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Journal articles on the topic 'Hamiltonien non convexe'

Author: Grafiati

Published: 18 May 2024

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1

Ishii, Hitoshi. "The vanishing discount problem for monotone systems of Hamilton-Jacobi equations: a counterexample to the full convergence." Mathematics in Engineering 5, no. 4 (2023): 1–10. http://dx.doi.org/10.3934/mine.2023072.

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<abstract><p>In recent years there has been intense interest in the vanishing discount problem for Hamilton-Jacobi equations. In the case of the scalar equation, B. Ziliotto has recently given an example of the Hamilton-Jacobi equation having non-convex Hamiltonian in the gradient variable, for which the full convergence of the solutions does not hold as the discount factor tends to zero. We give here an explicit example of nonlinear monotone systems of Hamilton-Jacobi equations having convex Hamiltonians in the gradient variable, for which the full convergence of the solutions fai

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2

Timoumi, Mohsen. "Solutions périodiques de systèmes hamiltoniens convexes non coercitifs." Bulletin de la Classe des sciences 75, no. 1 (1989): 463–81. http://dx.doi.org/10.3406/barb.1989.57866.

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3

Cirant, Marco, and Alessio Porretta. "Long time behavior and turnpike solutions in mildly non-monotone mean field games." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 86. http://dx.doi.org/10.1051/cocv/2021077.

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We consider mean field game systems in time-horizon (0, T), where the individual cost functional depends locally on the density distribution of the agents, and the Hamiltonian is locally uniformly convex. We show that, even if the coupling cost functions are mildly non-monotone, then the system is still well posed due to the effect of individual noise. The rate of anti-monotonicity (i.e. the aggregation rate of the cost functions) which can be afforded depends on the intensity of the diffusion and on global bounds of solutions. We give applications to either the case of globally Lipschitz Hami

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4

CONTRERAS, GONZALO, and RENATO ITURRIAGA. "Convex Hamiltonians without conjugate points." Ergodic Theory and Dynamical Systems 19, no. 4 (1999): 901–52. http://dx.doi.org/10.1017/s014338579913387x.

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We construct the Green bundles for an energy level without conjugate points of a convex Hamiltonian. In this case we give a formula for the metric entropy of the Liouville measure and prove that the exponential map is a local diffeomorphism. We prove that the Hamiltonian flow is Anosov if and only if the Green bundles are transversal. Using the Clebsch transformation of the index form we prove that if the unique minimizing measure of a generic Lagrangian is supported on a periodic orbit, then it is a hyperbolic periodic orbit.We also show some examples of differences with the behaviour of a ge

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5

Hayat, Sakander, Muhammad Yasir Hayat Malik, Ali Ahmad, Suliman Khan, Faisal Yousafzai, and Roslan Hasni. "On Hamilton-Connectivity and Detour Index of Certain Families of Convex Polytopes." Mathematical Problems in Engineering 2021 (July 17, 2021): 1–18. http://dx.doi.org/10.1155/2021/5553216.

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A convex polytope is the convex hull of a finite set of points in the Euclidean space ℝ n . By preserving the adjacency-incidence relation between vertices of a polytope, its structural graph is constructed. A graph is called Hamilton-connected if there exists at least one Hamiltonian path between any of its two vertices. The detour index is defined to be the sum of the lengths of longest distances, i.e., detours between vertices in a graph. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering, whereas the detour index has important

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6

Pittman, S. M., E. Tannenbaum, and E. J. Heller. "Dynamical tunneling versus fast diffusion for a non-convex Hamiltonian." Journal of Chemical Physics 145, no. 5 (2016): 054303. http://dx.doi.org/10.1063/1.4960134.

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7

Monthus, Cécile. "Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and via explicit large deviations at various levels." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 6 (2023): 063206. http://dx.doi.org/10.1088/1742-5468/acdcea.

