Canonical equations of Hamilton with beautiful symmetry
Liang, Guo; Guo, Qi
2012-01-01
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differe...
Canonical equations of Hamilton with beautiful symmetry
Liang, Guo
2012-01-01
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differential system. It is pointed out for the first time that the number of the canonical equations for the first-order differential system is half of that for the second-order differential system. The nonlinear Schr\\"{o}dinger equation, a universal first-order differential system, can be expressed with the new canonical equations in a consistent way.
Three-order pseudo-Hamilton canonical equations
Ma Shan-Jun; Huang Pei-Tian; Yan Rong; Zhao Hong-Xia
2006-01-01
Based on the three-order Lagrangian equations, Hamilton's function ofacceleration H* and generalized acceleration momentum P*α are defined, and pseudo-Hamilton canonical equations corresponding to three-order Lagrangian equations are obtained. The equations are similar to Hamilton's canonical equations of analytical mechanics in form.
Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
Chen, Hua; Sato, Yuki
2016-01-01
The canonical tensor model (CTM) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the ADM formalism of general relativity, and is studied as a discretized model for quantum gravity. In this paper, we analyze the classical equation of motion (EOM) of CTM in a formal continuum limit through a derivative expansion of the tensor up to the forth order, and show that it is the same as the EOM of a coupled system of gravity and a scalar field derived from the Hamilton-Jacobi equation with an appropriate choice of an action. The action contains a scalar field potential of an exponential form, and the system classically respects a dilatational symmetry. We find that the system has a critical dimension, given by six, over which it becomes unstable due to the wrong sign of the scalar kinetic term. In six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling the emergence of a conformal s...
Canonical equations of Hamilton for the nonlinear Schr\\"{o}dinger equation
Liang, Guo; Ren, Zhanmei
2013-01-01
We define two different systems of mathematical physics: the second-order differential system (SODS) and the first-order differential system (FODS). The Newton's second law of motion and the nonlinear Schr\\"{o}dinger equation (NLSE) are the exemplary SODS and FODS, respectively. We obtain a new kind of canonical equations of Hamilton (CEH), which are of some kind of symmetry in form and are formally different with the conventional CEH without symmetry [H. Goldstein, C. Poole, J. Safko, Classical Mechanics, third ed., Addison-Wesley, 2001]. We also prove that the number of the CEHs is equal to the number of the generalized coordinates for the FODS, but twice the number of the generalized coordinates for the SODS. We show that the FODS can only be expressed by the new CEH, but do not by the conventional CEH, while the SODS can be done by both the new and the conventional CEHs. As an example, we prove that the nonlinear Schr\\"{o}dinger equation can be expressed with the new CEH in a consistent way.
Canonical equations of Hamilton for the nonlinear Schrödinger equation
Liang, Guo; Guo, Qi; Ren, Zhanmei
2015-09-01
We define two different systems of mathematical physics: the second order differential system (SODS) and the first order differential system (FODS). The Newton's second law of motion and the nonlinear Schrödinger equation (NLSE) are the exemplary SODS and FODS, respectively. We obtain a new kind of canonical equations of Hamilton (CEH), which exhibit some kind of symmetry in form and are formally different from the conventional CEH without symmetry [H. Goldstein, C. Poole, J. Safko, Classical Mechanics, third ed., Addison- Wesley, 2001]. We also prove that the number of the CEHs is equal to the number of the generalized coordinates for the FODS, but twice the number of the generalized coordinates for the SODS. We show that the FODS can only be expressed by the new CEH, but not introduced by the conventional CEH, while the SODS can be done by both the new and the conventional CEHs. As an example, we prove that the nonlinear Schrödinger equation can be expressed with the new CEH in a consistent way.
Buenker, R J
2003-01-01
The erroneous prediction of the speed of light in dispersive media has been looked upon historically as unequivocal proof that Newton's corpuscular theory is incorrect. Examination of his arguments shows that they were only directly applicable to the momentum of photons, however, leaving open the possibility that the cause of his mistake was the unavailability of a suitable mechanical theory to enable a correct light speed prediction, rather than his use of a particle model. It is shown that Hamilton's canonical equations of motion remove Newton's error quantitatively, and also lead to the most basic formulas of quantum mechanics without reference to any of the pioneering experiments of the late nineteenth century. An alternative formulation of the wave-particle duality principle is then suggested which allows the phenomena of interference and diffraction to be understood in terms of statistical distributions of large populations of photons or other particles.
李仁杰; 乔永芬; 刘洋
2002-01-01
We present a general approach to the construction of conservation laws for variable mass nonholonomic noncon-servative systems. First, we give the definition of integrating factors, and we study in detail the necessary conditionsfor the existence of the conserved quantities. Then, we establish the conservation theorem and its inverse theorem forHamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems. Finally,we give an example to illustrate the application of the results.
九节点Hamilton等参元列式%9-node Isoparametric Element of Hamilton Canonical Equation
邢瑞山; 卿光辉
2012-01-01
结合弹性材料修正后的H-R变分原理和九节点四边形等参元二次插值函数,建立了九节点Hamilton等参元列式的正则方程.简要地介绍了弹性材料修正后的H-R变分原理.基于变分原理使用3×3的高斯积分详细地推导了Hamilton正则方程的九节点等参元列式,使得九节点等参元在有限元法中的优越性与弹性力学Hamihon正则方程的半解析法得到了有机的结合.数值实例的结果证明了本文九节点Hamilton等参元列式的正确性.%The 9-node isoparametric element of Hamiltonian canonical equation has been established by combining the modified Hellinger-Reissner (H-R) variational principle of elastic material and quadratic interpolation function of 9-node quadrilateral isoparametric element. Firstly, the modified H-R variational principle for the elastic material was briefly presented. Then, based on the variational principle and the 3 ×3 Guass integration, the Hamilton canonical equation of 9-node isoparametric element was derived in detail. The advantages of 9-node isoparametric element in finite element were combined with the semi-analytical method of elasticity Hamilton canoncial equation organically. The results of numerical examples prove the correctness of the 9-node isoparametric element formulation.
Conformal invariance and Hojman conserved quantities of canonical Hamilton systems
Liu Chang; Liu Shi-Xing; Mei Feng-Xiang; Guo Yong-Xin
2009-01-01
This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invariance being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.
Quantum Potential Via General Hamilton - Jacobi Equation
Mollai, Maedeh; Jami, Safa; Ahanj, Ali
2011-01-01
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The interpretation of QP in terms of independent entity is discussed along with the introduction of quantum kinetic energy. The method has been extended to relativistic regime, and same results have been concluded.
Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation
LIU Yan-hong; ZHANG Hui-ming
2007-01-01
Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.
Fu Jing-Li; Chen Li-Qun; Chen Xian-Wei
2006-01-01
This paper investigates the momentum-dependent symmetries for nonholonomic nonconservative Hamilton canonical systems. The definition and determining equations of the momentum-dependent symmetries are presented, based on the invariance of differential equations under infinitesimal transformations with respect to the generalized coordinates and generalized momentums. The structure equation and the non-Noether conserved quantities of the systems are obtained. The inverse issues associated with the momentum-dependent symmetries are discussed. Finally, an example is discussed to further illustrate the applications.
Covariant Hamilton equations for field theory
Giachetta, Giovanni [Department of Mathematics and Physics, University of Camerino, Camerino (Italy); Mangiarotti, Luigi [Department of Mathematics and Physics, University of Camerino, Camerino (Italy)]. E-mail: mangiaro@camserv.unicam.it; Sardanashvily, Gennadi [Department of Theoretical Physics, Physics Faculty, Moscow State University, Moscow (Russian Federation)]. E-mail: sard@grav.phys.msu.su
1999-09-24
We study the relations between the equations of first-order Lagrangian field theory on fibre bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. If a Lagrangian is hyperregular, these equations are equivalent. A degenerate Lagrangian requires a set of associated Hamiltonian forms in order to exhaust all solutions of the Euler-Lagrange equations. The case of quadratic degenerate Lagrangians is studied in detail. (author)
VIABILITY SOLUTIONS TO STRUCTURED HAMILTON-JACOBI EQUATIONS UNDER CONSTRAINTS
2011-01-01
International audience; Structured Hamilton-Jacobi partial differential equations are Hamilton-Jacobi equations where the time variable is replaced by a vector-valued variable "structuring" the system. It could be the time-age pair (Hamilton-Jacobi-McKendrick equations) or candidates for initial or terminal conditions (Hamilton-Jacobi-Cournot equations) among a manifold of examples. Here, we define the concept of "viability solution" which always exists and can be computed by viability algori...
Hamilton Jacobi method for solving ordinary differential equations
Mei, Feng-Xiang; Wu, Hui-Bin; Zhang, Yong-Fa
2006-08-01
The Hamilton-Jacobi method for solving ordinary differential equations is presented in this paper. A system of ordinary differential equations of first order or second order can be expressed as a Hamilton system under certain conditions. Then the Hamilton-Jacobi method is used in the integration of the Hamilton system and the solution of the original ordinary differential equations can be found. Finally, an example is given to illustrate the application of the result.
Hamilton's equations for a fluid membrane
Capovilla, R [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados, Apdo. Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo. Postal 70-543, 04510 Mexico, DF (Mexico); Rojas, E [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)
2005-10-14
Consider a homogeneous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature. We introduce a Hamiltonian formulation of this equation which dismantles it into a set of coupled first-order equations. This involves interpreting the Helfrich-Canham energy as an action; equilibrium surfaces are generated by the evolution of space curves. Two features complicate the implementation of a Hamiltonian framework. (i) The action involves second derivatives. This requires treating the velocity as a phase-space variable and the introduction of its conjugate momentum. The canonical Hamiltonian is constructed on this phase space. (ii) The action possesses a local symmetry-reparametrization invariance. The two labels we use to parametrize points on the surface are themselves physically irrelevant. This symmetry implies primary constraints, one for each label, that need to be implemented within the Hamiltonian. The two Lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface. The conservation of the primary constraints implies two secondary constraints, fixing the tangential components of the momentum conjugate to the position. Hamilton's equations are derived and the appropriate initial conditions on the phase-space variables are identified. Finally, it is shown how the shape equation can be reconstructed from these equations.
THE RELAXING SCHEMES FOR HAMILTON-JACOBI EQUATIONS
Hua-zhong Tang; Hua-mu Wu
2001-01-01
Hamilton-Jacobiequation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference approximations for Hamilton-Jacobi equation and hyperbolic conservation laws. In this paper we present the relaxing system for HamiltonJacobiequations in arbitrary space dimensions, and high resolution relaxing schemes for Hamilton-Jacobi equation, based on using the local relaxation approximation. The schemes are numerically tested on a variety of 1D and 2D problems, including a problem related to optimal control problem. High-order accuracy in smooth regions, good resolution of discontinuities, and convergence to viscosity solutions are observed.
Deriving the Hamilton equations of motion for a nonconservative system using a variational principle
Tveter, Frank Thomas
1998-03-01
The classical derivation of the canonical transformation theory [H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, 1981)] is based on Hamilton's principle which is only valid for conservative systems. This paper avoids this principle by using an approach that is basically reversed compared to the classical derivation. The Lagrange equations of motion are formulated in the undefined and general variable set {Q,P}, and the general Hamilton equations of motion are derived from the Lagrange equations by using a variational principle. The undefined general variables {Q,P} are defined through a transformation to a special (defined) variable set {q,p}. The transformation equations connecting the two sets are derived by using the invariants property of the value of the Lagrangian. This approach results in a more general interpretation of the generator function.
Solution Hamilton-Jacobi equation for oscillator Caldirola-Kanai
LEONARDO PASTRANA ARTEAGA
2016-12-01
Full Text Available The method allows Hamilton-Jacobi explicitly determine the generating function from which is possible to derive a transformation that makes soluble Hamilton's equations. Using the separation of variables the partial differential equation of the first order called Hamilton-Jacobi equation is solved; as a particular case consider the oscillator Caldirola-Kanai (CK, which is characterized in that the mass presents a temporal evolution exponentially . We demonstrate that the oscillator CK position presents an exponential decay in time similar to that obtained in the damped sub-critical oscillator, which reflects the dissipation of total mechanical energy. We found that in the limit that the damping factor is small, the behavior is the same as an oscillator with simple harmonic motion, where the effects of energy dissipation is negligible.
Numerical Solution of Hamilton-Jacobi Equations in High Dimension
2012-11-23
high dimension FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA-Universita di Roma P. Aldo Moro, 2 00185 ROMA AH930...solution of Hamilton-Jacobi equations in high dimension AFOSR contract n. FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA
Wave-Particle Duality and the Hamilton-Jacobi Equation
Sivashinsky, Gregory I
2009-01-01
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behavior. The de Broglie wave thus acquires a clear deterministic meaning of a wave-like excitation of the classical action function. The problem of quantization in terms of the breathing action function and the double-slit experiment are discussed.
Studying on Opinion Evolution by Hamilton-Jacobi Equation
Feng, Chen-Jie; Huo, Jie; Hao, Rui; Wang, Xu-Ming
2016-01-01
A physical description of an opinion evolution is conducted based on the Hamilton-Jacobi equation derived from a generalized potential and the corresponding Langevin equation. The investigation mainly focuses on the heterogeneities such as age, connection circle and overall quality of the participants involved in the opinion exchange process. The evolutionary patterns of opinion can be described by solution of the Hamilton-Jacobi equation, information entropy. The results show that the overall qualities of the participants play critical roles in forming an opinion. The higher the overall quality is, the easier the consensus can reach. The solution also demonstrates that the age and the connection circle of the agents play equally important roles in forming an opinion. The essence of the age, overall quality, and connection circle corresponds to the maturity of thought (opinion inertia), reason and intelligence, influence strength of the environment, respectively. So the information entropy distributes in the ...
Salisbury, Donald; Renn, Jürgen; Sundermeyer, Kurt
2016-02-01
Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord special privilege to any geometric structure. Intrinsic space-time curvature-based coordinates grant equal status to all geometric backgrounds. They play an essential role as a starting point for inequivalent semiclassical quantizations. The scheme calls into question Wheeler’s geometrodynamical approach and the associated Wheeler-DeWitt equation in which 3-metrics are featured geometrical objects. The formalism deals with variables that are manifestly invariant under the full diffeomorphism group. Yet, perhaps paradoxically, the liberty in selecting intrinsic coordinates is precisely as broad as is the original diffeomorphism freedom. We show how various ideas from the past five decades concerning the true degrees of freedom of general relativity can be interpreted in light of this new constrained Hamiltonian description. In particular, we show how the Kuchař multi-fingered time approach can be understood as a means of introducing full four-dimensional diffeomorphism invariants. Every choice of new phase space variables yields new Einstein-Hamilton-Jacobi constraining relations, and corresponding intrinsic Schrödinger equations. We show how to implement this freedom by canonical transformation of the intrinsic Hamiltonian. We also reinterpret and rectify significant work by Dittrich on the construction of “Dirac observables.”
DISCONTINUOUS SOLUTIONS IN L∞ FOR HAMILTON-JACOBI EQUATIONS
无
2000-01-01
An approach is introduced to construct global discontinuous solutions in L∞ for Hamilton Jacobi equations. This approach allows the initial data only in L∞ and applies to the equations with nonconvex Hamiltonians. The profit functions are introduced to formulate the notion of discontinuous solutions in L. The existence of global discontinuous solutions in L∞ is established. These solutions in L∞ coincide with the viscosity solutions and the minimax solutions, provided that the initial data are continuous. A prototypical equation is analyzed to examine the L∞ stability of our L∞ solutions. The analysis also shows that global discontinuous solutions are determined by the topology in which the initial data are approximated.
Beam dynamics with the Hamilton-Jacobi equation
Gabella, W.E.; Ruth, R.D.; Warnock, R.L.
1989-03-01
We describe a non-perturbative method to solve the Hamilton-Jacobi equation for invariant surfaces in phase space. The problem is formulated in action-angle variables with a general nonlinear perturbation. The solution of the Hamilton-Jacobi equation is regarded as the fixed point of a map on the Fourier coefficients of the generating function. Periodicity of the generator in the independent variable is enforced with a shooting method. We present two methods for finding the fixed point and hence the invariant surface. A solution by plain iteration is economical but has a restricted domain of convergence. The Newton iteration is costly but yields solutions up to the dynamic aperture. Examples of lattices with sextupoles for chromatic correction are discussed. 10 refs., 5 figs., 1 tab.
Hamilton-Jacobi equation, heteroclinic chains and Arnol'd diffusion in three time scales systems
Gallavotti, G; Mastropietro, V; Gallavotti, Giovanni; Gentile, Guido; Mastropietro, Vieri
1998-01-01
Interacting systems consisting of two rotators and a point mass near a hyperbolic fixed point are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of quasi periodic motions in phase space is studied via the Hamilton-Jacobi equation. The main result, a high density theorem of invariant tori, is derived by the classical canonical transformation method extending previous results. As an application the existence of long heteroclinic chains (and of Arnol'd diffusion) is proved for systems interacting through a trigonometric polynomial in the angle variables.
Fast methods for static Hamilton-Jacobi Partial Differential Equations
Vladimirsky, Alexander Boris
2001-05-01
The authors develop a family of fast methods approximating the solution to a wide class of static Hamilton-Jacobi partial differential equations. These partial differential equations are considered in the context of control-theoretic and front-propagation problems. In general, to produce a numerical solution to such a problem, one has to solve a large system of coupled non-linear discretized equations. The techniques use partial information about the characteristic directions to de-couple the system. Previously known fast methods, available for isotropic problems, are discussed in detail. They introduce a family of new Ordered Upwinding Methods (OUM) for general (anisotropic) problems and prove convergence to the viscosity solution of the corresponding Hamilton-Jacobi partial differential equation. The hybrid methods introduced here are based on the analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems. The performance of the methods is analyzed and compared to that of several other numerical approaches to these problems. Computational experiments are performed using test problems from control theory, computational geometry and seismology.
Fast methods for static Hamilton-Jacobi Partial Differential Equations
Vladimirsky, Alexander Boris [Univ. of California, Berkeley, CA (United States)
2001-01-01
The authors develop a family of fast methods approximating the solution to a wide class of static Hamilton-Jacobi partial differential equations. These partial differential equations are considered in the context of control-theoretic and front-propagation problems. In general, to produce a numerical solution to such a problem, one has to solve a large system of coupled non-linear discretized equations. The techniques use partial information about the characteristic directions to de-couple the system. Previously known fast methods, available for isotropic problems, are discussed in detail. They introduce a family of new Ordered Upwinding Methods (OUM) for general (anisotropic) problems and prove convergence to the viscosity solution of the corresponding Hamilton-Jacobi partial differential equation. The hybrid methods introduced here are based on the analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems. The performance of the methods is analyzed and compared to that of several other numerical approaches to these problems. Computational experiments are performed using test problems from control theory, computational geometry and seismology.
Unconditionally stable methods for Hamilton-Jacobi equations
Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik
2000-05-01
We present new numerical methods for constructing approximate solutions to the Cauchy problem for Hamilton-Jacobi equations of the form u{sub t} + H(D{sub x}u) = 0. The methods are based on dimensional splitting and front tracking for solving the associated (non-strictly hyperbolic) system of conservation laws p{sub t} + D{sub x}H(p) = 0, where p = D{sub x}u. In particular, our methods depend heavily on a front tracking method for one-dimensional scalar conservation laws with discontinuous coefficients. The proposed methods are unconditionally stable in the sense that the time step is not limited by the space discretization and they can be viewed as ''large time step'' Godunov type (or front tracking) methods. We present several numerical examples illustrating the main features of the proposed methods. We also compare our methods with several methods from the literature. (author)
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations
Fu Jing-Li; Chen Li-Qun; Xie Feng-Ping
2004-01-01
This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations,and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results.
Quantitative Compactness Estimates for Hamilton-Jacobi Equations
Ancona, Fabio; Cannarsa, Piermarco; Nguyen, Khai T.
2016-02-01
We study quantitative compactness estimates in {W^{1,1}_{loc}} for the map {S_t}, {t > 0} that is associated with the given initial data {u_0in Lip (R^N)} for the corresponding solution {S_t u_0} of a Hamilton-Jacobi equation u_t+Hbig(nabla_{x} ubig)=0, qquad t≥ 0,quad xinR^N, with a uniformly convex Hamiltonian {H=H(p)}. We provide upper and lower estimates of order {1/\\varepsilon^N} on the Kolmogorov {\\varepsilon}-entropy in {W^{1,1}} of the image through the map S t of sets of bounded, compactly supported initial data. Estimates of this type are inspired by a question posed by Lax (Course on Hyperbolic Systems of Conservation Laws. XXVII Scuola Estiva di Fisica Matematica, Ravello, 2002) within the context of conservation laws, and could provide a measure of the order of "resolution" of a numerical method implemented for this equation.
Singular Hamilton-Jacobi equation for the tail problem
Mirrahimi, Sepideh; Perthame, Benoit; Souganidis, Panagiotis E
2010-01-01
In this paper we study the long time-long range behavior of reaction diffusion equations with negative square root -type reaction terms. In particular we investigate the exponential behavior of the solutions after a standard hyperbolic scaling. This leads to a Hamilton-Jacobi variational inequality with an obstacle that depends on the solution itself and defines the open set where the limiting solution does not vanish. Counter-examples show a nontrivial lack of uniqueness for the variational inequality depending on the conditions imposed on the boundary of this open set. Both Dirichlet and state constraints boundary conditions play a role. When the competition term does not change sign, we can identify the limit, while, in general, we find lower and upper bounds for the limit. Although models of this type are rather old and extinction phenomena are as important as blow-up, our motivation comes from the so-called "tail problem" in population biology. One way to avoid meaningless exponential tails, is to impose...
Value Functions for Certain Class of Hamilton Jacobi Equations
Anup Biswas; Rajib Dutta; Prosenjit Roy
2011-08-01
We consider a class of Hamilton Jacobi equations (in short, HJE) of type $$u_t+\\frac{1}{2}\\left(|u_{x_n}|^2+\\cdots+|u_{x_{n-1}}|^2\\right)+\\frac{e^u}{m}|u_{x_n}|^m=0,$$ in $\\mathbb{R}^n×\\mathbb{R}_+$ and >1, with bounded, Lipschitz continuous initial data. We give a Hopf-Lax type representation for the value function and also characterize the set of minimizing paths. It is shown that the minimizing paths in the representation of value function need not be straight lines. Then we consider HJE with Hamiltonian decreasing in of type $$u_t+H_1(u_{x_1},\\ldots,u_{x_i})+e^{-u}H_2(u_{x_{i+1}},\\ldots,u_{x_n})=0$$ where $H_1,H_2$ are convex, homogeneous of degree $n,m>1$ respectively and the initial data is bounded, Lipschitz continuous. We prove that there exists a unique viscosity solution for this HJE in Lipschitz continuous class. We also give a representation formula for the value function.
The Hamiltonian Canonical Form for Euler-Lagrange Equations
ZHENG Yu
2002-01-01
Based on the theory of calculus of variation, some suffcient conditions are given for some Euler-Lagrangcequations to be equivalently represented by finite or even infinite many Hamiltonian canonical equations. Meanwhile,some further applications for equations such as the KdV equation, MKdV equation, the general linear Euler Lagrangeequation and the cylindric shell equations are given.
Hojman's conservation theorems for generalized Raitzin canonical equations of motion
Qiao Yong-Fen; Li Ren-Jie; Zhao Shu-Hong
2005-01-01
Using the Lie symmetry under infinitesimal transformations in which the time is not variable, Hojman's conservation theorems for Raitzin's canonical equations of motion in generalized classical mechanics are studied. The generalized Raitzin's canonical equations of motion are established. The determining equations of Lie symmetry under infinitesimal transformations are given. The Hojman conservation theorems of the system are established. Finally, an example is also presented to illustrate the application of the result.
Whittaker方程的Hamilton化%Hamiltonization of Whittaker equations
丁光涛
2010-01-01
引入Whittaker方程的Birkhoff表示,构造与该表示对应的Hamilton函数,并利用Hamilton-Poisson方法得到Whittaker方程的解.指出上述Hamilton函数与传统分析力学中Hamilton函数的区别.
An extended Hamilton — Jacobi method
Kozlov, Valery V.
2012-11-01
We develop a new method for solving Hamilton's canonical differential equations. The method is based on the search for invariant vortex manifolds of special type. In the case of Lagrangian (potential) manifolds, we arrive at the classical Hamilton — Jacobi method.
李仁杰; 刘洋; 等
2002-01-01
We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton's canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results.
Canonical averaging of the equations of quantum mechanics
Chirkov, A. G.
2005-01-01
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to receive asymptotic estimations of affinity of the precisian approximated solutions of Schrodinger equations
Extinction for viscous Hamilton-Jacobi equations%粘性Hamilton-Jacobi方程的熄灭
田娅; 穆春来
2009-01-01
Extinction in finite time for non-negative classical solutions p∈(0,1). The occurrence of these phenomena is shown to concerned with the domain Ω. For the Cauchy problem,extinction in finite time occurs to the classical solution of the above equation depends on the behavior of the initial data u0(x) as |x|→∞.%作者研究了初边值问题ut-Δu-u+|Δu|p=0,p∈(0,1) 的非负古典解的有限时间熄灭,证明了熄灭现象的发生与区域Ω有关.对于Cauchy问题,上述方程的古典解在有限时间熄灭与否依赖于初值u0(x)在|x|→∞时的性态.
On the convergence rate of operator splitting for Hamilton-Jacobi equations with source terms
Jakobsen, Espen R.; Karlsen, Kenneth H.; Risebro, Nils Henrik
2000-02-01
We establish a rate of convergence for a semi-discrete operator splitting method applied to Hamilton-Jacobi equations with source terms. The method is based on sequentially solving a Hamilton-Jacobi equation and an ordinary differential equation. The Hamilton-Jacobi equation is solved exactly while the ordinary differential equation is solved exactly or by an explicit Euler method. We prove that the L{sup {infinity}} error associated with the operator splitting method is bounded by O({delta}t), where {delta}t is the splitting (or time) step. This error bound is an improvement over the existing O((sqroot)({delta}t)) bound due to Souganidis [40]. In the one dimensional case, we present a fully discrete splitting method based on an unconditionally stable front tracking method for homogenuous Hamilton-Jacobi equations. It is proved that this fully discrete splitting method possesses a linear convergence rate. Moreover, numerical results are presented to illustrate the theoreticle convergence results. (author)
Yang, Shu-Zheng; Feng, Zhong-Wen; Li, Hui-Ling
2017-02-01
We derive the Hamilton-Jacobi equation from the Dirac equation, then, with the help of the Hamilton-Jacobi equation, the the tunneling radiation behavior of the non-stationary spherical symmetry de Sitter black hole is discussed, at last, we obtained the tunneling rate and Hawking temperature. Our results showed that the Hamilton-Jacobi equation is a fundamental dynamic equation, it can widely be derived from the dynamic equations which describe the particles with any spin. Therefore, people can easy calculate the tunneling behavior from the black holes.
Chou, Chia-Chun
2014-03-14
The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneously integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.
An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations
Guermond, Jean-Luc
2009-01-01
We describe an algorithm for solving steady one-dimensional convex-like Hamilton-Jacobi equations using a L1-minimization technique on piecewise linear approximations. For a large class of convex Hamiltonians, the algorithm is proven to be convergent and of optimal complexity whenever the viscosity solution is q-semiconcave. Numerical results are presented to illustrate the performance of the method.
Hamilton-Jacobi equation and the breaking of the WKB approximation
Canfora, F. [Istituto Nazionale di Fisica Nucleare, GC di Salerno (Italy) and Dipartimento di Fisica E.R. Caianiello, Universita di Salerno, Via S. Allende, 84081 Baronissi (Salerno) (Italy)]. E-mail: canfora@sa.infn.it
2005-03-17
A simple method to deal with four-dimensional Hamilton-Jacobi equation for null hypersurfaces is introduced. This method allows to find simple geometrical conditions which give rise to the failure of the WKB approximation on curved spacetimes. The relation between such failure, extreme blackholes and the Cosmic Censor hypothesis is briefly discussed.
Hamilton Systems of the Compound KdV Equation%组合KdV方程的Hamilton系统
吕书强; 蔡春; 马青华
2014-01-01
In this article, according to Hamilton Systems of the KdV Equation, and proved Hamilton Systems of the Compound KdV Equation.%本文根据KdV方程的Hamilton系统，构造并证明了组合KdV方程的Hamilton系统。
Superluminal Neutrinos and a Curious Phenomenon in the Relativistic Quantum Hamilton-Jacobi Equation
Matone, Marco
2011-01-01
OPERA's results, if confirmed, pose the question of superluminal neutrinos. We investigate the kinematics defined by the quantum version of the relativistic Hamilton-Jacobi equation, i.e. E^2=p^2c^2+m^2c^4+2mQc^2, with Q the quantum potential of the free particle. The key point is that the quantum version of the Hamilton-Jacobi equation is a third-order differential equation, so that it has integration constants which are missing in the Schr\\"odinger and Klein-Gordon equations. In particular, a non-vanishing imaginary part of an integration constant leads to a quantum correction to the expression of the velocity which is curiously in agreement with OPERA's results.
A Large Deviation, Hamilton-Jacobi Equation Approach to a Statistical Theory for Turbulence
2012-09-03
and its associated compressible Euler equations, Comptes Rendus Mathematique , (09 2011): 973. doi: 10.1016/j.crma.2011.08.013 2012/09/03 14:17:15 6...Hamilton-Jacobi PDE is shown to be well-posed. (joint work with T Nguyen, Journal de Mathematique Pures et Appliquees). Future works focusing on large time behavior for such equations is currently under its way. Technology Transfer
On the Hamilton-Jacobi-Bellman Equation by the Homotopy Perturbation Method
Abdon Atangana
2014-01-01
Full Text Available Our concern in this paper is to use the homotopy decomposition method to solve the Hamilton-Jacobi-Bellman equation (HJB. The approach is obviously extremely well organized and is an influential procedure in obtaining the solutions of the equations. We portrayed particular compensations that this technique has over the prevailing approaches. We presented that the complexity of the homotopy decomposition method is of order O(n. Furthermore, three explanatory examples established good outcomes and comparisons with exact solution.
Computational method for the quantum Hamilton-Jacobi equation: one-dimensional scattering problems.
Chou, Chia-Chun; Wyatt, Robert E
2006-12-01
One-dimensional scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. First, the pole structure of the quantum momentum function for scattering wave functions is analyzed. The significant differences of the pole structure of this function between scattering wave functions and bound state wave functions are pointed out. An accurate computational method for the quantum Hamilton-Jacobi equation for general one-dimensional scattering problems is presented to obtain the scattering wave function and the reflection and transmission coefficients. The computational approach is demonstrated by analysis of scattering from a one-dimensional potential barrier. We not only present an alternative approach to the numerical solution of the wave function and the reflection and transmission coefficients but also provide a computational aspect within the quantum Hamilton-Jacobi formalism. The method proposed here should be useful for general one-dimensional scattering problems.
许晶; 任文秀
2013-01-01
In this paper, we consider infinite-dimensional linear Hamiltonian canonical system , and put a linearization method which get recursion operator in the differential system into the Hamilton system , and get a determining equation ( group).Through solving the equation ( group), we win the matrix new form of recursion operator.Further more, through some examples, we verify that in Hamilton system, it is also consist with the relation which in the differential equation system .% 本文考虑了无穷维线性Hamilton正则系统，将微分方程系统下获得循环算子的线性化方法，移植到 Hamilton 系统下，并得到确定方程（组），通过解方程（组）获得了循环算子的矩阵新形式，进一步，通过算例，验证了在Hamilton体系下，依然符合在此类微分方程系统下的关系。
Salisbury, Donald; Sundermeyer, Kurt
2015-01-01
Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord special privilege to any geometric structure. Intrinsic spacetime curvature based coordinates grant equal status to all geometric backgrounds. They play an essential role as a starting point for inequivalent semi-classical quantizations. The scheme calls into question Wheeler's geometrodynamical approach and the associated Wheeler-DeWitt equation in which three-metrics are featured geometrical objects. The formalism deals with variables that are manifestly invariant under the full diffeomorphism group. Yet, perhaps paradoxically, the liberty in selecting intrinsic coordinates is precisely as broad as is the original diffeomorphism freedom. We show how various ideas from the past five decades concerning the true degrees of freedom of general relativity can be interpreted in light...
Computational method for the quantum Hamilton-Jacobi equation: bound states in one dimension.
Chou, Chia-Chun; Wyatt, Robert E
2006-11-07
An accurate computational method for the one-dimensional quantum Hamilton-Jacobi equation is presented. The Mobius propagation scheme, which can accurately pass through singularities, is used to numerically integrate the quantum Hamilton-Jacobi equation for the quantum momentum function. Bound state wave functions are then synthesized from the phase integral using the antithetic cancellation technique. Through this procedure, not only the quantum momentum functions but also the wave functions are accurately obtained. This computational approach is demonstrated through two solvable examples: the harmonic oscillator and the Morse potential. The excellent agreement between the computational and the exact analytical results shows that the method proposed here may be useful for solving similar quantum mechanical problems.
Relations between low-lying quantum wave functions and solutions of the Hamilton-Jacobi equation
Friedberg, R; Zhao Wei Qin
1999-01-01
We discuss a new relation between the low lying Schroedinger wave function of a particle in a one-dimentional potential V and the solution of the corresponding Hamilton-Jacobi equation with -V as its potential. The function V is $\\geq 0$, and can have several minina (V=0). We assume the problem to be characterized by a small anhamornicity parameter $g^{-1}$ and a much smaller quantum tunneling parameter $\\epsilon$ between these different minima. Expanding either the wave function or its energy as a formal double power series in $g^{-1}$ and $\\epsilon$, we show how the coefficients of $g^{-m}\\epsilon^n$ in such an expansion can be expressed in terms of definite integrals, with leading order term determined by the classical solution of the Hamilton-Jacobi equation. A detailed analysis is given for the particular example of quartic potential $V={1/2}g^2(x^2-a^2)^2$.
Large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations
Camilli, Fabio; Loreti, Paola; Nguyen, Vinh Duc
2011-01-01
We show a large time behavior result for class of weakly coupled systems of first-order Hamilton-Jacobi equations in the periodic setting. We use a PDE approach to extend the convergence result proved by Namah and Roquejoffre (1999) in the scalar case. Our proof is based on new comparison, existence and regularity results for systems. An interpretation of the solution of the system in terms of an optimal control problem with switching is given.
A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations
Hu, Changqing; Shu, Chi-Wang
1998-01-01
In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.
The Algebraic Riccati Matrix Equation for Eigendecomposition of Canonical Forms
M. Nouri
2013-01-01
Full Text Available The algebraic Riccati matrix equation is used for eigendecomposition of special structured matrices. This is achieved by similarity transformation and then using the algebraic Riccati matrix equation to the triangulation of matrices. The process is the decomposition of matrices into small and specially structured submatrices with low dimensions for easy finding of eigenpairs. Here, we show that previous canonical forms I, II, III, and so on are special cases of the presented method. Numerical and structural examples are included to show the efficiency of the present method.
On the Hamilton-Jacobi Treatment of Constrained Systems
Sami.I.Muslih; Hosam A.El-Zalan
2003-01-01
Systems with singular-higher order Lagrangians are investigated by two methods: Dirac method and Hamilton-Jacobi method. An example is studied and it is shown that the Hamilton-Jacobi method gives the correct canonical generalized equations of motion, contrary to Dirac method, where Dirac conjecture is invalid.
Viscosity solutions of two classes of coupled Hamilton-Jacobi-Bellman equations
Başar Tamer
2001-01-01
Full Text Available This paper studies viscosity solutions of two sets of linearly coupled Hamilton-Jacobi-Bellman (HJB equations (one for finite horizon and the other one for infinite horizon which arise in the optimal control of nonlinear piecewise deterministic systems where the controls could be unbounded. The controls enter through the system dynamics as well as the transitions for the underlying Markov chain process, and are allowed to depend on both the continuous state and the current state of the Markov chain. The paper establishes the existence and uniqueness of viscosity solutions for these two sets of HJB equations, whose Hamiltonian structures are different from the standard ones.
Fast methods for the Eikonal and related Hamilton- Jacobi equations on unstructured meshes.
Sethian, J A; Vladimirsky, A
2000-05-23
The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. The scheme relies on an upwind finite difference approximation to the gradient and a resulting causality relationship that lends itself to a Dijkstra-like programming approach. In this paper, we discuss several extensions to this technique, including higher order versions on unstructured meshes in Rn and on manifolds and connections to more general static Hamilton-Jacobi equations.
