or alternatively, one set for the isotopic spin state ι=ο and the other for the isotopic spin state ι=1. Clearly, if one or more of the above constraints are removed, there are additional amplitudes that need to be considered. To be meaningful, experiment requires observables that are particularly sensitive to the violation of a conservation law or symmetry principle. During the last decade a series of precision experiments has been performed to measure charge- symmetry breaking in n - p elastic scattering (corresponding to isotopic spin non-conservation), and to measure parity violation in p-p scattering. For a particle-anti-particle system,like the pp or λλ system one can raise the question of CP violation in a system other than the neutral kaon system may become possible in the near future through pp →λλ and pp→ ≡ ≡. A description is given of the ongoing efforts to measure charge symmetry breaking, parity violation and CP violation.(author). 42 refs., 6 figs
International Nuclear Information System (INIS)
Asanov, G.S.
1979-01-01
It is shown the description of gravitational field in the riemannian space-time by means of the absolute parallelism structure makes it possible to formulate an integrable covariant law of energy-momentum conservation for gravitational field, by imposing on the energy-momentum tensor the condition of vanishing of the covariant divergence (in the sense of the absolute parallelism). As a result of taking into account covariant constraints for the tetrads of the absolute parallelism, the Lagrangian density turns out to be not geometrised anymore and leads to the unambiguous conservation law of the type mentioned in the N-body problem. Covariant field equations imply the existence of the special euclidean coordinates outside of static neighbourhoods of gravitationing bodies. In these coordinates determined by the tetrads of the absolute parallelism, the linear approximation is not connected with any noncovariant assumptions
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.
A new six-component super soliton hierarchy and its self-consistent sources and conservation laws
International Nuclear Information System (INIS)
Wei Han-yu; Xia Tie-cheng
2016-01-01
A new six-component super soliton hierarchy is obtained based on matrix Lie super algebras. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy. After that, the self-consistent sources of the new six-component super soliton hierarchy are presented. Furthermore, we establish the infinitely many conservation laws for the integrable super soliton hierarchy. (paper)
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.
Lafitte, Pauline; Melis, Ward; Samaey, Giovanni
2017-07-01
We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.
Noether symmetries of discrete mechanico–electrical systems
International Nuclear Information System (INIS)
Fu Jingli; Xie Fengping; Chen Benyong
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. (general)
Symmetries, integrals, and three-dimensional reductions of Plebanski's second heavenly equation
International Nuclear Information System (INIS)
Neyzi, F.; Sheftel, M. B.; Yazici, D.
2007-01-01
We study symmetries and conservation laws for Plebanski's second heavenly equation written as a first-order nonlinear evolutionary system which admits a multi-Hamiltonian structure. We construct an optimal system of one-dimensional subalgebras and all inequivalent three-dimensional symmetry reductions of the original four-dimensional system. We consider these two-component evolutionary systems in three dimensions as natural candidates for integrable systems
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.
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...
Noteboom, H.P.
1985-01-01
The IUCN/WWF Plants Conservation Programme 1984 — 1985. World Wildlife Fund chose plants to be the subject of their fund-raising campaign in the period 1984 — 1985. The objectives were to: 1. Use information techniques to achieve the conservation objectives of the Plants Programme – to save plants;
National Audubon Society, New York, NY.
This set of teaching aids consists of seven Audubon Nature Bulletins, providing the teacher and student with informational reading on various topics in conservation. The bulletins have these titles: Plants as Makers of Soil, Water Pollution Control, The Ground Water Table, Conservation--To Keep This Earth Habitable, Our Threatened Air Supply,…
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.
International Nuclear Information System (INIS)
Belanger, M.
1998-09-01
The Union quebecoise pour la conservation de la nature (UQCN) is an association of 5000 members that is active in the field of nature conservation and environmental protection. Comments made by the UQCN to the Parliamentary Commission on Transport and the Environment on the proposed law on the security of dams are summarized. A number of general and specific comments were made concerning access to information, the process of authorisation, and the definition of high-volume dams. Concern was also expressed about the lack of clear indication of how the plans for the management of dam security and water reservoirs will be coordinated among the various agencies that represent the various users of the river system
A new six-component super soliton hierarchy and its self-consistent sources and conservation laws
Han-yu, Wei; Tie-cheng, Xia
2016-01-01
A new six-component super soliton hierarchy is obtained based on matrix Lie super algebras. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy. After that, the self-consistent sources of the new six-component super soliton hierarchy are presented. Furthermore, we establish the infinitely many conservation laws for the integrable super soliton hierarchy. Project supported by the National Natural Science Foundation of China (Grant Nos. 11547175, 11271008 and 61072147), the First-class Discipline of University in Shanghai, China, and the Science and Technology Department of Henan Province, China (Grant No. 152300410230).
International Nuclear Information System (INIS)
Fukutani, Yo; Imamura, Fumihiko; Tokunaga, Takeshi; Sato, Ichiro
2015-01-01
We propose a quantitative evaluation method of overall tsunami risk that the entire facility group over a wide area holds. We considerably reduced the calculation cost for tsunami inundation depth by adopting the evaluation method using energy conservation law as compared with the evaluation method using non-linear long wave equation. For financial institutions such as banks and insurance companies with contractors over a wide area and business companies with multiple their assets and facilities in various places, the proposed evaluation method in this study could be a useful approach to implement their risk-based management decisions for tsunami risk. (author)
Energy Technology Data Exchange (ETDEWEB)
Prior, C R [Cambridge Univ. (UK). Dept. of Applied Mathematics and Theoretical Physics
1977-06-27
Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptotically-flat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.
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.
Kuramochi, Yui; Ueda, Masahito
2015-03-01
We consider the information flow on a system observable X corresponding to a positive-operator-valued measure under a quantum measurement process Y described by a completely positive instrument from the viewpoint of the relative entropy. We establish a sufficient condition for the relative-entropy conservation law which states that the average decrease in the relative entropy of the system observable X equals the relative entropy of the measurement outcome of Y , i.e., the information gain due to measurement. This sufficient condition is interpreted as an assumption of classicality in the sense that there exists a sufficient statistic in a joint successive measurement of Y followed by X such that the probability distribution of the statistic coincides with that of a single measurement of X for the premeasurement state. We show that in the case when X is a discrete projection-valued measure and Y is discrete, the classicality condition is equivalent to the relative-entropy conservation for arbitrary states. The general theory on the relative-entropy conservation is applied to typical quantum measurement models, namely, quantum nondemolition measurement, destructive sharp measurements on two-level systems, a photon counting, a quantum counting, homodyne and heterodyne measurements. These examples except for the nondemolition and photon-counting measurements do not satisfy the known Shannon-entropy conservation law proposed by Ban [M. Ban, J. Phys. A: Math. Gen. 32, 1643 (1999), 10.1088/0305-4470/32/9/012], implying that our approach based on the relative entropy is applicable to a wider class of quantum measurements.
International Nuclear Information System (INIS)
Keraenen, A.; Suhonen, E.; Cleymans, J.
1999-01-01
The production of hadrons in relativistic heavy ion collisions is studied using a statistical ensemble with thermal and chemical equilibrium. Special attention is given to exact conservation laws, i.e. certain charges are treated canonically instead of using the usual grand canonical approach. For small systems, the exact conservation of baryon number, strangeness and electric charge is to be taken into account. We have derived compact, analytical expressions for particle abundances in such ensemble. As an application, the change in K/π ratios in AGS experiments with different interaction system sizes is well reproduced. The canonical treatment of three charges becomes impractical very quickly with increasing system size. Thus, we focus our attention on exact conservation of strangeness, and treat baryon number and electric charge grand canonically. We present expressions for particle abundances in such ensemble as well, and apply them to reproduce the large variety of particle ratios in GSI SIS 2 A GeV Ni-Ni experiments. At the energies considered here, the exact strangeness conservation fully accounts for strange particle suppression, and no extra chemical factor is needed. (author)
Conservation of energy and momentum in nonrelativistic plasmas
International Nuclear Information System (INIS)
Sugama, H.; Watanabe, T.-H.; Nunami, M.
2013-01-01
Conservation laws of energy and momentum for nonrelativistic plasmas are derived from applying Noether's theorem to the action integral for the Vlasov-Poisson-Ampère system [Sugama, Phys. Plasmas 7, 466 (2000)]. The symmetric pressure tensor is obtained from modifying the asymmetric canonical pressure tensor with using the rotational symmetry of the action integral. Differences between the resultant conservation laws and those for the Vlasov-Maxwell system including the Maxwell displacement current are clarified. These results provide a useful basis for gyrokinetic conservation laws because gyrokinetic equations are derived as an approximation of the Vlasov-Poisson-Ampère system.
Recent publications on environmental law
International Nuclear Information System (INIS)
Lohse, S.
1991-01-01
The bibliography contains references to publications covering the following subject fields: General environmental law; environmental law in relation to constitutional law, administrative law, procedural law, revenue law, criminal law, private law, industrial law; law of regional development; nature conservation law; law on water protection; waste management law; law on protection against harmful effects on the environment; atomic energy law and radiation protection law; law of the power industry and the mining industry; laws and regulations on hazardous material and environmental hygiene. (orig.) [de
Symmetry and symmetry breaking in quantum mechanics
International Nuclear Information System (INIS)
Chomaz, Philippe
1998-01-01
In the world of infinitely small, the world of atoms, nuclei and particles, the quantum mechanics enforces its laws. The discovery of Quanta, this unbelievable castration of the Possible in grains of matter and radiation, in discrete energy levels compels us of thinking the Single to comprehend the Universal. Quantum Numbers, magic Numbers and Numbers sign the wave. The matter is vibration. To describe the music of the world one needs keys, measures, notes, rules and partition: one needs quantum mechanics. The particles reduce themselves not in material points as the scholars of the past centuries thought, but they must be conceived throughout the space, in the accomplishment of shapes of volumes. When Einstein asked himself whether God plays dice, there was no doubt among its contemporaries that if He exists He is a geometer. In a Nature reduced to Geometry, the symmetries assume their role in servicing the Harmony. The symmetries allow ordering the energy levels to make them understandable. They impose there geometrical rules to the matter waves, giving them properties which sometimes astonish us. Hidden symmetries, internal symmetries and newly conceived symmetries have to be adopted subsequently to the observation of some order in this world of Quanta. In turn, the symmetries provide new observables which open new spaces of observation
Higher derivative extensions of 3d Chern-Simons models: conservation laws and stability
International Nuclear Information System (INIS)
Kaparulin, D.S.; Karataeva, I.Yu.; Lyakhovich, S.L.
2015-01-01
We consider the class of higher derivative 3d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability. (orig.)
Arnscheidt, Julia
2009-01-01
This book is about the politics of nature conservation in late New Order and early Reformasi Indonesia. It approaches the subject through discourse analysis. Understanding politics as a struggle for discourse hegemony it analyses both processes of policy- and lawmaking in Jakarta and of
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…
Covariant Conservation Laws and the Spin Hall Effect in Dirac-Rashba Systems
Milletarı, Mirco; Offidani, Manuel; Ferreira, Aires; Raimondi, Roberto
2017-12-01
We present a theoretical analysis of two-dimensional Dirac-Rashba systems in the presence of disorder and external perturbations. We unveil a set of exact symmetry relations (Ward identities) that impose strong constraints on the spin dynamics of Dirac fermions subject to proximity-induced interactions. This allows us to demonstrate that an arbitrary dilute concentration of scalar impurities results in the total suppression of nonequilibrium spin Hall currents when only Rashba spin-orbit coupling is present. Remarkably, a finite spin Hall conductivity is restored when the minimal Dirac-Rashba model is supplemented with a spin-valley interaction. The Ward identities provide a systematic way to predict the emergence of the spin Hall effect in a wider class of Dirac-Rashba systems of experimental relevance and represent an important benchmark for testing the validity of numerical methodologies.