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Abstract For boundary-driven non-equilibrium Markov models of non-interacting particles in one dimension, either in continuous space with the Fokker–Planck dynamics involving an arbitrary force F(x) and an arbitrary diffusion coefficient D(x), or in discrete space with the Markov jump dynamics involving arbitrary nearest-neighbor transition rates w ( x ± 1 , x ) , the Markov generator can be transformed via an appropriate similarity transformation into a quantum supersymmetric Hamiltonian with many remarkable properties. We first describe how the mapping from the boundary-driven non-equilibriu

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8

Hayat, Sakander, Asad Khan, Suliman Khan, and Jia-Bao Liu. "Hamilton Connectivity of Convex Polytopes with Applications to Their Detour Index." Complexity 2021 (January 23, 2021): 1–23. http://dx.doi.org/10.1155/2021/6684784.

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A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for a graph is also an NP-complete problem. In this paper, we study the Hamilton-connect

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9

Zhou, Min, and Binggui Zhong. "Regions of applicability of Aubry-Mather Theory for non-convex Hamiltonian." Chinese Annals of Mathematics, Series B 32, no. 4 (2011): 605–14. http://dx.doi.org/10.1007/s11401-011-0654-3.

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10

Entov, Michael, and Leonid Polterovich. "Contact topology and non-equilibrium thermodynamics." Nonlinearity 36, no. 6 (2023): 3349–75. http://dx.doi.org/10.1088/1361-6544/acd1ce.

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Abstract We describe a method, based on contact topology, of showing the existence of semi-infinite trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and asymptotically converge to another Legendrian submanifold. We discuss a mathematical model of non-equilibrium thermodynamics where such trajectories play a role of relaxation processes, and illustrate our results in the case of the Glauber dynamics for the mean field Ising model.

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11

You, Bo, Zhi Li, Liang Ding, Haibo Gao, and Jiazhong Xu. "A new optimization-driven path planning method with probabilistic completeness for wheeled mobile robots." Measurement and Control 52, no. 5-6 (2019): 317–25. http://dx.doi.org/10.1177/0020294019836127.

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Wheeled mobile robots are widely utilized for environment-exploring tasks both on earth and in space. As a basis for global path planning tasks for wheeled mobile robots, in this study we propose a method for establishing an energy-based cost map. Then, we utilize an improved dual covariant Hamiltonian optimization for motion planning method, to perform point-to-region path planning in energy-based maps. The method is capable of efficiently handling high-dimensional path planning tasks with non-convex cost functions through applying a robust active set algorithm, that is, non-monotone gradient

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12

Radjenovic, B., M. Radmilovic-Radjenovic, and M. Mitric. "Application of the level set method on the non-convex Hamiltonians." Facta universitatis - series: Physics, Chemistry and Technology 7, no. 1 (2009): 33–44. http://dx.doi.org/10.2298/fupct0901033r.

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Application of the level set method extended for the case of non-convex Hamiltonians is illustrated by the three dimensional (3D) simulation results of the profile evolution during anisotropic wet etching of silicon. Etching rate function is modeled on the basis of the silicon symmetry properties, by means of the interpolation technique using experimentally obtained values of the principal [100], [110], [111], and high index [311] directions in KOH solutions. The resulting level set equations are solved using an open source implementation of the sparse field method.

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13

Giuliani, Filippo. "Transfers of energy through fast diffusion channels in some resonant PDEs on the circle." Discrete & Continuous Dynamical Systems 41, no. 11 (2021): 5057. http://dx.doi.org/10.3934/dcds.2021068.

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<p style='text-indent:20px;'>In this paper we consider two classes of resonant Hamiltonian PDEs on the circle with non-convex (respect to actions) first order resonant Hamiltonian. We show that, for appropriate choices of the nonlinearities we can find time-independent linear potentials that enable the construction of solutions that undergo a prescribed growth in the Sobolev norms. The solutions that we provide follow closely the orbits of a nonlinear resonant model, which is a good approximation of the full equation. The non-convexity of the resonant Hamiltonian allows the existence of

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14

Bardi, Martino, and Markus Fischer. "On non-uniqueness and uniqueness of solutions in finite-horizon Mean Field Games." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 44. http://dx.doi.org/10.1051/cocv/2018026.

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This paper presents a class of evolutive Mean Field Games with multiple solutions for all time horizons T and convex but non-smooth Hamiltonian H, as well as for smooth H and T large enough. The phenomenon is analysed in both the PDE and the probabilistic setting. The examples are compared with the current theory about uniqueness of solutions. In particular, a new result on uniqueness for the MFG PDEs with small data, e.g., small T, is proved. Some results are also extended to MFGs with two populations.