Canonical conjugated Dirac equation in a curved space
Dzhunushaliev, Vladimir
2012-01-01
It is shown that the calculation of Dirac operator for the spherical coordinate system with spherical Dirac matrices and using the spin connection formalism is in the contradiction with the definition of standard Dirac operator in the spherical Minkowski coordinate system. It is shown that such contradiction one can avoid by introducing a canonical conjugated covariant derivative for the spinor field. The Dirac equation solution on the Reissner - Nordstr\\"om background is obtained. The solution describes a bound state of a charged particle.
On a Hamilton-Poisson Approach of the Maxwell-Bloch Equations with a Control
Lăzureanu, Cristian
2017-09-01
In this paper we consider the 3D real-valued Maxwell-Bloch equations with a parametric control given by \\dot {x}=y+az+byz,\\dot {y}=xz,\\dot {z}=-xy (a,b\\in \\mathbb {R}). We give two Lie-Poisson structures of this system that are related with well-known Lie algebras. Moreover, we construct infinitely many Hamilton-Poisson realizations of this system. We also analyze the stability of the equilibrium points, as well as the existence of periodic orbits. In addition, we emphasize some connections between the energy-Casimir mapping of the considered system and the above-mentioned dynamical elements.
Leclerc, M
2012-01-01
We introduce a symmetric Poisson bracket that allows us to describe anticommuting fields on a classical level in the same way as commuting fields, without the use of Grassmann variables. By means of a simple example, we show how the Dirac bracket for the elimination of the second class constraints can be introduced, how the classical Hamiltonian equations can be derived and how quantization can be achieved through a direct correspondence principle. Finally, we show that the semiclassical limit of the corresponding Schroedinger equation leads back to the Hamilton-Jacobi equation of the classical theory. Summarizing, it is shown that the relations between classical and quantum theory are valid for fermionic fields in exactly the same way as in the bosonic case, and that there is no need to introduce anticommuting variables on a classical level.
Dey, Bijoy K; Janicki, Marek R; Ayers, Paul W
2004-10-08
Classical dynamics can be described with Newton's equation of motion or, totally equivalently, using the Hamilton-Jacobi equation. Here, the possibility of using the Hamilton-Jacobi equation to describe chemical reaction dynamics is explored. This requires an efficient computational approach for constructing the physically and chemically relevant solutions to the Hamilton-Jacobi equation; here we solve Hamilton-Jacobi equations on a Cartesian grid using Sethian's fast marching method. Using this method, we can--starting from an arbitrary initial conformation--find reaction paths that minimize the action or the time. The method is demonstrated by computing the mechanism for two different systems: a model system with four different stationary configurations and the H+H(2)-->H(2)+H reaction. Least-time paths (termed brachistochrones in classical mechanics) seem to be a suitable chioce for the reaction coordinate, allowing one to determine the key intermediates and final product of a chemical reaction. For conservative systems the Hamilton-Jacobi equation does not depend on the time, so this approach may be useful for simulating systems where important motions occur on a variety of different time scales.
HERMITE WENO SCHEMES WITH LAX-WENDROFF TYPE TIME DISCRETIZATIONS FOR HAMILTON-JACOBI EQUATIONS
Jianxian Qiu
2007-01-01
In this paper, we use Hermite weighted essentially non-oscillatory (HWENO) schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and are used in the reconstruction. One major advantage of HWENO schemes is its compactness in the reconstruction. We explore the possibility in avoiding the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong discontinuous derivative. As a result,comparing with HWENO with Runge-Kutta time discretizations schemes (HWENO-RK) of Qiu and Shu [19] for Hamilton-Jacobi equations, the major advantages of HWENO-LW schemes are their saving of computational cost and their compactness in the reconstruction.Extensive numerical experiments are performed to illustrate the capability of the method.
Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming
Claudel, Christian G.
2014-01-01
This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.
Alba, David
2009-01-01
We study the coupling of N charged scalar particles plus the electro-magnetic field to ADM tetrad gravity and its canonical formulation in asymptotically Minkowskian space-times without super-translations. We make the canonical transformation to the York canonical basis, where there is a separation between the {\\it inertial} (gauge) variables and the {\\it tidal} ones inside the gravitational field and a special role of the Eulerian observers associated to the 3+1 splitting of space-time. The Dirac Hamiltonian is weakly equal to the weak ADM energy. The Hamilton equations in Schwinger time gauges are given explicitly. In the York basis they are naturally divided in four sets: a) the contracted Bianchi identities; b) the equations for the inertial gauge variables; c) the equations for the tidal ones; d) the equations for matter. Finally we give the restriction of the Hamilton equations and of the constraints to the family of {\\it non-harmonic 3-orthogonal} gauges, in which the instantaneous Riemannian 3-spaces ...
A canonical dilation of the Schrödinger equation
Brown, M. F.
2014-07-01
In this paper we shall re-visit the well-known Schrödinger equation of quantum mechanics. However, this shall be realized as a marginal dynamics of a more general, underlying stochastic counting process in a complex Minkowski space. One of the interesting things about this formalism is that its derivation has very deep roots in a new understanding of the differential calculus of time. This Minkowski-Hilbert representation of quantum dynamics is called the Belavkin formalism; a beautiful, but not well understood theory of mathematical physics that understands that both deterministic and stochastic dynamics may be formally represented by a counting process in a second-quantized Minkowski space. The Minkowski space arises as a canonical quantization of the clock, and this is derived naturally from the matrix-algebra representation [1, 2] of the Newton-Leibniz differential time increment, dt. And so the unitary dynamics of a quantum object, described by the Schrödinger equation, may be obtained as the expectation of a counting process of object-clock interactions.
Gabella, W.E.; Ruth, R.D.; Warnock, R.L.
1988-05-01
Periodic solutions of the Hamilton-Jacobi equation determine invariant tori in phase space. The Fourier spectrum of a torus with respect to angular coordinates gives useful information about nonlinear resonances and their potential for causing instabilities. We describe a method to solve the Hamilton-Jacobi equation for an arbitrary accelerator lattice. The method works with Fourier modes of the generating functions, and imposes periodicity in the machine azimuth by a shooting method. We give examples leading to three-dimensional plots in a surface of section. It is expected that the technique will be useful in lattice optimization. 14 refs., 6 figs., 1 tab.
Hybrid massively parallel fast sweeping method for static Hamilton-Jacobi equations
Detrixhe, Miles; Gibou, Frédéric
2016-10-01
The fast sweeping method is a popular algorithm for solving a variety of static Hamilton-Jacobi equations. Fast sweeping algorithms for parallel computing have been developed, but are severely limited. In this work, we present a multilevel, hybrid parallel algorithm that combines the desirable traits of two distinct parallel methods. The fine and coarse grained components of the algorithm take advantage of heterogeneous computer architecture common in high performance computing facilities. We present the algorithm and demonstrate its effectiveness on a set of example problems including optimal control, dynamic games, and seismic wave propagation. We give results for convergence, parallel scaling, and show state-of-the-art speedup values for the fast sweeping method.
Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations
Hofleitner, Aude
2012-12-01
This article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any point in the domain in which the solution is defined. The characterization of the distribution of the solution at any point is a first step towards the estimation of the parameters defining the random value conditions. This work has important applications for estimation in flow networks in which value conditions are noisy. In particular, we illustrate our derivations on a road segment with random capacity reductions. © 2012 IEEE.
Sakamoto, Noboru; Schaft, Arjan J. van der
2007-01-01
In this paper, an analytical approximation approach for the stabilizing solution of the Hamilton-Jacobi equation using stable manifold theory is proposed. The proposed method gives approximated flows on the stable manifold of the associated Hamiltonian system and provides approximations of the
Sakamoto, Noboru; Schaft, Arjan J. van der
2007-01-01
In this paper, an analytical approximation approach for the stabilizing solution of the Hamilton-Jacobi equation using stable manifold theory is proposed. The proposed method gives approximated flows on the stable manifold of the associated Hamiltonian system and provides approximations of the stabl
Cardaliaguet, Pierre
2008-01-01
We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally H\\"older continuous with H\\"older exponent depending only on the growth of the Hamiltonian. The proof relies on a reverse H\\"older inequality.
程晓良; 徐渊辑; 孟炳泉
2005-01-01
An algorithm for numerical solution of discrete Hamilton-Jacobi-Bellman equations is proposed.The method begins with a suitable initial guess value of the solution,then finds a suitable matrix to linearize the system and constructs an iteration algorithm to generate the monotone sequence.The convergence of the algorithm for nonlinear discrete Hamilton-Jacobi-Bellman equations is proved.Some numerical examples are presented to confirm the effciency of this algorithm.
Wave front-ray synthesis for solving the multidimensional quantum Hamilton-Jacobi equation.
Wyatt, Robert E; Chou, Chia-Chun
2011-08-21
A Cauchy initial-value approach to the complex-valued quantum Hamilton-Jacobi equation (QHJE) is investigated for multidimensional systems. In this approach, ray segments foliate configuration space which is laminated by surfaces of constant action. The QHJE incorporates all quantum effects through a term involving the divergence of the quantum momentum function (QMF). The divergence term may be expressed as a sum of two terms, one involving displacement along the ray and the other incorporating the local curvature of the action surface. It is shown that curvature of the wave front may be computed from coefficients of the first and second fundamental forms from differential geometry that are associated with the surface. Using the expression for the divergence, the QHJE becomes a Riccati-type ordinary differential equation (ODE) for the complex-valued QMF, which is parametrized by the arc length along the ray. In order to integrate over possible singularities in the QMF, a stable and accurate Möbius propagator is introduced. This method is then used to evolve rays and wave fronts for four systems in two and three dimensions. From the QMF along each ray, the wave function can be easily computed. Computational difficulties that may arise are described and some ways to circumvent them are presented. © 2011 American Institute of Physics
Singh, Parampreet
2015-01-01
The problem of obtaining canonical Hamiltonian structures from the equations of motion is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on its sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy condition, or more attractive than in the classical theory. Canonical structure of the modified theories is determined demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. Both of the repulsive modifications are found to yield singularity avoidance. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse trigonometric function of Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum ...
High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations
Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)
2002-01-01
We present the first fifth order, semi-discrete central upwind method for approximating solutions of multi-dimensional Hamilton-Jacobi equations. Unlike most of the commonly used high order upwind schemes, our scheme is formulated as a Godunov-type scheme. The scheme is based on the fluxes of Kurganov-Tadmor and Kurganov-Tadmor-Petrova, and is derived for an arbitrary number of space dimensions. A theorem establishing the monotonicity of these fluxes is provided. The spacial discretization is based on a weighted essentially non-oscillatory reconstruction of the derivative. The accuracy and stability properties of our scheme are demonstrated in a variety of examples. A comparison between our method and other fifth-order schemes for Hamilton-Jacobi equations shows that our method exhibits smaller errors without any increase in the complexity of the computations.
2016-05-01
Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games Yat Tin...complexity of the resulting algorithm is polynomial in the problem dimension; hence, it overcomes the curse of dimensionality [1, 2]. We extend previous work...compute the evolution of geometric objects [25], which was first used for reachability problems in [21, 22] to our knowledge . Numerical solutions to HJ PDE
Singh, Parampreet; Soni, S. K.
2016-06-01
The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann, ‘Robertson’, and Walker models. Modifications to the Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy conditions, or more attractive than in the classical theory. The canonical structure of the modified theories is determined by demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse a trigonometric function of the Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a ‘generalized polymerized’ canonical phase space. Both the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is nontrigonometric and singularities persist. Our results hint at connections between the repulsive/attractive nature of modifications to gravity arising from the gravitational sector and polymerized/non polymerized gravitational phase space.
Canonical structure of evolution equations with non-linear dispersive terms
B Talukdar; J Shamanna; S Ghosh
2003-07-01
The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The speciﬁc results presented refer to the third- and ﬁfth-order equations of the so-called distinguished subclass.
Transforming differential equations of multi-loop Feynman integrals into canonical form
Meyer, Christoph
2016-01-01
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
Canonical systems of differential equations with self-adjoint interface conditions on graphs
de Snoo, H; Winkler, Henrik
2005-01-01
For n canonical systems of differential equations, the corresponding n copies of their domain [0,∞) are thought of as a graph with vertex 0. An interface condition at 0 is given by a so-called Nevanlinna pair. Explicit formulae are deduced for the spectral representation of the corresponding underly
de Snoo, H; Winkler, Henrik
2005-01-01
The class of two-dimensional trace-normed canonical systems of differential equations on R is considered with selfadjoint interface conditions at 0. If one or both of the intervals around 0 are H-indivisible the interface conditions which give rise to selfadjoint relations (multi-valued operators) a
1 Taiwo O. A
2013-01-01
Full Text Available The problem of solving special nth-order linear integro-differential equations has special importance in engineering and sciences that constitutes a good model for many systems in various fields. In this paper, we construct canonical polynomial from the differential parts of special nth-order integro-differential equations and use it as our basis function for the numerical solutions of special nth-order integro-differential equations. The results obtained by this method are compared with those obtained by Adomian Decomposition method. It is also observed that the new method is an effective method with high accuracy. Some examples are given to illustrate the method.
Cagnetti, Filippo
2013-11-01
We consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L.C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(h) convergence rate in terms of the L∞ norm and O(h) in terms of the L1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper. © 2013 IMACS.
Osetrin, Konstantin; Osetrin, Evgeny
2015-01-01
The characteristics of dust matter in space-time models, admitting the existence of privilege coordinate systems are given, where the single-particle Hamilton-Jacobi equation can be integrated by the method of complete separation of variables. The resulting functional form of the 4-velocity field and energy density of matter for all types of spaces under consideration is presented.
Quesne, C
2008-01-01
On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schr\\"odinger equation and a deformation of the canonical commutation relations, a method based on deformed shape invariance has recently been devised for generating pairs of potential and PDM for which the Schr\\"odinger equation is exactly solvable. This approach has provided the bound-state energy spectrum, as well as the ground-state and the first few excited-state wavefunctions. The general wavefunctions have however remained unknown in explicit form because for their determination one would need the solutions of a rather tricky differential-difference equation. Here we show that solving this equation may be avoided by combining the deformed shape invariance technique with the point canonical transformation method in a novel way. It consists in employing our previous knowledge of the PDM problem energy spectrum to construct a constant-mass Schr\\"odinger equation with similar characteristics and in deducing the PD...
Canepa, Edward S.
2017-06-19
Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for highways modeled by a system of Lighthill Whitham Richards equations that is able to assimilate different sensor data available. We first present an equivalent formulation of the problem using a Hamilton–Jacobi equation. Then, using a semi-analytic formula, we show that the model constraints resulting from the Hamilton–Jacobi equation are linear ones. We then pose the problem of estimating the traffic density given incomplete and inaccurate traffic data as a Mixed Integer Program. We then extend the density estimation framework to highway networks with any available data constraint and modeling junctions. Finally, we present a travel estimation application for a small network using real traffic measurements obtained obtained during Mobile Century traffic experiment, and comparing the results with ground truth data.
ZHANG Li-Hua; LIU Xi-Qiang; BAI Cheng-Lin
2006-01-01
In this paper, the generalized tanh function method is extended to (2+1)-dimensional canonical generalized KP (CGKP) equation with variable coefficients. Taking advantage of the Riccati equation, many explicit exact solutions,which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional CGKP equation with variable coefficients.
Utility maximization with partial information: Hamilton-Jacobi-Bellman equation approach
BAI Lihua; GUO Junyi
2007-01-01
This paper deals with the problem of maximizing the expected utility of the terminal wealth when the stock price satisfies a stochastic differential equation with instantaneous rates of return modelled as an Ornstein-Uhlenbeck process.Here, only the stock price and interest rate can be observable for an investor.It is reduced to a partially observed stochastic control problem.Combining the filtering theory with the dynamic programming approach, explicit representations of the optimal value functions and corresponding optimal strategies are derived. Moreover, closed-form solutions are provided in two cases of exponential utility and logarithmic utility.In particular, logarithmic utility is considered under the restriction of shortselling and borrowing.
Heinz Toparkus
2014-04-01
Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.
A canonical system of differential equations arising from the Riemann zeta-function
Suzuki, Masatoshi
2012-01-01
This paper has two main results, which relate to a criteria for the Riemann hypothesis via the family of functions $\\Theta_\\omega(z)=\\xi(1/2-\\omega-iz)/\\xi(1/2+\\omega-iz)$, where $\\omega>0$ is a real parameter and $\\xi(s)$ is the Riemann xi-function. The first main result is necessary and sufficient conditions for $\\Theta_\\omega$ to be a meromorphic inner function in the upper half-plane. It is related to the Riemann hypothesis directly whether $\\Theta_\\omega$ is a meromorphic inner function. In comparison with this, a relation of the Riemann hypothesis and the second main result is indirect. It relates to the theory of de Branges, which associates a meromorphic inner function and a canonical system of linear differential equations (in the sense of de Branges). As the second main result, the canonical system associated with $\\Theta_\\omega$ is constructed explicitly and unconditionally under the restriction of the parameter $\\omega >1$ by applying a method of J.-F. Burnol in his recent work on the gamma functi...
The canonical equation of adaptive dynamics for Mendelian diploids and haplo-diploids
Metz, Johan A. J.; de Kovel, Carolien G. F.
2013-01-01
One of the powerful tools of adaptive dynamics is its so-called canonical equation (CE), a differential equation describing how the prevailing trait vector changes over evolutionary time. The derivation of the CE is based on two simplifying assumptions, separation of population dynamical and mutational time scales and small mutational steps. (It may appear that these two conditions rarely go together. However, for small step sizes the time-scale separation need not be very strict.) The CE was derived in 1996, with mathematical rigour being added in 2003. Both papers consider only well-mixed clonal populations with the simplest possible life histories. In 2008, the CE's reach was heuristically extended to locally well-mixed populations with general life histories. We, again heuristically, extend it further to Mendelian diploids and haplo-diploids. Away from strict time-scale separation the CE does an even better approximation job in the Mendelian than in the clonal case owing to gene substitutions occurring effectively in parallel, which obviates slowing down by clonal interference. PMID:24516713
Predictions of canonical wall bounded turbulent flows via a modified $k-\\omega$ equation
Chen, Xi; She, Zhen-Su
2016-01-01
A major challenge in computation of engineering flows is to derive and improve turbulence models built on turbulence physics. Here, we present a physics-based modified $k-\\omega$ equation for canonical wall bounded turbulent flows (boundary layer, channel and pipe), predicting both mean velocity profile (MVP) and streamwise mean kinetic energy profile (SMKP) with high accuracy over a wide range of Reynolds number ($Re$). The result builds on a multi-layer quantification of wall flows, which allows a significant modification of the $k-\\omega$ equation. Three innovations are introduced: First, an adjustment of the Karman constant to 0.45 is set for the overlap region with a logarithmic MVP. Second, a wake parameter models the turbulent transport near the centerline. Third, an anomalous dissipation factor represents the effect of a meso layer in the overlap region. Then, a highly accurate (above 99\\%) prediction of MVPs is obtained in Princeton pipes, improving the original model prediction by up to 10\\%. Moreov...
High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function
ZHANG Ming-Jiang; ZHAO Hong-Xia; FANG Jian-Hui; MA Shan-Jun; LU Kai
2008-01-01
In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton's principle. Finally, the Hamilton's principle of high-order Lagrangian function is given.
Variational principle and dynamical equations of discrete nonconservative holonomic systems
Liu Rong-Wan; Zhang Hong-Bin; Chen Li-Qun
2006-01-01
By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler-Lagrange equations and Hamilton's canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.
Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampère equations VIASM 2016
Tran, Hung
2017-01-01
Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the n...
E. W. Grafarend
1997-06-01
Full Text Available The length of the gravitational field lines/of the orthogonal trajectories of a family of gravity equipotential surfaces/of the plumbline between a terrestrial topographic point and a point on a reference equipotential surface like the geoid í also known as the orthometric height í plays a central role in Satellite Geodesy as well as in Physical Geodesy. As soon as we determine the geometry of the Earth pointwise by means of a satellite GPS (Global Positioning System: «global problem solver» we are left with the problem of converting ellipsoidal heights (geometric heights into orthometric heights (physical heights. For the computation of the plumbline we derive its three differential equations of first order as well as the three geodesic equations of second order. The three differential equations of second order take the form of a Newton differential equation when we introduce the parameter time via the Marussi gauge on a conformally flat three-dimensional Riemann manifold and the generalized force field, the gradient of the superpotential, namely the modulus of gravity squared and taken half. In particular, we compute curvature and torsion of the plumbline and prove their functional relationship to the second and third derivatives of the gravity potential. For a spherically symmetric gravity field, curvature and torsion of the plumbline are zero, the plumbline is straight. Finally we derive the three Lagrangean as well as the six Hamiltonian differential equations of the plumbline, in particular in their star form with respect to Marussi gauge.
Sloth, Peter
1990-01-01
Density profiles and partition coefficients are obtained for hard-sphere fluids inside hard, spherical pores of different sizes by grand canonical ensemble Monte Carlo calculations. The Monte Carlo results are compared to the results obtained by application of different kinds of integral equation...... approximations. Also, some exact, analytical results for the partition coefficients are given, which are valid in the case of (very) small pores or at low density, respectively. The Journal of Chemical Physics is copyrighted by The American Institute of Physics....
Nandi, Debottam; Shankaranarayanan, S.
2016-10-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
Nandi, Debottam
2016-01-01
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that our approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.
Al Mamon, Abdulla; Das, Sudipta [Visva-Bharati, Department of Physics, Santiniketan (India)
2015-06-15
In this present work, we try to build up a cosmological model using a non-canonical scalar field within the framework of a spatially flat FRW space-time. In this context, we have considered four different parametrizations of the equation of state parameter of the non-canonical scalar field. Under this scenario, analytical solutions for various cosmological parameters have been found out. It has been found that the deceleration parameter shows a smooth transition from a positive value to some negative value which indicates that the universe was undergoing an early deceleration followed by late time acceleration which is essential for the structure formation of the universe. With these four parametrizations, the future evolution of the models are also discussed. It has been found that one of the models (Generalized Chaplygin gas model, GCG) mimics the concordance ΛCDM in the near future, whereas two other models (CPL and JBP) diverge due to future singularity. Finally, we have studied these theoretical models with the latest datasets from SN Ia + H(z) + BAO/CMB. (orig.)
Dayi, O F
1995-01-01
The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Schr\\"{o}dinger equations for the Morse and the V=u^2+ 1/u^2 potentials were known to be related by a canonical transformation. q--deformed analog of this transformation connecting two different realizations of the sl_q(2) algebra is presented. By the virtue of the q--canonical transformation a q--deformed Schr\\"{o}dinger equation for the Morse potential is obtained from the q-deformed V=u^2+ 1/u^2 Schr\\"{o}dinger equation. Wave functions and eigenvalues of the q--Schr\\"{o}dinger equations yielding a new definition of the q--Laguerre polynomials are studied.
Metz, Johan A Jacob; Staňková, Kateřina; Johansson, Jacob
2016-03-01
This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value principle from evolutionary ecology, (4) show that the latter in turn is equivalent to Pontryagin's maximum principle, a well known equivalence that however in the literature is given either ex cathedra or is proven with more advanced tools, (5) connect the classical optimisation arguments of life history theory a little better to real biology (Mendelian populations with separate sexes subject to an environmental feedback loop), (6) make a minor improvement to the form of the CE for the examples in Dieckmann et al. and Parvinen et al.
丁金凤; 金世欣; 张毅
2016-01-01
The fractional Noether symmetries and fractional conserved quantities for Hamilton system with time delay based on Caputo derivatives are discussed.The fractional Hamilton canonical equations of the corresconding system with time delay are established base upon the fractional Hamilton principle of the Hamilton systems with time delay.Then,the fractional Noether symmetries of the Hamilton system with time delay are obtained,which based on the invariance of the fractional Hamilton action with time delay under the infinitesimal transformations of group.Finally,fractional Noether theorems with time delay of the Hamilton system are established.At the end,one example is given to illustrate the application of the results.%提出并讨论了Caputo导数定义下的含时滞的Hamilton系统的分数阶Noether对称性与守恒量。根据含时滞的Hamilton系统的分数阶Hamilton原理，建立了相应的含时滞的分数阶Hamilton 正则方程；依据分数阶Hamilton作用量在无限小变换下的不变性，得到了含时滞的Hamilton系统的分数阶Noether对称性；最后，建立了系统的含时滞的分数阶Noether理论，并举例说明结果的应用。
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy)
2016-02-15
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2015-01-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then, we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2016-02-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Stability of Controlled Hamilton Systems Excited by Gaussian White Noise
SHANG Mei; GUO Yong-xin; MEI Feng-xiang
2008-01-01
A new method is introduced in this paper. This method can be used to study the stability of controlled holonomic Hamilton systems under disturbance of Gaussian white noise. At first, the motion equation of controlled holonomic Hamilton systems excited by Gaussian noise is formulated. A theory to stabilize the system is provided. Finally, one example is given to illustrate the application procedures.
Invariant surfaces and tracking by the Hamilton-Jacobi method
Warnock, R.L.; Ruth, R.D.
1986-09-01
The Hamilton-Jacobi method is described for a model of betatron motion in one degree of freedom, namely, a harmonic oscillator perturbed by a lattice of sextupoles. The Hamilton-Jacobi equation is given in terms of Fourier amplitudes. Invariant surfaces have been obtained in phase space, and finite time symplectic maps were obtained for tracking of single particles. (LEW)
The Canonical Expanding Soliton and Harnack inequalities for Ricci flow
Cabezas-Rivas, Esther
2009-01-01
We introduce the notion of Canonical Expanding Ricci Soliton, and use it to derive new Harnack inequalities for Ricci flow. This viewpoint also gives geometric insight into the existing Harnack inequalities of Hamilton and Brendle.
Conformal invariance conserved quantity of Hamilton systems
Cai Jian-Le; Luo Shao-Kai; Mei Feng-Xiang
2008-01-01
This paper studies conformal invariance and comserved quantRies of Hamilton system.The definition and the determining equation of conformal invariance for Hamilton system are provided.The relationship between the conformal invariance and the Lie symmetry are discussed,and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced.It gives the conserved quantities of the system and an example for illustration.
Furmaniak, Sylwester; Terzyk, Artur P; Gauden, Piotr A [Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N Copernicus University, Gagarin Street 7, 87-100 Torun (Poland); Kowalczyk, Piotr [Nanochemistry Research Institute, Curtin University, PO Box U1987, Perth, WA 6845 (Australia); Harris, Peter J F, E-mail: aterzyk@chem.uni.torun.pl [Centre for Advanced Microscopy, University of Reading, Whiteknights, Reading RG6 6AF (United Kingdom)
2011-10-05
Using grand canonical Monte Carlo simulation we show, for the first time, the influence of the carbon porosity and surface oxidation on the parameters of the Dubinin-Astakhov (DA) adsorption isotherm equation. We conclude that upon carbon surface oxidation, the adsorption decreases for all carbons studied. Moreover, the parameters of the DA model depend on the number of surface oxygen groups. That is why in the case of carbons containing surface polar groups, SF{sub 6} adsorption isotherm data cannot be used for characterization of the porosity. (paper)
Elizabeth Hamilton: Enlightenment Educator.
Russell, Rosalind
1986-01-01
Elizabeth Hamilton, an eighteenth- and early nineteenth-century Scottish writer on education, was one of the first to advocate the application of educational psychology to teaching. She introduced Pestalozzi's method to the English-reading public and argued for equal education for all children of both sexes and all social backgrounds. (LFL)
Titchmarsh-Weyl theory for canonical systems
Keshav Raj Acharya
2014-11-01
Full Text Available The main purpose of this paper is to develop Titchmarsh- Weyl theory of canonical systems. To this end, we first observe the fact that Schrodinger and Jacobi equations can be written into canonical systems. We then discuss the theory of Weyl m-function for canonical systems and establish the relation between the Weyl m-functions of Schrodinger equations and that of canonical systems which involve Schrodinger equations.
Park, Chandeok
This dissertation presents a general methodology for solving the optimal feedback control problem in the context of Hamiltonian system theory. It is first formulated as a two point boundary value problem for a standard Hamiltonian system, and the associated phase flow is viewed as a canonical transformation. Then relying on the Hamilton-Jacobi theory, we employ generating functions to develop a unified methodology for solving a variety of optimal feedback control formulations with general types of boundary conditions. The major accomplishment is to establish a theoretical connection between the optimal cost function and a special kind of generating function. Guided by this recognition, we are ultimately led to a new flexible representation of the optimal feedback control law for a given system, which is adjustable to various types of boundary conditions by algebraic conversions and partial differentiations. This adaptive property provides a substantial advantage over the classical dynamic programming method in the sense that we do not need to solve the Hamilton-Jacobi-Bellman equation repetitively for varying types of boundary conditions. Furthermore for a special type of boundary condition, it also enables us to work around an inherent singularity of the Hamilton-Jacobi-Bellman equation by a special algebraic transformation. Taking full advantage of these theoretical insights, we develop a systematic algorithm for solving a class of optimal feedback control problems represented by smooth analytic Hamiltonians, and apply it to problems with different characteristics. Then, broadening the practical utility of generating functions for problems where the relevant Hamiltonian is non-smooth, we construct a pair of Cauchy problems from the associated Hamilton-Jacobi equations. This alternative formulation is justified by solving problems with control constraints which usually feature non-smoothness in the control logic. The main result of this research establishes that
P. G. L. Leach
2014-04-01
Full Text Available Dirac devised his theory of Quantum Mechanics and recognised that his operators resembled the canonical coordinates of Hamiltonian Mechanics. This gave the latter a new lease of life. We look at what happens to Dirac’s Quantum Mechanics if one starts from Hamiltonian Mechanics.
Kinetic derivation of a Hamilton-Jacobi traffic flow model
Borsche, Raul; Kimathi, Mark
2012-01-01
Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow equations leads to different types of equations: in certain situations modified Aw-Rascle equations are obtained. On the other hand, for several choices of kinetic parameters new Hamilton-Jacobi type traffic equations are found. Associated microscopic models are discussed and numerical experiments are presented discussing several situations for highway traffic and comparing the different models.
Sánchez Santos, José Manuel (1967-)
2012-01-01
A materia Mecánica Clásica II forma parte do bloque que no Grao en Física se dedica á Mecánica Clásica, que é a parte da Física que estuda o movemento das partículas e os corpos materiais e que comprende a teoría iniciada por Galileo e Newton e desenvolvida nos séculos XVIII e XIX por Lagrange e Hamilton, incluíndo tamén a Relatividade Especial de Einstein. A materia divídese en catro bloques temáticos de similar peso e duración temporal. O primeiro deles ten un marcado carácter teóric...
Covariant canonical quantization
Hippel, G.M. von [University of Regina, Department of Physics, Regina, Saskatchewan (Canada); Wohlfarth, M.N.R. [Universitaet Hamburg, Institut fuer Theoretische Physik, Hamburg (Germany)
2006-09-15
We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. This procedure agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and we apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses. Covariant canonical quantization can thus be understood as a ''first'' or pre-quantization within the framework of conventional QFT. (orig.)
Covariant canonical quantization
Von Hippel, G M; Hippel, Georg M. von; Wohlfarth, Mattias N.R.
2006-01-01
We present a manifestly covariant quantization procedure based on the de Donder-Weyl Hamiltonian formulation of classical field theory. Covariant canonical quantization agrees with conventional canonical quantization only if the parameter space is d=1 dimensional time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses.
Study of invariant surfaces and their break-up by the Hamilton-Jacobi method
Warnock, R.L.; Ruth, R.D.
1986-08-01
A method is described to compute invariant tori in phase space for calssical non-integrable Hamiltonian systems. Our procedure is to solve the Hamilton-Jacobi equation stated as a system of equations for Fourier coefficients of the generating function. The system is truncated to a finite number of Fourier modes and solved numerically by Newton's method. The resulting canonical transformation serves to reduce greatly the non-integrable part of the Hamiltonian. In examples studied to date the convergence properties of the method are excellent, even near chaotic regions and on the separatrices of isolated broad resonances. We propose a criterion for breakup of invariant surfaces, namely the vanishing of the Jacobian of the canonical transformation to new angle variables. By comparison with results from tracking, we find in an example with two nearly overlapping resonances that this criterion can be implemented with sufficient accuracy to determine critical parameters for the breakup ('transition to chaos') to an accuracy of 5 to 10%.
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
Lorz, Alexander
2011-01-17
Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses coexist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a kind of Lyapunov functional. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.
Dirac mass dynamics in a multidimensional nonlocal parabolic equation
Lorz, Alexander; Perthame, Benoit
2010-01-01
Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses co-exist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a structure of gradient flow. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models darwinian evolution.
Geometric Hamilton-Jacobi theory on Nambu-Poisson manifolds
de León, M.; Sardón, C.
2017-03-01
The Hamilton-Jacobi theory is a formulation of classical mechanics equivalent to other formulations as Newtonian, Lagrangian, or Hamiltonian mechanics. The primordial observation of a geometric Hamilton-Jacobi theory is that if a Hamiltonian vector field XH can be projected into the configuration manifold by means of a 1-form dW, then the integral curves of the projected vector field XHd Wcan be transformed into integral curves of XH provided that W is a solution of the Hamilton-Jacobi equation. Our aim is to derive a geometric Hamilton-Jacobi theory for physical systems that are compatible with a Nambu-Poisson structure. For it, we study Lagrangian submanifolds of a Nambu-Poisson manifold and obtain explicitly an expression for a Hamilton-Jacobi equation on such a manifold. We apply our results to two interesting examples in the physics literature: the third-order Kummer-Schwarz equations and a system of n copies of a first-order differential Riccati equation. From the first example, we retrieve the original Nambu bracket in three dimensions and from the second example, we retrieve Takhtajan's generalization of the Nambu bracket to n dimensions.
Viscosity Solutions of Hamilton-Jacobi Equations.
1981-08-01
the result follove. Remark 4.2. W* could replace u5 e c 2 ( ) above by uC e W 2 ,p(Q), p > N , via Bony’s boc maximum principle (5]. Remark 4.3. If...semigroup property S(t)S() S(t+T) for tr N 0 as usual. We remark that (6.7) also follows from (6.8) and the translation invariance of this model...Symposium, L. Cesari, J. Hale, J. LaSalle ode., Academic Press, New York, (1976), 131-165. a. Crandall, M. G. and P. L. Lions, Condition d’unicite pour
Goldstein, Sheldon; Lebowitz, Joel L.; Tumulka, Roderich; Zanghi, Nino
2005-01-01
It is well known that a system, S, weakly coupled to a heat bath, B, is described by the canonical ensemble when the composite, S+B, is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true both for classical distributions on the phase space and for quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced ...
Jordan Canonical Form Theory and Practice
Weintraub, Steven H
2009-01-01
Jordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. The JCF of a linear transformation, or of a matrix, encodes all of the structural information about that linear transformation, or matrix. This book is a careful development of JCF. After beginning with background material, we introduce Jordan Canonical Form and related notions: eigenvalues, (generalized) eigenvectors, and the characteristic and minimum polynomials. We decide the question of diagonalizability, and prove the Cayley-Hamilton theorem. Then we present a careful and complete proof of t
Geometric Hamilton-Jacobi theory for higher-order autonomous systems
Colombo, Leonardo; de León, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2014-06-01
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the background of higher-order mechanical systems, in both the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi equations in these formalisms and apply our results to analyze some particular physical examples.
Analytical mechanics and field theory: derivation of equations from energy conservation
Vinokurov, N. A.
2014-06-01
Equations of motion in mechanics and field equations in field theory are conventionally derived using the least action principle. This paper presents a nonvariational derivation of Hamilton's and Lagrange's equations. The derivation starts by specifying the system energy as a function of generalized coordinates and velocities and then introduces generalized momenta in such a way that the energy remains unchanged under variations of any degree of freedom. This immediately leads to Hamilton's equations with an as yet undefined Hamiltonian. The explicit dependence of generalized momenta on the coordinates and velocities is determined by first finding the Lagrangian from the known energy function. We discuss electrodynamics as an illustrative example. The proposed approach provides new insight into the nature of canonical momenta and offers a way to find the Lagrangian from the known energy of the system.
Canonical Chern-Simons gravity
Sarkar, Souvik; Vaz, Cenalo
2017-07-01
We study the canonical description of the axisymmetric vacuum in 2 +1 -dimensional gravity, treating Einstein's gravity as a Chern-Simons gauge theory on a manifold with the restriction that the dreibein is invertible. Our treatment is in the spirit of Kuchař's description of the Schwarzschild black hole in 3 +1 dimensions, where the mass and angular momentum are expressed in terms of the canonical variables and a series of canonical transformations that turn the curvature coordinates and their conjugate momenta into new canonical variables is performed. In their final form, the constraints are seen to require that the momenta conjugate to the Killing time and curvature radius vanish, and what remains is the mass, the angular momentum, and their conjugate momenta, which we derive. The Wheeler-DeWitt equation is trivial and describes time independent systems with wave functions described only by the total mass and total angular momentum.