MIGRATION AND CONSERVATION: FRAMEWORKS, GAPS, AND SYNERGIES IN SCIENCE, LAW, AND MANAGEMENT.
Meretsky, Vicky J; Atwell, Jonathan W; Hyman, Jeffrey B
2011-01-01
Migratory animals provide unique spectacles of cultural, ecological, and economic importance. However, the process of migration is a source of risk for migratory species as human actions increasingly destroy and fragment habitat, create obstacles to migration, and increase mortality along the migration corridor. As a result, many migratory species are declining in numbers. In the United States, the Endangered Species Act provides some protection against extinction for such species, but no protection until numbers are severely reduced, and no guarantee of recovery to population levels associated with cultural, ecological, or economic significance. Although groups of species receive some protection from statutes such as the Migratory Bird Treaty Act and Marine Mammal Protection Act, there is no coordinated system for conservation of migratory species. In addition, information needed to protect migratory species is often lacking, limiting options for land and wildlife managers who seek to support these species. In this Article, we outline the existing scientific, legal, and management information and approaches to migratory species. Our objective is to assess present capacity to protect the species and the phenomenon of migration, and we argue that al three disciplines are necessary for effective conservation. We find significant capacity to support conservation in all three disciplines, but no organization around conservation of migration within any discipline or among the three disciplines. Areas of synergy exist among the disciplines but not as a result of any attempt for coordination. As a result, significant gaps in information and capacity exist that must be addressed if effective conservation of migratory species is to be undertaken. We suggest that all three disciplines cooperate to identify the most pressing research needs, so that these can become targets for relevant funding sources. We identify areas of current risk to migratory species that represent gaps
On discrete symmetries for a whole Abelian model
International Nuclear Information System (INIS)
Chauca, J.; Doria, R.
2012-01-01
Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {D μ ,X i μ } and the physical basis {G μI }. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws driven for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {G μI } manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.
The role of Weyl symmetry in hydrodynamics
Diles, Saulo
2018-04-01
This article is dedicated to the analysis of Weyl symmetry in the context of relativistic hydrodynamics. Here is discussed how this symmetry is properly implemented using the prescription of minimal coupling: ∂ → ∂ + ωA. It is shown that this prescription has no problem to deal with curvature since it gives the correct expressions for the commutator of covariant derivatives. In hydrodynamics, Weyl gauge connection emerges from the degrees of freedom of the fluid: it is a combination of the expansion and entropy gradient. The remaining degrees of freedom, shear, vorticity and the metric tensor, are see in this context as charged fields under the Weyl gauge connection. The gauge nature of the connection provides natural dynamics to it via equations of motion analogous to the Maxwell equations for electromagnetism. As a consequence, a charge for the Weyl connection is defined and the notion of local charge is analyzed generating the conservation law for the Weyl charge.
Liu, Ren; Zhao, Yuejin; Chen, Haihong; Liang, Xiuying; Yang, Ming
2017-12-01
Industrial boilers are widely applied in such fields as factory power, building heating, and people’s lives; China is the world’s largest producer and user of industrial boilers, with very high annual energy consumption; clear requirements have been put forward by China on the energy efficiency since the “11th Five-year Plan” with the hope to save energy and reduce emission by means of energy efficiency standards and regulations on the supervision and control of various special equipment. So far, the energy efficiency of industrial boilers in China has been improved significantly but there is still a gap with the EU states. This paper analyzes the policies of energy efficiency, implementation models and methods of supervision and implementation at the EU level from laws, regulations, directives as well as standards; the paper also puts forward suggestions of energy conserving and emission reduction on the improvement of energy conserving capacity of industrial boilers in China through studying the legislations and measures of the developed countries in energy conserving of boilers.
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).
On conservation laws for models in discrete, noncommutative and fractional differential calculus
International Nuclear Information System (INIS)
Klimek, M.
2001-01-01
We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1+1 dimensions are studied
Construction of local and non-local conservation laws for non-linear field equations
International Nuclear Information System (INIS)
Vladimirov, V.S.; Volovich, I.V.
1984-08-01
A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)
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.
Balsara, Dinshaw S.; Dumbser, Michael
2015-04-01
Multidimensional Riemann solvers that have internal sub-structure in the strongly-interacting state have been formulated recently (D.S. Balsara (2012, 2014) [5,16]). Any multidimensional Riemann solver operates at the grid vertices and takes as its input all the states from its surrounding elements. It yields as its output an approximation of the strongly interacting state, as well as the numerical fluxes. The multidimensional Riemann problem produces a self-similar strongly-interacting state which is the result of several one-dimensional Riemann problems interacting with each other. To compute this strongly interacting state and its higher order moments we propose the use of a Galerkin-type formulation to compute the strongly interacting state and its higher order moments in terms of similarity variables. The use of substructure in the Riemann problem reduces numerical dissipation and, therefore, allows a better preservation of flow structures, like contact and shear waves. In this second part of a series of papers we describe how this technique is extended to unstructured triangular meshes. All necessary details for a practical computer code implementation are discussed. In particular, we explicitly present all the issues related to computational geometry. Because these Riemann solvers are Multidimensional and have Self-similar strongly-Interacting states that are obtained by Consistency with the conservation law, we call them MuSIC Riemann solvers. (A video introduction to multidimensional Riemann solvers is available on http://www.elsevier.com/xml/linking-roles/text/html". The MuSIC framework is sufficiently general to handle general nonlinear systems of hyperbolic conservation laws in multiple space dimensions. It can also accommodate all self-similar one-dimensional Riemann solvers and subsequently produces a multidimensional version of the same. In this paper we focus on unstructured triangular meshes. As examples of different systems of conservation laws we
Statistical symmetries in physics
International Nuclear Information System (INIS)
Green, H.S.; Adelaide Univ., SA
1994-01-01
Every law of physics is invariant under some group of transformations and is therefore the expression of some type of symmetry. Symmetries are classified as geometrical, dynamical or statistical. At the most fundamental level, statistical symmetries are expressed in the field theories of the elementary particles. This paper traces some of the developments from the discovery of Bose statistics, one of the two fundamental symmetries of physics. A series of generalizations of Bose statistics is described. A supersymmetric generalization accommodates fermions as well as bosons, and further generalizations, including parastatistics, modular statistics and graded statistics, accommodate particles with properties such as 'colour'. A factorization of elements of ggl(n b ,n f ) can be used to define truncated boson operators. A general construction is given for q-deformed boson operators, and explicit constructions of the same type are given for various 'deformed' algebras. A summary is given of some of the applications and potential applications. 39 refs., 2 figs
Cosmological constant is a conserved charge
Chernyavsky, Dmitry; Hajian, Kamal
2018-06-01
Cosmological constant can always be considered as the on-shell value of a top form in gravitational theories. The top form is the field strength of a gauge field, and the theory enjoys a gauge symmetry. We show that cosmological constant is the charge of the global part of the gauge symmetry, and is conserved irrespective of the dynamics of the metric and other fields. In addition, we introduce its conjugate chemical potential, and prove the generalized first law of thermodynamics which includes variation of cosmological constant as a conserved charge. We discuss how our new term in the first law is related to the volume–pressure term. In parallel with the seminal Wald entropy, this analysis suggests that pressure can also be considered as a conserved charge.
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...
A broken symmetry ontology: Quantum mechanics as a broken symmetry
International Nuclear Information System (INIS)
Buschmann, J.E.
1988-01-01
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance
Family of two-dimensional Born-Infeld equations and a system of conservation laws
International Nuclear Information System (INIS)
Koiv, M.; Rosenhaus, V.
1979-01-01
Lower-order conserved quantities, the ''currents'', for two-dimensional Lorentz-invariant Born-Infeld equation are considered. The currents are divided into pairs, which contain a class (basic currents) leading to the family equations. The basic currents determine the transformations between the solutions of the Born-Infeld eqution family. The equations belonging to the family are fully hodograph-invariant, partly hodograph-invariant, and effectively linear, i.e. non-linear equations with linear image of hodograph transformation
Energy Technology Data Exchange (ETDEWEB)
Fu, Yao, E-mail: Yao.Fu@colorado.edu; Song, Jeong-Hoon, E-mail: JH.Song@colorado.edu
2015-08-01
Heat flux expressions are derived for multibody potential systems by extending the original Hardy's methodology and modifying Admal & Tadmor's formulas. The continuum thermomechanical quantities obtained from these two approaches are easy to compute from molecular dynamics (MD) results, and have been tested for a constant heat flux model in two distinctive systems: crystalline iron and polyethylene (PE) polymer. The convergence criteria and affecting parameters, i.e. spatial and temporal window size, and specific forms of localization function are found to be different between the two systems. The conservation of mass, momentum, and energy are discussed and validated within this atomistic–continuum bridging.
International Nuclear Information System (INIS)
Fu, Yao; Song, Jeong-Hoon
2015-01-01
Heat flux expressions are derived for multibody potential systems by extending the original Hardy's methodology and modifying Admal & Tadmor's formulas. The continuum thermomechanical quantities obtained from these two approaches are easy to compute from molecular dynamics (MD) results, and have been tested for a constant heat flux model in two distinctive systems: crystalline iron and polyethylene (PE) polymer. The convergence criteria and affecting parameters, i.e. spatial and temporal window size, and specific forms of localization function are found to be different between the two systems. The conservation of mass, momentum, and energy are discussed and validated within this atomistic–continuum bridging
International Nuclear Information System (INIS)
Auluck, S. K. H.
2014-01-01
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
Energy Technology Data Exchange (ETDEWEB)
Auluck, S. K. H., E-mail: skhauluck@gmail.com, E-mail: skauluck@barc.gov.in [Physics Group, Bhabha Atomic Research Center, Mumbai (India)
2014-09-15
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.
International Nuclear Information System (INIS)
Ketteler, G.; Kippels, K.
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) [de
The nucleon- nucleon interaction and symmetries
Energy Technology Data Exchange (ETDEWEB)
Van Oers, W T.H.
1992-11-01
With the advent of the possibility to study nucleon-nucleon scattering at medium energies, its extension to investigate fundamental symmetries was recognized early on. It was precisely the introduction of rotational invariance, parity conservation, time reversal invariance, and isotopic spin conversation that led to the description of the N - N scattering matrix in terms of five complex amplitudes: one set of five for proton-proton scattering and one set of five for neutron-proton scattering, or alternatively, one set for the isotopic spin state {iota}={omicron} and the other for the isotopic spin state {iota}=1. Clearly, if one or more of the above constraints are removed, there are additional amplitudes that need to be considered. To be meaningful, experiment requires observables that are particularly sensitive to the violation of a conservation law or symmetry principle. During the last decade a series of precision experiments has been performed to measure charge- symmetry breaking in n - p elastic scattering (corresponding to isotopic spin non-conservation), and to measure parity violation in p-p scattering. For a particle-anti-particle system,like the pp or {lambda}{lambda} system one can raise the question of CP violation in a system other than the neutral kaon system may become possible in the near future through pp {yields}{lambda}{lambda} and pp{yields} {identical_to} {identical_to}. A description is given of the ongoing efforts to measure charge symmetry breaking, parity violation and CP violation.(author). 42 refs., 6 figs.