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15

Cordaro, Giuseppe. "Existence and location of periodic solutions to convex and non coercive Hamiltonian systems." Discrete & Continuous Dynamical Systems - A 12, no. 5 (2005): 983–96. http://dx.doi.org/10.3934/dcds.2005.12.983.

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16

Grotta-Ragazzo, C., and Pedro A. S. Salomão. "Global surfaces of section in non-regular convex energy levels of Hamiltonian systems." Mathematische Zeitschrift 255, no. 2 (2006): 323–34. http://dx.doi.org/10.1007/s00209-006-0026-y.

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17

Corsi, Livia, Roberto Feola, and Guido Gentile. "Lower-Dimensional Invariant Tori for Perturbations of a Class of Non-convex Hamiltonian Functions." Journal of Statistical Physics 150, no. 1 (2013): 156–80. http://dx.doi.org/10.1007/s10955-012-0682-8.

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18

KRITCHEVSKI, E., and S. STARR. "THE EXTENDED VARIATIONAL PRINCIPLE FOR MEAN-FIELD, CLASSICAL SPIN SYSTEMS." Reviews in Mathematical Physics 17, no. 10 (2005): 1209–39. http://dx.doi.org/10.1142/s0129055x05002510.

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The purpose of this article is to obtain a better understanding of the extended variational principle (EVP). The EVP is a formula for the thermodynamic pressure of a statistical mechanical system as a limit of a sequence of minimization problems. It was developed for disordered mean-field spin systems, spin systems where the underlying Hamiltonian is itself random, and whose distribution is permutation invariant. We present the EVP in the simpler setting of classical mean-field spin systems, where the Hamiltonian is non-random and symmetric. The EVP essentially solves these models. We compare

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19

Mongwe, Wilson Tsakane, Rendani Mbuvha, and Tshilidzi Marwala. "Quantum-Inspired Magnetic Hamiltonian Monte Carlo." PLOS ONE 16, no. 10 (2021): e0258277. http://dx.doi.org/10.1371/journal.pone.0258277.

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Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo algorithm that is able to generate distant proposals via the use of Hamiltonian dynamics, which are able to incorporate first-order gradient information about the target posterior. This has driven its rise in popularity in the machine learning community in recent times. It has been shown that making use of the energy-time uncertainty relation from quantum mechanics, one can devise an extension to HMC by allowing the mass matrix to be random with a probability distribution instead of a fixed mass. Furthermore, Magnetic Hamiltonian Mont

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20

Khanin, Konstantin, and Andrei Sobolevski. "Particle dynamics inside shocks in Hamilton–Jacobi equations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1916 (2010): 1579–93. http://dx.doi.org/10.1098/rsta.2009.0283.

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The characteristic curves of a Hamilton–Jacobi equation can be seen as action-minimizing trajectories of fluid particles. For non-smooth ‘viscosity’ solutions, which give rise to discontinuous velocity fields, this description is usually pursued only up to the moment when trajectories hit a shock and cease to minimize the Lagrangian action. In this paper we show that, for any convex Hamiltonian, there exists a uniquely defined canonical global non-smooth coalescing flow that extends particle trajectories and determines the dynamics inside shocks. We also provide a variational description of th

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21

Ennaji, Hamza, Noureddine Igbida, and Van Thanh Nguyen. "Beckmann-type problem for degenerate Hamilton-Jacobi equations." Quarterly of Applied Mathematics 80, no. 2 (2021): 201–20. http://dx.doi.org/10.1090/qam/1606.

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The aim of this note is to give a Beckmann-type problem as well as the corresponding optimal mass transportation problem associated with a degenerate Hamilton-Jacobi equation H ( x , ∇ u ) = 0 , H(x,\nabla u)=0, coupled with non-zero Dirichlet condition u = g u=g on ∂ Ω \partial \Omega . In this article, the Hamiltonian H H is continuous in both arguments, coercive and convex in the second, but not enjoying any property of existence of a smooth strict sub-solution. We also provide numerical examples to validate the correctness of theoretical formulations.