Hamilton-Jacobi formalism of tachyon inflation and cosmological perturbations
LIU Daojun
2014-08-01
Full Text Available We study the cosmological inflation models driven by the rolling tachyon field which has a Born-Infeld-type action.We drive the Hamilton-Jacobi equation for the cosmological dynamics of tachyon inflation and the mode equations for the scalar and tensor perturbations of tachyon field and spacetime, then a solution under the slow-roll condition is given. In the end,a realistic model from string theory is discussed.
Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation
Fathi, M.; Jalalzadeh, S.
2017-07-01
How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in Fathi et al. (Eur. Phys. J. C 76, 527 2016). In this paper we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics, applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.
Gharbi, A.; Touloum, S.; Bouda, A.
2015-04-01
We study the Klein-Gordon equation with noncentral and separable potential under the condition of equal scalar and vector potentials and we obtain the corresponding relativistic quantum Hamilton-Jacobi equation. The application of the quantum Hamilton-Jacobi formalism to the double ring-shaped Kratzer potential leads to its relativistic energy spectrum as well as the corresponding eigenfunctions.
A Hamilton-Jacobi Formalism for Thermodynamics
Rajeev, S G
2007-01-01
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with \\m{n} thermodynamic degrees of freedom it is \\m{2n+1}-dimensional. The equations of state of a substance pick out an \\m{n}-dimensional submanifold. A family of substances whose equations of state depend on \\m{n} parameters define a hypersurface of co-dimension one. This can be described by the vanishing of a function which plays the role of a Hamiltonian. The ordinary differential equations (characteristic equations) defined by this function describe a dynamical system on the hypersurface. Its orbits can be used to reconstruct the equations of state. The `time' variable associated to this dynamics is related to, but is not identical to, entropy. After developing this formalism on well-grounded systems such as the van der Waals gases...
Qin, Hong; Liu, Jian; Xiao, Jianyuan; Zhang, Ruili; He, Yang; Wang, Yulei; Sun, Yajuan; Burby, Joshua W.; Ellison, Leland; Zhou, Yao
2015-12-14
Particle-in-cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretising its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g. 10(9), degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinear Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.
Canonical transformation method in classical electrodynamics
Pavlenko, Yu. G.
1983-08-01
The solutions of Maxwell's equations in the parabolic equation approximation is obtained on the basis of the canonical transformation method. The Hamiltonian form of the equations for the field in an anisotropic stratified medium is also examined. The perturbation theory for the calculation of the wave reflection and transmission coefficients is developed.
The Hamilton principle for fluid binary mixtures with two temperatures
Gouin, Henri
2009-01-01
For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the total heat exchange between components. In this nonconservative case, a Gibbs dynamical identity connecting the equations of momenta, masses, energy and heat exchange allows to deduce the balance equation of energy of the mixture. Due to the unknown exchange of heat between components, the number of obtained equations is less than the number of field variables. The second law of thermodynamics constrains the possible expression of a supplementary constitutive equation closing the system of equations. The exchange of energy between components produces an increasing rate of entropy and creates a dynamical pressure term associated with the difference of temperature between components. This new dynamical pressure term fits with the results obtained by classical thermodynamical a...
The canonical form of the Rabi hamiltonian
Szopa, M; Ceulemans, A; Szopa, Marek; Mys, Geert; Ceulemans, Arnout
1996-01-01
The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.
Hamilton-Jacobi method for a simple resonance
Rudnev, Mischa
2003-01-01
It is well known that a generic small perturbation of a Liouville-integrable Hamiltonian system causes breakup of resonant and near-resonant invariant tori. A general approach to the simple resonance case in the convex real-analytic setting is developed, based on a new technique for solving the Hamilton-Jacobi equation. It is shown that a generic perturbation creates in the core of a resonance a partially hyperbolic lower-dimensional invariant torus, whose Lagrangian stable and unstable manif...
Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle
Wang, Hong
2017-09-01
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.
Determinant Sums for Undirected Hamiltonicity
Björklund, Andreas
2010-01-01
We present a Monte Carlo algorithm for Hamiltonicity detection in an $n$-vertex undirected graph running in $O^*(1.657^{n})$ time. To the best of our knowledge, this is the first superpolynomial improvement on the worst case runtime for the problem since the $O^*(2^n)$ bound established for TSP almost fifty years ago (Bellman 1962, Held and Karp 1962). It answers in part the first open problem in Woeginger's 2003 survey on exact algorithms for NP-hard problems. For bipartite graphs, we improve the bound to $O^*(1.414^{n})$ time. Both the bipartite and the general algorithm can be implemented to use space polynomial in $n$. We combine several recently resurrected ideas to get the results. Our main technical contribution is a new reduction inspired by the algebraic sieving method for $k$-Path (Koutis ICALP 2008, Williams IPL 2009). We introduce the Labeled Cycle Cover Sum in which we are set to count weighted arc labeled cycle covers over a finite field of characteristic two. We reduce Hamiltonicity to Labeled ...
2013-05-23
..., CT 06096-1010; or Hamilton Standard Division, One Hamilton Road, United Technologies Corporation, Mail Stop 1A-3-C63, Windsor Locks, CT 06096-1010; phone: 877-808-7575; fax: 860-660-0372; email: tech... corrosion to accumulate to critical limits. Hamilton Sundstrand developed, and we approved,...
Fitzpatrick, P. M.; Harmon, G. R.; Liu, J. J. F.; Cochran, J. E.
1974-01-01
The formalism for studying perturbations of a triaxial rigid body within the Hamilton-Jacobi framework is developed. The motion of a triaxial artificial earth satellite about its center of mass is studied. Variables are found which permit separation, and the Euler angles and associated conjugate momenta are obtained as functions of canonical constants and time.
Strebel differentials and Hamilton sequences
LI; Zhong(
2001-01-01
［1］Strebel, K., Point shift differentials and extremal quasiconformal mappings, Annale Acad. Scle. Fenn. Math., 1998, 23: 475 -494.［2］Gardiner, F. P., Approximation of infinite dimensional Teichmutller space, Trans. Amer. Soc., 1999, 282: 367-383.［3］Lakic, N. , The Strebel points, Comptemp. Math. , 1997, 211: 417-431.［4］Wu Sheng jian, Hamilton sequences for extremal quasiconformal mappings of the unit disc, Science in China, Ser. A, 1999,42(10): 1033-1042.［5］Li Zhong, Qi Yi, A note on point shift differentials, Science in China, Ser. A, 1999, 42(5): 449-455.［6］Hamilton, R. S., Extremal quasiconformal mappings with prescribed boundary values, Trans. Amer. Math. Soc. , 1969,138: 399-406.［7］Krushkal, S. , Extremal quasiconformal mappings, Sirbirsk. Mat. Zh., 1969, 10: 573-583.［8］Reich, E., Strebel, K., Extremal quasiconformal mappings with given boundary values, Contributions to Analysis, New York: Academic Press, 1974, 375-391.［9］Strebel, K. , On quasiconformal mappings of open Riemann surfaces, Commemt. Math. Helr., 1978, 53: 301-321.［10］Earle, C., Li Zhong, Extremal quasiconformal mappings in plane domains, Quasiconformal Mappings and Analysis A Col-lection of Papers Honoring F. W. Gehring, New York: Springer-Verlag, 1998, 141-158.［11］Strebel, K., On quadratic differentials and extremal quasiconforrnal mappings, in Proc. of the Intern. Congress of Math.,Vancouver, 1974.［12］Li Zhong, Some new results on the geometry of infinite dimensional Teichmuller space, in Proceedings of the 3rd International Colloquium on Finite or Infinite Dimensional Complex Analysis, 1995, 369-378.
Hamilton optics: transformational theory of optics
Winston, Roland; Ge, Wenjun
2013-09-01
In 1824 William Rowan Hamilton presented a memoir to the Royal Irish Academy on Optics(Trans. R. Irish. Acacamy, XV, 1828), which was the foundation for transformational optics, classical mechanics, nonimaging optics and thermodynamical foundation of nonimaging optics,etc. It is useful for us even in 2013 to revisit the Hamilton resolution.
Unconventional Hamilton-type variational principles for electromagnetic elastodynamics
无
2006-01-01
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.
[Canon Busting and Cultural Literacy.
National Forum: Phi Kappa Phi Journal, 1989
1989-01-01
Articles on literary canon include: "Educational Anomie" (Stephen W. White); "Why Western Civilization?" (William J. Bennett); "Peace Plan for Canon Wars" (Gerald Graff, William E. Cain); "Canons, Cultural Literacy, and Core Curriculum" (Lynne V. Cheney); "Canon Busting: Basic Issues" (Stanley…
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Digitization of the Mary Hamilton Papers
Gardner Anne-Christine
2017-03-01
Full Text Available Held at The John Rylands Library, Manchester, the Mary Hamilton Papers are a valuable, but still largely untapped resource for linguistic, cultural and literary studies focussing on the late eighteenth century. In her diaries Lady Mary Hamilton (1756-1816 documents daily life and friendships with intellectual figures of the time, for instance Horace Walpole and members of the Bluestocking circle, which included Elizabeth Montagu and Frances Burney. The archive also contains letters written to Lady Mary Hamilton by her family and other members of her social network.
Canonical Information Analysis
Vestergaard, Jacob Schack; Nielsen, Allan Aasbjerg
2015-01-01
Canonical correlation analysis is an established multivariate statistical method in which correlation between linear combinations of multivariate sets of variables is maximized. In canonical information analysis introduced here, linear correlation as a measure of association between variables is ...... airborne data. The simulation study shows that canonical information analysis is as accurate as and much faster than algorithms presented in previous work, especially for large sample sizes. URL: http://www.imm.dtu.dk/pubdb/p.php?6270...
Clean air Hamilton 2001 progress report
NONE
2002-05-01
This community initiative called Clean Air Hamilton was established to improve air quality in Hamilton, Ontario. It has been mandated to annually report on progress and provide advice with regard to current air quality issues. The quality of life of residents is improved as a result of the work performed by Clean Air Hamilton, and it also enhances Hamilton's image. Numerous inquiries have been received from City officials in several municipalities such as Toronto, Kitchener-Waterloo and Windsor as a testament to the success of the initiative. Financial support is received from all levels of government. The funding received from the Council has helped in attracting additional donations in support of this initiative. Clean Air Hamilton was involved in one capacity or another in research, emissions reduction projects and public awareness campaigns during 2001, and its contributions were valued at approximately 500,000 dollars. The City of Hamilton was awarded the United Nations for Human Settlements award as a result of Clean Air Hamilton's community process in local air quality improvement. In addition, the City received the Dubai International Award for Best Practices in Improving the Living Environment. Clean Air Hamilton is ready to move to the next phase, which requires moving current structures that supplements voluntary commitments with committed funding from key stakeholders. Since June 1996, the advisory level of 32 on the Air Pollution Index has not been reached, and rarely goes over 20. Throughout the 1990s, levels of toxics have decreased significantly. A three-year self-sustaining program should be developed and funding sought for those initiatives, discussions should be facilitated among industrial stakeholders when they address air quality issues, and research should continue to be supported and advice on current air quality issues be provided to City Council. 1 fig.
Epple, Mark Dominik
2008-12-03
In this work we examine the Yang-Mills-Schroedinger equation, which is a result from minimizing the vacuum energy density in Coulomb gauge. We use an ansatz for the vacuum wave functional which is motivated by the exact wave functional of quantum electrodynamics. The wave functional is by construction singular on the Gribov horizon and has a variational kernel in the exponent which represents the gluon energy. We derive the so-called Dyson-Schwinger-equations from the variational principle, that the vacuum energy density is stationary under variation with respect to the variational kernel. These Dyson-Schwinger-equations build a set of coupled integral equations for the gluon and ghost propagator, and for the curvature in gauge orbit space. These equations have been derived in the last few years, have been examined analytically in certain approximations, and first numerical results have been obtained. The case of the so-called horizon condition, which means that the ghost form factor is divergent in the infrared, has always been of special interest. But is has been found in certain approximations analytically as well als numerically that the fully coupled system has no self-consistent solution within the employed truncation on two-loop level in the energy. But one can obtain a solvable system by inserting the bare ghost-propagator into the Coulomb equation. This system possesses two different kind of infrared-divergent solutions which differ in the exponents of the power laws of the form factors in the infrared. The weaker divergent solution has previously been found, but not the stronger divergent solution. The subject of this work is to develop a deeper understanding of the presented system. We present a new renormalization scheme which enables us to reduce the number of renormalization parameters by one. This new system of integral equations is solved numerically with greatly increased precision. Doing so we found the stronger divergent solution for the first
Iemhoff, R.; Bezhanishvili, N.; Bezhanishvili, Guram
2016-01-01
We introduce stable canonical rules and prove that each normal modal multi-conclusion consequence relation is axiomatizable by stable canonical rules. We apply these results to construct finite refutation patterns for modal formulas, and prove that each normal modal logic is axiomatizable by stable
Multimodal electromechanical model of piezoelectric transformers by Hamilton's principle.
Nadal, Clement; Pigache, Francois
2009-11-01
This work deals with a general energetic approach to establish an accurate electromechanical model of a piezoelectric transformer (PT). Hamilton's principle is used to obtain the equations of motion for free vibrations. The modal characteristics (mass, stiffness, primary and secondary electromechanical conversion factors) are also deduced. Then, to illustrate this general electromechanical method, the variational principle is applied to both homogeneous and nonhomogeneous Rosen-type PT models. A comparison of modal parameters, mechanical displacements, and electrical potentials are presented for both models. Finally, the validity of the electrodynamical model of nonhomogeneous Rosen-type PT is confirmed by a numerical comparison based on a finite elements method and an experimental identification.
Hamilton-Jacobi method for curved domain walls and cosmologies
Skenderis, Kostas; Townsend, Paul K.
2006-12-01
We use Hamiltonian methods to study curved domain walls and cosmologies. This leads naturally to first-order equations for all domain walls and cosmologies foliated by slices of maximal symmetry. For Minkowski and AdS-sliced domain walls (flat and closed FLRW cosmologies) we recover a recent result concerning their (pseudo)supersymmetry. We show how domain-wall stability is consistent with the instability of AdS vacua that violate the Breitenlohner-Freedman bound. We also explore the relationship to Hamilton-Jacobi theory and compute the wave-function of a 3-dimensional closed universe evolving towards de Sitter spacetime.
Calculations of canonical averages from the grand canonical ensemble.
Kosov, D S; Gelin, M F; Vdovin, A I
2008-02-01
Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble provides an appropriate physical description but it is often much easier to perform the calculations in the corresponding grand canonical ensemble. We present a method to compute averages in the canonical ensemble based on calculations of the expectation values in the grand canonical ensemble. The number of particles, which is fixed in the canonical ensemble, is not necessarily the same as the average number of particles in the grand canonical ensemble.
Extension of warm inflation to non-canonical scalar fields
Zhang, Xiao-Min
2014-01-01
We extend the warm inflationary scenario to the case of the non-canonical scalar fields. The equation of motion and the other basic equations of this new scenario are obtained. The Hubble damped term is enhanced in non-canonical inflation. A linear stability analysis is performed to give the proper slow roll conditions in warm non-canonical inflation. We study the density fluctuations in the new picture and obtain an approximate analytic expression of the power spectrum. The energy scale at the horizon crossing is depressed by both non-canonical effect and thermal effect, so does the tensor-to-scalar ratio. Besides the synergy, the non-canonical effect and the thermal effect are competing in the case of the warm non-canonical inflation.
Canonical symmetry properties of the constrained singular generalized mechanical system
李爱民; 江金环; 李子平
2003-01-01
Based on generalized Apell-Chetaev constraint conditions and to take the inherent constrains for singular Lagrangian into account, the generalized canonical equations for a general mechanical system with a singular higher-order Lagrangian and subsidiary constrains are formulated. The canonical symmetries in phase space for such a system are studied and Noether theorem and its inversion theorem in the generalized canonical formalism have been established.
Canonical symmetry properties of the constrained singular generalized mechanical system
LiAi-Min; JiangJin-Huan; LiZi-Ping
2003-01-01
Based on generalized Apell-Chetaev constraint conditions and to take the inherent constrains for singular Lagrangian into account,the generalized canonical equations for a general mechanical system with a singular higher-order Lagrangian and subsidiary constrains are formulated. The canonical symmetries in phase space for such a system are studied and Noether theorem and its inversion theorem in the generalized canonical formalism have been established.
卿光辉; 王亚辉; 李顶河
2011-01-01
In the application of symplectic numerical methods to Hamiltonian systems, it is important to recognize that a nearby Hamiltonian is approximately conserved for.exponentially long times. The numerical result of separable differential equation is very accurate by using the symplectic numerical methods. Based on the modified Hellinger-Reissner (H-R) variational principle of piezoelectricity, Hamiltonian four-node rectangular element matrix was constructed in this paper. Then the separable K-canonical formulation of the Hamiltonian element was derived by exchanging the row-column of Hamiltonian element formulation. Finally, the explicit symplectic schemes was employed to solve the static problem of piezoelectric material laminated plate. The numerical examples show that the explicit symplectic method can be applied to the large-scale differential equation.%显式辛数值算法有一个重要的特性,即在长时间内保存Hamilton函数的指数幂,用这种方法求解可分的微分方程所得到的解逼近精确解.该文基于压电材料修正后的H-R混合变分原理,首先推导了Hamiltonian四节点有限元列式,然后通过对该列式进行行列变换,得到了K正则方程.最后将显式辛数值算法用于求解压电材料层合板的静力学问题,数值算例说明显式辛数值算法完全可以应用到高维的微分方程中.
Classifying Linear Canonical Relations
Lorand, Jonathan
2015-01-01
In this Master's thesis, we consider the problem of classifying, up to conjugation by linear symplectomorphisms, linear canonical relations (lagrangian correspondences) from a finite-dimensional symplectic vector space to itself. We give an elementary introduction to the theory of linear canonical relations and present partial results toward the classification problem. This exposition should be accessible to undergraduate students with a basic familiarity with linear algebra.
Hamilton's indicators of the force of selection
Baudisch, Annette
2005-01-01
To quantify the force of selection, Hamilton [Hamilton, W. D. (1966) J. Theor. Biol. 12, 12-45] derived expressions for the change in fitness with respect to age-specific mutations. Hamilton's indicators are decreasing functions of age. He concluded that senescence is inevitable: survival...... and fertility decline with age. I show that alternative parameterizations of mutational effects lead to indicators that can increase with age. I then consider the case of deleterious mutations with age-specific effects. In this case, it is the balance between mutation and selection pressure that determines...... the equilibrium number of mutations in a population. In this balance, the effects of different parameterizations cancel out, but only to a linear approximation. I show that mutation accumulation has little impact at ages when this linear approximation holds. When mutation accumulation matters, nonlinear effects...
Scalar potentials out of canonical quantum cosmology
Guzman, W; Socorro, J; Urena-Lopez, L A
2005-01-01
Using canonical quantization of a flat FRW cosmological model containing a real scalar field $\\phi$ endowed with a scalar potential $V(\\phi)$, we are able to obtain exact and semiclassical solutions of the so called Wheeler-DeWitt equation for a particular family of scalar potentials. Some features of the solutions and their classical limit are discussed.
Generalized canonical correlation analysis with missing values
M. van de Velden (Michel); Y. Takane
2009-01-01
textabstractTwo new methods for dealing with missing values in generalized canonical correlation analysis are introduced. The first approach, which does not require iterations, is a generalization of the Test Equating method available for principal component analysis. In the second approach, missing
Canonical Ensemble Model for Black Hole Radiation
Jingyi Zhang
2014-09-01
In this paper, a canonical ensemble model for the black hole quantum tunnelling radiation is introduced. In this model the probability distribution function corresponding to the emission shell is calculated to second order. The formula of pressure and internal energy of the thermal system is modified, and the fundamental equation of thermodynamics is also discussed.
Richard Hamilton: the Very Great Semiographer
Paul, Frédéric
2012-01-01
For fifty years and more, Richard Hamilton has been an enthralling artist. He was not only a Pop Art pioneer, but also one of its earliest theoreticians… before the United States pilfered the idea and turned it into a lucrative trademark—their industrial model inspiring the movement, but the formulae of Cubism and Surrealism, with the re-use of found objects by collage and assemblage, also playing their part. Hamilton is little known outside the United Kingdom, and has been signally overlooke...
Canonical coordinates for partial differential equations
Hunt, L. R.; Villarreal, Ramiro
1988-01-01
Necessary and sufficient conditions are found under which operators of the form Sigma (m, j=1) x (2) sub j + X sub O can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.
[Canon Busting and Cultural Literacy.
National Forum: Phi Kappa Phi Journal, 1989
1989-01-01
Articles on literary canon include: "Educational Anomie" (Stephen W. White); "Why Western Civilization?" (William J. Bennett); "Peace Plan for Canon Wars" (Gerald Graff, William E. Cain); "Canons, Cultural Literacy, and Core Curriculum" (Lynne V. Cheney); "Canon Busting: Basic Issues" (Stanley Fish); "A Truce in Curricular Wars" (Chester E. Finn,…
Measuring Social Capital in Hamilton, Ontario
Kitchen, Peter; Williams, Allison; Simone, Dylan
2012-01-01
Social capital has been studied by academics for more than 20 years and within the past decade there has been an explosion of growth in research linking social capital to health. This paper investigates social capital in Hamilton, Ontario by way of a telephone survey of 1,002 households in three neighbourhood groups representing high, mixed and…
Measuring Social Capital in Hamilton, Ontario
Kitchen, Peter; Williams, Allison; Simone, Dylan
2012-01-01
Social capital has been studied by academics for more than 20 years and within the past decade there has been an explosion of growth in research linking social capital to health. This paper investigates social capital in Hamilton, Ontario by way of a telephone survey of 1,002 households in three neighbourhood groups representing high, mixed and…
The face of energy poverty in Hamilton
Cooper, T. [McQuesten Legal and Community Services, Hamilton, ON (Canada)
2007-07-01
In 1907, Hamilton, Ontario was known as the electric city, where jobs were plentiful and where the cheapest hydro power in the world was produced. This presentation stated that currently, Hamilton which faces one of the highest poverty rates in the province of Ontario, with 96,000 residents living below the low income cutoff. Heat and hydro costs have escalated and have driven more Hamiltonians into deep poverty. Several quotes from residents were presented along with photographs to illustrate the situation. A graph depicting poverty by age demographics was also provided. The presentation emphasized that there is a need for a housing emergency loan program and a utility arrears program for the City of Hamilton, as many tenants are struggling to survive without heat, gas or electricity. The presentation concluded that Hamilton is in need of an effective heat strategy during the summer cooling months because senior citizens, persons with disabilities and families living in low-income, poorly ventilated housing are particularly at risk during an extreme heat event. refs., tabs., figs.
Hamilton County: A Rural School District Profile.
Harned, Catherine
Using state education agency, census, industry employment and occupational information data, this paper provides a detailed picture of a rural school district in Southern Illinois. Mining and agriculture are the major industries in Hamilton County. The major mining employer closed in February 1988, and the drought of 1988 is likely to adversely…
Hamilton-Jacobi renormalization for Lifshitz spacetime
Baggio, M.; de Boer, J.; Holsheimer, K.
2012-01-01
Just like AdS spacetimes, Lifshitz spacetimes require counterterms in order to make the on-shell value of the bulk action finite. We study these counterterms using the Hamilton-Jacobi method. Rather than imposing boundary conditions from the start, we will derive suitable boundary conditions by
On the Hamilton-Jacobi method in classical and quantum nonconservative systems
Dutra, A. de Souza; Correa, R. A. C.; Moraes, P. H. R. S.
2016-08-01
In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature, and we extend these complete solutions to the quantum mechanical case. In addition, we obtain the solution of the quantum Hamilton-Jacobi equation for an electric charge in an oscillating pulsing magnetic field. We also argue that for the case where a charged particle is under the action of an oscillating magnetic field, one can apply nuclear magnetic resonance techniques in order to find experimental results regarding this problem. We obtain all results analytically, showing that the quantum Hamilton-Jacobi formalism is a powerful tool to describe quantum mechanics.
Deformed Hamilton-Jacobi Method in Covariant Quantum Gravity Effective Models
Benrong, Mu; Yang, Haitang
2014-01-01
We first briefly revisit the original Hamilton-Jacobi method and show that the Hamilton-Jacobi equation for the action $I$ of tunnelings of a fermionic particle from a charged black hole can be written in the same form as that of a scalar particle. For the low energy quantum gravity effective models which respect covariance of the curved spacetime, we derive the deformed model-independent KG/Dirac and Hamilton-Jacobi equations using the methods of effective field theory. We then find that, to all orders of the effective theories, the deformed Hamilton-Jacobi equations can be obtained from the original ones by simply replacing the mass of emitted particles $m$ with a parameter $m_{eff}$ that includes all the quantum gravity corrections. Therefore, in this scenario, there will be no corrections to the Hawking temperature of a black hole from the quantum gravity effects if its original Hawking temperature is independent of the mass of emitted particles. As a consequence, our results show that breaking covariance...
An unusual ophthalmic finding in Lane-Hamilton syndrome.
Villegas, Victor M; Rachitskaya, Aleksandra V; Lam, Byron L; McKeown, Craig A; Berrocal, Audina M
2014-12-01
Lane-Hamilton syndrome is a rare condition that is characterized by idiopathic pulmonary hemosiderosis and celiac disease. We report the case of an 18-month-old girl with Lane-Hamilton syndrome who had unilateral pigmentary retinopathy.
Conformal invariance and Hamilton Jacobi theory for dissipative systems
Kiehn, R. M.
1975-01-01
For certain dissipative systems, a comparison can be made between the Hamilton-Jacobi theory and the conformal invariance of action theory. The two concepts are not identical, but the conformal action theory covers the Hamilton-Jacobi theory.
A hybrid-stress element based on Hamilton principle
Cen, Song; Zhang, Tao; Li, Chen-Feng; Fu, Xiang-Rong; Long, Yu-Qiu
2010-08-01
A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3 β here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3 β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.
Hopfion canonical quantization
Acus, A; Norvaisas, E; Shnir, Ya
2012-01-01
We study the effect of the canonical quantization of the rotational mode of the charge Q=1 and Q=2 spinning Hopfions. The axially-symmetric solutions are constructed numerically, it is shown the quantum corrections to the mass of the configurations are relatively large.
Hopfion canonical quantization
Acus, A. [Vilnius University, Institute of Theoretical Physics and Astronomy, Gostauto 12, Vilnius 01108 (Lithuania); Halavanau, A. [Department of Theoretical Physics and Astrophysics, BSU, Minsk (Belarus); Norvaisas, E. [Vilnius University, Institute of Theoretical Physics and Astronomy, Gostauto 12, Vilnius 01108 (Lithuania); Shnir, Ya., E-mail: shnir@maths.tcd.ie [Department of Theoretical Physics and Astrophysics, BSU, Minsk (Belarus); Institute of Physics, Carl von Ossietzky University Oldenburg (Germany)
2012-05-03
We study the effect of the canonical quantization of the rotational mode of the charge Q=1 and Q=2 spinning Hopfions. The axially-symmetric solutions are constructed numerically, it is shown the quantum corrections to the mass of the configurations are relatively large.
Revisiting Canonical Quantization
Klauder, John R
2012-01-01
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum theory with \\hbar>0. While keeping the good results of conventional procedures, some examples are noted where the new procedures offer better results than conventional ones.
On the use of the autonomous Birkhoff equations in Lie series perturbation theory
Boronenko, T. S.
2016-10-01
In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. The Birkhoff equations are derived from the linear first-order Pfaff-Birkhoff variational principle, which is more general than the Hamilton principle. The use of 1-form in formulating the equations of motion in dynamics makes the Birkhoff method more universal and flexible. Birkhoff's equations have a tensorial character, so their form is independent of the coordinate system used. Two examples of normalization in the restricted three-body problem are given to illustrate the application of the algorithm in perturbation theory. The efficiency of this algorithm for problems of asymptotic integration in dynamics is discussed for the case where there is a need to use non-canonical variables in phase space.
On the use of the autonomous Birkhoff equations in Lie series perturbation theory
Boronenko, T. S.
2017-02-01
In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. The Birkhoff equations are derived from the linear first-order Pfaff-Birkhoff variational principle, which is more general than the Hamilton principle. The use of 1-form in formulating the equations of motion in dynamics makes the Birkhoff method more universal and flexible. Birkhoff's equations have a tensorial character, so their form is independent of the coordinate system used. Two examples of normalization in the restricted three-body problem are given to illustrate the application of the algorithm in perturbation theory. The efficiency of this algorithm for problems of asymptotic integration in dynamics is discussed for the case where there is a need to use non-canonical variables in phase space.
Concept maps and canonical models in neuropsychiatry.
Marin-Sanguino, A; del Rosario, R C H; Mendoza, E R
2009-05-01
Most bioscientists engage in informal modelling in their research and explicitly document this activity's results in diagrams or "concept maps". While canonical modelling approaches such as Biochemical Systems Theory (BST) immediately allow the construction of a corresponding system of equations, the problem of determining appropriate parameter values remains. Goel et al. introduced Concept Map Modelling (CMM) as a framework to address this problem through an interactive dialogue between experimenters and modellers. The CMM dialogue extracts the experimenters' implicit knowledge about dynamical behaviour of the parts of the system being modelled in form of rough sketches and verbal statements, e.g. value ranges. These are then used as inputs for parameter and initial value estimates for the symbolic canonical model based on the diagram. Canonical models have the big advantage that a great variety of parameter estimation methods have been developed for them in recent years. The paper discusses the suitability of this approach for neuropsychiatry using recent work of Qi et al. on a canonical model of presynaptic dopamine metabolism. Due to the complexity of systems encountered in neuropsychiatry, hybrid models are often used to complement the canonical models discussed here.
Variational principle and phase space measure in non-canonical coordinates
Sergi, A
2005-11-01
Full Text Available Non-canonical equations of motion are derived from a variational principle written in symplectic form. The invariant measure of phase space and the covariant expression for the entropy are derived from non-canonical transformations of coordinates. This shows that the geometry of non-canonical phase space is non trivial even if dynamics has no compressibility.
Hamilton--Jacobi meet M\\"obius
Faraggi, Alon E
2015-01-01
Adaptation of the Hamilton--Jacobi formalism to quantum mechanics leads to a cocycle condition, which is invariant under $D$--dimensional M\\"obius transformations with Euclidean or Minkowski metrics. In this paper we aim to provide a pedagogical presentation of the proof of the M\\"obius symmetry underlying the cocycle condition. The M\\"obius symmetry implies energy quantization and undefinability of quantum trajectories, without assigning any prior interpretation to the wave function. As such, the Hamilton--Jacobi formalism, augmented with the global M\\"obius symmetry, provides an alternative starting point, to the axiomatic probability interpretation of the wave function, for the formulation of quantum mechanics and the quantum spacetime. The M\\"obius symmetry can only be implemented consistently if spatial space is compact, and correspondingly if there exist a finite ultraviolet length scale. Evidence for non--trivial space topology may exist in the cosmic microwave background radiation.
The canonical and grand canonical models for nuclear multifragmentation
G Chaudhuri; S Das Gupta
2010-08-01
Many observables seen in intermediate energy heavy-ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble, canonical ensemble or grand canonical ensemble. This paper deals with calculations with canonical and grand canonical ensembles. A recursive relation developed recently allows calculations with arbitrary precision for many nuclear problems. Calculations are done to study the nature of phase transition in nuclear matter.
Realizations of the Canonical Representation
M K Vemuri
2008-02-01
A characterisation of the maximal abelian subalgebras of the bounded operators on Hilbert space that are normalised by the canonical representation of the Heisenberg group is given. This is used to classify the perfect realizations of the canonical representation.
Higher Derivatives and Canonical Formalism
HAMAMOTO, Shinji
1995-01-01
A canonical formalism for higher-derivative theories is presented on the basis of Dirac's method for constrained systems. It is shown that this formalism shares a path integral expression with Ostrogradski's canonical formalism.
Canonical quantization of macroscopic electromagnetism
Philbin, T G, E-mail: tgp3@st-andrews.ac.u [School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS (United Kingdom)
2010-12-15
Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Kramers-Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.
Canonical quantization of macroscopic electromagnetism
Philbin, T G
2010-01-01
Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetoelectric medium with dielectric functions that obey the Kramers-Kronig relations. The prescriptions of the phenomenological approach are derived from the canonical theory.
Canonical Strangeness Enhancement
Sollfrank, J; Redlich, Krzysztof; Satz, Helmut
1998-01-01
According to recent experimental data and theoretical developments we discuss three distinct topics related to strangeness enhancement in nuclear reactions. We investigate the compatibility of multi-strange particle ratios measured in a restricted phase space with thermal model parameters extracted recently in 4pi. We study the canonical suppression as a possible reason for the observed strangeness enhancement and argue that a connection between QGP formation and the undersaturation of strangeness is not excluded.
2015-01-01
The traditional vision of Middleton as a playwright depicted him as an author of city comedies and tragicomedies, who in his very last years suddenly approached the tragic genre. Among his last four plays, three composed in succession are tragedies: Hengist, 1620, Women Beware Women, 1621 and The Changeling, 1622; the last two are recognized as masterpieces. In the last forty years, Middleton’s canon has changed with new attributions. This paper analyses the new pattern emerging in Middleton’...
Canonical Transformations of Kepler Trajectories
Mostowski, Jan
2010-01-01
In this paper, canonical transformations generated by constants of motion in the case of the Kepler problem are discussed. It is shown that canonical transformations generated by angular momentum are rotations of the trajectory. Particular attention is paid to canonical transformations generated by the Runge-Lenz vector. It is shown that these…
Fifty years with the Hamilton scales for anxiety and depression. A tribute to Max Hamilton
Bech, P
2009-01-01
From the moment Max Hamilton started his psychiatric education, he considered psychometrics to be a scientific discipline on a par with biochemistry or pharmacology in clinical research. His clinimetric skills were in operation in the 1950s when randomised clinical trials were established...... as the method for the evaluation of the clinical effects of psychotropic drugs. Inspired by Eysenck, Hamilton took the long route around factor analysis in order to qualify his scales for anxiety (HAM-A) and depression (HAM-D) as scientific tools. From the moment when, 50 years ago, Hamilton published his first...... placebo-controlled trial with an experimental anti-anxiety drug, he realized the dialectic problem in using the total score on HAM-A as a sufficient statistic for the measurement of outcome. This dialectic problem has been investigated for more than 50 years with different types of factor analyses without...
Whose Canon? Culturalization versus Democratization
Erling Bjurström
2012-06-01
Full Text Available Current accounts – and particularly the critique – of canon formation are primarily based on some form of identity politics. In the 20th century a representational model of social identities replaced cultivation as the primary means to democratize the canons of the fine arts. In a parallel development, the discourse on canons has shifted its focus from processes of inclusion to those of exclusion. This shift corresponds, on the one hand, to the construction of so-called alternative canons or counter-canons, and, on the other hand, to attempts to restore the authority of canons considered to be in a state of crisis or decaying. Regardless of the democratic stance of these efforts, the construction of alternatives or the reestablishment of decaying canons does not seem to achieve their aims, since they break with the explicit and implicit rules of canon formation. Politically motivated attempts to revise or restore a specific canon make the workings of canon formation too visible, transparent and calculated, thereby breaking the spell of its imaginary character. Retracing the history of the canonization of the fine arts reveals that it was originally tied to the disembedding of artists and artworks from social and worldly affairs, whereas debates about canons of the fine arts since the end of the 20th century are heavily dependent on their social, cultural and historical reembedding. The latter has the character of disenchantment, but has also fettered the canon debate in notions of “our” versus “their” culture. However, by emphasizing the dedifferentiation of contemporary processes of culturalization, the advancing canonization of popular culture seems to be able to break with identity politics that foster notions of “our” culture in the present thinking on canons, and push it in a more transgressive, syncretic or hybrid direction.
曹玉松
2013-01-01
从保险公司的角度出发,在投资基金价格服从带漂移的几何布朗运动的假定下,基于Hamilton-Jacobi-Bellman理论,给出了使得盈余终值的期望指数效用最大化的比例再保险函数的最优比例,及其各个风险市场的最优投资比例.%From the insurer's point of view,on the assumption that investment fund follows the Geometric Brownian motion,based on the theory of Hamilton-Jacobi-Bellman equation,the paper gives the optimal proportion of the proportional reinsurance and the capital amount of each risky investment markets,which can make the expected exponential utility of terminal wealth maximum.
Hamilton Graph Based on DNA Computing
ZHANGJia-xiu
2004-01-01
DNA computing is a novel method for solving a class of intractable computationalproblems in which the computing can grow exponentially with problem size. Up to now, manyaccomplishments have been achieved to improve its performance and increase its reliability.Hamilton Graph Problem has been solved by means of molecular biology techniques. A smallgraph was encoded in molecules of DNA, and the “operations” of the computation wereperformed with standard protocols and enzymes. This work represents further evidence forthe ability of DNA computing to solve NP-complete search problems.