Symmetries and groups in particle physics
International Nuclear Information System (INIS)
Scherer, Stefan
2016-01-01
The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to
A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions
Zborovský, I.
2018-04-01
Fractal self-similarity of hadron interactions demonstrated by the z-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable z is a function of the momentum fractions x1 and x2 of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions ya and yb of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the z-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.
Conservation laws and two-dimensional black holes in dilaton gravity
Mann, R. B.
1993-05-01
A very general class of Lagrangians which couple scalar fields to gravitation and matter in two spacetime dimensions is investigated. It is shown that a vector field exists along whose flow lines the stress-energy tensor is conserved, regardless of whether or not the equations of motion are satisfied or if any Killing vectors exist. Conditions necessary for the existence of Killing vectors are derived. A new set of two-dimensional (2D) black-hole solutions is obtained for one particular member within this class of Lagrangians, which couples a Liouville field to 2D gravity in a novel way. One solution of this theory bears an interesting resemblance to the 2D string-theoretic black hole, yet contains markedly different thermodynamic properties.
Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws
von Keyserlingk, C. W.; Rakovszky, Tibor; Pollmann, Frank; Sondhi, S. L.
2018-04-01
Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces ("spin chains"), quantum field theory, and holography. We tackle this problem in 1D spin chains evolving under random local unitary circuits and prove a number of exact results on the behavior of out-of-time-ordered commutators (OTOCs) and entanglement growth in this setting. These results follow from the observation that the spreading of operators in random circuits is described by a "hydrodynamical" equation of motion, despite the fact that random unitary circuits do not have locally conserved quantities (e.g., no conserved energy). In this hydrodynamic picture, quantum information travels in a front with a "butterfly velocity" vB that is smaller than the light-cone velocity of the system, while the front itself broadens diffusively in time. The OTOC increases sharply after the arrival of the light cone, but we do not observe a prolonged exponential regime of the form ˜eλL(t -x /v ) for a fixed Lyapunov exponent λL. We find that the diffusive broadening of the front has important consequences for entanglement growth, leading to an entanglement velocity that can be significantly smaller than the butterfly velocity. We conjecture that the hydrodynamical description applies to more generic Floquet ergodic systems, and we support this idea by verifying numerically that the diffusive broadening of the operator wavefront also holds in a more traditional nonrandom Floquet spin chain. We also compare our results to Clifford circuits, which have less rich hydrodynamics and consequently trivial OTOC behavior, but which can nevertheless exhibit linear entanglement growth and thermalization.
Contact symmetries and Hamiltonian thermodynamics
International Nuclear Information System (INIS)
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-01-01
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production
International Nuclear Information System (INIS)
Anon.
1980-01-01
This pocketbook contains major federal regulations on environmental protection. They serve to protect and cultivate mankind's natural foundations of life, to preserve the environment. The environmental law is devided as follows: Constitutional law on the environment, common administrative law on the environment, special administrative law on the environment including conservation of nature and preservation of rural amenities, protection of waters, waste management, protection against nuisances, nuclear energy and radiation protection, energy conservation, protection against dangerous substances, private law relating to the environment, criminal law relating to the environment. (HSCH) [de
Symmetry, from Euclid to Pierre Curie
International Nuclear Information System (INIS)
Sivardiere, J.
1997-01-01
A historical review of the principles of symmetry is presented, starting with Egyptian pavements and Euclid regular polyhedrons, 2 and 3 dimensional paving studies with Kepler in the 17. century, modern crystallography with the constant angle law and the rational truncations law in the 18. century, the identification of the various crystal symmetries (19. century), the discovery of liquid crystals, the relations between the symmetry and the physical and optical properties of systems, molecules, etc.. Finally, P. Curie has determined the general principle of symmetry, linking symmetry and its effects
International Nuclear Information System (INIS)
Uzhinskij, V.V.; Shmakov, S.Yu.
1988-01-01
A method is suggested which enables one to take unto account the Fermi motion of nuclear nucleons in Monte-Carlo simulation of exclusive states in hadron-nucleus and nucleus-nucleus interactions and, in hadron-hadron interaction simulation, to take into account the quark transverse momentum without violation of the energy-momentum conservation law
Quantum symmetry in quantum theory
International Nuclear Information System (INIS)
Schomerus, V.
1993-02-01
Symmetry concepts have always been of great importance for physical problems like explicit calculations, classification or model building. More recently, new 'quantum symmetries' ((quasi) quantum groups) attracted much interest in quantum theory. It is shown that all these quantum symmetries permit a conventional formulation as symmetry in quantum mechanics. Symmetry transformations can act on the Hilbert space H of physical states such that the ground state is invariant and field operators transform covariantly. Models show that one must allow for 'truncation' in the tensor product of representations of a quantum symmetry. This means that the dimension of the tensor product of two representations of dimension σ 1 and σ 2 may be strictly smaller than σ 1 σ 2 . Consistency of the transformation law of field operators local braid relations leads us to expect, that (weak) quasi quantum groups are the most general symmetries in local quantum theory. The elements of the R-matrix which appears in these local braid relations turn out to be operators on H in general. It will be explained in detail how examples of field algebras with weak quasi quantum group symmetry can be obtained. Given a set of observable field with a finite number of superselection sectors, a quantum symmetry together with a complete set of covariant field operators which obey local braid relations are constructed. A covariant transformation law for adjoint fields is not automatic but will follow when the existence of an appropriate antipode is assumed. At the example of the chiral critical Ising model, non-uniqueness of the quantum symmetry will be demonstrated. Generalized quantum symmetries yield examples of gauge symmetries in non-commutative geometry. Quasi-quantum planes are introduced as the simplest examples of quasi-associative differential geometry. (Weak) quasi quantum groups can act on them by generalized derivations much as quantum groups do in non-commutative (differential-) geometry
Aniello, Paolo; Chruściński, Dariusz
2017-07-01
A symmetry witness is a suitable subset of the space of selfadjoint trace class operators that allows one to determine whether a linear map is a symmetry transformation, in the sense of Wigner. More precisely, such a set is invariant with respect to an injective densely defined linear operator in the Banach space of selfadjoint trace class operators (if and) only if this operator is a symmetry transformation. According to a linear version of Wigner’s theorem, the set of pure states—the rank-one projections—is a symmetry witness. We show that an analogous result holds for the set of projections with a fixed rank (with some mild constraint on this rank, in the finite-dimensional case). It turns out that this result provides a complete classification of the sets of projections with a fixed rank that are symmetry witnesses. These particular symmetry witnesses are projectable; i.e. reasoning in terms of quantum states, the sets of ‘uniform’ density operators of corresponding fixed rank are symmetry witnesses too.
Equivalent conserved currents and generalized Noether's theorem
International Nuclear Information System (INIS)
Gordon, T.J.
1984-01-01
A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order
A high-order finite-volume method for hyperbolic conservation laws on locally-refined grids
Energy Technology Data Exchange (ETDEWEB)
McCorquodale, Peter; Colella, Phillip
2011-01-28
We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on Cartesian grids with multiple levels of refinement. The underlying method is a generalization of that in [5] to nonlinear systems, and is based on using fourth-order accurate quadratures for computing fluxes on faces, combined with fourth-order accurate Runge?Kutta discretization in time. To interpolate boundary conditions at refinement boundaries, we interpolate in time in a manner consistent with the individual stages of the Runge-Kutta method, and interpolate in space by solving a least-squares problem over a neighborhood of each target cell for the coefficients of a cubic polynomial. The method also uses a variation on the extremum-preserving limiter in [8], as well as slope flattening and a fourth-order accurate artificial viscosity for strong shocks. We show that the resulting method is fourth-order accurate for smooth solutions, and is robust in the presence of complex combinations of shocks and smooth flows.
International Nuclear Information System (INIS)
Yee, H.C.; Shinn, J.L.
1986-12-01
Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (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
International Nuclear Information System (INIS)
Yee, H.C.; Shinn, J.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. 46 references
Voisin, Claire
1999-01-01
This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the ...
Fifty years of symmetry operations
International Nuclear Information System (INIS)
Wigner, E.P.
1978-01-01
The author begins by discussing the application of symmetry principles in classical physics, which began 150 years ago. He then offers a few remarks on the essence of these principles and their role in the structure of physics; events, laws of nature, and invariance principles - kinematic and then dynamic - are treated. After this general discussion of the various types of symmetries, he considers the fundamental differences in their application in classical and quantum physics; the symmetry principles have greater effectiveness in quantum theory. After a few critical remarks of a general nature on the invariance principles, the author reviews the application of symmetry principles in various areas of quantum mechanics: atomic spectra, molecular physics, solid state physics, nuclear physics, and particle physics. He notes that the role of the different symmetries recognized to be approximate provide the most interesting conclusions
Conformal symmetry in quantum finance
International Nuclear Information System (INIS)
Romero, Juan M; Lavana, Ulises; Miranda, Elio Martínez
2014-01-01
The quantum finance symmetries are studied. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited and the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schrödinger algebra representation is constructed. In addition, it is shown that the operators of this last representation are not hermitian and not conserved.
Energy Technology Data Exchange (ETDEWEB)
Miller, G.A. [Department of Physics, University of Washington, Seattle (United States); Kolck, U. van [Department of Physics, University of Arizona, Tucson (United States)
2003-06-01
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 the down quark has a negative charge of -1/3. If charge symmetry was exact, the proton and the neutron would have the same mass and they would both be electrically neutral. This is because the proton is made of two up quarks and a down quark, while the neutron comprises two downs and an up. Replacing up quarks with down quarks, and vice versa, therefore transforms a proton into a neutron. Charge-symmetry breaking causes the neutron to be about 0.1% heavier than the proton because the down quark is slightly heavier than the up quark. Physicists had already elucidated certain aspects of charge-symmetry breaking, but our spirits were raised greatly when we heard of the recent work of Allena Opper of Ohio University in the US and co-workers at the TRIUMF laboratory in British Columbia, Canada. Her team has been trying to observe a small charge-symmetry-breaking effect for several years, using neutron beams at the TRIUMF accelerator. The researchers studied the
International Nuclear Information System (INIS)
Zhang Dajun; Chen Dengyuan
2004-01-01
Solitons, negatons, positons, rational-like solutions and mixed solutions of a non-isospectral equation, the Korteweg-de Vries equation with loss and non-uniformity terms, are obtained through the Wronskian technique. The non-isospectral characteristics of the motion behaviours of some solutions are described with some figures made by using Mathematica. We also derive an infinite number of conservation laws of the equation
Scale symmetry and virial theorem
International Nuclear Information System (INIS)
Westenholz, C. von
1978-01-01
Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework
Recent publications on environmental law
International Nuclear Information System (INIS)
Lohse, S.
1988-01-01
The bibliography contains 1235 references to publications covering the following subject fields: general environmental law; environmental law in relation to constitutional law, administrative law, procedural law, revenue law, criminal law, private law, industrial law; law of regional development; nature conservation law; law on water protection; waste management law; law on protection against harmful effects on the environment; atomic energy law and radiation protection law; law of the power industry and the mining industry; laws and regulations on hazardous material and environmental hygiene. (HP) [de
Recent publications on environmental law
International Nuclear Information System (INIS)
Lohse, S.