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22

Amick, C. J., and J. F. Toland. "Points of egress in problems of Hamiltonian dynamics." Mathematical Proceedings of the Cambridge Philosophical Society 109, no. 2 (1991): 405–17. http://dx.doi.org/10.1017/s030500410006984x.

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First we consider an elementary though delicate question about the trajectory in ℝn of a particle in a conservative field of force whose dynamics are governed by the equationHere the potential function V is supposed to have Lipschitz continuous first derivative at every point of ℝn. This is a natural assumption which ensures that the initial-value problem is well-posed. We suppose also that there is a closed convex set C with non-empty interior C° such that V ≥ 0 in C and V = 0 on the boundary ∂C of C. It is noteworthy that we make no assumptions about the degeneracy (or otherwise) of V on ∂C

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23

Chen, Qinbo, and Rafael de la Llave. "Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems." Nonlinearity 35, no. 4 (2022): 1986–2019. http://dx.doi.org/10.1088/1361-6544/ac50bb.

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Abstract The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the following a priori unstable Hamiltonian system with a time-periodic perturbation H ε ( p , q , I , φ , t ) = h ( I ) + ∑ i = 1 n ± 1 2 p i 2 + V i ( q i ) + ε H 1 ( p , q , I , φ , t ) , where ( p , q ) ∈ R n × T n , ( I , φ ) ∈ R d × T d with n, d ⩾ 1, V i are Morse potentials, and ɛ is a small non-zero parameter. The unperturbed Hamiltonian is not necessarily convex, and the induced inner dynamics does not need to satisfy a twist condition. Using geometric meth

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24

Bounemoura, Abed, and Vadim Kaloshin. "Generic Fast Diffusion for a Class of Non-Convex Hamiltonians with Two Degrees of Freedom." Moscow Mathematical Journal 14, no. 2 (2014): 181–203. http://dx.doi.org/10.17323/1609-4514-2014-14-2-181-203.

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25

Radjenović, Branislav, Jae Koo Lee, and Marija Radmilović-Radjenović. "Sparse field level set method for non-convex Hamiltonians in 3D plasma etching profile simulations." Computer Physics Communications 174, no. 2 (2006): 127–32. http://dx.doi.org/10.1016/j.cpc.2005.09.010.

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26

Mahmudov, Elimhan. "Optimization of Lagrange problem with higher order differential inclusions and endpoint constraints." Filomat 32, no. 7 (2018): 2367–82. http://dx.doi.org/10.2298/fil1807367m.

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In the paper minimization of a Lagrange type cost functional over the feasible set of solutions of higher order differential inclusions with endpoint constraints is studied. Our aim is to derive sufficient conditions of optimality for m th-order convex and non-convex differential inclusions. The sufficient conditions of optimality containing the Euler-Lagrange and Hamiltonian type inclusions as a result of endpoint constraints are accompanied by so-called ?endpoint? conditions. Here the basic apparatus of locally adjoint mappings is suggested. An application from the calculus of variations is

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27

De Blasi, Irene, Alessandra Celletti, and Christos Efthymiopoulos. "Satellites’ orbital stability through normal forms." Proceedings of the International Astronomical Union 15, S364 (2021): 146–51. http://dx.doi.org/10.1017/s174392132100137x.

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AbstractA powerful tool to investigate the stability of the orbits of natural and artificial bodies is represented by perturbation theory, which allows one to provide normal form estimates for nearly-integrable problems in Celestial Mechanics. In particular, we consider the orbital stability of point-mass satellites moving around the Earth. On the basis of the J2 model, we investigate the stability of the semimajor axis. Using a secular Hamiltonian model including also lunisolar perturbations, the so-called geolunisolar model, we study the stability of the other orbital elements, namely the ec

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28

NETO, JORGE ANANIAS, and WILSON OLIVEIRA. "DOES THE WEYL ORDERING PRESCRIPTION LEAD TO THE CORRECT ENERGY LEVELS FOR THE QUANTUM PARTICLE ON THE D-DIMENSIONAL SPHERE?" International Journal of Modern Physics A 14, no. 23 (1999): 3699–713. http://dx.doi.org/10.1142/s0217751x99001706.