Algebra and geometry of Hamilton's quaternions
Krishnaswami, Govind S
2016-01-01
Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations.
Hamilton-Jacobi Method and Gravitation
Di Criscienzo, R; Zerbini, S
2010-01-01
Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we possess the instruments to perform exact predictions in special, highly symmetric, conditions. Aim of the present contribution is to show how it is possible to extract quantitative information about a variety of physical phenomena in very general situations by virtue of the so-called Hamilton-Jacobi method. In particular, we shall prove the agreement of such semi-classical method with exact results of quantum field theoretic calculations.
Hamilton-Jacobi Method and Gravitation
di Criscienzo, R.; Vanzo, L.; Zerbini, S.
Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we possess the instruments to perform exact predictions in special, highly symmetric, conditions. Aim of the present contribution is to show how it is possible to extract quantitative information about a variety of physical phenomena in very general situations by virtue of the so-called Hamilton-Jacobi method. In particular, we shall prove the agreement of such semi-classical method with exact results of quantum field theoretic calculations.
Canonical formalism for coupled beam optics
Kheifets, S.A.
1989-09-01
Beam optics of a lattice with an inter-plane coupling is treated using canonical Hamiltonian formalism. The method developed is equally applicable both to a circular (periodic) machine and to an open transport line. A solution of the equation of a particle motion (and correspondingly transfer matrix between two arbitrary points of the lattice) are described in terms of two amplitude functions (and their derivatives and corresponding phases of oscillations) and four coupling functions, defined by a solution of the system of the first-order nonlinear differential equations derived in the paper. Thus total number of independent parameters is equal to ten. 8 refs.
Canonical energy and linear stability of Schwarzschild
Prabhu, Kartik; Wald, Robert
2017-01-01
Consider linearised perturbations of the Schwarzschild black hole in 4 dimensions. Using the linearised Newman-Penrose curvature component, which satisfies the Teukolsky equation, as a Hertz potential we generate a `new' metric perturbation satisfying the linearised Einstein equation. We show that the canonical energy, given by Hollands and Wald, of the `new' metric perturbation is the conserved Regge-Wheeler-like energy used by Dafermos, Holzegel and Rodnianski to prove linear stability and decay of perturbations of Schwarzschild. We comment on a generalisation of this strategy to prove the linear stability of the Kerr black hole.
An electromechanical model of neuronal dynamics using Hamilton's principle
Drapaca, Corina S.
2015-01-01
Damage of the brain may be caused by mechanical loads such as penetration, blunt force, shock loading from blast, and by chemical imbalances due to neurological diseases and aging that trigger not only neuronal degeneration but also changes in the mechanical properties of brain tissue. An understanding of the interconnected nature of the electro-chemo-mechanical processes that result in brain damage and ultimately loss of functionality is currently lacking. While modern mathematical models that focus on how to link brain mechanics to its biochemistry are essential in enhancing our understanding of brain science, the lack of experimental data required by these models as well as the complexity of the corresponding computations render these models hard to use in clinical applications. In this paper we propose a unified variational framework for the modeling of neuronal electromechanics. We introduce a constrained Lagrangian formulation that takes into account Newton's law of motion of a linear viscoelastic Kelvin–Voigt solid-state neuron as well as the classic Hodgkin–Huxley equations of the electronic neuron. The system of differential equations describing neuronal electromechanics is obtained by applying Hamilton's principle. Numerical simulations of possible damage dynamics in neurons will be presented. PMID:26236195
An electromechanical model of neuronal dynamics using Hamilton's principle.
Drapaca, Corina S
2015-01-01
Damage of the brain may be caused by mechanical loads such as penetration, blunt force, shock loading from blast, and by chemical imbalances due to neurological diseases and aging that trigger not only neuronal degeneration but also changes in the mechanical properties of brain tissue. An understanding of the interconnected nature of the electro-chemo-mechanical processes that result in brain damage and ultimately loss of functionality is currently lacking. While modern mathematical models that focus on how to link brain mechanics to its biochemistry are essential in enhancing our understanding of brain science, the lack of experimental data required by these models as well as the complexity of the corresponding computations render these models hard to use in clinical applications. In this paper we propose a unified variational framework for the modeling of neuronal electromechanics. We introduce a constrained Lagrangian formulation that takes into account Newton's law of motion of a linear viscoelastic Kelvin-Voigt solid-state neuron as well as the classic Hodgkin-Huxley equations of the electronic neuron. The system of differential equations describing neuronal electromechanics is obtained by applying Hamilton's principle. Numerical simulations of possible damage dynamics in neurons will be presented.
An Electromechanical Model of Neuronal Dynamics using Hamilton's Principle
Corina Stefania Drapaca
2015-07-01
Full Text Available Damage of the brain may be caused by mechanical loads such as penetration, blunt force, shock loading from blast, and by chemical imbalances due to neurological diseases and aging that trigger not only neuronal degeneration but also changes in the mechanical properties of brain tissue. An understanding of the interconnected nature of the electro-chemo-mechanical processes that result in brain damage and ultimately loss of functionality is currently lacking. While modern mathematical models that focus on how to link brain mechanics to its biochemistry are essential in enhancing our understanding of brain science, the lack of experimental data required by these models as well as the complexity of the corresponding computations render these models hard to use in clinical applications. In this paper we propose a unified variational framework for the modeling of neuronal electromechanics. We introduce a constrained Lagrangian formulation that takes into account Newton's law of motion of a linear viscoelastic Kelvin-Voigt solid-state neuron as well as the classic Hodgkin-Huxley equations of the electronic neuron. The system of differential equations describing neuronal electromechanics is obtained by applying Hamilton's principle. Numerical simulations of possible damage dynamics in neurons will be presented.
Hamilton y el Descubrimiento de los Cuaterniones
José Manuel Sánchez Muñoz
2011-10-01
Full Text Available Este artículo pretende ofrecer una visión general del descubrimiento de los llamados cuaterniones por parte del matemático irlandés William Rowan Hamilton. Se pretende dar al lector algunos detalles del nacimiento de los números imaginarios en el siglo XVI, su interpretación geométrica a principios del siglo XIX, y la extensión del plano complejo a las tres dimensiones a través de los cuaterniones, que abrirían el paso al estudio y el desarrollo de las nuevas álgebras no conmutativas y a una nueva interpretación tridimensional de la realidad física.
Viscous warm inflation: Hamilton-Jacobi formalism
Akhtari, L.; Mohammadi, A.; Sayar, K.; Saaidi, Kh.
2017-04-01
Using Hamilton-Jacobi formalism, the scenario of warm inflation with viscous pressure is considered. The formalism gives a way of computing the slow-rolling parameter without extra approximation, and it is well-known as a powerful method in cold inflation. The model is studied in detail for three different cases of the dissipation and bulk viscous pressure coefficients. In the first case where both coefficients are taken as constant, it is shown that the case could not portray warm inflationary scenario compatible with observational data even it is possible to restrict the model parameters. For other cases, the results shows that the model could properly predicts the perturbation parameters in which they stay in perfect agreement with Planck data. As a further argument, r -ns and αs -ns are drown that show the acquired result could stand in acceptable area expressing a compatibility with observational data.
Hamilton-Jacobi skeleton on cortical surfaces.
Shi, Y; Thompson, P M; Dinov, I; Toga, A W
2008-05-01
In this paper, we propose a new method to construct graphical representations of cortical folding patterns by computing skeletons on triangulated cortical surfaces. In our approach, a cortical surface is first partitioned into sulcal and gyral regions via the solution of a variational problem using graph cuts, which can guarantee global optimality. After that, we extend the method of Hamilton-Jacobi skeleton [1] to subsets of triangulated surfaces, together with a geometrically intuitive pruning process that can trade off between skeleton complexity and the completeness of representing folding patterns. Compared with previous work that uses skeletons of 3-D volumes to represent sulcal patterns, the skeletons on cortical surfaces can be easily decomposed into branches and provide a simpler way to construct graphical representations of cortical morphometry. In our experiments, we demonstrate our method on two different cortical surface models, its ability of capturing major sulcal patterns and its application to compute skeletons of gyral regions.
Analytical mechanics methods for solving Whittaker equations
2007-01-01
The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange-Noether method, Hamilton-Poisson method and potential integral method.
On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks
Annunziato, Mario
2014-09-01
In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.
78 FR 43838 - Airworthiness Directives; Hamilton Sundstrand Corporation Propellers
2013-07-22
..., Engine & Propeller Directorate, Aircraft Certification Service. BILLING CODE 4910-13-P ...-48-AD RIN 2120-AA64 Airworthiness Directives; Hamilton Sundstrand Corporation Propellers AGENCY... had applied to certain Hamilton Sundstrand Corporation 14SF-7, 14SF-15, and 14SF-23 series...
Non-linear canonical correlation
van der Burg, Eeke; de Leeuw, Jan
1983-01-01
Non-linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An
A Practical Approach to the Hamilton-Jacobi Formulation of Holographic Renormalization
Elvang, Henriette
2016-01-01
We revisit the subject of holographic renormalization for asymptotically AdS spacetimes. For many applications of holography, one has to handle the divergences associated with the on-shell gravitational action. The brute force approach uses the Fefferman-Graham (FG) expansion near the AdS boundary to identify the divergences, but subsequent reversal of the expansion is needed to construct the infinite counterterms. While in principle straightforward, the method is cumbersome and application/reversal of FG is formally unsatisfactory. Various authors have proposed an alternative method based on the Hamilton-Jacobi equation. However, this approach may appear to be abstract, difficult to implement, and in some cases limited in applicability. In this paper, we clarify the Hamilton-Jacobi formulation of holographic renormalization and present a simple algorithm for its implementation to extract cleanly the infinite counterterms. While the derivation of the method relies on the Hamiltonian formulation of general rel...
曾文平
2004-01-01
In this paper, we present two classes of symplectic schemes with high order accuracy for solving four-order rod vibration equation utt+uxxxx=0 via the third type generating function method. First, the equation of four order rod vibration is written into the canonical Hamilton system; second, overcoming successfully the essential difficult on the calculus of high order variations derivative, we get the semi-discretization with arbitrary order of accuracy in time direction for the PDEs by the third type generating function method. Furthermore the discretization of the related modified equation of original equation is obtained. Finally, arbitrary order accuracy symplectic schemes are obtained. Numerical results are also presented to show the effectiveness of the scheme, high order accuracy and properties of excellent long-time numerical behavior.
The fate of Hamilton's Hodograph in Special and General Relativity
Gibbons, G W
2015-01-01
The hodograph of a non-relativistic particle motion in Euclidean space is the curve described by its momentum vector. For a general central orbit problem the hodograph is the inverse of the pedal curve of the orbit, (i.e. its polar reciprocal), rotated through a right angle. Hamilton showed that for the Kepler/Coulomb problem, the hodograph is a circle whose centre is in the direction of a conserved eccentricity vector. The addition of an inverse cube law force induces the eccentricity vector to precess and with it the hodograph. The same effect is produced by a cosmic string. If one takes the relativistic momentum to define the hodograph, then for the Sommerfeld (i.e. the special relativistic Kepler/Coulomb problem) there is an effective inverse cube force which causes the hodograph to precess. If one uses Schwarzschild coordinates one may also define a a hodograph for timelike or null geodesics moving around a black hole. Iheir pedal equations are given. In special cases the hodograph may be found explicitl...
Canonical Height Functions For Monomial Maps
Lin, Jan-Li
2012-01-01
We show that the canonical height function defined by Silverman does not have the Northcott finiteness property in general. We develop a new canonical height function for monomial maps. In certain cases, this new canonical height function has nice properties.
Hitzl, D. L.; Zele, F.
Recently, the application of Hamilton's law of varying action to initial value problems in dynamics has been generalized and simplified. Using the Hitzl et al. (1984) new integral variation method, approximate solutions can be constructed to arbitrary initial value problems involving systems of first-order ordinary differential equations. The new constructive technique is briefly described, and the method is illustrated with two example problems: (1) the damped oscillator (two linear differential equations), and (2) the Lagrange planetary equations with zonal harmonics and drag (a highly nonlinear system of six coupled first-order differential equations). Numerical results confirm that the integral variation method indeed provides accurate approximate analytical solutions over a specified finite time interval.
Ren Wen-Xiu; Alatancang
2007-01-01
Using factorization viewpoint of differential operator, this paper discusses how ti transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical '(δ)/(δ)x'-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived fegibly.
Canonical quantization of constrained systems
Bouzas, A.; Epele, L.N.; Fanchiotti, H.; Canal, C.A.G. (Laboratorio de Fisica Teorica, Departamento de Fisica, Universidad Nacional de La Plata, Casilla de Correo No. 67, 1900 La Plata, Argentina (AR))
1990-07-01
The consideration of first-class constraints together with gauge conditions as a set of second-class constraints in a given system is shown to be incorrect when carrying out its canonical quantization.
Adaptive dynamics via Hamilton-Jacobi approach and entropy methods for a juvenile-adult model.
Carrillo, José Antonio; Cuadrado, Sílvia; Perthame, Benoît
2007-01-01
We consider a nonlinear system describing a juvenile-adult population undergoing small mutations. We analyze two aspects: from a mathematical point of view, we use an entropy method to prove that the population neither goes extinct nor blows-up; from an adaptive evolution point of view, we consider small mutations on a long time scale and study how a monomorphic or a dimorphic initial population evolves towards an Evolutionarily Stable State. Our method relies on an asymptotic analysis based on a constrained Hamilton-Jacobi equation. It allows to recover earlier predictions in Calsina and Cuadrado [A. Calsina, S. Cuadrado, Small mutation rate and evolutionarily stable strategies in infinite dimensional adaptive dynamics, J. Math. Biol. 48 (2004) 135; A. Calsina, S. Cuadrado, Stationary solutions of a selection mutation model: the pure mutation case, Math. Mod. Meth. Appl. Sci. 15(7) (2005) 1091.] that we also assert by direct numerical simulation. One of the interests here is to show that the Hamilton-Jacobi approach initiated in Diekmann et al. [O. Diekmann, P.-E. Jabin, S. Mischler, B. Perthame, The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach, Theor. Popul. Biol. 67(4) (2005) 257.] extends to populations described by systems.
Schmid, L. A.
1977-01-01
The first and second variations are calculated for the irreducible form of Hamilton's Principle that involves the minimum number of dependent variables necessary to describe the kinetmatics and thermodynamics of inviscid, compressible, baroclinic flow in a specified gravitational field. The form of the second variation shows that, in the neighborhood of a stationary point that corresponds to physically stable flow, the action integral is a complex saddle surface in parameter space. There exists a form of Hamilton's Principle for which a direct solution of a flow problem is possible. This second form is related to the first by a Friedrichs transformation of the thermodynamic variables. This introduces an extra dependent variable, but the first and second variations are shown to have direct physical significance, namely they are equal to the free energy of fluctuations about the equilibrium flow that satisfies the equations of motion. If this equilibrium flow is physically stable, and if a very weak second order integral constraint on the correlation between the fluctuations of otherwise independent variables is satisfied, then the second variation of the action integral for this free energy form of Hamilton's Principle is positive-definite, so the action integral is a minimum, and can serve as the basis for a direct trail and error solution. The second order integral constraint states that the unavailable energy must be maximum at equilibrium, i.e. the fluctuations must be so correlated as to produce a second order decrease in the total unavailable energy.
Sam D. Hamilton Noxubee National Wildlife Refuge: Comprehensive Conservation Plan
US Fish and Wildlife Service, Department of the Interior — This Comprehensive Conservation Plan (CCP) was written to guide management on Sam D. Hamilton Noxubee NWR for the next 15 years. This plan outlines the Refuge vision...
Hamilton-Jakobi method for classical mechanics in Grassmann algebra
Tabunshchyk, K. V.
1998-01-01
We present the Hamilton-Jakobi method for the classical mechanics with constrains in Grassmann algebra. In the frame of this method the solution for the classical system characterized by the SUSY Lagrangian is obtained.
Hamilton´s Principle and Electric Circuits Tudory
2006-01-01
In the theory of electrical or electromechanical circuits different methods are known for construction of mathematical model. In this paper another, alternative method is introduced that is based on Hamilton variational principle that is generally valid in physics.
Researcher Profile: An Interview with Axton Betz-Hamilton
Axton Betz-Hamilton
2015-07-01
Full Text Available Dr. Axton Betz-Hamilton teaches consumer studies courses at Eastern Illinois University, including Personal and Family Finance, Housing, and Consumer Issues. She conducts research on identity theft as well as financial abuse within families.
Packing tight Hamilton cycles in 3-uniform hypergraphs
Frieze, Alan; Loh, Po-Shen
2010-01-01
Let H be a 3-uniform hypergraph with N vertices. A tight Hamilton cycle C \\subset H is a collection of N edges for which there is an ordering of the vertices v_1, ..., v_N such that every triple of consecutive vertices {v_i, v_{i+1}, v_{i+2}} is an edge of C (indices are considered modulo N). We develop new techniques which enable us to prove that under certain natural pseudo-random conditions, almost all edges of H can be covered by edge-disjoint tight Hamilton cycles, for N divisible by 4. Consequently, we derive the corollary that random 3-uniform hypergraphs can be almost completely packed with tight Hamilton cycles w.h.p., for N divisible by 4 and P not too small. Along the way, we develop a similar result for packing Hamilton cycles in pseudo-random digraphs with even numbers of vertices.
Hamilton Place - Ontario Canadá
Garwood-Jones, T. P.
1975-04-01
Full Text Available Although comparatively modest as to its exterior, the interior of the theatre-auditorium Hamilton Place has been most successfully solved, both as regards design and acoustics. Construction techniques and elements have been utilized to achieve two different sections in one and the same hall with on one hand the capacity to be able to capture shades of the spoken word at theatrical functions and on the other to reproduce the sharpness and variety of orchestras and choirs. The following elements deserve special mention: the mobile wall which incorporates the orchestra into the hall by closing the proscenium arch; the two elevating platforms where the orchestra is placed; the vertical velvet surfaces, hung like banners which soften the repercussion of the sound; the mobile horizontal surfaces over the orchestra that direct and orient the sound. The most interesting construction techniques are: the subdivision of the building into different parts, each one with independent foundation so as to avoid the transmission of the sound from one section to the other; the texture of the brick walls that disperse the reflected sound; and the use of counterforts to create smaller more personal sections for varied use. The acoustic characteristics are improved by means of a sound installation, formed by small loudspeakers placed under each seat and by other bigger ones distributed in the walls that surround the hall. The building is completed by various service installations that are appropriate to this type of construction, as well as by a small theatre-studio for the rehearsals of the orchestra and the actors, while other functions are going on in the main hall.El teatro-auditorio Hamilton Place, aunque relativamente modesto por fuera, tiene soluciones muy afortunadas en el interior, tanto por su diseño como por su adecuación acústica. Se han utilizado elementos y técnicas constructivas destinadas a conseguir, en una única sala, dos espacios
Hamilton Jeffers and the Double Star Catalogues
Tenn, Joseph S.
2013-01-01
Astronomers have long tracked double stars in efforts to find those that are gravitationally-bound binaries and then to determine their orbits. Court reporter and amateur astronomer Shelburne Wesley Burnham (1838-1921) published a massive double star catalogue containing more than 13,000 systems in 1906. The next keeper of the double stars was Lick Observatory astronomer Robert Grant Aitken (1864-1951), who produced a much larger catalogue in 1932. Aitken maintained and expanded Burnham’s records of observations on handwritten file cards, eventually turning them over to Lick Observatory astrometrist Hamilton Moore Jeffers (1893-1976). Jeffers further expanded the collection and put all the observations on punched cards. With the aid of Frances M. "Rete" Greeby (1921-2002), he made two catalogues: an Index Catalogue with basic data about each star, and a complete catalogue of observations, with one observation per punched card. He enlisted Willem van den Bos of Johannesburg to add southern stars, and they published the Index Catalogue of Visual Double Stars, 1961.0. As Jeffers approached retirement he became greatly concerned about the disposition of the catalogues. He wanted to be replaced by another "double star man," but Lick Director Albert E. Whitford (1905-2002) had the new 120-inch reflector, the world’s second largest telescope, and he wanted to pursue modern astrophysics instead. Jeffers was vociferously opposed to turning over the card files to another institution, and especially against their coming under the control of Kaj Strand of the U.S. Naval Observatory. In the end the USNO got the files and has maintained the records ever since, first under Charles Worley (1935-1997), and, since 1997, under Brian Mason. Now called the Washington Double Star Catalog (WDS), it is completely online and currently contains more than 1,000,000 measures of more than 100,000 pairs.
Process modelling on a canonical basis[Process modelling; Canonical modelling
Siepmann, Volker
2006-12-20
Based on an equation oriented solving strategy, this thesis investigates a new approach to process modelling. Homogeneous thermodynamic state functions represent consistent mathematical models of thermodynamic properties. Such state functions of solely extensive canonical state variables are the basis of this work, as they are natural objective functions in optimisation nodes to calculate thermodynamic equilibrium regarding phase-interaction and chemical reactions. Analytical state function derivatives are utilised within the solution process as well as interpreted as physical properties. By this approach, only a limited range of imaginable process constraints are considered, namely linear balance equations of state variables. A second-order update of source contributions to these balance equations is obtained by an additional constitutive equation system. These equations are general dependent on state variables and first-order sensitivities, and cover therefore practically all potential process constraints. Symbolic computation technology efficiently provides sparsity and derivative information of active equations to avoid performance problems regarding robustness and computational effort. A benefit of detaching the constitutive equation system is that the structure of the main equation system remains unaffected by these constraints, and a priori information allows to implement an efficient solving strategy and a concise error diagnosis. A tailor-made linear algebra library handles the sparse recursive block structures efficiently. The optimisation principle for single modules of thermodynamic equilibrium is extended to host entire process models. State variables of different modules interact through balance equations, representing material flows from one module to the other. To account for reusability and encapsulation of process module details, modular process modelling is supported by a recursive module structure. The second-order solving algorithm makes it
Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity
Claudio Cremaschini
2017-07-01
Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.
Hamilton formalism and Noether symmetry for mechanico-electrical systems with fractional derivatives
Zhang Shi-Hua; Chen Ben-Yong; Fu Jing-Li
2012-01-01
This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives.The Euler-Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established.The definition and the criteria for the fractional generalized Noether quasisymmetry are presented. Furthermore,the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations.An example is presented to illustrate the application of the results.
Scalar particles emission from black holes with topological defects using Hamilton-Jacobi method
Jusufi, Kimet
2015-01-01
We study quantum tunneling of charged and uncharged scalar particles from the event horizon of Schwarzschild-de Sitter and Reissner-Nordstr\\"{o}m-de Sitter black holes pierced by an infinitely long spinning cosmic string and a global monopole. In order to find the Hawking temperature and the tunneling probability we solve the Klein-Gordon equation by using the Hamilton-Jacobi method and WKB approximation. We show that Hawking temperature is independent of the presence of topological defects in both cases.
Scalar particles emission from black holes with topological defects using Hamilton-Jacobi method
Jusufi, Kimet
2015-11-01
We study quantum tunneling of charged and uncharged scalar particles from the event horizon of Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black holes pierced by an infinitely long spinning cosmic string and a global monopole. In order to find the Hawking temperature and the tunneling probability we solve the Klein-Gordon equation by using the Hamilton-Jacobi method and WKB approximation. We show that Hawking temperature is independent of the presence of topological defects in both cases.
Spin Foams and Canonical Quantization
Alexandrov, Sergei; Noui, Karim
2011-01-01
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization \\`a la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.
Periodicity, the Canon and Sport
Thomas F. Scanlon
2015-10-01
Full Text Available The topic according to this title is admittedly a broad one, embracing two very general concepts of time and of the cultural valuation of artistic products. Both phenomena are, in the present view, largely constructed by their contemporary cultures, and given authority to a great extent from the prestige of the past. The antiquity of tradition brings with it a certain cachet. Even though there may be peripheral debates in any given society which question the specifics of periodization or canonicity, individuals generally accept the consensus designation of a sequence of historical periods and they accept a list of highly valued artistic works as canonical or authoritative. We will first examine some of the processes of periodization and of canon-formation, after which we will discuss some specific examples of how these processes have worked in the sport of two ancient cultures, namely Greece and Mesoamerica.
Estimating Resilience by Canonical Analysis
Fiering, Myron B.
1982-02-01
Canonical correlation analysis is used to formulate linear estimates of independent or orthogonal (incremental) information on the performance of water resource systems. Simple economic and resilience indicators are compared, and for the particular configurations chosen in this paper the replicated and independent information sets are explained in terms of the connectivity of the various reservoirs. The canonical correlations are relatively high, indicating that there is significant replication of information; a taxonomy is developed which suggests those basin and structural characteristics which would indicate less replication and consequently improved description of system performance. The procedure is based on simulation studies reported in an earlier paper in this series.
Sl$_{q}$(2) realizations for Kepler and oscillator potentials and q-canonical transformations
Dayi, O F; Dayi, O F; Duru, I H
1994-01-01
The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for q-canonical transformation is deduced. q-Schr\\"{o}dinger equation for a Kepler like potential is obtained from the q-oscillator Schr\\"{o}dinger equation. Energy spectrum and the ground state wave function are calculated.
Quantum canonical tensor model and an exact wave function
Sasakura, Naoki
2013-01-01
Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints has structure functions, and provides an algebraically consistent way of discretizing the Dirac first-class constraint algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt scheme of quantization of the canonical tensor model; the ordering of operators in the constraints is determined without ambiguity by imposing Hermiticity and covariance on the constraints, and the commutation algebra of constraints takes essentially the same from as the classical Poisson algebra, i.e. is first-class. Thus one could consistently obtain, at least locally in the configuration space, wave functions of "universe" by solving the partial differential equations representing the constraints, i.e. the Wheeler...
Canonical Transformations can Dramatically Simplify Supersymmetry
Dixon, John
2016-01-01
A useful way to keep track of the SUSY invariance of a theory is by formulating it with a BRST Poisson Bracket. It turns out that there is a crucial subtlety that is hidden in this formulation. When the theory contains a Chiral Multiplet, the relevant BRST Poisson Bracket has a very important Canonical Transformation that leaves it invariant. This Canonical Transformation takes all or part of the Scalar Field $A$ and replaces it with a Zinn Source $J_A$, and also takes the related Zinn Source $\\Gamma_A$ and replaces it with an `Antighost' Field $\\eta_A$. Naively, this looks like it is just a change of notation. But in fact the interpretation means that one has moved some of the conserved Noether SUSY current from the Field Action, and placed it partly in the Zinn Sources Action, and so the SUSY current in the Field part of the Action is no longer conserved, because the Zinn Sources do not satisfy any equations of motion. They are not quantized, because they are Sources. So it needs to be recognized that SUSY ...
Romanticism, Sexuality, and the Canon.
Rowe, Kathleen K.
1990-01-01
Traces the Romanticism in the work and persona of film director Jean-Luc Godard. Examines the contradictions posed by Godard's politics and representations of sexuality. Asserts, that by bringing an ironic distance to the works of such canonized directors, viewers can take pleasure in those works despite their contradictions. (MM)
Romanticism, Sexuality, and the Canon.
Rowe, Kathleen K.
1990-01-01
Traces the Romanticism in the work and persona of film director Jean-Luc Godard. Examines the contradictions posed by Godard's politics and representations of sexuality. Asserts, that by bringing an ironic distance to the works of such canonized directors, viewers can take pleasure in those works despite their contradictions. (MM)
Resistant multiple sparse canonical correlation.
Coleman, Jacob; Replogle, Joseph; Chandler, Gabriel; Hardin, Johanna
2016-04-01
Canonical correlation analysis (CCA) is a multivariate technique that takes two datasets and forms the most highly correlated possible pairs of linear combinations between them. Each subsequent pair of linear combinations is orthogonal to the preceding pair, meaning that new information is gleaned from each pair. By looking at the magnitude of coefficient values, we can find out which variables can be grouped together, thus better understanding multiple interactions that are otherwise difficult to compute or grasp intuitively. CCA appears to have quite powerful applications to high-throughput data, as we can use it to discover, for example, relationships between gene expression and gene copy number variation. One of the biggest problems of CCA is that the number of variables (often upwards of 10,000) makes biological interpretation of linear combinations nearly impossible. To limit variable output, we have employed a method known as sparse canonical correlation analysis (SCCA), while adding estimation which is resistant to extreme observations or other types of deviant data. In this paper, we have demonstrated the success of resistant estimation in variable selection using SCCA. Additionally, we have used SCCA to find multiple canonical pairs for extended knowledge about the datasets at hand. Again, using resistant estimators provided more accurate estimates than standard estimators in the multiple canonical correlation setting. R code is available and documented at https://github.com/hardin47/rmscca.
Geometrical Field Theory of Hamilton Dynamic System In Rational Mechanics
Jianhua, Xiao
2011-01-01
When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is originated from the fact that the motion in time domain and the motion in spatial domain are coupled together completely. Generally, for a Hamilton dynamic system established by a set of general velocity functions, several abstract theories have been well established, such as Lie algebra, Symplectic manifold, Poisson brackets, and others. However, mathematically, to find out a general Hamilton function is very difficult even for very simple problems. Inspired by these abstract mathematic researches, the Hamilton dynamic system is studied by geometrical field theory of deformation. Firstly, referring to the instant configuration, the deformation tensor in spatial domain and the velocity transformation tensor in time domain are established for a dynamic system defined by a set of gen...
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Klein-Gordon-Wheeler-DeWitt-Schroedinger Equation
Pavsic, Matej
2011-01-01
We start from the Einstein-Hilbert action for the gravitational field in the presence of a point particle source, and cast the action into the corresponding phase space form. The dynamical variables of such a system satisfy the point particle mass shell constraint, the Hamilton and the momentum constraints of the canonical gravity. In the quantized theory, those constraints become operators that annihilate a state. A state can be represented by a wave functional $\\Psi$ that simultaneously satisfies the Klein-Gordon and the Wheeler-DeWitt-Schr\\"odinger equation. The latter equation, besides the term due to gravity, also contains the Schr\\"odinger like term, namely the derivative of $\\Psi$ with respect to time, that occurs because of the presence of the point particle. The particle's time coordinate, $X^0$, serves the role of time. Next, we generalize the system to $p$-branes, and find out that for a quantized spacetime filling brane there occurs an effective cosmological constant, proportional to the expectati...
The Transport of Relative Canonical Helicity
You, Setthivoine
2012-01-01
The evolution of relative canonical helicity is examined in the two-fluid magnetohydrodynamic formalism. Canonical helicity is defined here as the helicity of the plasma species' canonical momentum. The species' canonical helicity are coupled together and can be converted from one into the other while the total gauge-invariant relative canonical helicity remains globally invariant. The conversion is driven by enthalpy differences at a surface common to ion and electron canonical flux tubes. The model provides an explanation for why the threshold for bifurcation in counter-helicity merging depends on the size parameter. The size parameter determines whether magnetic helicity annihilation channels enthalpy into the magnetic flux tube or into the vorticity flow tube components of the canonical flux tube. The transport of relative canonical helicity constrains the interaction between plasma flows and magnetic fields, and provides a more general framework for driving flows and currents from enthalpy or inductive b...
Modern Canonical Quantum General Relativity
Thiemann, Thomas
2008-11-01
Preface; Notation and conventions; Introduction; Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity; 2. The problem of time, locality and the interpretation of quantum mechanics; 3. The programme of canonical quantisation; 4. The new canonical variables of Ashtekar for general relativity; Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II: quantum-algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1. Implementation and solution of the kinematical constraints; 10. Step V: 2. Implementation and solution of the Hamiltonian constraint; 11. Step VI: semiclassical analysis; Part III. Physical Applications: 12. Extension to standard matter; 13. Kinematical geometrical operators; 14. Spin foam models; 15. Quantum black hole physics; 16. Applications to particle physics and quantum cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology; 19. Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field theories with constraints; 25. Tools from measure theory; 26. Elementary introduction to Gel'fand theory for Abelean C* algebras; 27. Bohr compactification of the real line; 28. Operatir -algebras and spectral theorem; 29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network functions for SU(2); 32. + Functional analytical description of classical connection dynamics; Bibliography; Index.
Canonical reduction for dilatonic gravity in 3+1 dimensions
Scott, T C; Mann, R B; Fee, G J
2016-01-01
We generalize the 1+1-dimensional gravity formalism of Ohta and Mann to 3+1 dimensions by developing the canonical reduction of a proposed formalism applied to a system coupled with a set of point particles. This is done via the Arnowitt-Deser-Misner method and by eliminating the resulting constraints and imposing coordinate conditions. The reduced Hamiltonian is completely determined in terms of the particles' canonical variables (coordinates, dilaton field and momenta). It is found that the equation governing the dilaton field under suitable gauge and coordinate conditions, including the absence of transverse-traceless metric components, is a logarithmic Schroedinger equation. Thus, although different, the 3+1 formalism retains some essential features of the earlier 1+1 formalism, in particular the means of obtaining a quantum theory for dilatonic gravity.
Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
Kober, Martin
2011-01-01
General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the noncommutativity algebra of the coordinates in the canonical case of noncommutative geometry, this idea is closely related to noncommutative geometry as well as to canonical quantization of gravity. According to this presupposition there are derived generalized field equations for general relativity which are obtained by replacing the usual tetrad field by the tetrad field operator within the actions and then building expectation values of the corresponding field equations between coherent states. These coherent states refer to creation and annihilation operators created from the components of the tetrad field operator. In this sense the obtained theory could be regarded as a kind of semiclassical approximation of a complete quantum description of gravity. The consideration pr...
A Quantum Algorithm for Finding a Hamilton Circuit
GUO Hao; LONG Gui-Lu; SUN Yang; XIU Xiao-Lin
2001-01-01
A quantum algorithm for solving the classical NP-complete problem - the Hamilton circuit is presented. The algorithm employs the quantum SAT and the quantum search algorithms. The algorithm is square-root faster than classical algorithm, and becomes exponentially faster than classical algorithm if nonlinear quantum mechanical computer is used.
Hamilton´s Principle and Electric Circuits Tudory
Daniel Mayer
2006-01-01
Full Text Available In the theory of electrical or electromechanical circuits different methods are known for construction of mathematical model. In this paper another, alternative method is introduced that is based on Hamilton variational principle that is generally valid in physics.
Spin Hamilton Operators, Symmetry Breaking, Energy Level Crossing and Entanglement
Steeb, Willi-Hans; Hardy, Yorick; de Greef, Jacqueline
2011-01-01
We study finite-dimensional product Hilbert spaces, coupled spin systems, entanglement and energy level crossing. The Hamilton operators are based on the Pauli group. We show that swapping the interacting term can lead from unentangled eigenstates to entangled eigenstates and from an energy spectrum with energy level crossing to avoided energy level crossing.
Hojman Exact Invariants and Adiabatic Invariants of Hamilton System
无
2007-01-01
The perturbation to Lie symmetry and adiabatic invariants are studied. Based on the concept of higherorder adiabatic invariants of mechanical systems with action of a small perturbation, the perturbation to Lie symmetry is studied, and Hojman adiabatic invariants of Hamilton system are obtained. An example is given to illustrate the application of the results.
Hamilton,Sir William Rowan(1805-1865)
2002-01-01
Shortly after Hamilton submitted his paper and while still an undergraduate,Trinity College elected him to the post of Andrews professor of astronomy and royal astronomer of Ireland’ to succeed Brinkley,who had been made a bishop. Thus an undergraduate(not quite 22years old) became ex officio an examiner of graduates who were candidates
Unconventional Hamilton-type variational principles for analytical mechanics
2007-01-01
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper.
Unconventional Hamilton-type variational principles for analytical mechanics
LUO En; LIANG LiFu; LI WeiHua
2007-01-01
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper.
Dirac equation of spin particles and tunneling radiation from a Kinnersly black hole
Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Feng, Zhong-Wen [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Li, Hui-Ling [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Shenyang Normal University, College of Physics Science and Technology, Shenyang (China)
2017-04-15
In curved space-time, the Hamilton-Jacobi equation is a semi-classical particle equation of motion, which plays an important role in the research of black hole physics. In this paper, starting from the Dirac equation of spin 1/2 fermions and the Rarita-Schwinger equation of spin 3/2 fermions, respectively, we derive a Hamilton-Jacobi equation for the non-stationary spherically symmetric gravitational field background. Furthermore, the quantum tunneling of a charged spherically symmetric Kinnersly black hole is investigated by using the Hamilton-Jacobi equation. The result shows that the Hamilton-Jacobi equation is helpful to understand the thermodynamic properties and the radiation characteristics of a black hole. (orig.)