1989-01-01
The bibliography contains 1160 references to publications covering the following subject fields: General environmental law; environmental law in relation to constitutional law, administrative law, procedural law, revenue law, criminal law, private law, industrial law; law of regional development; nature conservation law; law on water protection; waste management law; law on protection against harmful effects on the environment; atomic energy law and radiation protection law; law of the power industry and the mining industry; laws and regulations on hazardous material and environmental hygiene. (orig./HP) [de
Symmetries and casimir of an extended classical long wave system
Indian Academy of Sciences (India)
Keywords. Dispersionless equations; symmetries; casimir; conserved quantities. ... Application of Lie symmetry analysis to integro-differential equations or infinite systems ..... The financial support in the form of Senior Research Fellowship.
Symmetry, Symmetry Breaking and Topology
Directory of Open Access Journals (Sweden)
Siddhartha Sen
2010-07-01
Full Text Available The ground state of a system with symmetry can be described by a group G. This symmetry group G can be discrete or continuous. Thus for a crystal G is a finite group while for the vacuum state of a grand unified theory G is a continuous Lie group. The ground state symmetry described by G can change spontaneously from G to one of its subgroups H as the external parameters of the system are modified. Such a macroscopic change of the ground state symmetry of a system from G to H correspond to a “phase transition”. Such phase transitions have been extensively studied within a framework due to Landau. A vast range of systems can be described using Landau’s approach, however there are also systems where the framework does not work. Recently there has been growing interest in looking at such non-Landau type of phase transitions. For instance there are several “quantum phase transitions” that are not of the Landau type. In this short review we first describe a refined version of Landau’s approach in which topological ideas are used together with group theory. The combined use of group theory and topological arguments allows us to determine selection rule which forbid transitions from G to certain of its subgroups. We end by making a few brief remarks about non-Landau type of phase transition.
Dynamics symmetries of Hamiltonian system on time scales
Energy Technology Data Exchange (ETDEWEB)
Peng, Keke, E-mail: pengkeke88@126.com; Luo, Yiping, E-mail: zjstulyp@126.com [Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)
2014-04-15
In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.
Symmetries in discrete-time mechanics
International Nuclear Information System (INIS)
Khorrami, M.
1996-01-01
Based on a general formulation for discrete-time quantum mechanics, introduced by M. Khorrami (Annals Phys. 224 (1995), 101), symmetries in discrete-time quantum mechanics are investigated. It is shown that any classical continuous symmetry leads to a conserved quantity in classical mechanics, as well as quantum mechanics. The transformed wave function, however, has the correct evolution if and only if the symmetry is nonanomalous. Copyright copyright 1996 Academic Press, Inc
Peculiar symmetry structure of some known discrete nonautonomous equations
International Nuclear Information System (INIS)
Garifullin, R N; Habibullin, I T; Yamilov, R I
2015-01-01
We study the generalized symmetry structure of three known discrete nonautonomous equations. One of them is the semidiscrete dressing chain of Shabat. Two others are completely discrete equations defined on the square lattice. The first one is a discrete analogue of the dressing chain introduced by Levi and Yamilov. The second one is a nonautonomous generalization of the potential discrete KdV equation or, in other words, the H1 equation of the well-known Adler−Bobenko−Suris list. We demonstrate that these equations have generalized symmetries in both directions if and only if their coefficients, depending on the discrete variables, are periodic. The order of the simplest generalized symmetry in at least one direction depends on the period and may be arbitrarily high. We substantiate this picture by some theorems in the case of small periods. In case of an arbitrarily large period, we show that it is possible to construct two hierarchies of generalized symmetries and conservation laws. The same picture should take place in case of any nonautonomous equation of the Adler−Bobenko−Suris list. (paper)
Conjuring the universe the origins of the laws of nature
Atkins, Peter
2018-01-01
The marvellous complexity of the Universe emerges from several deep laws and a handful of fundamental constants that fix its shape, scale, and destiny. There is a deep structure to the world which at the same time is simple, elegant, and beautiful. Where did these laws and these constants come from? And why are the laws so fruitful when written in the language of mathematics? Peter Atkins considers the minimum effort needed to equip the Universe with its laws and its constants. He explores the origin of the conservation of energy, of electromagnetism, of classical and quantum mechanics, and of thermodynamics, showing how all these laws spring from deep symmetries. The revolutionary result is a short but immensely rich weaving together of the fundamental ideas of physics. With his characteristic wit, erudition, and economy, Atkins sketches out how the laws of Nature can spring from very little. Or arguably from nothing at all.
Relabeling symmetries in hydrodynamics and magnetohydrodynamics
International Nuclear Information System (INIS)
Padhye, N.; Morrison, P.J.
1996-04-01
Lagrangian symmetries and concomitant generalized Bianchi identities associated with the relabeling of fluid elements are found for hydrodynamics and magnetohydrodynamics (MHD). In hydrodynamics relabeling results in Ertel's theorem of conservation of potential vorticity, while in MHD it yields the conservation of cross helicity. The symmetries of the reduction from Lagrangian (material) to Eulerian variables are used to construct the Casimir invariants of the Hamiltonian formalism
Directory of Open Access Journals (Sweden)
Angel Garrido
2011-01-01
Full Text Available In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brain's systems have complex network features—such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure, with the degree distribution following a Power Law. How can very different systems have the same underlying topological features? Modeling and characterizing these networks, looking for their governing laws, are the current lines of research. So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.
Quantized Dirac field in curved Riemann--Cartan background. I. Symmetry properties, Green's function
International Nuclear Information System (INIS)
Nieh, H.T.; Yan, M.L.
1982-01-01
In the present series of papers, we study the properties of quantized Dirac field in curved Riemann--Cartan space, with particular attention on the role played by torsion. In this paper, we give, in the spirit of the original work of Weyl, a systematic presentation of Dirac's theory in curved Riemann--Cartan space. We discuss symmetry properties of the system, and derive conservation laws as direct consequences of these symmetries. Also discussed is conformal gauge symmetry, with torsion effectively playing the role of a conformal gauge field. To obtain short-distance behavior, we calculate the spinor Green's function, in curved Riemann--Cartan background, using the Schwinger--DeWitt method of proper-time expansion. The calculation corresponds to a generalization of DeWitt's calculation for a Riemannian background
NHEG mechanics: laws of near horizon extremal geometry (thermo)dynamics
International Nuclear Information System (INIS)
Hajian, K.; Seraj, A.; Sheikh-Jabbari, M.M.
2014-01-01
Near Horizon Extremal Geometries (NHEG) are solutions to gravity theories with SL(2,ℝ)×U(1) N (for some N) symmetry, are smooth geometries and have no event horizon, unlike black holes. Following the ideas by R. M. Wald, we derive laws of NHEG dynamics, the analogs of laws of black hole dynamics for the NHEG. Despite the absence of horizon in the NHEG, one may associate an entropy to the NHEG, as a Noether-Wald conserved charge. We work out “entropy” and “entropy perturbation” laws, which are respectively universal relations between conserved Noether charges corresponding to the NHEG and a system probing the NHEG. Our entropy law is closely related to Sen’s entropy function. We also discuss whether the laws of NHEG dynamics can be obtained from the laws of black hole thermodynamics in the extremal limit
Delzanno, G. L.
2015-11-01
A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.
On the Definition of Energy for a Continuum, Its Conservation Laws, and the Energy-Momentum Tensor
Directory of Open Access Journals (Sweden)
Mayeul Arminjon
2016-01-01
Full Text Available We review the energy concept in the case of a continuum or a system of fields. First, we analyze the emergence of a true local conservation equation for the energy of a continuous medium, taking the example of an isentropic continuum in Newtonian gravity. Next, we consider a continuum or a system of fields in special relativity: we recall that the conservation of the energy-momentum tensor contains two local conservation equations of the same kind as before. We show that both of these equations depend on the reference frame and that, however, they can be given a rigorous meaning. Then, we review the definitions of the canonical and Hilbert energy-momentum tensors from a Lagrangian through the principle of stationary action in general space-time. Using relatively elementary mathematics, we prove precise results regarding the definition of the Hilbert tensor field, its uniqueness, and its tensoriality. We recall the meaning of its covariant conservation equation. We end with a proof of uniqueness of the energy density and flux, when both depend polynomially on the fields.
Laurençot, Philippe
2018-03-01
Uniqueness of mass-conserving self-similar solutions to Smoluchowski's coagulation equation is shown when the coagulation kernel K is given by K(x,x_*)=2(x x_*)^{-α } , (x,x_*)\\in (0,∞)^2 , for some α >0.
Augousti, A. T.; Radosz, A.; Ostasiewicz, K.
2011-01-01
By using the symmetry and time-independence properties of Schwarzschild spacetime it is demonstrated that an energy conservation law may be expressed in terms of local velocity. From this form three important results may be derived very concisely. This highlights analogies and differences between relativistic and classical approaches to mechanics…
Chiral symmetry breaking for domain wall fermions in quenched lattice QCD
International Nuclear Information System (INIS)
Wu Lingling
2001-01-01
The domain wall fermion formulation exhibits full chiral symmetry for finite lattice spacing except for the effects of mixing between the domain walls. Close to the continuum limit these symmetry breaking effects should be described by a single residual mass. We determine this mass from the conservation law obeyed by the conserved axial current in quenched simulations with β = 5.7 and 6.0 and domain wall separations varying between 12 and 48 on 8 3 x 32 and 16 3 x 32 lattices. Using the resulting values for the residual mass we perform two complete and independent calculations of the pion decay constant. Good agreement is found between these two methods and with experiment
Directory of Open Access Journals (Sweden)
Waldyr A. Rodrigues
2016-01-01
Full Text Available We discuss the physics of interacting fields and particles living in a de Sitter Lorentzian manifold (dSLM, a submanifold of a 5-dimensional pseudo-Euclidean (5dPE equipped with a metric tensor inherited from the metric of the 5dPE space. The dSLM is naturally oriented and time oriented and is the arena used to study the energy-momentum conservation law and equations of motion for physical systems living there. Two distinct de Sitter space-time structures MdSL and MdSTP are introduced given dSLM, the first equipped with the Levi-Civita connection of its metric field and the second with a metric compatible parallel connection. Both connections are used only as mathematical devices. Thus, for example, MdSL is not supposed to be the model of any gravitational field in the General Relativity Theory (GRT. Misconceptions appearing in the literature concerning the motion of free particles in dSLM are clarified. Komar currents are introduced within Clifford bundle formalism permitting the presentation of Einstein equation as a Maxwell like equation and proving that in GRT there are infinitely many conserved currents. We prove that in GRT even when the appropriate Killing vector fields exist it is not possible to define a conserved energy-momentum covector as in special relativistic theories.
Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations
Alghamdi, Moataz
2017-06-18
We introduce a symbolic computational approach to detecting all permutation and parity symmetries in any general evolution equation, and to generating associated invariant polynomials, from given monomials, under the action of these symmetries. Traditionally, discrete point symmetries of differential equations are systemically found by solving complicated nonlinear systems of partial differential equations; in the presence of Lie symmetries, the process can be simplified further. Here, we show how to find parity- and permutation-type discrete symmetries purely based on algebraic calculations. Furthermore, we show that such symmetries always form groups, thereby allowing for the generation of new group-invariant conserved quantities from known conserved quantities. This work also contains an implementation of the said results in Mathematica. In addition, it includes, as a motivation for this work, an investigation of the connection between variational symmetries, described by local Lie groups, and conserved quantities in Hamiltonian systems.