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The energy eigenvalues of the quantum particle constrained in a surface of the sphere of D dimensions embedded in a RD+1 space are obtained by using two different procedures: in the first, we derive the Hamiltonian operator by squaring the expression of the momentum, written in Cartesian components, which satisfies the Dirac brackets between the canonical operators of this second-class system. We use the Weyl ordering prescription to construct the Hermitian operators. When D=2 we verify that there is no constant parameter in the expression of the eigenvalues energy, a result that is in agreeme

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Stark, Colin P., and Gavin J. Stark. "The direction of landscape erosion." Earth Surface Dynamics 10, no. 3 (2022): 383–419. http://dx.doi.org/10.5194/esurf-10-383-2022.

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Abstract. The rate of erosion of a landscape depends largely on local gradient and material fluxes. Since both quantities are functions of the shape of the catchment surface, this dependence constitutes a mathematical straitjacket, in the sense that – subject to simplifying assumptions about the erosion process, and absent variations in external forcing and erodibility – the rate of change of surface geometry is solely a function of surface geometry. Here we demonstrate how to use this geometric self-constraint to convert a gradient-dependent erosion model into its equivalent Hamiltonian, and

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30

Rouleux, Michel. "Semi-classical Integrability, Hyperbolic Flows and the Birkhoff Normal Form." Canadian Journal of Mathematics 56, no. 5 (2004): 1034–67. http://dx.doi.org/10.4153/cjm-2004-047-6.

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AbstractWe prove that a Hamiltonianp∈C∞(T*Rn) is locally integrable near a non-degenerate critical point ρ0of the energy, provided that the fundamental matrix at ρ0has rationally independent eigenvalues, none purely imaginary. This is done by using Birkhoff normal forms, which turn out to be convergent in theC∞sense. We also give versions of the Lewis-Sternberg normal form near a hyperbolic fixed point of a canonical transformation. Then we investigate the complex case, showing that whenpis holomorphic near ρ0∈T*Cn, then Repbecomes integrable in the complex domain for real times, while the Bir

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31

Sreedharan Kallyadan, Sreethin, and Priyanka Shukla. "Dynamical aspects of a restricted three-vortex problem." IMA Journal of Applied Mathematics 87, no. 1 (2021): 1–19. http://dx.doi.org/10.1093/imamat/hxab043.

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Abstract Point vortex systems that include vortices with constant coordinate functions are largely unexplored, even though they have reasonable physical interpretations in the geophysical context. Here, we investigate the dynamical aspects of the restricted three-vortex problem when one of the point vortices is assumed to be fixed at a location in the plane. The motion of the passive tracer is explored from a rotating frame of reference within which the free vortex with non-zero circulation remains stationary. By using basic dynamical system theory, it is shown that the vortex motion is always

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32

Jezequel, Lucien, Clément Tauber, and Pierre Delplace. "Estimating bulk and edge topological indices in finite open chiral chains." Journal of Mathematical Physics 63, no. 12 (2022): 121901. http://dx.doi.org/10.1063/5.0096720.

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We develop a formalism to estimate, simultaneously, the usual bulk and edge indices from topological insulators in the case of a finite sample with open boundary conditions and provide a physical interpretation of these quantities. We then show that they converge exponentially fast to an integer value when we increase the system size and also show that bulk and edge index estimates coincide at finite size. The theorem applies to any non-homogeneous system, such as disordered or defect configurations. We focus on one-dimensional chains with chiral symmetry, such as the Su–Schrieffer–Heeger mode

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33

Dunn, Katherine, Martin Trefzer, Steven Johnson, and Andy Tyrrell. "Towards a Bioelectronic Computer: A Theoretical Study of a Multi-Layer Biomolecular Computing System That Can Process Electronic Inputs." International Journal of Molecular Sciences 19, no. 9 (2018): 2620. http://dx.doi.org/10.3390/ijms19092620.