A Spectral Canonical Electrostatic Algorithm
Webb, Stephen D
2015-01-01
Studying single-particle dynamics over many periods of oscillations is a well-understood problem solved using symplectic integration. Such integration schemes derive their update sequence from an approximate Hamiltonian, guaranteeing that the geometric structure of the underlying problem is preserved. Simulating a self-consistent system over many oscillations can introduce numerical artifacts such as grid heating. This unphysical heating stems from using non-symplectic methods on Hamiltonian systems. With this guidance, we derive an electrostatic algorithm using a discrete form of Hamilton's Principle. The resulting algorithm, a gridless spectral electrostatic macroparticle model, does not exhibit the unphysical heating typical of most particle-in-cell methods. We present results of this using a two-body problem as an example of the algorithm's energy- and momentum-conserving properties.
Derivation of Mayer Series from Canonical Ensemble
Wang, Xian-Zhi
2016-02-01
Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid (X.Z. Wang, Phys. Rev. E 66 (2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.
A practical approach to the Hamilton-Jacobi formulation of holographic renormalization
Elvang, Henriette; Hadjiantonis, Marios
2016-06-01
We revisit the subject of holographic renormalization for asymptotically AdS spacetimes. For many applications of holography, one has to handle the divergences associated with the on-shell gravitational action. The brute force approach uses the Fefferman- Graham (FG) expansion near the AdS boundary to identify the divergences, but subsequent reversal of the expansion is needed to construct the infinite counterterms. While in principle straightforward, the method is cumbersome and application/reversal of FG is formally unsatisfactory. Various authors have proposed an alternative method based on the Hamilton-Jacobi equation. However, this approach may appear to be abstract, difficult to implement, and in some cases limited in applicability. In this paper, we clarify the Hamilton-Jacobi formulation of holographic renormalization and present a simple algorithm for its implementation to extract cleanly the infinite counterterms. While the derivation of the method relies on the Hamiltonian formulation of general relativity, the actual application of our algorithm does not. The work applies to any D-dimensional holographic dual with asymptotic AdS boundary, Euclidean or Lorentzian, and arbitrary slicing. We illustrate the method in several examples, including the FGPW model, a holographic model of 3d ABJM theory, and cases with marginal scalars such as a dilaton-axion system.
A practical approach to the Hamilton-Jacobi formulation of holographic renormalization
Elvang, Henriette; Hadjiantonis, Marios [Department of Physics and Michigan Center for Theoretical Physics, University of Michigan,450 Church Str., Ann Arbor MI 48109 (United States)
2016-06-08
We revisit the subject of holographic renormalization for asymptotically AdS spacetimes. For many applications of holography, one has to handle the divergences associated with the on-shell gravitational action. The brute force approach uses the Fefferman-Graham (FG) expansion near the AdS boundary to identify the divergences, but subsequent reversal of the expansion is needed to construct the infinite counterterms. While in principle straightforward, the method is cumbersome and application/reversal of FG is formally unsatisfactory. Various authors have proposed an alternative method based on the Hamilton-Jacobi equation. However, this approach may appear to be abstract, difficult to implement, and in some cases limited in applicability. In this paper, we clarify the Hamilton-Jacobi formulation of holographic renormalization and present a simple algorithm for its implementation to extract cleanly the infinite counterterms. While the derivation of the method relies on the Hamiltonian formulation of general relativity, the actual application of our algorithm does not. The work applies to any D-dimensional holographic dual with asymptotic AdS boundary, Euclidean or Lorentzian, and arbitrary slicing. We illustrate the method in several examples, including the FGPW model, a holographic model of 3d ABJM theory, and cases with marginal scalars such as a dilaton-axion system.
Grand canonical Molecular Dynamics Simulations
Fritsch, S; Junghans, C; Ciccotti, G; Site, L Delle; Kremer, K
2011-01-01
For simulation studies of (macro-) molecular liquids it would be of significant interest to be able to adjust/increase the level of resolution within one region of space, while allowing for the free exchange of molecules between (open) regions of different resolution/representation. In the present work we generalize the adaptive resolution idea in terms of a generalized Grand Canonical approach. This provides a robust framework for truly open Molecular Dynamics systems. We apply the method to liquid water at ambient conditions.
Canonical metrics on complex manifold
YAU Shing-Tung
2008-01-01
@@ Complex manifolds are topological spaces that are covered by coordinate charts where the Coordinate changes are given by holomorphic transformations. For example, Riemann surfaces are one dimensional complex manifolds. In order to understand complex manifolds, it is useful to introduce metrics that are compatible with the complex structure. In general, we should have a pair (M, ds2M) where ds2M is the metric. The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries. Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
Canonical metrics on complex manifold
YAU; Shing-Tung(Yau; S.-T.)
2008-01-01
Complex manifolds are topological spaces that are covered by coordinate charts where the coordinate changes are given by holomorphic transformations.For example,Riemann surfaces are one dimensional complex manifolds.In order to understand complex manifolds,it is useful to introduce metrics that are compatible with the complex structure.In general,we should have a pair(M,ds~2_M)where ds~2_M is the metric.The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries.Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
What is "Relativistic Canonical Quantization"?
Arbatsky, D. A.
2005-01-01
The purpose of this review is to give the most popular description of the scheme of quantization of relativistic fields that was named relativistic canonical quantization (RCQ). I do not give here the full exact account of this scheme. But with the help of this review any physicist, even not a specialist in the relativistic quantum theory, will be able to get a general view of the content of RCQ, of its connection with other known approaches, of its novelty and of its fruitfulness.
A field theory approach to the evolution of canonical helicity and energy
You, Setthivoine
2016-01-01
A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.
A field theory approach to the evolution of canonical helicity and energy
You, S.
2016-07-01
A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.
A field theory approach to the evolution of canonical helicity and energy
You, S. [William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States)
2016-07-15
A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.
Almost Periodic Viscosity Solutions of Nonlinear Parabolic Equations
Zhang Shilin
2009-01-01
Full Text Available We generalize the comparison result 2007 on Hamilton-Jacobi equations to nonlinear parabolic equations, then by using Perron's method to study the existence and uniqueness of time almost periodic viscosity solutions of nonlinear parabolic equations under usual hypotheses.
Exact Vacuum Solutions to the Einstein Equation
无
2007-01-01
In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations,which are much convenient for the resolution.
Hamilton geometry: Phase space geometry from modified dispersion relations
Barcaroli, Leonardo; Gubitosi, Giulia; Loret, Niccoló; Pfeifer, Christian
2015-01-01
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\\kappa$-Poincar\\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.
Canonical and alternative MAPK signaling.
Pimienta, Genaro; Pascual, Jaime
2007-11-01
The archetype of MAPK cascade activation is somewhat challenged by the most recent discovery of unexpected phosphorylation patterns, alternative activation mechanisms and sub-cellular localization, in various members of this protein kinase family. In particular, activation by autophosphorylation pathways has now been described for the three best understood MAPK subgroups: ERK1/2; JNK1/2 and p38 alpha/beta. Also, a form of dosage compensation between homologs has been shown to occur in the case of ERK1/2 and JNK1/2. In this paper we summarize the MAPK activation pathway, with an emphasis on non-canonical examples. We use this information to propose a model for MAPK signal transduction that considers a cross-talk between MAPKs with different activation loop sequence motifs and unique C-terminal extensions. We highlight the occurrence of non-canonical substrate specificity during MAPK auto-activation, in strong connection with MAPK homo- and hetero-dimerization events.
Propagation of singularities for Schr\\"odinger equations with modestly long range type potentials
2013-01-01
In a previous paper by the second author, we discussed a characterization of the microlocal singularities for solutions to Schr\\"odinger equations with long range type perturbations, using solutions to a Hamilton-Jacobi equation. In this paper we show that we may use Dollard type approximate solutions to the Hamilton-Jacobi equation if the perturbation satisfies somewhat stronger conditions. As applications, we describe the propagation of microlocal singularities for $e^{itH_0}e^{-itH}$ when ...
Hamilton-Jacobi Many-Worlds Theory and the Heisenberg Uncertainty Principle
Tipler, Frank J
2010-01-01
I show that the classical Hamilton-Jacobi (H-J) equation can be used as a technique to study quantum mechanical problems. I first show that the the Schr\\"odinger equation is just the classical H-J equation, constrained by a condition that forces the solutions of the H-J equation to be everywhere $C^2$. That is, quantum mechanics is just classical mechanics constrained to ensure that ``God does not play dice with the universe.'' I show that this condition, which imposes global determinism, strongly suggests that $\\psi^*\\psi$ measures the density of universes in a multiverse. I show that this interpretation implies the Born Interpretation, and that the function space for $\\psi$ is larger than a Hilbert space, with plane waves automatically included. Finally, I use H-J theory to derive the momentum-position uncertainty relation, thus proving that in quantum mechanics, uncertainty arises from the interference of the other universes of the multiverse, not from some intrinsic indeterminism in nature.
Sir William Rowan Hamilton: Life, Achievements, Stature in Physics
2016-06-01
Against the background of the development ofphysics, and in particular of mechanics, over thecenturies since Galileo and Newton, we describethe life and work of William Rowan Hamilton inthe 19th century. The depth of his ideas whichbrought together the understanding of ray opticsand classical mechanics, and the remarkableways in which his work paved the way to theconstruction of quantum mechanics in the 20thcentury, are emphasized.
Hamilton,Sir William Rowan(1805-1865)
2002-01-01
Irish mathematician and astronomer who developed the theory of quaternions, a landmark in the development of algebra,and discovered the phenomenon of conical refraction. His unification of dynamics and optics,moreover,has had alasting influence on mathematical physics, even though the full significance of his work was not fully appreciated until after the risd of quantum mechanics. Like his English contemporaries Thomas Babington Macaulay and John Stuart Mill,Hamilton showed
Hamilton-Jacobi method for molecular distribution function in a chemical oscillator.
Nakanishi, Hiizu; Sakaue, Takahiro; Wakou, Jun'ichi
2013-12-07
Using the Hamilton-Jacobi method, we solve chemical Fokker-Planck equations within the Gaussian approximation and obtain a simple and compact formula for a conditional probability distribution. The formula holds in general transient situations, and can be applied not only to a steady state but also to an oscillatory state. By analyzing the long time behavior of the solution in the oscillatory case, we obtain the phase diffusion constant along the periodic orbit and the steady distribution perpendicular to it. A simple method for numerical evaluation of these formulas are devised, and they are compared with Monte Carlo simulations in the case of Brusselator as an example. Some results are shown to be identical to previously obtained expressions.
Initialization of the Shooting Method via the Hamilton-Jacobi-Bellman Approach
Cristiani, Emiliano
2009-01-01
The aim of this paper is to investigate from the numerical point of view the possibility of coupling the Hamilton-Jacobi-Bellman (HJB) equation and Pontryagin's Minimum Principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniques (such as continuation or direct methods) is to provide an initial guess close to the global minimum. Numerical tests involving multiple minima, discontinuous control, singular arcs and state constraints are considered. The CPU time for the proposed method is less than four minutes up to dimension four, without code parallelization.
Hamilton-Jacobi formalism for inflation with non-minimal derivative coupling
Sheikhahmadi, Haidar; Saridakis, Emmanuel N.; Aghamohammadi, Ali; Saaidi, Khaled
2016-10-01
In inflation with nonminimal derivative coupling there is not a conformal transformation to the Einstein frame where calculations are straightforward, and thus in order to extract inflationary observables one needs to perform a detailed and lengthy perturbation investigation. In this work we bypass this problem by performing a Hamilton-Jacobi analysis, namely rewriting the cosmological equations considering the scalar field to be the time variable. We apply the method to two specific models, namely the power-law and the exponential cases, and for each model we calculate various observables such as the tensor-to-scalar ratio, and the spectral index and its running. We compare them with 2013 and 2015 Planck data, and we show that they are in a very good agreement with observations.
Holographic renormalization and Ward identities with the Hamilton-Jacobi method
Martelli, Dario E-mail: d.martelli@qmul.ac.uk; Mueck, Wolfgang E-mail: mueck@na.infn.it
2003-03-24
A systematic procedure for performing holographic renormalization, which makes use of the Hamilton-Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U(1) gauge field in the Stueckelberg formalism. We describe how the power divergences are obtained as solutions of a set of 'descent equations' stemming from the radial Hamiltonian constraint of the theory. In addition, we isolate the logarithmic divergences, which are closely related to anomalies. The method allows to determine also the exact one-point functions of the dual field theory. Using the other Hamiltonian constraints of the bulk theory, we derive the Ward identities for diffeomorphisms and gauge invariance. In particular, we demonstrate the breaking of U(1){sub R} current conservation, recovering the holographic chiral anomaly recently discussed in and.
Hamilton-Jacobi method for molecular distribution function in a chemical oscillator
Nakanishi, Hiizu; Sakaue, Takahiro; Wakou, Jun'ichi
2013-12-01
Using the Hamilton-Jacobi method, we solve chemical Fokker-Planck equations within the Gaussian approximation and obtain a simple and compact formula for a conditional probability distribution. The formula holds in general transient situations, and can be applied not only to a steady state but also to an oscillatory state. By analyzing the long time behavior of the solution in the oscillatory case, we obtain the phase diffusion constant along the periodic orbit and the steady distribution perpendicular to it. A simple method for numerical evaluation of these formulas are devised, and they are compared with Monte Carlo simulations in the case of Brusselator as an example. Some results are shown to be identical to previously obtained expressions.
The classical limit of minimal length uncertainty relation: revisit with the Hamilton-Jacobi method
Guo, Xiaobo; Wang, Peng; Yang, Haitang
2016-05-01
The existence of a minimum measurable length could deform not only the standard quantum mechanics but also classical physics. The effects of the minimal length on classical orbits of particles in a gravitation field have been investigated before, using the deformed Poisson bracket or Schwarzschild metric. In this paper, we first use the Hamilton-Jacobi method to derive the deformed equations of motion in the context of Newtonian mechanics and general relativity. We then employ them to study the precession of planetary orbits, deflection of light, and time delay in radar propagation. We also set limits on the deformation parameter by comparing our results with the observational measurements. Finally, comparison with results from previous papers is given at the end of this paper.
On a Lagrange-Hamilton formalism describing position and momentum uncertainties
Schuch, Dieter
1993-01-01
According to Heisenberg's uncertainty relation, in quantum mechanics it is not possible to determine, simultaneously, exact values for the position and the momentum of a material system. Calculating the mean value of the Hamiltonian operator with the aid of exact analytic Gaussian wave packet solutions, these uncertainties cause an energy contribution additional to the classical energy of the system. For the harmonic oscillator, e.g., this nonclassical energy represents the ground state energy. It will be shown that this additional energy contribution can be considered as a Hamiltonian function, if it is written in appropriate variables. With the help of the usual Lagrange-Hamilton formalism known from classical particle mechanics, but now considering this new Hamiltonian function, it is possible to obtain the equations of motion for position and momentum uncertainties.
Hamilton-Jacobi formalism for inflation with non-minimal derivative coupling
Sheikhahmadi, Haidar; Aghamohammadi, Ali; Saaidi, Khaled
2016-01-01
In inflation with nonminimal derivative coupling there is not a conformal transformation to the Einstein frame where calculations are straightforward, and thus in order to extract inflationary observables one needs to perform a detailed and lengthy perturbation investigation. In this work we bypass this problem by performing a Hamilton-Jacobi analysis, namely rewriting the cosmological equations considering the scalar field to be the time variable. We apply the method to two specific models, namely the power-law and the exponential cases, and for each model we calculate various observables such as the tensor-to-scalar ratio, and the spectral index and its running. We compare them with 2013 and 2015 Planck data, and we show that they are in a very good agreement with observations.
Unconventional Hamilton-type variational principles for nonlinear coupled thermoelastodynamics
罗恩; 邝君尚; 黄伟江; 罗志国
2002-01-01
According to the basic idea of classical yin-yang complementarity and modem dual-com plementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type vari ational principles for geometrically nonlinear coupled thermoelastodynamics can be established system atically. The new unconventional Hamilton-type variational principle can fully characterize the initia boundary-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for geometrically nonlin ear coupled thermodynamics. Based on this relation, it is possible not only to obtain the principle of vir tual work in geometrically nonlinear coupled thermodynamics, but also to derive systematically the complementary functionals for eight-field, six-field, four-field and two-field unconventional Hamilton type variational principles by the generalized Legendre transformations given in this paper. Further more, with this approach, the intrinsic relationship among various principles can be explained clearly.
Ignat'ev, Yu G
2013-01-01
On the basis of Hamilton a formalism the dynamic equations of movement scalar charged particles in a classical scalar field are formulated. Unlike earlier published works of the author the model with zero own weight of particles is considered. Linear integrals of movement are found and ambiguity of communication between kinematic speed and an impulse of particles is specified.
Dynamic equations for curved submerged floating tunnel
无
2007-01-01
In virtue of reference Cartesian coordinates, geometrical relations of spatial curved structure are presented in orthogonal curvilinear coordinates. Dynamic equations for helical girder are derived by Hamilton principle. These equations indicate that four generalized displacements are coupled with each other. When spatial structure degenerates into planar curvilinear structure, two generalized displacements in two perpendicular planes are coupled with each other. Dynamic equations for arbitrary curvilinear structure may be obtained by the method used in this paper.
Knud Jeppesen
2003-11-01
Full Text Available The Psalter, read as a coherent book instead of being read as 150 independent poems, reveals some patterns and a continuum of ideas, which might not express the editors’ original intention, but support the readers’ understanding of this canonical book. The article suggests that, even if the majority of texts are laments, the Psalter is a book of praise, underlined for instance by the endings of the Psalter’s five books. The five books relate the Psalter to the Pentateuch, and a form of competition between David and Moses is found (see esp Book 4, of which David was the winner. This is one of the reasons why the Christians were able to read the Psalter as a Christian book.
Canonical curves with low apolarity
Ballico, Edoardo; Notari, Roberto
2010-01-01
Let $k$ be an algebraically closed field and let $C$ be a non--hyperelliptic smooth projective curve of genus $g$ defined over $k$. Since the canonical model of $C$ is arithmetically Gorenstein, Macaulay's theory of inverse systems allows to associate to $C$ a cubic form $f$ in the divided power $k$--algebra $R$ in $g-2$ variables. The apolarity of $C$ is the minimal number $t$ of linear form in $R$ needed to write $f$ as sum of their divided power cubes. It is easy to see that the apolarity of $C$ is at least $g-2$ and P. De Poi and F. Zucconi classified curves with apolarity $g-2$ when $k$ is the complex field. In this paper, we give a complete, characteristic free, classification of curves $C$ with apolarity $g-1$ (and $g-2$).
Hansen, Jesper Bent; Bech, Per
2011-01-01
-reporting versions (definitely and semidefinitely anchored) corresponding to the Hamilton Depression Scale (HAMD), the Hamilton Subscale (HAM6), and the Bech-Rafaelsen Melancholia Scale (MES) were compared to each other and the clinician-rated version. The unidimensional property of the sum score in each scale...
Nimon, Kim; Henson, Robin K.; Gates, Michael S.
2010-01-01
In the face of multicollinearity, researchers face challenges interpreting canonical correlation analysis (CCA) results. Although standardized function and structure coefficients provide insight into the canonical variates produced, they fall short when researchers want to fully report canonical effects. This article revisits the interpretation of…
Guibout, Vincent M.
This dissertation has been motivated by the need for new methods to address complex problems that arise in spacecraft formation design. As a direct result of this motivation, a general methodology for solving two-point boundary value problems for Hamiltonian systems has been found. Using the Hamilton-Jacobi theory in conjunction with the canonical transformation induced by the phase flow, it is shown that generating functions solve two-point boundary value problems. Traditional techniques for addressing these problems are iterative and require an initial guess. The method presented in this dissertation solves boundary value problems at the cost of a single function evaluation, although it requires knowledge of at least one generating function. Properties of this method are presented. Specifically, we show that it includes perturbation theory and generalizes it to nonlinear systems. Most importantly, it predicts the existence of multiple solutions and allows one to recover all of these solutions. To demonstrate the efficiency of this approach, an algorithm for computing the generating functions is proposed and its convergence properties are studied. As the method developed in this work is based on the Hamiltonian structure of the problem, particular attention must be paid to the numerics of the algorithm. To address this, a general framework for studying the discretization of certain dynamical systems is developed. This framework generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent and cotangent bundles respectively. In addition, it provides new insights into some symplectic integrators and leads to a new discrete Hamilton-Jacobi theory. Most importantly, it allows one to discretize optimal control problems. In particular, a discrete maximum principle is presented. This dissertation also investigates applications of the proposed method to solve two-point boundary value problems. In particular, new techniques for designing
Hamilton principle for the dual electrodynamics; Principio de Hamilton para a eletrodinamica dual
Souza Silva, Saulo Carneiro de
1995-12-31
The present work discusses the classical electromagnetic theory in the presence of magnetic monopoles. We review the connection between such objects and the long standing problem of charge quantization and the main theoretical difficulties in formulating the classical dual electromagnetic theory in terms of an action principle. We show that a deeper understanding of the source of such difficulties leads naturally to the construction of a variational principle for a non-local Lagrangian from which all the (local) dynamical equations for electric, magnetic charges and fields can be obtained. (author) 53 refs.
McGann, M; Dewar, R L; von Nessi, G
2010-01-01
The vanishing of the divergence of the total stress tensor (magnetic plus kinetic) in a neighborhood of an equilibrium plasma containing a toroidal surface of discontinuity gives boundary and jump conditions that strongly constrain allowable continuations of the magnetic field across the surface. The boundary conditions allow the magnetic fields on either side of the discontinuity surface to be described by surface magnetic potentials, reducing the continuation problem to that of solving a Hamilton--Jacobi equation. The characteristics of this equation obey Hamiltonian equations of motion, and a necessary condition for the existence of a continued field across a general toroidal surface is that there exist invariant tori in the phase space of this Hamiltonian system. It is argued from the Birkhoff theorem that existence of such an invariant torus is also, in general, sufficient for continuation to be possible. An important corollary is that the rotational transform of the continued field on a surface of disco...
The Current Canon in British Romantics Studies.
Linkin, Harriet Kramer
1991-01-01
Describes and reports on a survey of 164 U.S. universities to ascertain what is taught as the current canon of British Romantic literature. Asserts that the canon may now include Mary Shelley with the former standard six major male Romantic poets, indicating a significant emergence of a feminist perspective on British Romanticism in the classroom.…
De canon : een oude katholieke kerkstructuur?
Smit, P.B.A.
2011-01-01
Op 30 november 2011 houdt theoloog prof. dr. Peter-Ben Smit zijn oratie aan de Universiteit Utrecht. Daarin gaat hij na hoe de canon van het Nieuwe Testament tot stand kwam binnen de vroege kerk, en wat de functie van de canon was bij de uitleg - oftewel exegese - van de Schrift. Dit onderwerp kwam
CANONICAL EXTENSIONS OF SYMMETRIC LINEAR RELATIONS
Sandovici, Adrian; Davidson, KR; Gaspar, D; Stratila, S; Timotin, D; Vasilescu, FH
2006-01-01
The concept of canonical extension of Hermitian operators has been recently introduced by A. Kuzhel. This paper deals with a generalization of this notion to the case of symmetric linear relations. Namely, canonical regular extensions of symmetric linear relations in Hilbert spaces are studied. The
Canonical structure of 2D black holes
Navarro-Salas, J; Talavera, C F
1994-01-01
We determine the canonical structure of two-dimensional black-hole solutions arising in $2D$ dilaton gravity. By choosing the Cauchy surface appropriately we find that the canonically conjugate variable to the black hole mass is given by the difference of local (Schwarzschild) time translations at right and left spatial infinities. This can be regarded as a generalization of Birkhoff's theorem.
Subsets of configurations and canonical partition functions
Bloch, J.; Bruckmann, F.; Kieburg, M.;
2013-01-01
We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: the subset sum over configurations is shown to project out the canonical determinant with zero quark charge from a given configuration. As the grand canonical chiral random matrix partition...
The canonical controller and its regularity
Willems, Jan C.; Belur, Madhu N.; Anak Agung Julius, A.A.J.; Trentelman, Harry L.
2003-01-01
This paper deals with properties of canonical controllers. We first specify the behavior that they implement. It follows that a canonical controller implements the desired controlled behavior if and only if the desired behavior is implementable. We subsequently investigate the regularity of the cont
A Graphical representation of the grand canonical partition function
Smii, Boubaker
2010-01-01
In this paper we consider a stochastic partial differential equation defined on a Lattice $L_\\delta$ with coefficients of non-linearity with degree $p$. An analytic solution in the sense of formal power series is given. The obtained series can be re-expressed in terms of rooted trees with two types of leaves. Under the use of the so-called Cole-Hopf transformation and for the particular case $p=2$, one thus get the generalized Burger equation. A graphical representation of the solution and its logarithm is done in this paper. A discussion of the summability of the previous formal solutions is done in this paper using Borel sum. A graphical calculus of the correlation function is given. The special case when the noise is of L\\'evy type gives a simplified representations of the solution of the generalized Burger equation. From the previous results we recall a graphical representation of the grand canonical partition function.
Canon, Jubilees 23 and Psalm 90
Pieter M. Venter
2014-02-01
Full Text Available There never existed only one form of the biblical canon. This can be seen in the versions as well as editions of the Hebrew and Greek Bibles. History and circumstances played a central role in the gradual growth of eventually different forms of the biblical canon. This process can be studied using the discipline of intertextuality. There always was a movement from traditum to traditio in the growth of these variant forms of biblical canon. This can be seen in an analysis of the intertextuality in Jubilees 23:8–32. The available canon of the day was interpreted there, not according to a specific demarcated volume of canonical scriptures, but in line with the theology presented in those materials, especially that of Psalm 90.
Nuclear power and the Hamilton-Jefferson debate
Hacker, A.
The basic sources of nuclear opposition derive from the philosophical arguments of Thomas Jefferson against Alexander Hamilton's vision of an industrial society with a strong central authority. Today's young people continue Jefferson's radical plea for the individual freedoms associated with personal ownership and limited government, but they accept the structure of the former while searching for the romanticism of the latter. The nuclear debate reflects this dichotomy and will continue even if the issues of waste disposal and safety are resolved. (DCK)
The Hamilton-Jacobi method and Hamiltonian maps
Abdullaev, S.S. [Institut fuer Plasmaphysik, Forschungszentrum Juelich GmbH, EURATOM Association, Trilateral Euregio Cluster, Juelich (Germany)
2002-03-29
A method for constructing time-step-based symplectic maps for a generic Hamiltonian system subjected to perturbation is developed. Using the Hamilton-Jacobi method and Jacobi's theorem in finite periodic time intervals, the general form of the symplectic maps is established. The generating function of the map is found by the perturbation method in the finite time intervals. The accuracy of the maps is studied for fully integrable and partially chaotic Hamiltonian systems and compared to that of the symplectic integration method. (author)
The Hamilton-Jacobi method and Hamiltonian maps
Abdullaev, S. S.
2002-03-01
A method for constructing time-step-based symplectic maps for a generic Hamiltonian system subjected to perturbation is developed. Using the Hamilton-Jacobi method and Jacobi's theorem in finite periodic time intervals, the general form of the symplectic maps is established. The generating function of the map is found by the perturbation method in the finite time intervals. The accuracy of the maps is studied for fully integrable and partially chaotic Hamiltonian systems and compared to that of the symplectic integration method.
Hamilton and Hardy for the 21st Century
Ogden, Trevor
2016-01-01
Hamilton and Hardy’s Industrial Toxicology is now 80 years old, and the new sixth edition links us with a pioneer era. This is an impressive book, but the usefulness of the hardback version as a reference book is unfortunately limited by its poor index. There is now an ebook version, and for the practitioner on the move this has the great advantages of searchability and portability. However, Wiley ebooks can apparently only be downloaded when first purchased, so their lifetime is limited to that of the device. The Kindle edition should avoid this shortcoming.
Multiplicity fluctuations in heavy-ion collisions using canonical and grand-canonical ensemble
Garg, P. [Indian Institute of Technology Indore, Discipline of Physics, School of Basic Science, Simrol (India); Mishra, D.K.; Netrakanti, P.K.; Mohanty, A.K. [Bhabha Atomic Research Center, Nuclear Physics Division, Mumbai (India)
2016-02-15
We report the higher-order cumulants and their ratios for baryon, charge and strangeness multiplicity in canonical and grand-canonical ensembles in ideal thermal model including all the resonances. When the number of conserved quanta is small, an explicit treatment of these conserved charges is required, which leads to a canonical description of the system and the fluctuations are significantly different from the grand-canonical ensemble. Cumulant ratios of total-charge and net-charge multiplicity as a function of collision energies are also compared in grand-canonical ensemble. (orig.)
Towards a loop representation for quantum canonical supergravity
Gambini, R; Pullin, J
1995-01-01
We study several aspects of the canonical quantization of supergravity in terms of the Asthekar variables. We cast the theory in terms of a GSU(2) connection and we introduce a loop representation. The solution space is remarkably similar to the loop representation of ordinary gravity, the main difference being the form of the Mandelstam identities. Physical states are in general given by knot invariants that are compatible with the GSU(2) Mandelstam identities. There is an explicit solution to all the quantum constraint equations connected with the Chern-Simons form, which leads to a new knot invariant polynomial in the loop representation.
Parametric Potential Determination by the Canonical Function Method
Tannous, C; Langlois, J M
1999-01-01
The canonical function method (CFM) is a powerful means for solving the Radial Schrodinger Equation. The mathematical difficulty of the RSE lies in the fact it is a singular boundary value problem. The CFM turns it into a regular initial value problem and allows the full determination of the spectrum of the Schrodinger operator without calculating the eigenfunctions. Following the parametrisation suggested by Klapisch and Green, Sellin and Zachor we develop a CFM to optimise the potential parameters in order to reproduce the experimental Quantum Defect results for various Rydberg series of He, Ne and Ar as evaluated from Moore's data.
Energy Conservation Equations of Motion
Vinokurov, Nikolay A
2015-01-01
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities that is called energy is constant. This paper presents an alternative approach, namely derivation of a general form of equations of motion that keep the system energy, expressed as a function of generalized coordinates and corresponding velocities, constant. These are Lagrange equations with addition of gyroscopic forces. The important fact, that the energy is defined as the function on the tangent bundle of configuration manifold, is used explicitly for the derivation. The Lagrangian is derived from a known energy function. A development of generalized Hamilton and Lagrange equations without the use of variational principles is proposed. The use of new technique is applied to derivation of some equations.
THE HAMILTONIAN EQUATIONS IN SOME MATHEMATICS AND PHYSICS PROBLEMS
陈勇; 郑宇; 张鸿庆
2003-01-01
Some new Hamiltonian canonical system are discussed for a series of partialdifferential equations in Mathematics and Physics. It includes the Hamiltonian formalism forthe symmetry second-order equation with the variable coefficients, the new nonhomogeneousHamiltonian representation for fourth-order symmetry equation with constant coefficients,the one of MKdV equation and KP equation.
Li, Zhendong; Liu, Wenjian
2016-01-01
Complicated mathematical equations involving tensors with permutation symmetries are frequently encountered in fields such as quantum chemistry, e.g., those in coupled cluster theories and derivatives of wavefunction parameters. In automatic derivations of these equations, a key step is the collection of product terms that can be found identical by using permutation symmetries or relabelling dummy indices. In the present work, we define a canonical form for a general tensor product in the presence of permutation symmetries as a result of the classification of all tensor products from a group theoretical point of view. To make such definition of practical use, we provide an efficient algorithm to compute the canonical form by combining the classical backtrack search for permutation groups and the idea of partitions used in graph isomorphism algorithms. The resulted algorithm can compute canonical forms and generators of the automorphism groups of tensor expressions. Moreover, for tensor products with external ...
Regularized canonical correlation analysis with unlabeled data
Xi-chuan ZHOU; Hai-bin SHEN
2009-01-01
In standard canonical correlation analysis (CCA), the data from definite datasets are used to estimate their canonical correlation. In real applications, for example in bilingual text retrieval, it may have a great portion of data that we do not know which set it belongs to. This part of data is called unlabeled data, while the rest from definite datasets is called labeled data. We propose a novel method called regularized canonical correlation analysis (RCCA), which makes use of both labeled and unlabeled samples. Specifically, we learn to approximate canonical correlation as if all data were labeled. Then. we describe a generalization of RCCA for the multi-set situation. Experiments on four real world datasets, Yeast, Cloud, Iris, and Haberman, demonstrate that,by incorporating the unlabeled data points, the accuracy of correlation coefficients can be improved by over 30%.
Hamilton-Jacobi method and effective actions of D-brane and M-brane in supergravity
Sato, Matsuo E-mail: machan@het.phys.sci.osaka-u.ac.jp; Tsuchiya, Asato E-mail: tsuchiya@het.phys.sci.osaka-u.ac.jp
2003-11-03
We show that the effective actions of D-brane and M-brane are solutions to the Hamilton-Jacobi (H-J) equations in supergravities. This fact means that these effective actions are on-shell actions in supergravities. These solutions to the H-J equations reproduce the supergravity solutions that represent D-branes in a B{sub 2} field, M2 branes and the M2-M5 bound states. The effective actions in these solutions are those of a probe D-brane and a probe M-brane. Our findings can be applied to the study of the gauge/gravity correspondence, especially the holographic renormalization group, and a search for new solutions of supergravity.
Hamilton-Jacobi method and effective actions of D-brane and M-brane in supergravity
Sato, Matsuo; Tsuchiya, Asato
2003-11-01
We show that the effective actions of D-brane and M-brane are solutions to the Hamilton-Jacobi (H-J) equations in supergravities. This fact means that these effective actions are on-shell actions in supergravities. These solutions to the H-J equations reproduce the supergravity solutions that represent D-branes in a B2 field, M2 branes and the M2-M5 bound states. The effective actions in these solutions are those of a probe D-brane and a probe M-brane. Our findings can be applied to the study of the gauge/gravity correspondence, especially the holographic renormalization group, and a search for new solutions of supergravity.
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Arithmetic partial differential equations
Buium, Alexandru; Simanca, Santiago R.
2006-01-01
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to ``flow'' integers or, more generally, points on algebraic groups with coordinates in rings with arithmetic flavor. In particular, we show that elliptic curves have certain canonical ``flows'' on them that are the arithmetic analogues of the heat and wave...
Investigating the Dynamics of Canonical Flux Tubes
von der Linden, Jens; Sears, Jason; Intrator, Thomas; You, Setthivoine
2016-10-01
Canonical flux tubes are flux tubes of the circulation of a species' canonical momentum. They provide a convenient generalization of magnetic flux tubes to regimes beyond magnetohydrodynamics (MHD). We hypothesize that hierarchies of instabilities which couple disparate scales could transfer magnetic pitch into helical flows and vice versa while conserving the total canonical helicity. This work first explores the possibility of a sausage instability existing on top of a kink as mechanism for coupling scales, then presents the evolution of canonical helicity in a gyrating kinked flux rope. Analytical and numerical stability spaces derived for magnetic flux tubes with core and skin currents indicate that, as a flux tube lengthens and collimates, it may become kink unstable with a sausage instability developing on top of the kink. A new analysis of 3D magnetic field and ion flow data on gyrating kinked magnetic flux ropes from the Reconnection Scaling Experiment tracks the evolution of canonical flux tubes and their helicity. These results and methodology are being developed as part of the Mochi experiment specifically designed to observe the dynamics of canonical flux tubes. This work is supported by DOE Grant DE-SC0010340 and the DOE Office of Science Graduate Student Research Program and prepared in part by LLNL under Contract DE-AC52-07NA27344. LLNL-ABS-697161.
The dark sector from interacting canonical and non-canonical scalar fields
De Souza, Rudinei C; Kremer, Gilberto M, E-mail: kremer@Fisica.ufpr.b [Departamento de Fisica, Universidade Federal do Parana, Curitiba (Brazil)
2010-09-07
In this work general models with interactions between two canonical scalar fields and between one non-canonical (tachyon type) and one canonical scalar field are investigated. The potentials and couplings to the gravity are selected through the Noether symmetry approach. These general models are employed to describe interactions between dark energy and dark matter, with the fields being constrained by the astronomical data. The cosmological solutions of some cases are compared with the observed evolution of the late Universe.
Dark Sector from Interacting Canonical and Non-Canonical Scalar Fields
de Souza, Rudinei C
2010-01-01
In this work it is investigated general models with interactions between two canonical scalar fields and between one non-canonical (tachyon-type) and one canonical scalar field. The potentials and couplings to the gravity are selected through the Noether symmetry approach. These general models are employed to describe interactions between dark energy and dark matter, with the fields being constrained by the astronomical data. The cosmological solutions of some cases are compared with the observed evolution of the late Universe.