International Nuclear Information System (INIS)
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces
International Nuclear Information System (INIS)
Panov, E Yu
1999-01-01
We consider a hyperbolic system of conservation laws on the space of symmetric second-order matrices. The right-hand side of this system contains the functional calculus operator f-bar(U) generated in the general case only by a continuous scalar function f(u). For these systems we define and describe the set of singular entropies, introduce the concept of generalized entropy solutions of the corresponding Cauchy problem, and investigate the properties of generalized entropy solutions. We define the class of strong generalized entropy solutions, in which the Cauchy problem has precisely one solution. We suggest a condition on the initial data under which any generalized entropy solution is strong, which implies its uniqueness. Under this condition we establish that the 'vanishing viscosity' method converges. An example shows that in the general case there can be more than one generalized entropy solution
International Nuclear Information System (INIS)
Panov, E Yu
2000-01-01
Many-dimensional non-strictly hyperbolic systems of conservation laws with a radially degenerate flux function are considered. For such systems the set of entropies is defined and described, the concept of generalized entropy solution of the Cauchy problem is introduced, and the properties of generalized entropy solutions are studied. The class of strong generalized entropy solutions is distinguished, in which the Cauchy problem in question is uniquely soluble. A condition on the initial data is described that ensures that the generalized entropy solution is strong and therefore unique. Under this condition the convergence of the 'vanishing viscosity' method is established. An example presented in the paper shows that a generalized entropy solution is not necessarily unique in the general case
Motsepa, Tanki; Masood Khalique, Chaudry
2018-05-01
In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.
Siswaningsih, W.; Nahadi; Firmansyah, D. R.
2018-05-01
The purpose of this research is to develop the instrument of performance assessment of law of mass conservation using self and peer assessment technique that meet valid and reliable criteria. The instrument components consist of task and rubric. The method used is development and validation.Value of the instrument reliability obtained from twice observations that are at four and six students every group with three same observers. Cronbach alpha value for four and six students every group consecutively are 0.94 and 0.76, indicating that value shows that the instrument is reliable. Optimum amount of the students that can be observed are four students. The implementation of the instrument to limited group of students showed that All of the students give positive responses to the instrument used with the interpretation of questionnaire scores >90% that categorized as good.
Chiral symmetry and chiral-symmetry breaking
International Nuclear Information System (INIS)
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed
International Nuclear Information System (INIS)
Henley, E.M.
1987-01-01
Nuclei are very useful for testing symmetries, and for studies of symmetry breaking. This thesis is illustrated for two improper space-time transformations, parity and time-reversal and for one internal symmetry: charge symmetry and independence. Recent progress and present interest is reviewed. 23 refs., 8 figs., 2 tabs
Wiafe, Edward Debrah
2016-01-01
The wildlife laws of Ghana alienated the rural communities from forests and material well-being depended upon for their livelihood and this manifests itself in the progressive conflict between the park patrol staff and poachers from the fringes of the protected areas. The main aim of this study was to determine the impact of quantification of patrol efforts on indicators of illegal hunting activities that occur in rainforest protected areas, as a result of monitoring patrol operations and modifying the original plan. The specific objectives were to determine the optimal patrol efforts necessary to reduce illegal wildlife use to minimal; and the influence of the rainfall and seasonal activities on illegal wildlife use. The results indicated that as the patrol efforts increased the encounter with illegal wildlife use also increased until a certain point that the encounter rates started decreasing. Neither rainfall nor seasonal activities influenced the illegal activities and the patrol efforts. The protection staff of rainforest protected areas would work effectively to bring down illegal wildlife off-take to the barest minimum if monitored, quantified and provide feed-back. Illegal wildlife off-take can also be reduced by the protection staff if the original plans are made flexible to be adjusted. Recommendations for further studies have been made.
Directory of Open Access Journals (Sweden)
Alina BOGOI
2016-12-01
Full Text Available Supersonic/hypersonic flows with strong shocks need special treatment in Computational Fluid Dynamics (CFD in order to accurately capture the discontinuity location and his magnitude. To avoid numerical instabilities in the presence of discontinuities, the numerical schemes must generate low dissipation and low dispersion error. Consequently, the algorithms used to calculate the time and space-derivatives, should exhibit a low amplitude and phase error. This paper focuses on the comparison of the numerical results obtained by simulations with some high resolution numerical schemes applied on linear and non-linear one-dimensional conservation low. The analytical solutions are provided for all benchmark tests considering smooth periodical conditions. All the schemes converge to the proper weak solution for linear flux and smooth initial conditions. However, when the flux is non-linear, the discontinuities may develop from smooth initial conditions and the shock must be correctly captured. All the schemes accurately identify the shock position, with the price of the numerical oscillation in the vicinity of the sudden variation. We believe that the identification of this pure numerical behavior, without physical relevance, in 1D case is extremely useful to avoid problems related to the stability and convergence of the solution in the general 3D case.
Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.
2018-01-01
The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.
Interdependence of different symmetry energy elements
Mondal, C.; Agrawal, B. K.; De, J. N.; Samaddar, S. K.; Centelles, M.; Viñas, X.
2017-08-01
Relations between the nuclear symmetry energy coefficient and its density derivatives are derived. The relations hold for a class of interactions with quadratic momentum dependence and a power-law density dependence. The structural connection between the different symmetry energy elements as obtained seems to be followed by almost all reasonable nuclear energy density functionals, both relativistic and nonrelativistic, suggesting a universality in the correlation structure. This, coupled with known values of some well-accepted constants related to nuclear matter, helps in constraining values of different density derivatives of the nuclear symmetry energy, shedding light on the isovector part of the nuclear interaction.
International Nuclear Information System (INIS)
Hsu, J.P.
1976-01-01
A new picture of nature is proposed in which there are only two fundamental universal constants anti e (identical with e/c) and dirac constant (identical with dirac constant/c). The theory is developed within the framework of a new four-dimensional symmetry which is constructed on the basis of the Poincare--Einstein principle of relativity for the laws of physics and the Newtonian concept of time. One obtains a new space--light transformation law, a velocity-addition law, and so on. In this symmetry scheme, the speed of light is constant and is completely relative. The new theory is logically self-consistent, and it moreover is in agreement with all previously established experimental facts, such as the ''lifetime dilatation'' of unstable particles, the Michelson--Morley experiment, etc. There is a difference relative to the usual theory, though, in that our theory predicts a new law for the Doppler frequency shift, which can be tested experimentally by measuring the second-order frequency shift
Law behind second law of thermodynamics - unification with cosmology
International Nuclear Information System (INIS)
Nielsen, Holger B.; Ninomiya, Masao
2006-01-01
In an abstract setting of a general classical mechanical system as a model for the universe we set up a general formalism for a law behind the second law of thermodynamics, i.e. really for 'initial conditions'. We propose a unification with the other laws by requiring similar symmetry and locality properties
Hairs of discrete symmetries and gravity
Energy Technology Data Exchange (ETDEWEB)
Choi, Kang Sin [Scranton Honors Program, Ewha Womans University, Seodaemun-Gu, Seoul 03760 (Korea, Republic of); Center for Fields, Gravity and Strings, CTPU, Institute for Basic Sciences, Yuseong-Gu, Daejeon 34047 (Korea, Republic of); Kim, Jihn E., E-mail: jihnekim@gmail.com [Department of Physics, Kyung Hee University, 26 Gyungheedaero, Dongdaemun-Gu, Seoul 02447 (Korea, Republic of); Center for Axion and Precision Physics Research (IBS), 291 Daehakro, Yuseong-Gu, Daejeon 34141 (Korea, Republic of); Kyae, Bumseok [Department of Physics, Pusan National University, 2 Busandaehakro-63-Gil, Geumjeong-Gu, Busan 46241 (Korea, Republic of); Nam, Soonkeon [Department of Physics, Kyung Hee University, 26 Gyungheedaero, Dongdaemun-Gu, Seoul 02447 (Korea, Republic of)
2017-06-10
Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair) at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.
Hairs of discrete symmetries and gravity
Directory of Open Access Journals (Sweden)
Kang Sin Choi
2017-06-01
Full Text Available Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.
Ermolenko, Alexander E; Perepada, Elena A
2007-01-01
The paper contains a description of basic regularities in the manifestation of symmetry of human structural organization and its ontogenetic and phylogenetic development. A concept of macrobiocrystalloid with inherent complex symmetry is proposed for the description of the human organism in its integrity. The symmetry can be characterized as two-plane radial (quadrilateral), where the planar symmetry is predominant while the layout of organs of radial symmetry is subordinated to it. Out of the two planes of symmetry (sagittal and horizontal), the sagittal plane is predominant. The symmetry of the chromosome, of the embrio at the early stages of cell cleavage as well as of some organs and systems in their phylogenetic development is described. An hypothesis is postulated that the two-plane symmetry is formed by two mechanisms: a) the impact of morphogenetic fields of the whole crystalloid organism during embriogenesis and, b) genetic mechanisms of the development of chromosomes having two-plane symmetry.
Energy Technology Data Exchange (ETDEWEB)
Matsuta, K., E-mail: matsuta@vg.phys.sci.osaka-u.ac.jp; Minamisono, T.; Mihara, M.; Fukuda, M. [Osaka Univ., Dept. of Physics (Japan); Zhu, Shengyun [CIAE (China); Masuda, Y. [High Energy Accelerator Research Organization (KEK) (Japan); Hatanaka, K. [Osaka Univ., RCNP (Japan); Yuan Daqing; Zheng Yongnan; Zuo Yi; Fang Ping; Zhou Dongmei [CIAE (China); Ohtsubo, T. [Niigata Univ., Dept. of Physics (Japan); Izumikawa, T. [Niigata Univ., RI Center (Japan); Momota, S. [Kochi Univ. of Technology (Japan); Nishimura, D. [Tokyo Univ. of Science (Japan); Matsumiya, R. [Osaka Univ., RCNP (Japan); Kitagawa, A.; Sato, S.; Kanazawa, M. [Nat. Inst. Radiological Sciences (Japan); Collaboration: Osaka-CIAE-NIRS-Niigata-Kochi-LBL Collaboration; and others
2013-05-15
We report our studies in various fields of Physics through nuclear moments utilizing the {beta}-NMR technique, including material sciences, nuclear structures and fundamental symmetries. Especially, we focus on the recent progress in the studies on the electronic structure in Pt through Knight shifts of various impurities, lattice locations of impurities, electric field gradients, the analysis of nuclear spin in terms of its components, anomaly in the spin expectation value for {sup 9}C-{sup 9}Li mirror pair, the G-parity conservation law, and the Ramsey resonance on UCN for future neutron EDM measurements.