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DNA molecular machines have great potential for use in computing systems. Since Adleman originally introduced the concept of DNA computing through his use of DNA strands to solve a Hamiltonian path problem, a range of DNA-based computing elements have been developed, including logic gates, neural networks, finite state machines (FSMs) and non-deterministic universal Turing machines. DNA molecular machines can be controlled using electrical signals and the state of DNA nanodevices can be measured using electrochemical means. However, to the best of our knowledge there has as yet been no demonst

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34

Nooijen, Marcel, and K. R. Shamasundar. "A Case Study of State-Specific and State-Averaged Brueckner Equation-of-Motion Coupled-Cluster Theory: The Ionic-Covalent Avoided Crossing in Lithium Fluoride." Collection of Czechoslovak Chemical Communications 70, no. 8 (2005): 1082–108. http://dx.doi.org/10.1135/cccc20051082.

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State-specific Brueckner equation-of-motion coupled-cluster theory (SS-B-EOMCC) is summarized, which can be considered an internally contracted version of a state-selective multireference coupled-cluster theory, which, however, is not entirely size-consistent. The method is applicable to general multireference problems, adheres to the space and spin symmetries of the molecular system, is straightforwardly extended to a state-averaged version, and has an associated perturbative variant which yields results close to the full coupled-cluster treatment. A key strength is that Brueckner orbitals ar

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35

Roy, Rhombik, Camille Lévêque, Axel U. J. Lode, Arnaldo Gammal, and Barnali Chakrabarti. "Fidelity and Entropy Production in Quench Dynamics of Interacting Bosons in an Optical Lattice." Quantum Reports 1, no. 2 (2019): 304–16. http://dx.doi.org/10.3390/quantum1020028.

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We investigate the dynamics of a few bosons in an optical lattice induced by a quantum quench of a parameter of the many-body Hamiltonian. The evolution of the many-body wave function is obtained by solving the time-dependent many-body Schrödinger equation numerically, using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We report the time evolution of three key quantities, namely, the occupations of the natural orbitals, that is, the eigenvalues of the one-body reduced density matrix, the many-body Shannon information entropy, and the quantum fidelity for a wide r

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36

Aslani, Shahriar, and Patrick Bernard. "Normal Form Near Orbit Segments of Convex Hamiltonian Systems." International Mathematics Research Notices, January 18, 2021. http://dx.doi.org/10.1093/imrn/rnaa344.

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Abstract In the study of Hamiltonian systems on cotangent bundles, it is natural to perturb Hamiltonians by adding potentials (functions depending only on the base point). This led to the definition of Mañé genericity [ 8]: a property is generic if, given a Hamiltonian $H$, the set of potentials $g$ such that $H+g$ satisfies the property is generic. This notion is mostly used in the context of Hamiltonians that are convex in $p$, in the sense that $\partial ^2_{pp} H$ is positive definite at each point. We will also restrict our study to this situation. There is a close relation between pertur

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37

Bolten, M., O. T. Doganay, H. Gottschalk, and K. Klamroth. "Non-convex shape optimization by dissipative Hamiltonian flows." Engineering Optimization, February 18, 2024, 1–20. http://dx.doi.org/10.1080/0305215x.2024.2304135.

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38

Boyer, Mark A., and Edwin L. Sibert. "A general expression for vibrational Hamiltonians expressed in oblique coordinates." Journal of Chemical Physics 159, no. 23 (2023). http://dx.doi.org/10.1063/5.0181135.

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We examine the properties of oblique coordinates. The coordinates, introduced by Zúñiga et al. [J. Phys. B: At., Mol. Opt. Phys. 52, 055101, (2019)], reduce vibrational mode-mixing and enhance the quality of vibrational assignments in quantum mechanical investigations of two-dimensional model Hamiltonians. Oblique coordinates are obtained by making non-orthogonal rotations of the original coordinates that convert the matrix representation of the quadratic Hamiltonian operator into a block-diagonal matrix where the blocks are distinguished by the total quanta of vibrational excitation. Using te

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39

Chau, Huy N., and Miklós Rásonyi. "Stochastic Gradient Hamiltonian Monte Carlo for non-convex learning." Stochastic Processes and their Applications, April 2022. http://dx.doi.org/10.1016/j.spa.2022.04.001.

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40

Ratiu, Tudor, Christophe Wacheux, and Nguyen Zung. "Convexity of Singular Affine Structures and Toric-Focus Integrable Hamiltonian Systems." Memoirs of the American Mathematical Society 287, no. 1424 (2023). http://dx.doi.org/10.1090/memo/1424.