Alexander M Many
Full Text Available The characterization of mammary stem cells, and signals that regulate their behavior, is of central importance in understanding developmental changes in the mammary gland and possibly for targeting stem-like cells in breast cancer. The canonical Wnt/β-catenin pathway is a signaling mechanism associated with maintenance of self-renewing stem cells in many tissues, including mammary epithelium, and can be oncogenic when deregulated. Wnt1 and Wnt3a are examples of ligands that activate the canonical pathway. Other Wnt ligands, such as Wnt5a, typically signal via non-canonical, β-catenin-independent, pathways that in some cases can antagonize canonical signaling. Since the role of non-canonical Wnt signaling in stem cell regulation is not well characterized, we set out to investigate this using mammosphere formation assays that reflect and quantify stem cell properties. Ex vivo mammosphere cultures were established from both wild-type and Wnt1 transgenic mice and were analyzed in response to manipulation of both canonical and non-canonical Wnt signaling. An increased level of mammosphere formation was observed in cultures derived from MMTV-Wnt1 versus wild-type animals, and this was blocked by treatment with Dkk1, a selective inhibitor of canonical Wnt signaling. Consistent with this, we found that a single dose of recombinant Wnt3a was sufficient to increase mammosphere formation in wild-type cultures. Surprisingly, we found that Wnt5a also increased mammosphere formation in these assays. We confirmed that this was not caused by an increase in canonical Wnt/β-catenin signaling but was instead mediated by non-canonical Wnt signals requiring the receptor tyrosine kinase Ror2 and activity of the Jun N-terminal kinase, JNK. We conclude that both canonical and non-canonical Wnt signals have positive effects promoting stem cell activity in mammosphere assays and that they do so via independent signaling mechanisms.
Surface Modification of ZnO Nanorods with Hamilton Receptors
Lukas Zeininger
2015-04-01
Full Text Available A new prototype of a Hamilton receptor suitable for the functionalization of inorganic nanoparticles was synthesized and characterized. The hydrogen bonding receptor was coupled to a catechol moiety, which served as anchor group for the functionalization of metal oxides, in particular zinc oxide. Synthesized zinc oxide nanorods [ZnO] were used for surface functionalization. The wet-chemical functionalization procedure towards monolayer-grafted particles [ZnO-HR] is described and a detailed characterization study is presented. In addition, the detection of specific cyanurate molecules is demonstrated. The hybrid structures [ZnO-HR-CA] were stable towards agglomeration and exhibited enhanced dispersability in apolar solvents. This observation, in combination with several spectroscopic experiments gave evidence of the highly directional supramolecular recognition at the surface of nanoparticles.
Square-integrable solutions and Weyl functions for singular canonical systems
Behrndt, Jussi; Hassi, Seppo; de Snoo, Henk; Wietsma, Rudi
2011-01-01
Boundary value problems for singular canonical systems of differential equations of the form Jf'(t) - H(t)f(t) = lambda Delta(t)f(t), t is an element of i, lambda is an element of C, are studied in the associated Hilbert space L(Delta)(2)(i). With the help of a monotonicity principle for matrix func
Kheirandish, Fardin; Amooshahi, Majid; Soltani, Morteza [Department of Physics, University of Isfahan, Hezar Jarib Ave., Isfahan (Iran, Islamic Republic of)], E-mail: fardinkh@phys.ui.ac.ir, E-mail: amooshahi@phys.ui.ac.ir, E-mail: m.soltani@phys.ui.ac.ir
2009-04-14
In this paper, by extending the Lagrangian of the Huttner-Barnett model an electromagnetic field in a nonhomogeneous and anisotropic magnetodielectric medium is quantized canonically. In this model, Maxwell equations in the medium are obtained and solved using the Green function technique. The noise operators are found and the results are compared with the phenomenological method.
Sense of Belonging and Mental Health in Hamilton, Ontario: An Intra-Urban Analysis
Kitchen, Peter; Williams, Allison; Chowhan, James
2012-01-01
This paper examines geographic variations in sense of community belonging in Hamilton, Ontario. It also identifies the most significant health and social factors associated with belonging in the city. The research employs data from the 2007/08 Canadian Community Health Survey for respondents aged 18 or over living in the Hamilton Census…
BOOK REVIEW: Modern Canonical Quantum General Relativity
Kiefer, Claus
2008-06-01
the geometrical nature of gravity, no such background exists in quantum gravity. Instead, the notion of a background is supposed to emerge a posteriori as an approximate notion from quantum states of geometry. As a consequence, the standard ultraviolet divergences of quantum field theory do not show up because there is no limit of Δx → 0 to be taken in a given spacetime. On the other hand, it is open whether the theory is free of any type of divergences and anomalies. A central feature of any canonical approach, independent of the choice of variables, is the existence of constraints. In geometrodynamics, these are the Hamiltonian and diffeomorphism constraints. They also hold in loop quantum gravity, but are supplemented there by the Gauss constraint, which emerges due to the use of triads in the formalism. These constraints capture all the physics of the quantum theory because no spacetime is present anymore (analogous to the absence of trajectories in quantum mechanics), so no additional equations of motion are needed. This book presents a careful and comprehensive discussion of these constraints. In particular, the constraint algebra is calculated in a transparent and explicit way. The author makes the important assumption that a Hilbert-space structure is still needed on the fundamental level of quantum gravity. In ordinary quantum theory, such a structure is needed for the probability interpretation, in particular for the conservation of probability with respect to external time. It is thus interesting to see how far this concept can be extrapolated into the timeless realm of quantum gravity. On the kinematical level, that is, before the constraints are imposed, an essentially unique Hilbert space can be constructed in terms of spin-network states. Potentially problematic features are the implementation of the diffeomorphism and Hamiltonian constraints. The Hilbert space Hdiff defined on the diffeomorphism subspace can throw states out of the kinematical
Hamilton's equations for a fluid membrane: axial symmetry
Capovilla, R [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico); Rojas, E [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)
2005-09-23
Consider a homogeneous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an 'action' describing the motion of a particle; the contours of equilibrium geometries are identified with particle trajectories. A novel Hamiltonian formulation of the problem is presented which exhibits the following two features: (i) the second derivatives appearing in the action through the mean curvature are accommodated in a natural phase space and (ii) the intrinsic freedom associated with the choice of evolution parameter along the contour is preserved. As a result, the phase space involves momenta conjugate not only to the particle position but also to its velocity, and there are constraints on the phase space variables. This formulation provides the groundwork for a field theoretical generalization to arbitrary configurations, with the particle replaced by a loop in space.
Hamilton's Equations with Euler Parameters for Rigid Body Dynamics Modeling. Chapter 3
Shivarama, Ravishankar; Fahrenthold, Eric P.
2004-01-01
A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.
Some Inverse Problems in Periodic Homogenization of Hamilton-Jacobi Equations
Luo, Songting; Tran, Hung V.; Yu, Yifeng
2016-09-01
We look at the effective Hamiltonian {overline{H}} associated with the Hamiltonian {H(p,x)=H(p)+V(x)} in the periodic homogenization theory. Our central goal is to understand the relation between {V} and {overline{H}}. We formulate some inverse problems concerning this relation. Such types of inverse problems are, in general, very challenging. In this paper, we discuss several special cases in both convex and nonconvex settings.
1985-10-01
many more resu -s of this kind, including existence results in cases where nonuniqueness is possible and the existence of minimal solutions. We also...in these works. -4- . .. . . . . . . . . * .. ..-.. .. ... . .. . .. . .. . .. . .. . .. . . H CONTENTS I. Lipschitz Hamiltonians and the stationary...condition~s at infinity VII. Further remarks on the Cauchy problem V -5-r 1. LIPSCHITZ HAMILTONIANS AN-D THE STATIONARY PROBLEM. wilIn this section we
Gallavotti, G
1997-01-01
Local integrability of hyperbolic oscillators is discussed to provide an introductory example of the Arnold's diffusion phenomenon in a forced pendulum. This is a text prepared for the the ISI summer school of June 1997 and deals with developments of the topics treated in the lectures.
Lindstedt series and Hamilton-Jacobi equation for hyperbolic tori in three time scales problems
Gallavotti, G; Mastropietro, V; Gallavotti, Giovannni; Gentile, Guido; Astropietro, Vieri M
1998-01-01
Interacting systems consisting of two rotators and a pendulum are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of unstable quasi periodic motions in phase space is studied via Lindstedt series. The result is a strong improvement, compared to our previous results, on the domain of validity of bounds that imply existence of invariant tori, large homoclinic angles, long heteroclinic chains and drift--diffusion in phase space.
Saroj K. Ghosh
2015-05-01
Full Text Available The histological features and histochemical characterization of the stomach were investigated in Mystus cavasius (Hamilton, Oreochromis niloticus (Linnaeus and Gudusia chapra (Hamilton having different feeding habits. Histologically the stomach of all the three fishes was made up of mucosa, submucosa, muscularis and serosa. The mucosa of superficial epithelium consists of a single layer of compactly arranged columnar epithelial cells. Prominent gastric glands are present in M. cavasius whereas in G. chapra the gastric glands are totally absent in the gizzard like stomach. However, in O. niloticus tubular gastric glands are present in the glandular epithelium of caecal like stomach. The distribution and chemical nature of mucopolysaccharides in the aforementioned fishes were studied histochemically by employing Periodic Acid Schiff’s in combination with the Alcian Blue (PAS–AB technique. Columnar epithelial cells lining the mucosa of the stomach including mucosal border were provided with exclusively neutral mucin which was probably involved in the protective functions against acid and enzymes. The different intensities of reaction of Best Carmine (BC for glycogen in the epithelial lining and gastric glands of the stomach of the aforesaid three fish species under study were discussed. The intense reaction for protein and tryptophan was noticed in the gastric epithelium and gastric glands of M. cavasius probably due to accumulation of zymogen granules in the gastric glands. On the contrary, moderate reaction for protein and tryptophan was associated with the epithelial cells and gastric glands of O. niloticus and G. chapra. The cytoarchitecture and different degrees of localization of mucopolysaccharides, glycogen, protein and tryptophan in the stomach of M. cavasius, O. niloticus and G. chapra were correlated with the functional significance of the region concerned.
New Perspectives in Canonical Gravity
Ashtekar, A.
A new approach to non-perturbative quantum gravity is developed. The key idea is to express general relativity inÂ·terms of variables which are similar to those used in Yang-Mills theory. In terms of these variables, Einstein's equation simplifies considerably and this enables one to deal with the exact theory, without having to make an essential use of perturbation expansions. Furthermore, one can import into quantum gravity several ideas and techniques from gauge theories. The framework also has applications to classical generaI relativity and differential geometry. The first four parts of the book are based on a special topics course that Abhay Ashtekar taught at Syracuse University in the spring of 1987. The last part contains invited contributions from Ted Jacobson, Paul Renteln, David C. Robinson, Carlo Rovelli, Lee Smolin and Charles Torre. These reports discuss the current research in this area.
Ohta, Tadayuki; Kimura, Toshiei
1993-10-01
The second post-Coulombian Lagrangian of Wheeler-Feynman electrodynamics for a many-particle system is treated according to a canonical formalism of a singular Lagrangian with higher derivatives. The canonical equations are given in terms of a reduced Hamiltonian with Dirac brackets, but they are transformed to be expressed in terms of ordinary Poisson brackets by redefinition of canonical variables. The reduced Hamiltonian includes a characteristic form of three-particle and four-particle potentials. Finally a direct pathway to the reduced Hamiltonian is presented via first-order formalism of the Maxwell theory with charged particles.
Multi-symplectic method for generalized Boussinesq equation
HU Wei-peng; DENG Zi-chen
2008-01-01
The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations (PDEs) derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.
Agonistic and antagonistic roles for TNIK and MINK in non-canonical and canonical Wnt signalling.
Alexander Mikryukov
Full Text Available Wnt signalling is a key regulatory factor in animal development and homeostasis and plays an important role in the establishment and progression of cancer. Wnt signals are predominantly transduced via the Frizzled family of serpentine receptors to two distinct pathways, the canonical ß-catenin pathway and a non-canonical pathway controlling planar cell polarity and convergent extension. Interference between these pathways is an important determinant of cellular and phenotypic responses, but is poorly understood. Here we show that TNIK (Traf2 and Nck-interacting kinase and MINK (Misshapen/NIKs-related kinase MAP4K signalling kinases are integral components of both canonical and non-canonical pathways in Xenopus. xTNIK and xMINK interact and are proteolytically cleaved in vivo to generate Kinase domain fragments that are active in signal transduction, and Citron-NIK-Homology (CNH Domain fragments that are suppressive. The catalytic activity of the Kinase domain fragments of both xTNIK and xMINK mediate non-canonical signalling. However, while the Kinase domain fragments of xTNIK also mediate canonical signalling, the analogous fragments derived from xMINK strongly antagonize this signalling. Our data suggest that the proteolytic cleavage of xTNIK and xMINK determines their respective activities and is an important factor in controlling the balance between canonical and non-canonical Wnt signalling in vivo.
Canonical and micro-canonical typical entanglement of continuous variable systems
Serafini, A [Institute for Mathematical Sciences, 53 Prince' s Gate, Imperial College London, London SW7 2PG (United Kingdom); Dahlsten, O C O [Institute for Mathematical Sciences, 53 Prince' s Gate, Imperial College London, London SW7 2PG (United Kingdom); Gross, D [Institute for Mathematical Sciences, 53 Prince' s Gate, Imperial College London, London SW7 2PG (United Kingdom); Plenio, M B [Institute for Mathematical Sciences, 53 Prince' s Gate, Imperial College London, London SW7 2PG (United Kingdom)
2007-08-03
We present a framework, compliant with the general canonical principle of statistical mechanics, to define measures on the set of pure Gaussian states of continuous variable systems. Within such a framework, we define two specific measures, referred to as 'micro-canonical' and 'canonical', and apply them to study systematically the statistical properties of the bipartite entanglement of n-mode pure Gaussian states at, respectively, given maximal energy and given temperature. We prove the 'concentration of measure' around a finite average, occurring for the entanglement in the thermodynamical limit in both the canonical and the micro-canonical approach. For finite n, we determine analytically the average and standard deviation of the entanglement (as quantified by the reduced purity) between one mode and all the other modes. Furthermore, we numerically investigate more general situations, clearly showing that the onset of the concentration of measure already occurs at relatively small n.
Król, Magdalena; Mucha, Joanna; Majchrzak, Kinga; Homa, Agata; Bulkowska, Małgorzata; Majewska, Alicja; Gajewska, Małgorzata; Pietrzak, Marta; Perszko, Mikołaj; Romanowska, Karolina; Pawłowski, Karol; Manuali, Elisabetta; Hellmen, Eva; Motyl, Tomasz
2014-01-01
Objective According to the current hypothesis, tumor-associated macrophages (TAMs) are “corrupted” by cancer cells and subsequently facilitate, rather than inhibit, tumor metastasis. Because the molecular mechanisms of cancer cell–TAM interactions are complicated and controversial we aimed to better define this phenomenon. Methods and Results Using microRNA microarrays, Real-time qPCR and Western blot we showed that co-culture of canine mammary tumor cells with TAMs or treatment with macrophage-conditioned medium inhibited the canonical Wnt pathway and activated the non-canonical Wnt pathway in tumor cells. We also showed that co-culture of TAMs with tumor cells increased expression of canonical Wnt inhibitors in TAMs. Subsequently, we demonstrated macrophage-induced invasive growth patterns and epithelial–mesenchymal transition of tumor cells. Validation of these results in canine mammary carcinoma tissues (n = 50) and xenograft tumors indicated the activation of non-canonical and canonical Wnt pathways in metastatic tumors and non-metastatic malignancies, respectively. Activation of non-canonical Wnt pathway correlated with number of TAMs. Conclusions We demonstrated that TAMs mediate a “switch” between canonical and non-canonical Wnt signaling pathways in canine mammary tumors, leading to increased tumor invasion and metastasis. Interestingly, similar changes in neoplastic cells were observed in the presence of macrophage-conditioned medium or live macrophages. These observations indicate that rather than being “corrupted” by cancer cells, TAMs constitutively secrete canonical Wnt inhibitors that decrease tumor proliferation and development, but as a side effect, they induce the non-canonical Wnt pathway, which leads to tumor metastasis. These data challenge the conventional understanding of TAM–cancer cell interactions. PMID:24404146
Universal canonical entropy for gravitating systems
Ashok Chatterjee; Parthasarathi Majumdar
2004-10-01
The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of the boundary, (a) an area spectrum as determined by non-perturbative canonical quantum general relativity (NCQGR), (b) an energy spectrum that bears a power law relation to the area spectrum, (c) an area law for the leading order microcanonical entropy, leading thermal fluctuation corrections to the canonical entropy are shown to be logarithmic in area with a universal coefficient. Since the microcanonical entropy also has universal logarithmic corrections to the area law (from quantum space-time fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.
Functional linear regression via canonical analysis
He, Guozhong; Wang, Jane-Ling; Yang, Wenjing; 10.3150/09-BEJ228
2011-01-01
We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical components of the processes involved. This representation establishes a connection between functional regression and functional canonical analysis and suggests alternative approaches for the implementation of functional linear regression analysis. A specific procedure for the estimation of the regression parameter function using canonical expansions is proposed and compared with an established functional principal component regression approach. As an example of an application, we present an analysis of mortality data for cohorts of medflies, obtained in experimental studies of aging and longevity.
Global canonical symmetry in a quantum system
李子平
1996-01-01
Based on the phase-space path integral for a system with a regular or singular Lagrangian the generalized canonical Ward identities under the global symmetry transformation in extended phase space are deduced respectively, thus the relations among Green functions can be found. The connection between canonical symmetries and conservation laws at the quantum level is established. It is pointed out that this connection in classical theories, in general, is no longer always preserved in quantum theories. The advantage of our formulation is that we do not need to carry out the integration over the canonical momenta in phase-space generating functional as usually performed. A precise discussion of quantization for a nonlinear sigma model with Hopf and Chern-Simons terms is reexamined. The property of fractional spin at quantum level has been clarified.
无向完全图的哈密顿回路%Hamilton Circles of No Direction Graph
梁震; 陈新军
2000-01-01
In this article,a way of finding all Hamilton cycles of a perfect no direction graph will be presented.Then we can find out the formula of all Hamilton circles of a perfect no direction graph.Finally the way will be expanded to other cases like finding whether a graph has Hamilton cycles or not.
Dispersion Operators Algebra and Linear Canonical Transformations
Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo
2017-02-01
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.
Dispersion Operators Algebra and Linear Canonical Transformations
Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo
2017-04-01
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.
The Hamilton depression scale. Evaluation of objectivity using logistic models.
Bech, P; Allerup, P; Gram, L F; Reisby, N; Rosenberg, R; Jacobsen, O; Nagy, A
1981-03-01
The consistency of the Hamilton Depression Scale (HDS) as a measure of the severity of depressive states has been examined when the scale was used weekly during a trial when imipramine. By use of logistic models (Rasch) the consistency of the HDS has been considered across patient-variables as age, sex, plasma levels of imipramine, and diagnosis. The results showed that the original 17-item HDS was without adequate consistency, i.e. the total score of the sample of items was no one-dimensional measure of depressive states. However, a melancholia subscale of the HDS contained items the total of which can be used to compare patients quantitatively, although in some part of the analysis one of these items showed ceiling effect. It was concluded that the melancholia subscale (containing the items depressed mood, guilt, work and interests, retardation, psychic anxiety, and general somatic symptoms) can form the basis for further improvements in the field of quantitative rating scales for depressive states.
New facility in Hamilton to generate electricity from biosolids
Nolan, W. [Liberty Energy, Hamilton, ON (Canada); Thomson, M.; Ahluwalia, J. [Environ EC Canada, Mississauga, ON (Canada)
2009-07-15
Ontario's Green Energy Act was introduced in 2009 to facilitate progress toward greenhouse gas (GHG) reduction and to increase the amount of energy produced from renewable energy sources. This article described a technology that can be used to generate electricity from the biosolids that are generated at wastewater treatment plants and pulp and paper mills across Ontario. Liberty Energy Inc. is proposing to build a new renewable energy thermal electric power plant in Hamilton, Ontario. The facility will use waste biomass as fuel consisting of biosolids, or sewage sludge. These materials have traditionally been managed through land filling, land application, or incineration. The use of waste biomass for power generation will provide a long term, sustainable and environmentally friendly method to manage these waste materials. This article reviewed some of the thermal treatment technologies, including fixed hearth, multiple hearth, rotary kilns and fluidized bed reactors. The odour management plan for the facility includes sealed storage of biosolids and indoor receiving of both biosolids and biomass, with all venting to either the gasifier or a biofilter. The exhaust from the gasifier will be treated by selective catalytic and non-catalytic reduction technology, lime slurry wet scrubbers, fabric filters and powdered activated carbon scrubbers. 2 figs.
Geometric integrator for simulations in the canonical ensemble
Tapias, Diego; Sanders, David P.; Bravetti, Alessandro
2016-08-01
We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of a system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results. Moreover, to show the advantage of our geometric integrator over a non-geometric one, we compare the results with those obtained by using the non-geometric Gear integrator, which is frequently used to perform simulations in the canonical ensemble. The non-geometric integrator induces a drift in the invariant quantity, while our integrator has no such drift, thus ensuring that the system is effectively sampling the correct ensemble.
Geometric integrator for simulations in the canonical ensemble.
Tapias, Diego; Sanders, David P; Bravetti, Alessandro
2016-08-28
We introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble that preserves the invariant distribution in equations arising from the density dynamics algorithm, with any possible type of thermostat. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of a system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results. Moreover, to show the advantage of our geometric integrator over a non-geometric one, we compare the results with those obtained by using the non-geometric Gear integrator, which is frequently used to perform simulations in the canonical ensemble. The non-geometric integrator induces a drift in the invariant quantity, while our integrator has no such drift, thus ensuring that the system is effectively sampling the correct ensemble.
Rahman, M Atiqur
2013-01-01
The massive particles tunneling method has been used to investigate the Hawking non-thermal and purely thermal radiations of Schwarzschild Anti-de Sitter (SAdS) black hole. Considering the spacetime background to be dynamical, incorporate the self-gravitation effect of the emitted particles the imaginary part of the action has been derived from Hamilton-Jacobi equation. Using the conservation laws of energy and angular momentum we have showed that the non-thermal and purely thermal tunneling rates are related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum. The result obtained for SAdS black hole is also in accordance with Parikh and Wilczek\\rq s opinion and gives a correction to the Hawking radiation of SAdS black hole.
Rahman, M. Atiqur; Hossain, M. Ilias
2013-06-01
The massive particles tunneling method has been used to investigate the Hawking non-thermal and purely thermal radiations of Schwarzschild Anti-de Sitter (SAdS) black hole. Considering the spacetime background to be dynamical, incorporate the self-gravitation effect of the emitted particles the imaginary part of the action has been derived from Hamilton-Jacobi equation. Using the conservation laws of energy and angular momentum we have showed that the non-thermal and purely thermal tunneling rates are related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum. The result obtained for SAdS black hole is also in accordance with Parikh and Wilczek's opinion and gives a correction to the Hawking radiation of SAdS black hole.
Kuidas Canon suureks kasvas / Andres Eilart
Eilart, Andres
2004-01-01
Jaapani kaamerate ja büroomasinate tootja Canon Groupi arengust, tegevusest kolmes regioonis - USA-s, Euroopas ja Aasias ning ettevõtte pikaajalise edu põhjustest - ärifilosoofiast ning ajastatud tootearendusest. Vt. samas: Firma esialgne nimi oli Kwanon; Konkurendid koonduvad
Probing the small distance structure of canonical
t Hooft, G.
2010-01-01
In canonical quantum gravity, the formal functional integral includes an integration over the local conformal factor, and we propose to perform the functional integral over this factor before doing any of the other functional integrals. By construction, the resulting effective theory would be expect
Green's Conjecture for the generic canonical curve
Teixidor-I-Bigas, Montserrat
1998-01-01
Green's Conjecture states the following : syzygies of the canonical model of a curve are simple up to the p^th stage if and only if the Clifford index of C is greater than p. We prove that the generic curve of genus g satisfies Green's conjecture.
Canonical analysis based on mutual information
Nielsen, Allan Aasbjerg; Vestergaard, Jacob Schack
2015-01-01
combinations with the information theoretical measure mutual information (MI). We term this type of analysis canonical information analysis (CIA). MI allows for the actual joint distribution of the variables involved and not just second order statistics. While CCA is ideal for Gaussian data, CIA facilitates...
Infants' Recognition of Objects Using Canonical Color
Kimura, Atsushi; Wada, Yuji; Yang, Jiale; Otsuka, Yumiko; Dan, Ippeita; Masuda, Tomohiro; Kanazawa, So; Yamaguchi, Masami K.
2010-01-01
We explored infants' ability to recognize the canonical colors of daily objects, including two color-specific objects (human face and fruit) and a non-color-specific object (flower), by using a preferential looking technique. A total of 58 infants between 5 and 8 months of age were tested with a stimulus composed of two color pictures of an object…
Regularized Multiple-Set Canonical Correlation Analysis
Takane, Yoshio; Hwang, Heungsun; Abdi, Herve
2008-01-01
Multiple-set canonical correlation analysis (Generalized CANO or GCANO for short) is an important technique because it subsumes a number of interesting multivariate data analysis techniques as special cases. More recently, it has also been recognized as an important technique for integrating information from multiple sources. In this paper, we…
Canonical duties, liabilities of trustees and administrators.
Morrisey, F G
1985-06-01
The new Code of Canon Law outlines a number of duties of those who have responsibility for administering the Church's temporal goods. Before assuming office, administrators must pledge to be efficient and faithful, and they must prepare an inventory of goods belonging to the juridic person they serve. Among their duties, administrators must: Ensure that adequate insurance is provided; Use civilly valid methods to protect canonical ownership of the goods; Observe civil and canon law prescriptions as well as donors' intentions; Collect and safeguard revenues, repay debts, and invest funds securely; Maintain accurate records, keep documents secure, and prepare an annual budget; Prepare an annual report and present it to the Ordinary where prescribed; Observe civil law concerning labor and social policy, and pay employees a just and decent wage. Administrators who carry out acts that are invalid canonically are liable for such acts. The juridic person is not liable, unless it derived benefit from the transaction. Liability is especially high when the sale of property is involved or when a contract is entered into without proper cannonical consent. Although Church law is relatively powerless to punish those who have been negligent, stewards, administrators, and trustees must do all they can to be truthful to the responsibility with which they have been entrusted.
Canonical equivalence between massive spin 1 theories
Arias, P J; Arias, Pio J.; Perez-Mosquera, Jean C.
2004-01-01
The model of Cremmer-Scherck and Proca are considered in dimensions greater than 3+1. It is obtained that the Proca model correspond to a gauged fixed version of the Cremmer-Scherck one, and we show their canonical equivalence.
Quantum canonical ensemble: A projection operator approach
Magnus, Wim; Lemmens, Lucien; Brosens, Fons
2017-09-01
Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration. Introduced in the recent past to handle various issues related to particle-number projected statistics, the projection operator approach proves beneficial to a wide variety of problems in condensed matter physics for which the canonical ensemble offers a natural and appropriate environment. In this light, we present a systematic treatment of the canonical ensemble that embeds the projection operator into the formalism of second quantization while explicitly fixing N, the very number of particles rather than the average. Being applicable to both bosonic and fermionic systems in arbitrary dimensions, transparent integral representations are provided for the partition function ZN and the Helmholtz free energy FN as well as for two- and four-point correlation functions. The chemical potential is not a Lagrange multiplier regulating the average particle number but can be extracted from FN+1 -FN, as illustrated for a two-dimensional fermion gas.
刘道军
2014-01-01
讨论带有Born-Infeld作用量的快子场所驱动的暴涨模型.首先给出了快子暴涨方程的Hamilton-Jacobi形式并且考虑如何去解Hamilton-Jacobi方程;然后讨论快子场的宇宙学扰动给出扰动场的模方程;最后,讨论了一个真实的由弦理论得来的滚动快子模型.
Geometric integrator for simulations in the canonical ensemble
Tapias, Diego; Bravetti, Alessandro
2016-01-01
In this work we introduce a geometric integrator for molecular dynamics simulations of physical systems in the canonical ensemble. In particular, we consider the equations arising from the so-called density dynamics algorithm with any possible type of thermostat and provide an integrator that preserves the invariant distribution. Our integrator thus constitutes a unified framework that allows the study and comparison of different thermostats and of their influence on the equilibrium and non-equilibrium (thermo-)dynamic properties of the system. To show the validity and the generality of the integrator, we implement it with a second-order, time-reversible method and apply it to the simulation of a Lennard-Jones system with three different thermostats, obtaining good conservation of the geometrical properties and recovering the expected thermodynamic results.
NUMERICAL METHOD BASED ON HAMILTON SYSTEM AND SYMPLECTIC ALGORITHM TO DIFFERENTIAL GAMES
无
2006-01-01
The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.
Hamilton-Jacobi method for classical mechanics in Grassmann algebra (in English)
Tabunshchyk, K. V.
We present the Hamilton--Jacobi method for the classical mechanics with the constrains in Grassmann algebra. Within the framework of this method the solution for the classical system characterized by the SUSY Lagrangian is obtained.
Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics
Schlitt, D. W.
1977-01-01
Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH)
Thomas, Marion
2006-06-01
Robert Yerkes is a pivotal figure in American psychology and primatology in the first half of the twentieth century. As is well known, Yerkes first studied ape intelligence in 1915, on a visit to the private California laboratory of the psychiatrist Gilbert Hamilton, a former student. Less widely appreciated is how far the work done at the Hamilton lab, in its aims and ambitions as well as its techniques, served as a template for much of Yerkes's research thereafter. This paper uses the Hamilton-Yerkes relationship to re-examine Yerkes's career and, more generally, that of American psychology in the early twentieth century. Three points especially are emphasized: first, the role of Freudian psychoanalysis as a spur to Hamilton's experimental studies of ape intelligence; second, the importance of Hamilton's laboratory, with its semi-wild population of monkeys and ape, as a model for Yerkes's efforts to create a laboratory of his own; and third, the influence on Yerkes of Hamilton's optimism about experimental psychological studies of nonhuman primates as a source of lessons beneficial to a troubled human world.
Exact periodic solution in coupled nonlinear Schrodinger equations
Li Qi-Liang; Chen Jun-Lang; Sun Li-Li; Yu Shu-Yi; Qian Sheng
2007-01-01
The coupled nonlinear Schrodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.
Field, J H [Departement de Physique Nucleaire et Corpusculaire, Universite de Geneve, 24, quai Ernest-Ansermet CH-1211 Geneva 4 (Switzerland)
2006-12-15
It is demonstrated how all the mechanical equations of classical electromagnetism (CEM) may be derived from only Coulomb's inverse square force law, special relativity and Hamilton's principle. The instantaneous nature of the Coulomb force in the centre-of-mass frame of two interacting charged objects, mediated by the exchange of space-like virtual photons, is predicted by quantum electrodynamics (QED). The interaction Lagrangian of QED is shown to be identical, in the appropriate limit, to the potential energy term in the Lorentz-invariant Lagrangian of CEM. A comparison is made with the Feynman-Wheeler action-at-a-distance formulation of CEM.
Canonical sound speed profile for the central Bay of Bengal
Murty, T.V.R.; PrasannaKumar, S.; Somayajulu, Y.K.; Sastry, J.S.; De Figueiredo, R.J.P.
Following Munk's canonical theory, an algorithm has been presented for computing sound channel parameters in the western and southern Bay of Bengal. The estimated canonical sound speed profile using these parameters has been compared with computed...
An introduction to the theory of canonical matrices
Turnbull, H W
2004-01-01
Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory's principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations. 1952 edition. Index. Appendix. Historical notes. Bibliographies. 275 problems.
Gravitational closure of matter field equations
Schuller, F P; Wolz, F; Düll, M
2016-01-01
We show how to unlock the hidden information about gravity in one's choice of matter dynamics. Restricting attention to canonically quantizable matter field equations, but therefore being able to admit any tensorial background geometry, one is left with very little choice for the dynamics of the geometry. Indeed, the physical requirement that the common canonical evolution of matter and geometry can start and end on shared Cauchy surfaces imposes consistency conditions so strong that the Lagrangian for the geometry arises as the solution of a particular system of linear partial differential equations. Employing a suitable associated bundle to encode the canonical configuration degrees of freedom of the geometry, this system can be set up without additional constraints and with coefficient functions that indeed only depend on the causal structure of the chosen matter dynamics. Through these equations, the Lagrangian for the geometry is thus determined by the stipulated matter field dynamics, up to typically on...
Non-canonical modulators of nuclear receptors.
Tice, Colin M; Zheng, Ya-Jun
2016-09-01
Like G protein-coupled receptors (GPCRs) and protein kinases, nuclear receptors (NRs) are a rich source of pharmaceutical targets. Over 80 NR-targeting drugs have been approved for 18 NRs. The focus of drug discovery in NRs has hitherto been on identifying ligands that bind to the canonical ligand binding pockets of the C-terminal ligand binding domains (LBDs). Due to the development of drug resistance and selectivity concerns, there has been considerable interest in exploring other, non-canonical ligand binding sites. Unfortunately, the potencies of compounds binding at other sites have generally not been sufficient for clinical development. However, the situation has changed dramatically over the last 3years, as compounds with sufficient potency have been reported for several NR targets. Here we review recent developments in this area from a medicinal chemistry point of view in the hope of stimulating further interest in this area of research.
Microcanonical and canonical approach to traffic flow
Surda, Anton
2007-01-01
A system of identical cars on a single-lane road is treated as a microcanonical and canonical ensemble. Behaviour of the cars is characterized by the probability of car velocity as a function of distance and velocity of the car ahead. The calculations a performed on a discrete 1D lattice with discrete car velocities. Probability of total velocity of a group of cars as a function of density is calculated in microcanonical approach. For a canonical ensemble, fluctuations of car density as a function of total velocity is found. Phase transitions between free and jammed flow for large deceleration rate of cars and formation of queues of cars with the same velocity for low deceleration rate are described.
Deformed Special Relativity in a Canonical Framework
Ghosh, S; Ghosh, Subir; Pal, Probir
2007-01-01
In this paper we have studied the nature of kinematical and dynamical laws in $\\kappa $-Minkowski spacetime from a new perspective: the canonical phase space approach. We have introduced a new form of $\\kappa$-Minkowski phase space algebra from which we recover the $\\kappa$-extended finite Lorentz transformations derived in \\cite{kim}. This is a particular form of a Deformed Special Relativity model that admits a modified energy-momentum dispersion law as well as noncommutative $\\kappa$-Minkowski phase space. We show that this system can be completely mapped to a set of phase space variables that obey canonical (and {\\it{not}} $\\kappa$-Minkowski) phase space algebra and Special Relativity Lorentz transformation (and {\\it{not}} $\\kappa$-extended Lorentz transformation). We demonstrate the usefulness and simplicity of this approach through a number of applications both in classical and quantum mechanics. We also construct a Lagrangian for the $\\kappa$-particle.
Canonical Quantum Gravity on Noncommutative Spacetime
Kober, Martin
2014-01-01
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the moyal star product, which enables the representation of the field quantities depending on noncommuting coordinates by generalized quantities depending on usual coordinates. But not only the classical theory has to be generalized in analogy to other field theories. Besides, the necessity arises to replace the commutator between the gravitational field operator and its canonical conjugated quantity by a corresponding generalized expression on noncommutative space-time. Accordingly the transition to the quantum theory has also to be performed in a generalized way and leads to extended representations of the quantum theoretical operators. If the generalized representations of the operators are inserted to the generalized constraints, one obtains the corresponding generalized quantum constraints including the Hamiltonian constraint as dynamical constraint. Af...
Observables in classical canonical gravity: folklore demystified
Pons, J M; Sundermeyer, K A
2010-01-01
We give an overview of some conceptual difficulties, sometimes called paradoxes, that have puzzled for years the physical interpetation of classical canonical gravity and, by extension, the canonical formulation of generally covariant theories. We identify these difficulties as stemming form some terminological misunderstandings as to what is meant by "gauge invariance", or what is understood classically by a "physical state". We make a thorough analysis of the issue and show that all purported paradoxes disappear when the right terminology is in place. Since this issue is connected with the search of observables - gauge invariant quantities - for these theories, we formally show that time evolving observables can be constructed for every observer. This construction relies on the fixation of the gauge freedom of diffeomorphism invariance by means of a scalar coordinatization. We stress the condition that the coordinatization must be made with scalars. As an example of our method for obtaining observables we d...