The priority of internal symmetries in particle physics
Kantorovich, Aharon
2003-12-01
In this paper, I try to decipher the role of internal symmetries in the ontological maze of particle physics. The relationship between internal symmetries and laws of nature is discussed within the framework of ;Platonic realism.; The notion of physical ;structure; is introduced as representing a deeper ontological layer behind the observable world. I argue that an internal symmetry is a structure encompassing laws of nature. The application of internal symmetry groups to particle physics came about in two revolutionary steps. The first was the introduction of the internal symmetries of hadrons in the early 1960s. These global and approximate symmetries served as means of bypassing the dynamics. I argue that the realist could interpret these symmetries as ontologically prior to the hadrons. The second step was the gauge revolution in the 1970s, where symmetries became local and exact and were integrated with the dynamics. I argue that the symmetries of the second generation are fundamental in the following two respects: (1) According to the so-called ;gauge argument,; gauge symmetry dictates the existence of gauge bosons, which determine the nature of the forces. This view, which has been recently criticized by some philosophers, is widely accepted in particle physics at least as a heuristic principle. (2) In view of grand unified theories, the new symmetries can be interpreted as ontologically prior to baryon matter.
Du, Zhong; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Sun, Yan
2017-07-01
Subpicosecond or femtosecond optical pulse propagation in the inhomogeneous fiber can be described by a higher-order nonlinear Schrödinger equation with variable coefficients, which is investigated in the paper. Via the Ablowitz-Kaup-Newell-Segur system and symbolic computation, the Lax pair and infinitely-many conservation laws are deduced. Based on the Lax pair and a modified Darboux transformation technique, the first- and second-order rogue wave solutions are constructed. Effects of the groupvelocity dispersion and third-order dispersion on the properties of the first- and second-order rouge waves are graphically presented and analyzed: The groupvelocity dispersion and third-order dispersion both affect the ranges and shapes of the first- and second-order rogue waves: The third-order dispersion can produce a skew angle of the first-order rogue wave and the skew angle rotates counterclockwise with the increase of the groupvelocity dispersion, when the groupvelocity dispersion and third-order dispersion are chosen as the constants; When the groupvelocity dispersion and third-order dispersion are taken as the functions of the propagation distance, the linear, X-shaped and parabolic trajectories of the rogue waves are obtained.
Extended constitutive laws for lamellar phases
Directory of Open Access Journals (Sweden)
Chi-Deuk Yoo
2013-10-01
Full Text Available Classically, stress and strain rate in linear viscoelastic materials are related by a constitutive relationship involving the viscoelastic modulus G(t. The same constitutive law, within Linear Response Theory, relates currents of conserved quantities and gradients of existing conjugate variables, and it involves the autocorrelation functions of the currents in equilibrium. We explore the consequences of the latter relationship in the case of a mesoscale model of a block copolymer, and derive the resulting relationship between viscous friction and order parameter diffusion that would result in a lamellar phase. We also explicitly consider in our derivation the fact that the dissipative part of the stress tensor must be consistent with the uniaxial symmetry of the phase. We then obtain a relationship between the stress and order parameter autocorrelation functions that can be interpreted as an extended constitutive law, one that offers a way to determine them from microscopic experiment or numerical simulation.
International Nuclear Information System (INIS)
Nilles, Hans Peter
2012-04-01
Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.
Energy Technology Data Exchange (ETDEWEB)
Nilles, Hans Peter [Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Bonn Univ. (Germany). Physikalisches Inst.; Ratz, Michael [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-04-15
Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.
An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry
International Nuclear Information System (INIS)
Bernard-Champmartin, Aude; Ghidaglia, Jean-Michel; Braeunig, Jean-Philippe
2013-01-01
In this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable h), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific up-winding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity uh. (authors)
Symmetry, asymmetry and dissymmetry
International Nuclear Information System (INIS)
Wackenheim, A.; Zollner, G.
1987-01-01
The authors discuss the concept of symmetry and defect of symmetry in radiological imaging and recall the definition of asymmetry (congenital or constitutional) and dissymmetry (acquired). They then describe a rule designed for the cognitive method of automatic evaluation of shape recognition data and propose the use of reversal symmetry [fr
International Nuclear Information System (INIS)
Fuentes Cobas, L.E.; Font Hernandez, R.
1993-01-01
An analytical treatment of electrostatic and magnetostatic field symmetry, as a function of charge and current distribution symmetry, is proposed. The Newmann Principle, related to the cause-effect symmetry relation, is presented and applied to the characterization of simple configurations. (Author) 5 refs
Rehren, K. -H.
1996-01-01
Weak C* Hopf algebras can act as global symmetries in low-dimensional quantum field theories, when braid group statistics prevents group symmetries. Possibilities to construct field algebras with weak C* Hopf symmetry from a given theory of local observables are discussed.
International Nuclear Information System (INIS)
Weinberg, S.
1976-01-01
The problem of how gauge symmetries of the weak interactions get broken is discussed. Some reasons why such a heirarchy of gauge symmetry breaking is needed, the reason gauge heirarchies do not seem to arise in theories of a given and related type, and the implications of theories with dynamical symmetry breaking, which can exhibit a gauge hierarchy
CP properties of symmetry-constrained two-Higgs-doublet models
Ferreira, P M; Nachtmann, O; Silva, Joao P
2010-01-01
The two-Higgs-doublet model can be constrained by imposing Higgs-family symmetries and/or generalized CP symmetries. It is known that there are only six independent classes of such symmetry-constrained models. We study the CP properties of all cases in the bilinear formalism. An exact symmetry implies CP conservation. We show that soft breaking of the symmetry can lead to spontaneous CP violation (CPV) in three of the classes.
Chiral symmetry breaking and confinement - solutions of relativistic wave equations
International Nuclear Information System (INIS)
Murugesan, P.
1983-01-01
In this thesis, an attempt is made to explore the question whether confinement automatically leads to chiral symmetry breaking. While it should be accepted that chiral symmetry breaking manifests in nature in the absence of scalar partners of pseudoscalar mesons, it does not necessarily follow that confinement should lead to chiral symmetry breaking. If chiral conserving forces give rise to observed spectrum of hadrons, then the conjuncture that confinement is responsible for chiral symmetry breaking is not valid. The method employed to answer the question whether confinement leads to chiral symmetry breaking or not is to solve relativistic wave equations by introducing chiral conserving as well as chiral breaking confining potentials and compare the results with experimental observations. It is concluded that even though chiral symmetry is broken in nature, confinement of quarks need not be the cause of it
Raibert, M H
1986-03-14
Symmetry plays a key role in simplifying the control of legged robots and in giving them the ability to run and balance. The symmetries studied describe motion of the body and legs in terms of even and odd functions of time. A legged system running with these symmetries travels with a fixed forward speed and a stable upright posture. The symmetries used for controlling legged robots may help in elucidating the legged behavior of animals. Measurements of running in the cat and human show that the feet and body sometimes move as predicted by the even and odd symmetry functions.
Kemeth, Felix P.; Haugland, Sindre W.; Krischer, Katharina
2018-05-01
Symmetry broken states arise naturally in oscillatory networks. In this Letter, we investigate chaotic attractors in an ensemble of four mean-coupled Stuart-Landau oscillators with two oscillators being synchronized. We report that these states with partially broken symmetry, so-called chimera states, have different setwise symmetries in the incoherent oscillators, and in particular, some are and some are not invariant under a permutation symmetry on average. This allows for a classification of different chimera states in small networks. We conclude our report with a discussion of related states in spatially extended systems, which seem to inherit the symmetry properties of their counterparts in small networks.
Parastatistics and gauge symmetries
International Nuclear Information System (INIS)
Govorkov, A.B.
1982-01-01
A possible formulation of gauge symmetries in the Green parafield theory is analysed and the SO(3) gauge symmetry is shown to be on a distinct status. The Greenberg paraquark hypothesis turns out to be not equivalent to the hypothesis of quark colour SU(3)sub(c) symmetry. Specific features of the gauge SO(3) symmetry are discussed, and a possible scheme where it is an exact subgroup of the broken SU(3)sub(c) symmetry is proposed. The direct formulation of the gauge principle for the parafield represented by quaternions is also discussed
Nonlinearity, Conservation Law and Shocks
Indian Academy of Sciences (India)
Almost all natural phenomena, and social and economic changes, .... reference moving with velocity c also by the same symbol x and ... abstract as can be seen from the publication of the book Shock Waves and Reaction Diffusion Equation.
Conservation laws and gravitational radiation
International Nuclear Information System (INIS)
Rastall, P.
1977-01-01
A total stress-momentum is defined for gravitational fields and their sources. The Lagrangian density is slightly different from that in the previous version of the theory, and the field equations are considerably simplified. The post-Newtonian approximation of the theory is unchanged. The existence and nature of weak gravitational waves are discussed. (author)
Lie-algebra approach to symmetry breaking
International Nuclear Information System (INIS)
Anderson, J.T.
1981-01-01
A formal Lie-algebra approach to symmetry breaking is studied in an attempt to reduce the arbitrariness of Lagrangian (Hamiltonian) models which include several free parameters and/or ad hoc symmetry groups. From Lie algebra it is shown that the unbroken Lagrangian vacuum symmetry can be identified from a linear function of integers which are Cartan matrix elements. In broken symmetry if the breaking operators form an algebra then the breaking symmetry (or symmetries) can be identified from linear functions of integers characteristic of the breaking symmetries. The results are applied to the Dirac Hamiltonian of a sum of flavored fermions and colored bosons in the absence of dynamical symmetry breaking. In the partially reduced quadratic Hamiltonian the breaking-operator functions are shown to consist of terms of order g 2 , g, and g 0 in the color coupling constants and identified with strong (boson-boson), medium strong (boson-fermion), and fine-structure (fermion-fermion) interactions. The breaking operators include a boson helicity operator in addition to the familiar fermion helicity and ''spin-orbit'' terms. Within the broken vacuum defined by the conventional formalism, the field divergence yields a gauge which is a linear function of Cartan matrix integers and which specifies the vacuum symmetry. We find that the vacuum symmetry is chiral SU(3) x SU(3) and the axial-vector-current divergence gives a PCAC -like function of the Cartan matrix integers which reduces to PCAC for SU(2) x SU(2) breaking. For the mass spectra of the nonets J/sup P/ = 0 - ,1/2 + ,1 - the integer runs through the sequence 3,0,-1,-2, which indicates that the breaking subgroups are the simple Lie groups. Exact axial-vector-current conservation indicates a breaking sum rule which generates octet enhancement. Finally, the second-order breaking terms are obtained from the second-order spin tensor sum of the completely reduced quartic Hamiltonian
International Nuclear Information System (INIS)
Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan; Willett, Brian
2015-01-01
A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (q=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have ’t Hooft anomalies, which prevent us from gauging them, but lead to ’t Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.
R-charge Conservation and More in Factorizable and Non-Factorizable Orbifolds
Bizet, Nana Geraldine Cabo; Pena, Damian Kaloni Mayorga; Parameswaran, Susha L; Schmitz, Matthias; Zavala, Ivonne
2013-01-01
We consider the string theory origin of R-charge conservation laws in heterotic orbifold compactifications, deriving the corresponding string coupling selection rule for factorizable and non-factorizable orbifolds, with prime ordered and non-prime ordered point groups. R-charge conservation arises due to symmetries among the worldsheet instantons that can mediate the couplings. Among our results is a previously missed non-trivial contribution to the conserved R-charges from the Gamma-phases in non-prime orbifolds, which weakens the R-charge selection rule. Symmetries among the worldsheet instantons can also lead to additional selection rules for some couplings. We make a similar analysis for Rule 4 or the 'torus lattice selection rule'. Moreover, we identify a new string selection rule, that we call Rule 6 or the 'coset vector selection rule'.
Movsesyan, Arsen A.
2015-01-01
The purpose of this article is to tell briefly about the newly discovered fundamental Laws of Sociodynamics, which are the driving force of the evolution of society and the determining factor of world historic process. Based on the principle of symmetry of the laws of nature the relationship between the Laws of Thermodynamics and Sociodynamics is shown, due to which the fifth Law of Thermodynamics has been formulated. In doing so the objectivity of the concept of «spirituality» has been subst...
Unified Symmetry of Nonholonomic Mechanical Systems with Non-Chetaev's Type Constraints
International Nuclear Information System (INIS)
Xia Lili; Li Yuancheng; Hou Qibao; Wang Jing
2006-01-01
Based on the total time derivative along the trajectory of the system, the unified symmetry of nonholonomic mechanical system with non-Chetaev's type constraints is studied. The definition and criterion of the unified symmetry of nonholonomic mechanical systems with non-Chetaev's type constraints are given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. Two examples are given to illustrate the application of the results.
Symmetries and groups in particle physics; Symmetrien und Gruppen in der Teilchenphysik
Energy Technology Data Exchange (ETDEWEB)
Scherer, Stefan [Mainz Univ. (Germany)
2016-07-01
The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to
International Nuclear Information System (INIS)
Mainzer, K.
1988-01-01
Symmetry, disymmetry, chirality etc. are well-known topics in chemistry. But they cannot only be found on the molecular level of matter. Atoms and elementary particles in physics are also characterized by particular symmetry groups. Even living organisms and populations on the macroscopic level have functional properties of symmetry. The whole physical, chemical, and biological evolution seems to be regulated by the emergence of new symmetries and the breaking down of old ones. One is reminded of Heisenberg's famous statement: 'Die letzte Wurzel der Erscheinungen ist also nicht die Materie, sondern das mathematische Gesetz, die Symmetrie, die mathematische Form' (Wandlungen in den Grundlagen der Naturwissenschaften, 1959). Historically the belief in symmetry and simplicity of nature has a long philosophical tradition from the Pythagoreans, Plato and Greek astronomers to Kepler and modern scientists. Today, 'symmetries in nature' is a common topic of mathematics, physics, chemistry, and biology. A lot of Nobel prizes were given in honour of inquiries concerning symmetries in nature. The fascination of symmetries is not only motivated by science, but by art and religion too. Therefore 'symmetris in nature' is an interdisciplinary topic which may help to overcome C.P. Snow's 'Two Cultures' of natural sciences and humanities. (author) 17 refs., 21 figs
Energy Technology Data Exchange (ETDEWEB)
Mainzer, K
1988-05-01
Symmetry, disymmetry, chirality etc. are well-known topics in chemistry. But they cannot only be found on the molecular level of matter. Atoms and elementary particles in physics are also characterized by particular symmetry groups. Even living organisms and populations on the macroscopic level have functional properties of symmetry. The whole physical, chemical, and biological evolution seems to be regulated by the emergence of new symmetries and the breaking down of old ones. One is reminded of Heisenberg's famous statement: 'Die letzte Wurzel der Erscheinungen ist also nicht die Materie, sondern das mathematische Gesetz, die Symmetrie, die mathematische Form' (Wandlungen in den Grundlagen der Naturwissenschaften, 1959). Historically the belief in symmetry and simplicity of nature has a long philosophical tradition from the Pythagoreans, Plato and Greek astronomers to Kepler and modern scientists. Today, 'symmetries in nature' is a common topic of mathematics, physics, chemistry, and biology. A lot of Nobel prizes were given in honour of inquiries concerning symmetries in nature. The fascination of symmetries is not only motivated by science, but by art and religion too. Therefore 'symmetris in nature' is an interdisciplinary topic which may help to overcome C.P. Snow's 'Two Cultures' of natural sciences and humanities. (author) 17 refs., 21 figs.
International Nuclear Information System (INIS)
Arima, A.
2003-01-01
(1) There are symmetries in nature, and the concept of symmetry has been used in art and architecture. The symmetry is evaluated high in the European culture. In China, the symmetry is broken in the paintings but it is valued in the architecture. In Japan, however, the symmetry has been broken everywhere. The serious and interesting question is why these differences happens? (2) In this lecture, I reviewed from the very beginning the importance of the rotational symmetry in quantum mechanics. I am sorry to be too fundamental for specialists of nuclear physics. But for people who do not use these theories, I think that you could understand the mathematical aspects of quantum mechanics and the relation between the angular momentum and the rotational symmetry. (3) To the specialists of nuclear physics, I talked about my idea as follows: dynamical treatment of collective motions in nuclei by IBM, especially the meaning of the degeneracy observed in the rotation bands top of γ vibration and β vibration, and the origin of pseudo-spin symmetry. Namely, if there is a symmetry, a degeneracy occurs. Conversely, if there is a degeneracy, there must be a symmetry. I discussed some details of the observed evidence and this correspondence is my strong belief in physics. (author)
CP -symmetry of order 4 and its consequences
International Nuclear Information System (INIS)
Ivanov, Igor P.
2017-01-01
Extended Higgs sectors offer rich opportunities for various forms of CP -violation. Here, we describe a new form of CP-conservation and discuss its consequences. We give a concrete example of a three-Higgs-doublet model dubbed CP4-3HDM with a CP -symmetry of order 4 and no other other accidental symmetries. If the vacuum conserves this symmetry, the model is CP -conserving with pairwise mass-degenerate extra neutral Higgs bosons. These fields cannot be classified as CP -even or CP -odd but they can be combined into complex physical fields which are CP -half-odd, that is, they pick up the i factor upon CP transformation. These CP -half-odd scalars can be Yukawa-coupled to the fermion bilinears in a CP -conserving way. We discuss fundamental and phenomenological features of the model, and stress a peculiar clash between the CP -symmetry and any convention for the particle-antiparticle assignment. (paper)
Superconducting cosmic strings in models with spontaneously broken family symmetry
International Nuclear Information System (INIS)
Bibilashvili, T.M.; Dvali, G.R.
1990-01-01
It is shown that superconducting cosmic strings with some specific properties naturally exist in models of spontaneously broken family symmetry. Superconductivity may be of both types - bosonic and fermionic. There exists a possible mechanism of string conservation. (orig.)
Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations
Alghamdi, Moataz
2017-01-01
conserved quantities. This work also contains an implementation of the said results in Mathematica. In addition, it includes, as a motivation for this work, an investigation of the connection between variational symmetries, described by local Lie groups
Light-front realization of chiral symmetry breaking
International Nuclear Information System (INIS)
Itakura, Kazunori; Maedan, Shinji
2001-01-01
We discuss a description of chiral symmetry breaking in the light-front (LF) formalism. Based on careful analyses of several modes, we give clear answers to the following three fundamental questions: (i) What is the difference between the LF chiral transformation and the ordinary chiral transformation? (ii) How does a gap equation for the chiral condensate emerge? (iii) What is the consequence of the coexistence of a nonzero chiral condensate and the trivial Fock vacuum? The answer to Question (i) is given through a classical analysis of each model. Question (ii) is answered based on our recognition of the importance of characteristic constraints, such as the zero-mode and fermionic constraints. Question (iii) is intimately related to another important problem, reconciliation of the nonzero chiral condensate ≠ 0 and the invariance of the vacuum under the LF chiral transformation Q 5 LF | 0> = 0. This and Question (iii) are understood in terms of the modified chiral transformation laws of the dependent variables. The characteristic ways in which the chiral symmetry breaking is realized are that the chiral charge Q 5 LF is no longer conserved and that the transformation of the scalar and pseudoscalar fields is modified. We also discuss other outcomes, such as the light-cone wave function of the pseudoscalar meson in the Nambu-Jona-Lasinio model. (author)
Weak interaction models with spontaneously broken left-right symmetry
International Nuclear Information System (INIS)
Mohapatra, R.H.
1978-01-01
The present status of weak interaction models with spontaneously broken left-right symmetry is reviewed. The theoretical basis for asymptotic parity conservation, manifest left-right symmetry in charged current weak interactions, natural parity conservation in neutral currents and CP-violation in the context of SU(2)/sub L/ circled x SU (2)/sub R/ circled x U(1) models are outlined in detail. Various directions for further research in the theoretical and experimental side are indicated
From physical symmetries to emergent gauge symmetries
International Nuclear Information System (INIS)
Barceló, Carlos; Carballo-Rubio, Raúl; Di Filippo, Francesco; Garay, Luis J.
2016-01-01
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
Harris, A. Brooks
2006-01-01
This paper represents a detailed instruction manual for constructing the Landau expansion for magnetoelectric coupling in incommensurate ferroelectric magnets. The first step is to describe the magnetic ordering in terms of symmetry adapted coordinates which serve as complex valued magnetic order parameters whose transformation properties are displayed. In so doing we use the previously proposed technique to exploit inversion symmetry, since this symmetry had been universally overlooked. Havi...
Quasi Hopf quantum symmetry in quantum theory
International Nuclear Information System (INIS)
Mack, G.; Schomerus, V.
1991-05-01
In quantum theory, internal symmetries more general than groups are possible. We show that quasitriangular quasi Hopf algebras G * as introduced by Drinfeld permit a consistent formulation of a transformation law of states in the physical Hilbert space H, of invariance of the ground state, and of a transformation law of field operators which is consistent with local braid relations of field operators as proposed by Froehlich. All this remains true when Drinfelds axioms are suitably weakened in order to build in truncated tensor products. Conversely, all the axioms of a weak quasitriangular quasi Hopf algebra are motivated from what physics demands of a symmetry. Unitarity requires in addition that G * admits a * -operation with certain properties. Invariance properties of Greens functions follow from invariance of the ground state and covariance of field operators as usual. Covariant adjoints and covariant products of field operators can be defined. The R-matrix elements in the local braid relations are in general operators in H. They are determined by the symmetry up to a phase factor. Quantum group algebras like U q (sl 2 ) with vertical strokeqvertical stroke=1 are examples of symmetries with special properties. We show that a weak quasitriangular quasi Hopf algebra G * is canonically associated with U q (sl 2 ) if q P =-1. We argue that these weak quasi Hopf algebras are the true symmetries of minimal conformal models. Their dual algebras G ('functions on the group') are neither commutative nor associative. (orig.)
PREFACE: Symmetries and Integrability of Difference Equations
Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane
2007-10-01
M Sergeev on quantization of three-wave equations. Random matrix theory. This section contains a paper by A V Kitaev on the boundary conditions for scaled random matrix ensembles in the bulk of the spectrum. Symmetries and conservation laws. In this section we have five articles. H Gegen, X-B Hu, D Levi and S Tsujimoto consider a difference-analogue of Davey-Stewartson system giving its discrete Gram-type determinant solution and Lax pair. The paper by D Levi, M Petrera, and C Scimiterna is about the lattice Schwarzian KDV equation and its symmetries, while O G Rasin and P E Hydon study the conservation laws for integrable difference equations. S Saito and N Saitoh discuss recurrence equations associated with invariant varieties of periodic points, and P H van der Kamp presents closed-form expressions for integrals of MKDV and sine-Gordon maps. Ultra-discrete systems. This final category contains an article by C Ormerod on connection matrices for ultradiscrete linear problems. We would like to express our sincerest thanks to all contributors, and to everyone involved in compiling this special issue.
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximate and renormgroup symmetries
International Nuclear Information System (INIS)
Ibragimov, Nail H.; Kovalev, Vladimir F.