DNA pattern recognition using canonical correlation algorithm
B K Sarkar; Chiranjib Chakraborty
2015-10-01
We performed canonical correlation analysis as an unsupervised statistical tool to describe related views of the same semantic object for identifying patterns. A pattern recognition technique based on canonical correlation analysis (CCA) was proposed for finding required genetic code in the DNA sequence. Two related but different objects were considered: one was a particular pattern, and other was test DNA sequence. CCA found correlations between two observations of the same semantic pattern and test sequence. It is concluded that the relationship possesses maximum value in the position where the pattern exists. As a case study, the potential of CCA was demonstrated on the sequence found from HIV-1 preferred integration sites. The subsequences on the left and right flanking from the integration site were considered as the two views, and statistically significant relationships were established between these two views to elucidate the viral preference as an important factor for the correlation.
Canonical approach to 2D induced gravity
Popovic, D
2001-01-01
Using canonical method the Liouville theory has been obtained as a gravitational Wess-Zumino action of the Polyakov string. From this approach it is clear that the form of the Liouville action is the consequence of the bosonic representation of the Virasoro algebra, and that the coefficient in front of the action is proportional to the central charge and measures the quantum braking of the classical symmetry.
Canonical Formulation of pp-waves
Balasin, Herbert
2007-01-01
We construct a Hamiltonian formulation for the class of plane-fronted gravitational waves with parallel rays (pp-waves). Because of the existence of a light-like Killing vector, the dynamics is effectively reduced to a 2+1 evolution with "time" chosen to be light-like. In spite of the vanishing action this allows us to geometrically identify a symplectic form as well as dynamical Hamiltonian, thus casting the system into canonical form.
On Complex Supermanifolds with Trivial Canonical Bundle
Groeger, Josua
2016-01-01
We give an algebraic characterisation for the triviality of the canonical bundle of a complex supermanifold in terms of a certain Batalin-Vilkovisky superalgebra structure. As an application, we study the Calabi-Yau case, in which an explicit formula in terms of the Levi-Civita connection is achieved. Our methods include the use of complex integral forms and the recently developed theory of superholonomy.
CANONICAL FORMULATION OF NONHOLONOMIC CONSTRAINED SYSTEMS
GUO YONG-XIN; YU YING; HUANG HAI-JUN
2001-01-01
Based on the Ehresmann connection theory and symplectic geometry, the canonical formulation of nonholonomic constrained mechanical systems is described. Following the Lagrangian formulation of the constrained system, the Hamiltonian formulation is given by Legendre transformation. The Poisson bracket defined by an anti-symmetric tensor does not satisfy the Jacobi identity for the nonintegrability of nonholonomic constraints. The constraint manifold can admit symplectic submanifold for some cases, in which the Lie algebraic structure exists.
Baby Skyrmions stabilized by canonical quantization
Acus, A.; Norvaisas, E. [Vilnius University, Institute of Theoretical Physics and Astronomy, Gostauto 12, Vilnius 01108 (Lithuania); Shnir, Ya., E-mail: shnir@maths.tcd.i [School of Theoretical Physics - DIAS, 10 Burlington Road, Dublin 4 (Ireland); Institute of Physics, Jagiellonian University, Krakow (Poland)
2009-11-23
We analyse the effect of the canonical quantization of the rotational mode of the O(3)sigma-model which includes the Skyrme term. Numerical evidence is presented that the quantum correction to the mass of the rotationally-invariant charge n=1,2 configurations may stabilize the solution even in the limit of vanishing potential. The corresponding range of values of the parameters is discussed.
Baby Skyrmions stabilized by canonical quantization
Acus, A; Shnir, Ya
2009-01-01
We analyse the effect of the canonical quantization of the rotational mode of the O(3) $\\sigma$-model which includes the Skyrme term. Numerical evidence is presented that the quantum correction to the mass of the rotationally-invariant charge $n=1,2$ configurations may stabilize the solution even in the limit of vanishing potential. The corresponding range of values of the parameters is discussed.
Il Canone Linguistico Boccacciano, Non Senza Dissenso
Cecilia Casini
2015-06-01
Full Text Available Author of prose’s greatest masterpiece of medieval literature in the vernacular, Giovanni Boccaccio was crucial to defining the Italian language canon, especially since Pietro Bembo proposed its coding in the sixteenth century. Not without controversy, however, since shortly after the publication of Prose Della Volgar Language, Bembo presents the first contrasting theories that support the linguistic model presented by Machiavelli
Cluster expansion in the canonical ensemble
Pulvirenti, Elena
2011-01-01
We consider a system of particles confined in a box $\\La\\subset\\R^d$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime. The convergence is uniform in the volume and in the thermodynamic limit it reproduces Mayer's virial expansion providing an alternative and more direct derivation which avoids the deep combinatorial issues present in the original proof.
Canonical transfer and multiscale energetics for primitive and quasi-geostrophic atmospheres
Liang, X San
2016-01-01
The past years have seen the success of a novel multiscale energetic formalism in a variety of ocean and engineering fluid applications. In a self-contained way, this study introduces it to the atmospheric dynamical diagnostics, with important theoretical updates. Multiscale energy equations are derived using a new analysis apparatus, namely, multiscale window transform, with respect to both the primitive equation and quasi-geostrophic models. A reconstruction of the "atomic" energy fluxes on the multiple scale windows allows for a natural and unique separation of the in-scale transports and cross-scale transfers from the intertwined nonlinear processes. The resulting energy transfers bear a Lie bracket form, reminiscent of the Poisson bracket in Hamiltonian mechanics, we hence would call them "canonical". A canonical transfer process is a mere redistribution of energy among scale windows, without generating or destroying energy as a whole. By classification, a multiscale energetic cycle comprises of availabl...
Canonical Sets of Best L1-Approximation
Dimiter Dryanov
2012-01-01
Full Text Available In mathematics, the term approximation usually means either interpolation on a point set or approximation with respect to a given distance. There is a concept, which joins the two approaches together, and this is the concept of characterization of the best approximants via interpolation. It turns out that for some large classes of functions the best approximants with respect to a certain distance can be constructed by interpolation on a point set that does not depend on the choice of the function to be approximated. Such point sets are called canonical sets of best approximation. The present paper summarizes results on canonical sets of best L1-approximation with emphasis on multivariate interpolation and best L1-approximation by blending functions. The best L1-approximants are characterized as transfinite interpolants on canonical sets. The notion of a Haar-Chebyshev system in the multivariate case is discussed also. In this context, it is shown that some multivariate interpolation spaces share properties of univariate Haar-Chebyshev systems. We study also the problem of best one-sided multivariate L1-approximation by sums of univariate functions. Explicit constructions of best one-sided L1-approximants give rise to well-known and new inequalities.
2015-09-24
19. Colloquium lecture at College of Management , National Chiao Tung University, June 22, 2012. Title: Unified Framework in Global Supply Chain and...the well-known logistic equation in population dynamical systems can be reformulated as a global optimization problem, which could have at most 2n...making, supply chain , scheduling problems, and computational mechanics, etc. Impacts to the communities: The canonical duality theory is now
Da Lio, Francesca; 10.1137/S0363012904440897
2010-01-01
In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman and Isaacs equations. As an application, we characterize the value function of a finite horizon stochastic control problem with unbounded controls as the unique viscosity solution of the corresponding dynamic programming equation.
Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)
2016-07-01
The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.
Extension of the Schrodinger equation
Somsikov, Vyacheslav
2017-03-01
Extension of the Schrodinger equation is submitted by removing its limitations appearing due to the limitations of the formalism of Hamilton, based on which this equation was obtained. For this purpose the problems of quantum mechanics arising from the limitations of classical mechanics are discussed. These limitations, in particular, preclude the use of the Schrodinger equation to describe the time symmetry violation. The extension of the Schrodinger equation is realized based on the principle of duality symmetry. According to this principle the dynamics of the systems is determined by the symmetry of the system and by the symmetry of the space. The extension of the Schrodinger equation was obtained from the dual expression of energy, represented in operator form. For this purpose the independent micro - and macro-variables that determine respectively the dynamics of quantum particle system relative to its center of mass and the movement of the center of mass in space are used. The solution of the extended Schrodinger equation for the system near equilibrium is submitted. The main advantage of the extended Schrodinger equation is that it is applicable to describe the interaction and evolution of quantum systems in inhomogeneous field of external forces.
Theory of extreme correlations using canonical Fermions and path integrals
Shastry, B. Sriram, E-mail: sriram@physics.ucsc.edu
2014-04-15
The t–J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson–Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitian quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further, a transparent physical interpretation of the previously introduced auxiliary Greens function and the ‘caparison factor’, is obtained. The low energy electron spectral function in this theory, with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale Δ{sub 0} that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying very low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function, related simply to the Fano line shape, has a peculiar energy dependence unlike that of a Lorentzian. The resulting energy dispersion obtained by maximization is a hybrid of a massive and a massless Dirac spectrum E{sub Q}{sup ∗}∼γQ−√(Γ{sub 0}{sup 2}+Q{sup 2}), where the vanishing of Q, a momentum type variable, locates the kink minimum. Therefore the quasiparticle velocity interpolates between (γ∓1) over a width Γ{sub 0} on the two sides of Q=0, implying a kink there that strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations. -- Highlights: •Spectral function of the Extremely Correlated Fermi Liquid theory at low energy.
A quantitative test of Hamilton's rule for the evolution of altruism.
Markus Waibel
2011-05-01
Full Text Available The evolution of altruism is a fundamental and enduring puzzle in biology. In a seminal paper Hamilton showed that altruism can be selected for when rb - c > 0, where c is the fitness cost to the altruist, b is the fitness benefit to the beneficiary, and r is their genetic relatedness. While many studies have provided qualitative support for Hamilton's rule, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. Here we use a simulated system of foraging robots to experimentally manipulate the costs and benefits of helping and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different c/b ratios, we show that Hamilton's rule always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects as well as mutations with strong effects on behavior and fitness (effects not directly taken into account in Hamilton's original 1964 rule. In addition to providing the first quantitative test of Hamilton's rule in a system with a complex mapping between genotype and phenotype, these experiments demonstrate the wide applicability of kin selection theory.
Burg, van der Eeke; Leeuw, de Jan
1988-01-01
In this paper we discuss the estimation of mean and standard errors of the eigenvalues and category quantifications in generalized non-linear canonical correlation analysis (OVERALS). Starting points are the delta method equations, but the jack-knife and bootstrap are used to provide finite differen
Pool, René; Heringa, Jaap; Hoefling, Martin; Schulz, Roland; Smith, Jeremy C; Feenstra, K Anton
2012-05-01
We report on a python interface to the GROMACS molecular simulation package, GromPy (available at https://github.com/GromPy). This application programming interface (API) uses the ctypes python module that allows function calls to shared libraries, for example, written in C. To the best of our knowledge, this is the first reported interface to the GROMACS library that uses direct library calls. GromPy can be used for extending the current GROMACS simulation and analysis modes. In this work, we demonstrate that the interface enables hybrid Monte-Carlo/molecular dynamics (MD) simulations in the grand-canonical ensemble, a simulation mode that is currently not implemented in GROMACS. For this application, the interplay between GromPy and GROMACS requires only minor modifications of the GROMACS source code, not affecting the operation, efficiency, and performance of the GROMACS applications. We validate the grand-canonical application against MD in the canonical ensemble by comparison of equations of state. The results of the grand-canonical simulations are in complete agreement with MD in the canonical ensemble. The python overhead of the grand-canonical scheme is only minimal.
A Canonical Biomechanical Vocal Fold Model
Bhattacharya, Pinaki; Siegmund, Thomas H.
2012-01-01
Summary The present article aimed at constructing a canonical geometry of the human vocal fold (VF) from subject-specific image slice data. A computer-aided design approach automated the model construction. A subject-specific geometry available in literature, three abstractions (which successively diminished in geometric detail) derived from it, and a widely used quasi two-dimensional VF model geometry were used to create computational models. The first three natural frequencies of the models were used to characterize their mechanical response. These frequencies were determined for a representative range of tissue biomechanical properties, accounting for underlying VF histology. Compared with the subject-specific geometry model (baseline), a higher degree of abstraction was found to always correspond to a larger deviation in model frequency (up to 50% in the relevant range of tissue biomechanical properties). The model we deemed canonical was optimally abstracted, in that it significantly simplified the VF geometry compared with the baseline geometry but can be recalibrated in a consistent manner to match the baseline response. Models providing only a marginally higher degree of abstraction were found to have significant deviation in predicted frequency response. The quasi two-dimensional model presented an extreme situation: it could not be recalibrated for its frequency response to match the subject-specific model. This deficiency was attributed to complex support conditions at anterior-posterior extremities of the VFs, accentuated by further issues introduced through the tissue biomechanical properties. In creating canonical models by leveraging advances in clinical imaging techniques, the automated design procedure makes VF modeling based on subject-specific geometry more realizable. PMID:22209063
Canonical group quantization and boundary conditions
Jung, Florian
2012-07-16
In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.
Fractional-calculus diffusion equation
Ajlouni, Abdul-Wali MS; Al-Rabai'ah, Hussam A
2010-01-01
Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive...
Kato expansion in quantum canonical perturbation theory
Nikolaev, A S
2015-01-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. The corresponding computational algorithm is more efficient for high perturbative orders than the algorithms of Van Vleck and Magnus methods.
Kato expansion in quantum canonical perturbation theory
Nikolaev, Andrey
2016-06-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson's ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Women and Textiles: Warping the Architectural Canon
Aron, Jamie
2012-01-01
Textiles have long been a part of the canon of Western architecture—from the folds of draped female forms in ancient Greek temples to the abstract Mayan patterns “knitted” together in Frank Lloyd Wright’s textile block houses of the 1920s. Yet just as any façade may conceal what’s inside, architecture’s shared history with weaving is often obscured. Today architecture sits at the top alongside the “fine arts” of painting and sculpture, while woven textiles occupy a less prominent position in ...
UNCONVENTIONAL HAMILTON-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF REISSNER SANDWICH PLATE
HUANG Wei-jiang; LUO En; SHE Hui
2006-01-01
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo(1987), some unconventional Hamilton-type variational principles for dynamics of Reissner sandwich plate can be established systematically. The unconventional Hamilton-type variation principle can fully characterize the initial-boundary-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work in dynamics of Reissner sandwich plate, but also to derive systematically the complementary functionals for five-field, two-field and one-field unconventional Hamilton-type variational principles by the generalized Legender transformations. Furthermore, with this approach, the intrinsic relationship among the various principles can be explained clearly.
Hamilton and Hardy: Mentoring and Friendship in the Service of Occupational Health.
Sullivan, Marianne
This article explores the mentoring relationship between Alice Hamilton and Harriet Hardy, two female physician-researchers who had a tremendous impact on the development of the field of occupational health in the United States during the 20th century. The article relies on letters the women wrote to each other. Hamilton, the elder, supported and furthered Hardy's career by asking her to coauthor the second edition of a seminal occupational health text. After beginning this intellectual collaboration, Hamilton remained a mentor to Hardy, and a decades-long friendship ensued. The article explores their relationship within the historical, political, and social context in which the women worked and made remarkable contributions to public health.
Glaucoma at the Hamilton Glaucoma Center and the University of California, San Diego
Robert N. Weinreb
2011-01-01
@@ Known for its unique cross-disciplinary investigative programs and clinical excellence, the scientists and clinicians at the Hamilton Glaucoma Center of the University of California, San Diego seek to enhance the discovery and translation of innovative research to clinical glaucoma care to prevent and cure glaucoma blindness.With state of the art laboratory and clinical facilities located on the La Jolla campus (Figure 1), the Center is a home for a worldrenowned team of scientists and staff.More than 100 post-doctoral fellows in Glaucoma, many of whom hold distinguished academic positions throughout the world, have been trained at the Hamilton Glaucoma Center and the University of California, San Diego.At the core of Hamilton Glaucoma Center activities are the outstanding faculty that are described below.
Hawking radiation of Kerr-de Sitter black holes using Hamilton-Jacobi method
Ibungochouba Singh, T.; Ablu Meitei, I.; Yugindro Singh, K.
2013-05-01
Hawking radiation of Kerr-de Sitter black hole is investigated using Hamilton-Jacobi method. When the well-behaved Painleve coordinate system and Eddington coordinate are used, we get the correct result of Bekenstein-Hawking entropy before and after radiation but a direct computation will lead to a wrong result via Hamilton-Jacobi method. Our results show that the tunneling probability is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal but it is consistent with underlying unitary theory.
Respiratory Medicine at McMaster University, Hamilton, Ontario: 1968 To 2013
Jones, Norman L.; Paul M O’Byrne
2014-01-01
The medical school at McMaster University (Hamilton, Ontario) was conceived in 1965 and admitted the first class in 1969. John Evans became the founding Dean and he invited Moran Campbell to be the first Chairman of the Department of Medicine. Moran Campbell, already a world figure in respiratory medicine and physiology, arrived at McMaster in September 1968, and he invited Norman Jones to be Coordinator of the Respiratory Programme.At that time, Hamilton had a population of 300,000, with two...
Power, Gender, and Canon Formation in Mexico
Cynthia Steele
1996-01-01
Full Text Available I propose to analyze Castellanos's trajectory from marginalized ethnographer and critic of "latino" society, to presidential insider and ambassador, and the first modern Mexican woman writer to be accepted into the literary canon. I will explore the intersection of politics, gender, and the (self- creation of a literary persona with regard to the following issues: 1 the tension between self-exposure and self-censorship in Castellanos's literary work; 2 Castellanos's intense and problematic relationship with her illegitimate, mestizo half-brother; 3 the coincidences and contradictions between Castellanos's journalistic account of her relationship with her servant Maria Escandon, and Maria's own oral history twenty years later; 4 the tension between depression and dependency, on the one hand, and self-assertiveness and audacity, on the other; 5 the relation between Castellanos's role as ambassador and the personal, apolitical, often frivolous character of her journalistic articles written in Israel; 6 the contradictory readings of Castellanos's death, and the respective implications for her place in the canon; and 7 the implications, for their reception, of the love letters published in Cartas a Ricardo 1994, as opposed to 1974.
Face hallucination using orthogonal canonical correlation analysis
Zhou, Huiling; Lam, Kin-Man
2016-05-01
A two-step face-hallucination framework is proposed to reconstruct a high-resolution (HR) version of a face from an input low-resolution (LR) face, based on learning from LR-HR example face pairs using orthogonal canonical correlation analysis (orthogonal CCA) and linear mapping. In the proposed algorithm, face images are first represented using principal component analysis (PCA). Canonical correlation analysis (CCA) with the orthogonality property is then employed, to maximize the correlation between the PCA coefficients of the LR and the HR face pairs to improve the hallucination performance. The original CCA does not own the orthogonality property, which is crucial for information reconstruction. We propose using orthogonal CCA, which is proven by experiments to achieve a better performance in terms of global face reconstruction. In addition, in the residual-compensation process, a linear-mapping method is proposed to include both the inter- and intrainformation about manifolds of different resolutions. Compared with other state-of-the-art approaches, the proposed framework can achieve a comparable, or even better, performance in terms of global face reconstruction and the visual quality of face hallucination. Experiments on images with various parameter settings and blurring distortions show that the proposed approach is robust and has great potential for real-world applications.
Observables in classical canonical gravity: Folklore demystified
Pons, J. M.; Salisbury, D. C.; Sundermeyer, K. A.
2010-04-01
We give an overview of some conceptual difficulties, sometimes called paradoxes, that have puzzled for years the physical interpetation of classical canonical gravity and, by extension, the canonical formulation of generally covariant theories. We identify these difficulties as stemming form some terminological misunderstandings as to what is meant by "gauge invariance", or what is understood classically by a "physical state". We make a thorough analysis of the issue and show that all purported paradoxes disappear when the right terminology is in place. Since this issue is connected with the search of observables - gauge invariant quantities - for these theories, we formally show that time evolving observables can be constructed for every observer. This construction relies on the fixation of the gauge freedom of diffeomorphism invariance by means of a scalar coordinatization. We stress the condition that the coordinatization must be made with scalars. As an example of our method for obtaining observables we discuss the case of the massive particle in AdS spacetime.
Observables in classical canonical gravity: Folklore demystified
Pons, J M [Departament d' Estructura i Constituents de la Materia and Institut de Ciencies del Cosmos, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Catalonia (Spain); Salisbury, D C [Department of Physics, Austin College, Sherman, Texas 75090-4440, USA, and Max-Planck-Institut fuer Wissenschaftsgeschichte, Boltzmannstrasse 22, 14195 Berlin (Germany); Sundermeyer, K A, E-mail: pons@ecm.ub.e, E-mail: dsalisbury@austincollege.ed, E-mail: ksun@gmx.d [Freie Universitaet Berlin, Fachbereich Physik, Institute for Theoretical Physics, Arnimallee 14, 14195 Berlin (Germany)
2010-04-01
We give an overview of some conceptual difficulties, sometimes called paradoxes, that have puzzled for years the physical interpetation of classical canonical gravity and, by extension, the canonical formulation of generally covariant theories. We identify these difficulties as stemming form some terminological misunderstandings as to what is meant by 'gauge invariance', or what is understood classically by a 'physical state'. We make a thorough analysis of the issue and show that all purported paradoxes disappear when the right terminology is in place. Since this issue is connected with the search of observables - gauge invariant quantities - for these theories, we formally show that time evolving observables can be constructed for every observer. This construction relies on the fixation of the gauge freedom of diffeomorphism invariance by means of a scalar coordinatization. We stress the condition that the coordinatization must be made with scalars. As an example of our method for obtaining observables we discuss the case of the massive particle in AdS spacetime.
Non-canonical RAN Translation of CGG Repeats Has Canonical Requirements.
Cox, Diana C; Cooper, Thomas A
2016-04-21
Repeat expansions cause dominantly inherited neurological disorders. In this issue of Molecular Cell, Kearse et al. (2016) examine the requirements for RAN translation of the CGG repeats that cause fragile X-associated tremor/ataxia syndrome, revealing similarities and differences with canonical translation.
Canon Fodder: Young Adult Literature as a Tool for Critiquing Canonicity
Hateley, Erica
2013-01-01
Young adult literature is a tool of socialisation and acculturation for young readers. This extends to endowing "reading" with particular significance in terms of what literature should be read and why. This paper considers some recent young adult fiction with an eye to its engagement with canonical literature and its representations of…
Obituary: George Hamilton Bowen Jr. (1925-2009)
Willson, Lee Anne; Struck, Curtis
2011-12-01
Our colleague and collaborator George Hamilton Bowen, Jr., passed away November 1, 2009 in Ames, Iowa. George was born June 20, 1925 in Tulsa, Oklahoma to George and Dorothy (Huntington) Bowen. He married Marjorie Brown June 19, 1948 in Redondo Beach, California; they had five children, with eight grandchildren and five great-grandchildren at the time of his death. George H. Bowen's third or perhaps his fourth career was in astronomy. He was drafted into the navy in 1944, at the end of his first year as a student at Caltech, and ended his war-time service as an electronic technician on the aircraft carrier Shangri-La. He later said "In just nine months, starting from scratch (Ohm's law!), we learned an amazing amount - not by memorization, of course, but by study and real understanding of the basic function of the most advanced AC circuits then being used for instrumentation, measurements, communications, control systems, and much more." He gained a confidence that he could quickly and accurately diagnose and solve technical problems that stood him well in future work. One accomplishment he took particular pride in was figuring out how the radar control used cams and gears to solve the trigonometry for accurate pointing. He also described how the captain was alarmed when weather conditions changed so that refraction no longer showed them distant, small boats around the curvature of Earth. After the war, George Bowen returned to undergraduate and eventually graduate study at Caltech, where he was recruited to the biophysics research group headed by future Nobel Laureate Max Delbrück. George often described his joy in working with these first-rate scientists and finding himself accepted as a part of the effort. He finished his BS with honors in 1949 and his PhD in 1953 with a thesis on "Kinetic Studies on the Mechanism of Photoreactivation of Bacteriophase T2 Inactivated by Ultraviolet Light" involving work with E Coli. This work was supported by grants from the U
Essén, Hanno; Nordmark, Arne B.
2016-09-01
The canonical Poisson bracket algebra of four-dimensional relativistic mechanics is used to derive the equation of motion for a charged particle, with the Lorentz force, and the homogeneous Maxwell equations.
When Canonical Quantization Fails, Here is How to Fix It
Klauder, John R.
2016-01-01
Following Dirac, the rules of canonical quantization include classical and quantum contact transformations of classical and quantum phase space variables. While arbitrary classical canonical coordinate transformations exist that is not the case for some analogous quantum canonical coordinate transformations. This failure is due to the rigid connection of quantum variables arising by promoting the corresponding classical variable from a $c$-number to a $q$-number. A different relationship of $...
Canonical terminal patterning is an evolutionary novelty.
Duncan, Elizabeth J; Benton, Matthew A; Dearden, Peter K
2013-05-01
Patterning of the terminal regions of the Drosophila embryo is achieved by an exquisitely regulated signal that passes between the follicle cells of the ovary, and the developing embryo. This pathway, however, is missing or modified in other insects. Here we trace the evolution of this pathway by examining the origins and expression of its components. The three core components of this pathway: trunk, torso and torso-like have different evolutionary histories and have been assembled step-wise to form the canonical terminal patterning pathway of Drosophila and Tribolium. Trunk, torso and a gene unrelated to terminal patterning, prothoraciotrophic hormone (PTTH), show an intimately linked evolutionary history, with every holometabolous insect, except the honeybee, possessing both PTTH and torso genes. Trunk is more restricted in its phylogenetic distribution, present only in the Diptera and Tribolium and, surprisingly, in the chelicerate Ixodes scapularis, raising the possibility that trunk and torso evolved earlier than previously thought. In Drosophila torso-like restricts the activation of the terminal patterning pathway to the poles of the embryo. Torso-like evolved in the pan-crustacean lineage, but based on expression of components of the canonical terminal patterning system in the hemimetabolous insect Acyrthosiphon pisum and the holometabolous insect Apis mellifera, we find that the canonical terminal-patterning system is not active in these insects. We therefore propose that the ancestral function of torso-like is unrelated to terminal patterning and that torso-like has become co-opted into terminal patterning in the lineage leading to Coleoptera and Diptera. We also show that this co-option has not resulted in changes to the molecular function of this protein. Torso-like from the pea aphid, honeybee and Drosophila, despite being expressed in different patterns, are functionally equivalent. We propose that co-option of torso-like into restricting the activity
The Literary Canon in the Age of New Media
Backe, Hans-Joachim
2015-01-01
and mediality of the canon. In a development that has largely gone unnoticed outside German speaking countries, new approaches for discussing current and future processes of canonization have been developed in recent years. One pivotal element of this process has been a thorough re-evaluation new media...... as a touchstone for both defining literature in the digital age and inquiring into the mechanisms of contemporary canon formation. The article is thus aimed at introducing both the specifically German approach to canon developed in recent years and its results to a larger scholarly community....
Update on non-canonical microRNAs
2014-01-01
Non-canonical microRNAs are a recently-discovered subset of microRNAs. They structurally and functionally resemble canonical miRNAs, but were found to follow distinct maturation pathways, typically bypassing one or more steps of the classic canonical biogenesis pathway. Non-canonical miRNAs were found to have diverse origins, including introns, snoRNAs, endogenous shRNAs and tRNAs. Our knowledge about their functions remains relatively primitive; however, many interesting discoveries have tak...
The Topology of Canonical Flux Tubes in Flared Jet Geometry
Sander Lavine, Eric; You, Setthivoine
2017-01-01
Magnetized plasma jets are generally modeled as magnetic flux tubes filled with flowing plasma governed by magnetohydrodynamics (MHD). We outline here a more fundamental approach based on flux tubes of canonical vorticity, where canonical vorticity is defined as the circulation of the species’ canonical momentum. This approach extends the concept of magnetic flux tube evolution to include the effects of finite particle momentum and enables visualization of the topology of plasma jets in regimes beyond MHD. A flared, current-carrying magnetic flux tube in an ion-electron plasma with finite ion momentum is thus equivalent to either a pair of electron and ion flow flux tubes, a pair of electron and ion canonical momentum flux tubes, or a pair of electron and ion canonical vorticity flux tubes. We examine the morphology of all these flux tubes for increasing electrical currents, different radial current profiles, different electron Mach numbers, and a fixed, flared, axisymmetric magnetic geometry. Calculations of gauge-invariant relative canonical helicities track the evolution of magnetic, cross, and kinetic helicities in the system, and show that ion flow fields can unwind to compensate for an increasing magnetic twist. The results demonstrate that including a species’ finite momentum can result in a very long collimated canonical vorticity flux tube even if the magnetic flux tube is flared. With finite momentum, particle density gradients must be normal to canonical vorticities, not to magnetic fields, so observations of collimated astrophysical jets could be images of canonical vorticity flux tubes instead of magnetic flux tubes.
Hamilton体系下压电材料层合板特征值灵敏度分析%SENSITIVITY ANALYSIS OF EIGENVALUE FOR PIEZOELECTRIC IN HAMILTON SYSTEMS
卢翔; 李顶河; 徐建新; 卿光辉
2011-01-01
在Hamilton体系下,基于区间B(B-spline wavelet on the interval)-样条小波有限元法研究压电材料特征值的灵敏度分析问题,推导压电材料特征值响应灵敏度系数的控制方程.利用二分法求得压电材料层合板前4阶特征值对材料密度的灵敏度系数,并与有限差分法所得结果相比较,证明所提方法的可靠性.结果表明,在Hamilton体系下求解特征值的灵敏度系数是可行的.%In the structural shape optimization (SSO) procedures, one of the main difficulties is to perform an accurate sensitivity analysis for the structural response with respect to some parameters. At present, the analytical, semi-analytical and finite difference methods are the most commonly used. In Hamilton systems, the sensitivity analysis of eigenvalue response was studied for piezoelectric laminated plates, and the governing equation of sensitivity coefficients of eigenvalue for piezoelectric laminated plates was derived based on B-spline wavelet on the interval (BSWI) wavelets element methods in the present work. So the sensitivity coefficients of eigenvalue would be obtained in Hamilton system, while it just would be gained in Lagrange system before. Sensitivity coefficients of eigenvalue of first 4 ranks with respect to density are obtained by bisection mehtod. And the numerical results of bisection mehtod are compared with that of the finite difference methods. The reliability of this eigenvalue sensitivity analysis method which based on wavelets and Hamilton systems is proved by this compare.
Gnutzmann, Sven; Waltner, Daniel
2016-12-01
We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016), 10.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.
Hamilton decompositions of regular expanders: a proof of Kelly's conjecture for large tournaments
Kühn, Daniela
2012-01-01
A long-standing conjecture of Kelly states that every regular tournament on n vertices can be decomposed into (n-1)/2 edge-disjoint Hamilton cycles. We prove this conjecture for large n. In fact, we prove a far more general result, based on our recent concept of robust expansion and a new method for decomposing graphs. We show that every sufficiently large regular digraph G on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into edge-disjoint Hamilton cycles. This enables us to obtain numerous further results, e.g. as a special case we confirm a conjecture of Erdos on packing Hamilton cycles in random tournaments. As corollaries to the main result, we also obtain several results on packing Hamilton cycles in undirected graphs, giving e.g. the best known result on a conjecture of Nash-Williams. We also apply our result to solve a problem on the domination ratio of the Asymmetric Travelling Salesman problem, which was raised e.g. by Glover and Punnen as well as Alon,...
Mobile Air Monitoring: Measuring Change in Air Quality in the City of Hamilton, 2005-2010
Adams, Matthew D.; DeLuca, Patrick F.; Corr, Denis; Kanaroglou, Pavlos S.
2012-01-01
This paper examines the change in air pollutant concentrations between 2005 and 2010 occurring in the City of Hamilton, Ontario, Canada. After analysis of stationary air pollutant concentration data, we analyze mobile air pollutant concentration data. Air pollutants included in the analysis are CO, PM[subscript 2.5], SO[subscript 2], NO,…
Air Quality in Hamilton: Who Is Concerned? Perceptions from Three Neighbourhoods
Simone, Dylan; Eyles, John; Newbold, K. Bruce; Kitchen, Peter; Williams, Allison
2012-01-01
This study investigates the factors influencing perceptions of air quality in the industrial city of Hamilton, Canada. The research employs data collected via a telephone survey of 1,002 adult residents in three neighbourhoods. Perceptions in the neighbourhoods were examined by individual socio-demographic factors (age, gender, marital and…
LI Wei-hua; LUO En; HUANG Wei-jiang
2007-01-01
According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An important integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper. Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.
Octavia Butler and Virginia Hamilton: Black Women Writers and Science Fiction.
Hampton, Gregory Jerome; Brooks, Wanda M.
2003-01-01
Notes that African American literature has always had science fiction elements in its focus on narratives of the alienated and marginalized "other." Contends that Octavia Butler and Virginia Hamilton are two African American writers of science fiction who examine the connections between the stories of a culture and the genre of science…
Excellent reliability of the Hamilton Depression Rating Scale (HDRS-21) in Indonesia after training
Istriana, E.; Kurnia, A.; Weijers, A.; Hidayat, T.; Pinxten, W.J.L.; Jong, C.A.J. de; Schellekens, A.F.A.
2013-01-01
Introduction: The Hamilton Depression Rating Scale (HDRS) is the most widely used depression rating scale worldwide. Reliability of HDRS has been reported mainly from Western countries. The current study tested the reliability of HDRS ratings among psychiatric residents in Indonesia, before and afte
And Others; Gilmartin, Harvey
1979-01-01
Presented is a form of Hamilton's principle for classical mechanics appropriate to the study of arbitrary self-sustained vibrations in one dimension. It is applied as an approximate computational tool to the study of several examples of anharmonic oscillation. (Author/GA)
Helping in cooperatively breeding long-tailed tits: a test of Hamilton's rule.
Hatchwell, Ben J; Gullett, Philippa R; Adams, Mark J
2014-05-19
Inclusive fitness theory provides the conceptual framework for our current understanding of social evolution, and empirical studies suggest that kin selection is a critical process in the evolution of animal sociality. A key prediction of inclusive fitness theory is that altruistic behaviour evolves when the costs incurred by an altruist (c) are outweighed by the benefit to the recipient (b), weighted by the relatedness of altruist to recipient (r), i.e. Hamilton's rule rb > c. Despite its central importance in social evolution theory, there have been relatively few empirical tests of Hamilton's rule, and hardly any among cooperatively breeding vertebrates, leading some authors to question its utility. Here, we use data from a long-term study of cooperatively breeding long-tailed tits Aegithalos caudatus to examine whether helping behaviour satisfies Hamilton's condition for the evolution of altruism. We show that helpers are altruistic because they incur survival costs through the provision of alloparental care for offspring. However, they also accrue substantial benefits through increased survival of related breeders and offspring, and despite the low average relatedness of helpers to recipients, these benefits of helping outweigh the costs incurred. We conclude that Hamilton's rule for the evolution of altruistic helping behaviour is satisfied in this species.
Light Rail Transit in Hamilton: Health, Environmental and Economic Impact Analysis
Topalovic, P.; Carter, J.; Topalovic, M.; Krantzberg, G.
2012-01-01
Hamilton's historical roots as an electric, industrial and transportation-oriented city provide it with a high potential for rapid transit, especially when combined with its growing population, developing economy, redeveloping downtown core and its plans for sustainable growth. This paper explores the health, environmental, social and economic…
Two-item discrimination and Hamilton search learning in infant pigtailed macaque monkeys
Ha, J.C.; Mandell, D.J.; Gray, J.
2011-01-01
This study investigated how infant pigtailed macaque monkeys performed on two separate learning assessments, two-object discrimination/reversal and Hamilton search learning. Although the learning tasks have been tested on several species, including non-human primates, there have been no normative
Perceptions of Quality Life in Hamilton's Neighbourhood Hubs: A Qualitative Analysis
Eby, Jeanette; Kitchen, Peter; Williams, Allison
2012-01-01
This paper examines perceptions of quality of life in Hamilton, Ontario, Canada from the perspective of residents and key community stakeholders. A series of eight focus groups were conducted. Six sessions were held with residents of neighbourhood "hubs", areas characterized by high levels of poverty. The following themes were highlighted as…
Perceptions of Quality Life in Hamilton's Neighbourhood Hubs: A Qualitative Analysis
Eby, Jeanette; Kitchen, Peter; Williams, Allison
2012-01-01
This paper examines perceptions of quality of life in Hamilton, Ontario, Canada from the perspective of residents and key community stakeholders. A series of eight focus groups were conducted. Six sessions were held with residents of neighbourhood "hubs", areas characterized by high levels of poverty. The following themes were…
Angel, V.; Garvey, A.; Sydor, M.