2009-01-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Revisiting conserved charges in higher curvature gravitational theories
Energy Technology Data Exchange (ETDEWEB)
Ghodrati, M. [University of Michigan, Michigan Center for Theoretical Physics, Randall Laboratory of Physics, Ann Arbor, MI (United States); Hajian, K. [Institute for Research in Fundamental Sciences (IPM), School of Physics, P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Setare, M.R. [University of Kurdistan, Department of Science, Campus of Bijar, Bijar (Iran, Islamic Republic of)
2016-12-15
Restricting the covariant gravitational phase spaces to the manifold of parametrized families of solutions, the mass, angular momenta, entropies, and electric charges can be calculated by a single and simple method. In this method, which has been called the ''solution phase space method,'' conserved charges are unambiguous and regular. Moreover, assuming the generators of the charges to be exact symmetries, entropies and other conserved charges can be calculated on almost arbitrary surfaces, not necessarily horizons or asymptotics. Hence, the first law of thermodynamics would be a local identity relating the exact symmetries to which the mass, angular momentum, electric charge, and entropy are attributed. In this paper, we apply this powerful method to the f(R) gravitational theories accompanied by the terms quadratic in the Riemann and Ricci tensors. Furthermore, conserved charges and the first law of thermodynamics for some of their black hole solutions are exemplified. The examples include warped AdS{sub 3}, charged static BTZ, and 3-dimensional z = 3 Lifshitz black holes. (orig.)
Revisiting conserved charges in higher curvature gravitational theories
International Nuclear Information System (INIS)
Ghodrati, M.; Hajian, K.; Setare, M.R.
2016-01-01
Restricting the covariant gravitational phase spaces to the manifold of parametrized families of solutions, the mass, angular momenta, entropies, and electric charges can be calculated by a single and simple method. In this method, which has been called the ''solution phase space method,'' conserved charges are unambiguous and regular. Moreover, assuming the generators of the charges to be exact symmetries, entropies and other conserved charges can be calculated on almost arbitrary surfaces, not necessarily horizons or asymptotics. Hence, the first law of thermodynamics would be a local identity relating the exact symmetries to which the mass, angular momentum, electric charge, and entropy are attributed. In this paper, we apply this powerful method to the f(R) gravitational theories accompanied by the terms quadratic in the Riemann and Ricci tensors. Furthermore, conserved charges and the first law of thermodynamics for some of their black hole solutions are exemplified. The examples include warped AdS 3 , charged static BTZ, and 3-dimensional z = 3 Lifshitz black holes. (orig.)
Revisiting conserved charges in higher curvature gravitational theories
Ghodrati, M.; Hajian, K.; Setare, M. R.
2016-12-01
Restricting the covariant gravitational phase spaces to the manifold of parametrized families of solutions, the mass, angular momenta, entropies, and electric charges can be calculated by a single and simple method. In this method, which has been called the "solution phase space method," conserved charges are unambiguous and regular. Moreover, assuming the generators of the charges to be exact symmetries, entropies and other conserved charges can be calculated on almost arbitrary surfaces, not necessarily horizons or asymptotics. Hence, the first law of thermodynamics would be a local identity relating the exact symmetries to which the mass, angular momentum, electric charge, and entropy are attributed. In this paper, we apply this powerful method to the f( R) gravitational theories accompanied by the terms quadratic in the Riemann and Ricci tensors. Furthermore, conserved charges and the first law of thermodynamics for some of their black hole solutions are exemplified. The examples include warped AdS_3, charged static BTZ, and 3-dimensional z=3 Lifshitz black holes.
International Nuclear Information System (INIS)
Haxton, W.C.
1988-01-01
I discuss a number of the themes of the Symmetries and Spin session of the 8th International Symposium on High Energy Spin Physics: parity nonconservation, CP/T nonconservation, and tests of charge symmetry and charge independence. 28 refs., 1 fig
2016-01-01
The Symmetry Festival is a science and art program series, the most important periodic event (see its history) to bring together scientists, artists, educators and practitioners interested in symmetry (its roots, what is behind, applications, etc.), or in the consequences of its absence.
Quantum symmetry for pedestrians
International Nuclear Information System (INIS)
Mack, G.; Schomerus, V.
1992-03-01
Symmetries more general than groups are possible in quantum therory. Quantum symmetries in the narrow sense are compatible with braid statistics. They are theoretically consistent much as supersymmetry is, and they could lead to degenerate multiplets of excitations with fractional spin in thin films. (orig.)
Charged fluids with symmetries
Indian Academy of Sciences (India)
It is possible to introduce many types of symmetries on the manifold which restrict the ... metric tensor field and generate constants of the motion along null geodesics .... In this analysis we have studied the role of symmetries for charged perfect ...
Marchis, Iuliana
2009-01-01
Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.
Brock, Phyllis; And Others
This instructional unit for secondary school students is designed to integrate facts and concepts of energy, environment, and economics into the study of the process of making and applying a law (the fifty-five mile-per-hour speed limit law). The unit contains activities on the legislative process designed to fit into traditional segments of…
Symmetry and symmetry breaking in modern physics
International Nuclear Information System (INIS)
Barone, M; Theophilou, A K
2008-01-01
In modern physics, the theory of symmetry, i.e. group theory, is a basic tool for understanding and formulating the fundamental principles of Physics, like Relativity, Quantum Mechanics and Particle Physics. In this work we focus on the relation between Mathematics, Physics and objective reality
On the Relativistic Origin of Pseudo spin Symmetry in Nuclei
International Nuclear Information System (INIS)
Leviatan, A.
1998-01-01
We review the concept of pseudo spin symmetry and its role in nuclear spectroscopy. We survey the attempts to arrive at a microscopic understanding of this symmetry. In particular, we show that pseudo spin symmetry in nuclei could arise from nucleons moving in a relativistic mean field which has an attractive scalar (Vs) and repulsive vector (Vv) potential nearly equal in magnitude but opposite in sign. We show that the generators of pseudo spin symmetry are the non-relativistic limit of the generators of an SU(2) symmetry which leaves invariant the Dirac Hamiltonian with Vs 2= -Vv. Furthermore within this framework, we demonstrate that this symmetry may be approximately conserved for realistic scalar and vector potentials
DEFF Research Database (Denmark)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey
2004-01-01
the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr nonlinearity, are shown to reduce...... the properties of Maxwell's equations in nonlinear optics, without resorting to the commonly used nonlinear Schr\\"odinger (NLS) equation approximation in which a high frequency carrier wave is modulated on long length and time scales due to nonlinear sideband wave interactions. This is important in femto......-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field $E$, in terms of the the canonical variables, with possible multiple real roots for $E$. In order...
Statistical Equilibria of Turbulence on Surfaces of Different Symmetry
Qi, Wanming; Marston, Brad
2012-02-01
We test the validity of statistical descriptions of freely decaying 2D turbulence by performing direct numerical simulations (DNS) of the Euler equation with hyperviscosity on a square torus and on a sphere. DNS shows, at long times, a dipolar coherent structure in the vorticity field on the torus but a quadrapole on the sphereootnotetextJ. Y-K. Cho and L. Polvani, Phys. Fluids 8, 1531 (1996).. A truncated Miller-Robert-Sommeria theoryootnotetextA. J. Majda and X. Wang, Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows (Cambridge University Press, 2006). can explain the difference. The theory conserves up to the second-order Casimir, while also respecting conservation laws that reflect the symmetry of the domain. We further show that it is equivalent to the phenomenological minimum-enstrophy principle by generalizing the work by Naso et al.ootnotetextA. Naso, P. H. Chavanis, and B. Dubrulle, Eur. Phys. J. B 77, 284 (2010). to the sphere. To explain finer structures of the coherent states seen in DNS, especially the phenomenon of confinement, we investigate the perturbative inclusion of the higher Casimir constraints.
Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model
International Nuclear Information System (INIS)
Ivanov, Igor P.; Vdovin, E.
2013-01-01
Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized-CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the Z 4 symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM. (orig.)
The Influence of Natural User Experience on Information Laws
Directory of Open Access Journals (Sweden)
Eglė Švedaitė
2012-04-01
Full Text Available This article reviews the main cause of user experience on development methods and laws, including Fitt’s Law, Hick-Hyman Law, Accot’s Law, Gestalt Law, proximity, similarity, closure, continuity, figure and ground, simplicity, symmetry and experience.Article in Lithuanian
Environmental law. 3. rev. ed.
International Nuclear Information System (INIS)
Anon.
1985-01-01
This pocketbook contains major federal regulations on environmental protection. They serve to protect and cultivate mankind's natural foundations of life, to preserve the environment. The environmental law is devided as follows: Constitutional law on the environment, common administrative law on the environment, special administrative law on the environment including conservation of nature and preservation of rural amenities, protection of waters, waste management, protection against nuisances, nuclear energy and radiation protection, energy conservation, protection against dangerous substances, private law relating to the environment, criminal law relating to the environment. (orig.) [de
International Nuclear Information System (INIS)
O'Raifeartaigh, L.
1979-01-01
This review describes the principles of hidden gauge symmetry and of its application to the fundamental interactions. The emphasis is on the structure of the theory rather than on the technical details and, in order to emphasise the structure, gauge symmetry and hidden symmetry are first treated as independent phenomena before being combined into a single (hidden gauge symmetric) theory. The main application of the theory is to the weak and electromagnetic interactions of the elementary particles, and although models are used for comparison with experiment and for illustration, emphasis is placed on those features of the application which are model-independent. (author)
Sequential flavor symmetry breaking
International Nuclear Information System (INIS)
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-01-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
Sequential flavor symmetry breaking
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-08-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
Schwichtenberg, Jakob
2015-01-01
This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.
Directory of Open Access Journals (Sweden)
Shu-Kun Lin
2001-03-01
Full Text Available Abstract: Symmetry is a measure of indistinguishability. Similarity is a continuous measure of imperfect symmetry. Lewis' remark that Ã¢Â€Âœgain of entropy means loss of informationÃ¢Â€Â defines the relationship of entropy and information. Three laws of information theory have been proposed. Labeling by introducing nonsymmetry and formatting by introducing symmetry are defined. The function L ( L=lnw, w is the number of microstates, or the sum of entropy and information, L=S+I of the universe is a constant (the first law of information theory. The entropy S of the universe tends toward a maximum (the second law law of information theory. For a perfect symmetric static structure, the information is zero and the static entropy is the maximum (the third law law of information theory. Based on the Gibbs inequality and the second law of the revised information theory we have proved the similarity principle (a continuous higher similarityÃ¢ÂˆÂ’higher entropy relation after the rejection of the Gibbs paradox and proved the Curie-Rosen symmetry principle (a higher symmetryÃ¢ÂˆÂ’higher stability relation as a special case of the similarity principle. The principles of information minimization and potential energy minimization are compared. Entropy is the degree of symmetry and information is the degree of nonsymmetry. There are two kinds of symmetries: dynamic and static symmetries. Any kind of symmetry will define an entropy and, corresponding to the dynamic and static symmetries, there are static entropy and dynamic entropy. Entropy in thermodynamics is a special kind of dynamic entropy. Any spontaneous process will evolve towards the highest possible symmetry, either dynamic or static or both. Therefore the revised information theory can be applied to characterizing all kinds of structural stability and process spontaneity. Some examples in chemical physics have been given. Spontaneous processes of all kinds of molecular