2017-08-01
In the face of changing economies and patterns of development, the definition of heritage is diversifying, and the role of inventories in local heritage planning is coming to the fore. The Durand neighbourhood is a layered and complex area located in inner-city Hamilton, Ontario, Canada, and the second subject area in a set of pilot inventory studies to develop a new city-wide inventory strategy for the City of Hamilton,. This paper presents an innovative digital workflow developed to undertake the Durand Built Heritage Inventory project. An online database was developed to be at the centre of all processes, including digital documentation, record management, analysis and variable outputs. Digital tools were employed for survey work in the field and analytical work in the office, resulting in a GIS-based dataset that can be integrated into Hamilton's larger municipal planning system. Together with digital mapping and digitized historical resources, the Durand database has been leveraged to produce both digital and static outputs to shape recommendations for the protection of Hamilton's heritage resources.
Octavia Butler and Virginia Hamilton: Black Women Writers and Science Fiction.
Hampton, Gregory Jerome; Brooks, Wanda M.
2003-01-01
Notes that African American literature has always had science fiction elements in its focus on narratives of the alienated and marginalized "other." Contends that Octavia Butler and Virginia Hamilton are two African American writers of science fiction who examine the connections between the stories of a culture and the genre of science fiction.…
Air Quality in Hamilton: Who Is Concerned? Perceptions from Three Neighbourhoods
Simone, Dylan; Eyles, John; Newbold, K. Bruce; Kitchen, Peter; Williams, Allison
2012-01-01
This study investigates the factors influencing perceptions of air quality in the industrial city of Hamilton, Canada. The research employs data collected via a telephone survey of 1,002 adult residents in three neighbourhoods. Perceptions in the neighbourhoods were examined by individual socio-demographic factors (age, gender, marital and…
Two-item discrimination and Hamilton search learning in infant pigtailed macaque monkeys
Ha, J.C.; Mandell, D.J.; Gray, J.
2011-01-01
This study investigated how infant pigtailed macaque monkeys performed on two separate learning assessments, two-object discrimination/reversal and Hamilton search learning. Although the learning tasks have been tested on several species, including non-human primates, there have been no normative re
Enhanced Preliminary Assessment. Task Order 2. Hamilton Army Airfield, Novato, California
1990-01-01
that Novato and San Rafael will likely continue to be the population centers of the county. 2.4.2 CIUMATE Hamilton Army Airfield is located...Sacramento Reserve Center (2) Modesto Reserve Center (1) San Pablo Reserve Center (2) Concord Reserve Center (4) Santa Rosa Reserve Center (4) A-7 -4 - IEI
Linear canonical transforms theory and applications
Kutay, M; Ozaktas, Haldun; Sheridan, John
2016-01-01
This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications. This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.
New Canonical Variables for d=11 Supergravity
Melosch, S; Melosch, Stephan; Nicolai, Hermann
1998-01-01
A set of new canonical variables for $d=11$ supergravity is proposed which renders the supersymmetry variations and the supersymmetry constraint polynomial. The construction is based on the $SO(1,2)\\times SO(16)$ invariant reformulation of $d=11$ supergravity given in previous work, and has some similarities with Ashtekar's reformulation of Einstein's theory. The new bosonic variables fuse the gravitational degrees of freedom with those of the three-index photon $A_{MNP}$ in accordance with the hidden symmetries of the dimensionally reduced theory. Although $E_8$ is not a symmetry of the theory, the bosonic sector exhibits a remarkable $E_8$ structure, hinting at the existence of a novel type of ``exceptional geometry''.
The Deuteron as a Canonically Quantized Biskyrmion
Acus, A; Norvaisas, E; Riska, D O
2003-01-01
The ground state configurations of the solution to Skyrme's topological soliton model for systems with baryon number larger than 1 are well approximated with rational map ans"atze, without individual baryon coordinates. Here canonical quantization of the baryon number 2 system, which represents the deuteron, is carried out in the rational map approximation. The solution, which is described by the 6 parameters of the chiral group SU(2)$times$SU(2), is stabilized by the quantum corrections. The matter density of the variational quantized solution has the required exponential large distance falloff and the quantum numbers of the deuteron. Similarly to the axially symmetric semiclassical solution, the radius and the quadrupole moment are, however, only about half as large as the corresponding empirical values. The quantized deuteron solution is constructed for representations of arbitrary dimension of the chiral group.
Consistency of canonical formulation of Horava gravity
Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Tainan, Taiwan (China)
2011-09-22
Both the non-projectable and projectable version of Horava gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra graviton mode which can be problematic. A new formulation (based on arXiv:1007.1563) of Horava gravity which is naturally realized as a representation of the master constraint algebra (instead of the Dirac algebra) studied by loop quantum gravity researchers is presented. This formulation yields a consistent canonical theory with first class constraints; and captures the essence of Horava gravity in retaining only spatial diffeomorphisms as the physically relevant non-trivial gauge symmetry. At the same time the local Hamiltonian constraint is equivalently enforced by the master constraint.
Families of Log Canonically Polarized Varieties
Dundon, Ariana
2011-01-01
Determining the number of singular fibers in a family of varieties over a curve is a generalization of Shafarevich's Conjecture and has implications for the types of subvarieties that can appear in the corresponding moduli stack. We consider families of log canonically polarized varieties over $\\P^1$, i.e. families $g:(Y,D)\\to \\P^1$ where $D$ is an effective snc divisor and the sheaf $\\omega_{Y/\\P^1}(D)$ is $g$-ample. After first defining what it means for fibers of such a family to be singular, we show that with the addition of certain mild hypotheses (the fibers have finite automorphism group, $\\sO_Y(D)$ is semi-ample, and the components of $D$ must avoid the singular locus of the fibers and intersect the fibers transversely), such a family must either be isotrivial or contain at least 3 singular fibers.
An extension of the Noether theorem: Accompanying equations possessing conservation laws
Dorodnitsyn, V. A.; Ibragimov, N. H.
2014-02-01
It is shown that the Noether theorem can be extended for some equations associated (accompanying) with Euler-Lagrange equation. Each symmetry of Lagrangian yields a class of accompanying equations possessing conservation law (first integral). The generalization is done for canonical Hamiltonian equations as well.
Towards a 'canonical' agranular cortical microcircuit
Sarah F. Beul
2015-01-01
Full Text Available Based on regularities in the intrinsic microcircuitry of cortical areas, variants of a 'canonical' cortical microcircuit have been proposed and widely adopted, particularly in computational neuroscience and neuroinformatics. However, this circuit is founded on striate cortex, which manifests perhaps the most extreme instance of cortical organization, in terms of a very high density of cells in highly differentiated cortical layers. Most other cortical regions have a less well differentiated architecture, stretching in gradients from the very dense eulaminate primary cortical areas to the other extreme of dysgranular and agranular areas of low density and poor laminar differentiation. It is unlikely for the patterns of inter- and intra-laminar connections to be uniform in spite of strong variations of their structural substrate. This assumption is corroborated by reports of divergence in intrinsic circuitry across the cortex. Consequently, it remains an important goal to define local microcircuits for a variety of cortical types, in particular, agranular cortical regions. As a counterpoint to the striate microcircuit, which may be anchored in an exceptional cytoarchitecture, we here outline a tentative microcircuit for agranular cortex. The circuit is based on a synthesis of the available literature on the local microcircuitry in agranular cortical areas of the rodent brain, investigated by anatomical and electrophysiological approaches. A central observation of these investigations is a weakening of interlaminar inhibition as cortical cytoarchitecture becomes less distinctive. Thus, our study of agranular microcircuitry revealed deviations from the well-known 'canonical' microcircuit established for striate cortex, suggesting variations in the intrinsic circuitry across the cortex that may be functionally relevant.
Canonical quantization of a string describing N branes at angles
Pesando, Igor
2014-12-01
We study the canonical quantization of a bosonic string in presence of N twist fields. This generalizes the quantization of the twisted string in two ways: the in and out states are not necessarily twisted and the number of twist fields N can be bigger than 2. In order to quantize the theory we need to find the normal modes. Then we need to define a product between two modes which is conserved. Because of this we need to use the Klein-Gordon product and to separate the string coordinate into the classical and the quantum part. The quantum part has different boundary conditions than the original string coordinates but these boundary conditions are precisely those which make the operator describing the equation of motion self adjoint. The splitting of the string coordinates into a classical and quantum part allows the formulation of an improved overlap principle. Using this approach we then proceed in computing the generating function for the generic correlator with L untwisted operators and N (excited) twist fields for branes at angles. We recover as expected the results previously obtained using the path integral. This construction explains why these correlators are given by a generalization of the Wick theorem.
Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation
Yong, Jiongmin
2012-01-01
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value function of the problem. Well-posedness and some properties of such an equation is studied, and time-consistent equilibrium strategies are constructed. As special cases, the linear-quadratic problem and a generalized Merton's portfolio problem are investigated.
Canonical connection on a class of Riemannian almost product manifolds
Mekerov, Dimitar
2009-01-01
The canonical connection on a Riemannian almost product manifolds is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with nonintegrable almost product structure.
Iterative algorithms to approximate canonical Gabor windows: Computational aspects
Janssen, A.J.E.M; Søndergaard, Peter Lempel
In this paper we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g,a,b). The iterations start with the window g while the iteration steps comprise the window g, the k^th iterand...
The Literary Canon in the Age of New Media
Backe, Hans-Joachim
2015-01-01
and mediality of the canon. In a development that has largely gone unnoticed outside German speaking countries, new approaches for discussing current and future processes of canonization have been developed in recent years. One pivotal element of this process has been a thorough re-evaluation new media...
CERN Photo Club (CPC) / Canon Contest - My View of CERN
Steyaert, Didier
2016-01-01
The CERN Photo Club has organized in collaboration with Canon Switzerland a photo contest open to all members of the CERN (Persons with a CERN access card). The only restriction is that the photos must have been taken with a CANON camera (DSLR, bridge or compact) between 1 and 31 October 2016.
Critical Literature Pedagogy: Teaching Canonical Literature for Critical Literacy
Borsheim-Black, Carlin; Macaluso, Michael; Petrone, Robert
2014-01-01
This article introduces Critical Literature Pedagogy (CLP), a pedagogical framework for applying goals of critical literacy within the context of teaching canonical literature. Critical literacies encompass skills and dispositions to understand, question, and critique ideological messages of texts; because canonical literature is often…
Canonical Quantum Teleportation of Two-Particle Arbitrary State
HAO Xiang; ZHU Shi-Qun
2005-01-01
The canonical quantum teleportation of two-particle arbitrary state is realized by means of phase operator and number operator. The maximally entangled eigenstates between the difference of phase operators and the sum of number operators are considered as the quantum channels. In contrast to the standard quantum teleportation, the different unitary local operation of canonical teleportation can be simplified by a general expression.
Relativistic Spinning Particle without Grassmann Variables and the Dirac Equation
A. A. Deriglazov
2011-01-01
Full Text Available We present the relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. Classical equations for the spin tensor are the same as those of the Barut-Zanghi model of spinning particle.
Canonical correlations between chemical and energetic characteristics of lignocellulosic wastes
Thiago de Paula Protásio
2012-09-01
Full Text Available Canonical correlation analysis is a statistical multivariate procedure that allows analyzing linear correlation that may exist between two groups or sets of variables (X and Y. This paper aimed to provide canonical correlation analysis between a group comprised of lignin and total extractives contents and higher heating value (HHV with a group of elemental components (carbon, hydrogen, nitrogen and sulfur for lignocellulosic wastes. The following wastes were used: eucalyptus shavings; pine shavings; red cedar shavings; sugar cane bagasse; residual bamboo cellulose pulp; coffee husk and parchment; maize harvesting wastes; and rice husk. Only the first canonical function was significant, but it presented a low canonical R². High carbon, hydrogen and sulfur contents and low nitrogen contents seem to be related to high total extractives contents of the lignocellulosic wastes. The preliminary results found in this paper indicate that the canonical correlations were not efficient to explain the correlations between the chemical elemental components and lignin contents and higher heating values.
A Canonical Approach to the Argument/Adjunct Distinction
Diana Forker
2014-01-01
Full Text Available This paper provides an account of the argument/adjunct distinction implementing the 'canonical approach'. I identify five criteria (obligatoriness, latency, co-occurrence restrictions, grammatical relations, and iterability and seven diagnostic tendencies that can be used to distinguish canonical arguments from canonical adjuncts. I then apply the criteria and tendencies to data from the Nakh-Daghestanian language Hinuq. Hinuq makes extensive use of spatial cases for marking adjunct-like and argument-like NPs. By means of the criteria and tendencies it is possible to distinguish spatial NPs that come close to canonical arguments from those that are canonical adjuncts, and to place the remaining NPs bearing spatial cases within the argument-adjunct continuum.
Matrix product purifications for canonical ensembles and quantum number distributions
Barthel, Thomas
2016-09-01
Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs substantially. It is straightforward to compute an MPP of a grand-canonical ensemble, also when symmetries are exploited. This paper provides and demonstrates methods for the efficient computation of MPPs of canonical ensembles under utilization of symmetries. Furthermore, we present a scheme for the evaluation of global quantum number distributions using matrix product density operators (MPDOs). We provide exact matrix product representations for canonical infinite-temperature states, and discuss how they can be constructed alternatively by applying matrix product operators to vacuum-type states or by using entangler Hamiltonians. A demonstration of the techniques for Heisenberg spin-1 /2 chains explains why the difference in the energy densities of canonical and grand-canonical ensembles decays as 1 /L .
The canon as text for a biblical theology
James A. Loader
2005-10-01
Full Text Available The novelty of the canonical approach is questioned and its fascination at least partly traced to the Reformation, as well as to the post-Reformation’s need for a clear and authoritative canon to perform the function previously performed by the church. This does not minimise the elusiveness and deeply contradictory positions both within the canon and triggered by it. On the one hand, the canon itself is a centripetal phenomenon and does play an important role in exegesis and theology. Even so, on the other hand, it not only contains many difficulties, but also causes various additional problems of a formal as well as a theological nature. The question is mooted whether the canonical approach alleviates or aggravates the dilemma. Since this approach has become a major factor in Christian theology, aspects of the Christian canon are used to gauge whether “canon” is an appropriate category for eliminating difficulties that arise by virtue of its own existence. Problematic uses and appropriations of several Old Testament canons are advanced, as well as evidence in the New Testament of a consciousness that the “old” has been surpassed(“Überbietungsbewußtsein”. It is maintained that at least the Childs version of the canonical approach fails to smooth out these and similar difficulties. As a method it can cater for the New Testament’s (superior role as the hermeneutical standard for evaluating the Old, but flounders on its inability to create the theological unity it claims can solve religious problems exposed by Old Testament historical criticism. It is concluded that canon as a category cannot be dispensed with, but is useful for the opposite of the purpose to which it is conventionally put: far from bringing about theological “unity” or producing a standard for “correct” exegesis, it requires different readings of different canons.
Wheeler-DeWitt equation and Feynman diagrams
Barvinsky, A O
1998-01-01
We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the conventional Feynman diagrammatic technique involving graviton loops and vertices. It also reveals explicitly the back reaction effects of quantized matter and graviton vacuum polarization. This provides an explicit correspondence between the frameworks of canonical and covariant quantum gravity in the semiclassical limit.
Wheeler-DeWitt equation and Feynman diagrams
Barvinsky, Andrei O.; Kiefer, Claus
1998-08-01
We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the Feynman diagrammatic technique involving graviton loops and vertices. It also reveals explicitly the back-reaction effects of quantized matter and graviton vacuum polarization. This provides an explicit correspondence between the frameworks of canonical and covariant quantum gravity in the semiclassical limit.
Swenson, Sarah A
2015-02-01
W.D. Hamilton's theory of inclusive fitness aimed to define the evolved limits of altruism with mathematical precision. Although it was meant to apply universally, it has been almost irretrievably entwined with the particular case of social insects that featured in his famous 1964 papers. The assumption that social insects were central to Hamilton's early work contradicts material in his rich personal archive. In fact, careful study of Hamilton's notes, letters, diaries, and early essays indicates the extent to which he had humans in mind when he decided altruism was a topic worthy of biological inquiry. For this reason, this article reconsiders the role of extra-scientific factors in Hamilton's early theorizing. In doing so, it offers an alternative perspective as to why Hamilton saw self-sacrifice to be an important subject. Although the traditional narrative prioritizes his distaste for benefit-of-the-species explanations as a motivating factor behind his foundational work, I argue that greater attention ought to be given to Hamilton's hope that science could be used to address social ills. By reconsidering the meaning Hamilton intended inclusive fitness to have, we see that while he was no political ideologue, the socio-political relevance of his theory was nevertheless integral to its development.
A Note on Four-Dimensional Symmetry Algebras and Fourth-Order Ordinary Differential Equations
A. Fatima
2013-01-01
Full Text Available We provide a supplementation of the results on the canonical forms for scalar fourth-order ordinary differential equations (ODEs which admit four-dimensional Lie algebras obtained recently. Together with these new canonical forms, a complete list of scalar fourth-order ODEs that admit four-dimensional Lie algebras is available.
El Escritor y las Normas del Canon Literario (The Writer and the Norms of the Literary Canon).
Policarpo, Alcibiades
This paper speculates about whether a literary canon exists in contemporary Latin American literature, particularly in the prose genre. The paper points to Carlos Fuentes, Gabriel Garcia Marquez, and Mario Vargas Llosa as the three authors who might form this traditional and liberal canon with their works "La Muerte de Artemio Cruz"…
Canonical Coordinates for Retino-Cortical Magnification
Luc Florack
2014-02-01
Full Text Available A geometric model for a biologically-inspired visual front-end is proposed, based on an isotropic, scale-invariant two-form field. The model incorporates a foveal property typical of biological visual systems, with an approximately linear decrease of resolution as a function of eccentricity, and by a physical size constant that measures the radius of the geometric foveola, the central region characterized by maximal resolving power. It admits a description in singularity-free canonical coordinates generalizing the familiar log-polar coordinates and reducing to these in the asymptotic case of negligibly-sized geometric foveola or, equivalently, at peripheral locations in the visual field. It has predictive power to the extent that quantitative geometric relationships pertaining to retino-cortical magnification along the primary visual pathway, such as receptive field size distribution and spatial arrangement in retina and striate cortex, can be deduced in a principled manner. The biological plausibility of the model is demonstrated by comparison with known facts of human vision.
Dissolution of Marriage According to Canon Law
MSc. Sulejman Ahmedi
2013-12-01
Full Text Available In the Canon law, dissolution of marriage is not allowed since it was considered sacred and as such cannot break until the two spouses are alive, except only if one of the spouses passes away. But throughout history we find cases when allowed dissolution of the marriage and causes specific conditions set by the church. Thus, according to the Old Testament, if, a man married to a woman, didn’t like something about his wife, should write a request for divorce and allow her to leave his home. Meanwhile according to the New Testament records, divorce is prohibited. Although most Protestants continue to espouse the view that marriage was sacred and as such should not be divorced, from those who had supported the idea of granting the divorce. One of them was Luther, who in his remarks before his preachers said: "In my opinion, the issue of divorce belongs to the law, are not they to whom called for regulation of parental relationships, why not have they the authority to regulate the relations between spouses". Protestant churches allow the dissolution of marriage: a Because of adultery by the wife; allowed by Jesus, b Unjustified abandonment of the marital community; c If there were other reasons: if one spouse refuses to have sexual marriage, if the husband abuses his wife repeatedly and without cause, severe illness of one spouse.
Finite Canonical Measure for Nonsingular Cosmologies
Page, Don N
2011-01-01
The total canonical (Liouville-Henneaux-Gibbons-Hawking-Stewart) measure is finite for completely nonsingular Friedmann-Robertson-Walker classical universes with a minimally coupled massive scalar field and a positive cosmological constant. For a cosmological constant very small in units of the square of the scalar field mass, most of the measure is for nearly de Sitter solutions with no inflation at a much more rapid rate. However, if one restricts to solutions in which the scalar field energy density is ever more than twice the equivalent energy density of the cosmological constant, then the number of e-folds of rapid inflation must be large, and the fraction of the measure is low in which the spatial curvature is comparable to the cosmological constant at the time when it is comparable to the energy density of the scalar field. The measure for such classical FRW-Lambda-phi models with both a big bang and a big crunch is also finite. Only the solutions with a big bang that expand forever, or the time-revers...
The canonical equilibrium of constrained molecular models
Echenique, Pablo; García-Risueño, Pablo
2011-01-01
In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. However, as any other element that affects the physical model, the imposition of constraints must be assessed from the point of view of accuracy: both the dynamics and the equilibrium statistical mechanics are model-dependent, and they will be changed if constraints are used. In this review, we investigate the accuracy of constrained models at the level of the equilibrium statistical mechanics distributions produced by the different dynamics. We carefully derive the canonical equilibrium distributions of both the constrained and unconstrained dynamics, comparing the two of them by means of a "stiff" approximation to the latter. We do so both in the case of flexible and hard constraints, i.e., when the value of the constrained coordinates depends on the conformation and when it is a cons...
An $OSp$ extension of Canonical Tensor Model
Narain, Gaurav
2015-01-01
Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally constrained system with a number of first-class constraints, which have a similar algebraic structure as the constraints of the ADM formalism of general relativity. In this paper, we formulate a super-extension of CTM as an attempt to incorporate fermionic degrees of freedom. The kinematical symmetry group is extended from $O(N)$ to $OSp(N,\\tilde N)$, and the constraints are constructed so that they form a first-class constraint super-Poisson algebra. This is a straightforward super-extension, and the constraints and their algebraic structure are formally unchanged from the purely bosonic case, except for the additional signs associated to the order of the fermionic indices and dynamical variables. However, this extension of CTM leads to the existence of negative norm state...
First-order partial differential equations in classical dynamics
Smith, B. R.
2009-12-01
Carathèodory's classic work on the calculus of variations explores in depth the connection between ordinary differential equations and first-order partial differential equations. The n second-order ordinary differential equations of a classical dynamical system reduce to a single first-order differential equation in 2n independent variables. The general solution of first-order partial differential equations touches on many concepts central to graduate-level courses in analytical dynamics including the Hamiltonian, Lagrange and Poisson brackets, and the Hamilton-Jacobi equation. For all but the simplest dynamical systems the solution requires one or more of these techniques. Three elementary dynamical problems (uniform acceleration, harmonic motion, and cyclotron motion) can be solved directly from the appropriate first-order partial differential equation without the use of advanced methods. The process offers an unusual perspective on classical dynamics, which is readily accessible to intermediate students who are not yet fully conversant with advanced approaches.
Chen, Qiang; Liu, Jian; Xiao, Jianyuan; Zhang, Ruili; He, Yang; Wang, Yulei
2016-01-01
An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon-matter interactions described by the Schr\\"odinger-Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. This new numerical capability enables us to carry out first-principle based simulation study of important photon-matter interactions, such at the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.
Domanov, Ignat; De Lathauwer, Lieven
2013-01-01
Canonical Polyadic Decomposition (CPD) of a third-order tensor is decomposition in a minimal number of rank-$1$ tensors. We call an algorithm algebraic if it is guaranteed to find the decomposition when it is exact and if it only relies on standard linear algebra (essentially sets of linear equations and matrix factorizations). The known algebraic algorithms for the computation of the CPD are limited to cases where at least one of the factor matrices has full column rank. In the paper we pres...
The geometry of ordinary variational equations
Krupková, Olga
1997-01-01
The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The reader should be familiar with elements of differential geometry, global analysis and the calculus of variations.
Generalisations of Hamilton's Rule Applied to Non-Additive Public Goods Games with Random Group Size
James A R Marshall
2014-07-01
Full Text Available Inclusive fitness theory has been described as being limited to certain special cases of social evolution. In particular some authors argue that the theory can only be applied to social interactions having additive fitness effects, and involving only pairs of individuals. This article takes an elegant formulation of non-additive public goods games from the literature, and shows how the two main generalisations of Hamilton's rule can be applied to such games when group sizes are random. In doing so inclusive fitness theory is thus applied to a very general class of social dilemmas, thereby providing further evidence for its generality. Interestingly, one of the two predominant versions of Hamilton's rule is found to be mathematically easier to apply to the scenario considered, despite both necessarily giving equivalent predictions.
Fleck, Marcelo Pio de Almeida; Chaves, Márcia Lorena Fagundes; Poirier-Littré, Marie France; Bourdel, Marie Chantal; Loo, Henri; Guelfi, Julien Daniel
2004-02-01
Among various research strategies for depression, the cross-cultural approach is a useful tool to investigate depressive disorders. The Hamilton Rating Scale for Depression was applied to 130 depressed inpatients in France and Brazil. Items were factorized by principal component analysis with Varimax rotation using the Kaiser or simulation method for factor sorting. Three factors were obtained in France, and four in Brazil. The first factor includes the core symptoms of depression in both samples. Qualitative and quantitative differences appeared in the anxiety factor between Brazilian and French samples. Insomnia items appeared as another factor for both groups. A limitation of this study is that it was conducted with small inpatient samples. Principal component analysis of the Hamilton Rating Scale for Depression for depressive inpatients in these two countries showed a similar structure. Differences observed were in the way anxiety items were distributed.
图的谱半径和Hamilton性%Spectral radius and Hamiltonicity of a graph
朱五华
2011-01-01
从图G的闭包理论角度去研究图的Hamilton性。利用图的补图谱半径的界，讨论了Hamilton图存在的谱条件，证明了n阶图G，如果它的补图的谱半径小于或等于（n-3）的算术平方根，则G是Hamilton图。%The Hamihonicity is studied from the closure theory of a graph G. We discuss some spectral conditions for the existence of Hamilton graph by using bounds of spectral radius of the Complement of a graph, and show that if G is a graph of order n with spectral radius of its complement is less than or equal to the arithmetic square root of （ n - 3） , then G is a Hamilton graph.
The Wasserstein geometry of nonlinear σ models and the Hamilton-Perelman Ricci flow
Carfora, Mauro
Nonlinear sigma models are quantum field theories describing, in the large deviation sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci flow. By exploiting the heat kernel embedding introduced by Gigli and Mantegazza, we show that the Wasserstein geometry of the space of probability measures over Riemannian metric measure spaces provides a natural setting for discussing the relation between nonlinear sigma models and Ricci flow theory. In particular, we analyze the embedding of Ricci flow into a heat kernel renormalization group flow for dilatonic nonlinear sigma models, and characterize a non-trivial generalization of the Hamilton-Perelman version of the Ricci flow. We discuss in detail the monotonicity and gradient flow properties of this extended flow.
Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems
Chen Rong; Xu Xue-Jun
2012-01-01
In this paper,the relation of the conformal invariance,the Noether symmetry,and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given.The relation between the conformal invariance and the Noether symmetry is discussed,the conformal factors of the determining expressions are found by using the Noether symmetry,and the Noether conserved quantity resulted from the conformal invariance is obtained.The relation between the conformal invariance and the Lie symmetry is discussed,the conformal factors are found by using the Lie symmetry,and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained.Two examples are given to illustrate the application of the results.
Non-canonical WNT signalling in the lung
Li, Changgong; Bellusci, Saverio; Borok, Zea; Minoo, Parviz
2015-01-01
The role of WNT signalling in metazoan organogenesis has been a topic of widespread interest. In the lung, while the role of canonical WNT signalling has been examined in some detail by multiple studies, the non-canonical WNT signalling has received limited attention. Reliable evidence shows that this important signalling mechanism constitutes a major regulatory pathway in lung development. In addition, accumulating evidence has also shown that the non-canonical WNT pathway is critical for maintaining lung homeostasis and that aberrant activation of this pathway may underlie several debilitating lung diseases. Functional analyses have further revealed that the non-canonical WNT pathway regulates multiple cellular activities in the lung that are dependent on the specific cellular context. In most cell types, non-canonical WNT signalling regulates canonical WNT activity, which is also critical for many aspects of lung biology. This review will summarize what is currently known about the role of non-canonical WNT signalling in lung development, homeostasis and pathogenesis of disease. PMID:26261051
AN APOLOGY OF THE LITERARY CANON IN A LINGUISTIC STUDY
Alexey Vladimirovich Sosnin
2015-01-01
Full Text Available The article highlights the principles of selecting practical material for a linguistic study aspiring to objectivity and states that in such a study orientation to the literary text is absolutely essential, as a solid corpus of literary texts is indispensable for describing complicated linguistic phenomena and mental structures standing behind them. The article puts forward the postulate that any serious study into the English language should be constructed on the English literary canon – a global textual corpus on the basis of which the greatest part of the educated speakers’ conceptual sphere is formed. At the same time, the article considers certain problems related to the Anglicist’s orientation towards the canon – its definition, limits, central and peripheral authors, the criteria of a literary work canonic status, arguments of those opposing any canonicity in literature, reconstruction of the canon in other cultures. The article also analyzes the cognitive aspect and tells about the key transformation of the English mentality, which gave rise to thinking in the terms of the time, cause-and-effect, and probability in canonic literature. The author of the article comes up with a principal conclusion: orientation to the literary canon in a linguistic study allows reconciling of linguistics and literature studies and including into the analysis nonlinguistic semiotic systems as well as idiolectal systems of conceptualizing the world in literary works.
Bound States and Band Structure - a Unified Treatment through the Quantum Hamilton - Jacobi Approach
Ranjani, S S; Panigrahi, P K
2005-01-01
We analyze the Scarf potential, which exhibits both discrete energy bound states and energy bands, through the quantum Hamilton-Jacobi approach. The singularity structure and the boundary conditions in the above approach, naturally isolate the bound and periodic states, once the problem is mapped to the zero energy sector of another quasi-exactly solvable quantum problem. The energy eigenvalues are obtained without having to solve for the corresponding eigenfunctions explicitly. We also demonstrate how to find the eigenfunctions through this method.
Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems
ZHANG Ming-Jiang; FANG Jian-Hui; LU Kai; PANG Ting; LIN Peng
2009-01-01
Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.
WANG Yu-Sheng; ZHANG Xiao-Ni; YUAN Bao-He; FANG Jian-Hui; YANG Guo-Hong; LIN Peng; PANG Ting
2008-01-01
Based on the concept of higher-order adiabatic invariants of mechanical system with action of a small perturbation, the perturbation to Lie symmetry and generalized Hojman adiabatic invariants for the relativistic Hamilton system are studied. Perturbation to Lie symmetry is discussed under general infinitesimal transformation of groups in which time is variable. The form and the criterion of generalized Hojman adiabatic invariants for this system are obtained. Finally, an example is given to illustrate the results.
Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method
Fukushima, Kenji
2015-01-01
The Lefschetz thimble method, i.e., the integration along the steepest descent cycles, is an idea to evade the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state wave-functions of a supersymmetric Hamilton dynamics, which is described with a framework akin to the complex Langevin method. We numerically construct the wave-functions on a grid using a toy model and confirm their well-localized behavior.
Grajevskaja, Viktorija
2017-01-01
Danio rerio (Hamilton, 1822) is a powerful vertebrate model system, which provides a unique combination of advantages that are important for an investigation of cardiovascular development and regeneration. However, conditional mutagenesis, which is essential for dissecting a role of developmental genes in regeneration, has not been demonstrated in the adult zebrafish. This remains a main disadvantage of D. rerio model system. The main aim of this research project was to use insertional ge...
Ilias Hossain, M.; Atiqur Rahman, M.
2013-09-01
We have investigated Hawking non-thermal and purely thermal Radiations of Reissner Nordström anti-de Sitter (RNAdS) black hole by massive particles tunneling method. The spacetime background has taken as dynamical, incorporate the self-gravitation effect of the emitted particles the imaginary part of the action has derived from Hamilton-Jacobi equation. We have supposed that energy and angular momentum are conserved and have shown that the non-thermal and thermal tunneling rates are related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum. The results for RNAdS black hole is also in the same manner with Parikh and Wilczek's opinion and explored the new result for Hawking radiation of RNAdS black hole.
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey
2004-01-01
The vector Maxwell equations of nonlinear optics coupled to a single Lorentz oscillator and with instantaneous Kerr nonlinearity are investigated by using Lie symmetry group methods. Lagrangian and Hamiltonian formulations of the equations are obtained. The aim of the analysis is to explore......-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...... to circumvent this problem, non-canonical Poisson bracket formulations of the equations are obtained in which the electric field is one of the non-canonical variables. Noether's theorem, and the Lie point symmetries admitted by the equations are used to obtain four conservation laws, including...
Kaneko, Yuta
2014-01-01
Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term -{\\Delta}Q, just representing the current density (Q is a Clebsch variable, and {\\Delta} is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensional Euler vorticity equation of a neutral fluid. A heuristic estimate shows that current sheets grow exponentially (even in a fully nonlinear regime) together with the action variable P that is conjugate to Q. By numerical simulation, the predicted behavior of the canonical variables, yielding exponential growth of current sheets, has been demonstrated.
Canonical approach to finite density QCD with multiple precision computation
Fukuda, Ryutaro; Oka, Shotaro
2015-01-01
We calculate the baryon chemical potential ($\\mu_B$) dependence of thermodynamic observables, i.e., pressure, baryon number density and susceptibility by lattice QCD using the canonical approach. We compare the results with those by the multi parameter reweighting (MPR) method; Both methods give very consistent values in the regions where errors of the MPR are under control. The canonical method gives reliable results over $\\mu_ B/T=3$,with $T$ being temperature. Multiple precision operations play an important roll in the evaluation of canonical partition functions.
Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations
Vasily E. Tarasov
2016-06-01
Full Text Available An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are represented by infinite series. This new mathematical tool allows us to build sensible discrete quantum mechanics based on the suggested differences and includes the correct canonical commutation and uncertainty relations.
Chondrules: The canonical and noncanonical views
Connolly, Harold C.; Jones, Rhian H.
2016-10-01
Millimeter-scale rock particles called chondrules are the principal components of the most common meteorites, chondrites. Hence, chondrules were arguably the most abundant components of the early solar system at the time of planetesimal accretion. Despite their fundamental importance, the existence of chondrules would not be predicted from current observations and models of young planetary systems. There are many different models for chondrule formation, but no single model satisfies the many constraints determined from their mineralogical and chemical properties and from chondrule analog experiments. Significant recent progress has shown that several models can satisfy first-order constraints and successfully reproduce chondrule thermal histories. However, second- and third-order constraints such as chondrule size ranges, open system behavior, oxidation states, reheating, and chemical diversity have not generally been addressed. Chondrule formation models include those based on processes that are known to occur in protoplanetary disk environments, including interactions with the early active Sun, impacts and collisions between planetary bodies, and radiative heating. Other models for chondrule heating mechanisms are based on hypothetical processes that are possible but have not been observed, like shock waves, planetesimal bow shocks, and lightning. We examine the evidence for the canonical view of chondrule formation, in which chondrules were free-floating particles in the protoplanetary disk, and the noncanonical view, in which chondrules were the by-products of planetesimal formation. The fundamental difference between these approaches has a bearing on the importance of chondrules during planet formation and the relevance of chondrules to interpreting the evolution of protoplanetary disks and planetary systems.
MBARI CANON Experiment Visualization and Analysis
Fatland, R.; Oscar, N.; Ryan, J. P.; Bellingham, J. G.
2013-12-01
We describe the task of understanding a marine drift experiment conducted by MBARI in Fall 2012 ('CANON'). Datasets were aggregated from a drifting ADCP, from the MBARI Environmental Sample Processor, from Long Range Autonomous Underwater Vehicles (LRAUVs), from other in situ sensors, from NASA and NOAA remote sensing platforms, from moorings, from shipboard CTD casts and from post-experiment metagenomic analysis. We seek to combine existing approaches to data synthesis -- visual inspection, cross correlation and co.-- with three new ideas. This approach has the purpose of differentiating biological signals into three causal categories: Microcurrent advection, physical factors and microbe metabolism. Respective examples are aberrance from Lagrangian frame drift due to windage, changes in solar flux over several days, and microbial population responses to shifts in nitrate concentration. The three ideas we implemented are as follows: First, we advect LRAUV data to look for patterns in time series data for conserved quanitities such as salinity. We investigate whether such patterns can be used to support or undermine the premise of Lagrangian motion of the experiment ensemble. Second we built a set of configurable filters that enable us to visually isolate segments of data: By type, value, time, anomaly and location. Third we associated data hypotheses with a Bayesian inferrence engine for the purpose of model validation, again across sections taken from within the complete data complex. The end result is towards a free-form exploration of experimental data with low latency: from question to view, from hypothesis to test (albeit with considerable preparatory effort.) Preliminary results show the three causal categories shifting in relative influence.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
On Global Smooth Solution of A Semi-Linear System of Wave Equations in R3
WU Haigen
2009-01-01
In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth so-lution of the system for subcritical case by using conservation of energy and Strichartz's estimate. On the basis of Morawetz-Poho2ev identity, we obtain the same result for the critical case.
Exact solution to the one-dimensional Dirac equation of linear potential
Long Chao-Yun; Qin Shui-Jie
2007-01-01
In this paper the one-dimensional Dirac equation with linear potential has been solved by the method of canonical transformation. The bound-state wavefunctions and the corresponding energy spectrum have been obtained for all bound states.