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This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds (with boundary and corners), analogous to the toric case, but their associated integral affine structures are singular, with non-trivial monodromy, due to focus singularities. We obtain a series of convexity results, both positive and negative, for such singular integral affine base spaces. In particular, near a focus singular point, they are locally convex a

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41

Fabila-Monroy, Ruy, David Flores-Peñaloza, Clemens Huemer, Ferran Hurtado, Jorge Urrutia, and David R. Wood. "On the chromatic number of some flip graphs." Discrete Mathematics & Theoretical Computer Science Vol. 11 no. 2, Graph and Algorithms (2009). http://dx.doi.org/10.46298/dmtcs.460.

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Graphs and Algorithms International audience This paper studies the chromatic number of the following four flip graphs (under suitable definitions of a flip): the flip graph of perfect matchings of a complete graph of even order, the flip graph of triangulations of a convex polygon (the associahedron), the flip graph of non-crossing Hamiltonian paths of a set of points in convex position, and the flip graph of triangles in a convex point set. We give tight bounds for the latter two cases and upper bounds for the first two.

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42

TAPIA-GARCÍA, SEBASTIÁN. "REGULARITY OF AML FUNCTIONS IN TWO-DIMENSIONAL NORMED SPACES." Journal of the Australian Mathematical Society, May 20, 2022, 1–25. http://dx.doi.org/10.1017/s1446788722000088.

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Abstract Savin [‘ $\mathcal {C}^{1}$ regularity for infinity harmonic functions in two dimensions’, Arch. Ration. Mech. Anal.3(176) (2005), 351–361] proved that every planar absolutely minimizing Lipschitz (AML) function is continuously differentiable whenever the ambient space is Euclidean. More recently, Peng et al. [‘Regularity of absolute minimizers for continuous convex Hamiltonians’, J. Differential Equations274 (2021), 1115–1164] proved that this property remains true for planar AML functions for certain convex Hamiltonians, using some Euclidean techniques. Their result can be applied t

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Giambò, Roberto, Fabio Giannoni, and Paolo Piccione. "On the Least Action Principle – Hamiltonian Dynamics on Fixed Energy Levels in the Non-convex Case." Advanced Nonlinear Studies 6, no. 2 (2006). http://dx.doi.org/10.1515/ans-2006-0208.

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AbstractWe review the classical Principle of the Least Action in a general context where the Hamilton functionH is possibly non-convex. We show how the van Groesen [6] principle follows as a particular case where H is hyperregular and of homogeneous type. Homogeneous scalar field spacetimes in spherical symmetry are derived as an application.

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Odavić, Jovan, Tobias Haug, Gianpaolo Torre, Alioscia Hamma, Fabio Franchini, and Salvatore Marco Giampaolo. "Complexity of frustration: A new source of non-local non-stabilizerness." SciPost Physics 15, no. 4 (2023). http://dx.doi.org/10.21468/scipostphys.15.4.131.

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We advance the characterization of complexity in quantum many-body systems by examining WW-states embedded in a spin chain. Such states show an amount of non-stabilizerness or “magic”, measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a WW-state, while in the rest of the phase to which the classical point belongs, it is dressed with local quantum correlations. Topological frustrated

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De Blasi, Irene, Alessandra Celletti, and Christos Efthymiopoulos. "Semi-Analytical Estimates for the Orbital Stability of Earth’s Satellites." Journal of Nonlinear Science 31, no. 6 (2021). http://dx.doi.org/10.1007/s00332-021-09738-w.

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AbstractNormal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different estimates for the orbital stability of point-mass satellites orbiting around the Earth. (i) We demonstrate the long-term stability of the semimajor axis within the framework of the $$J_2$$ J 2 problem, by a normal form construction eliminating the fast angle in the corresponding Hamiltonian and obtaining $${\mathcal {H}}_{J_2}$$ H J 2 . (ii) We demonstrate

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Wen, Xueda, Yingfei Gu, Ashvin Vishwanath, and Ruihua Fan. "Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases." SciPost Physics 13, no. 4 (2022). http://dx.doi.org/10.21468/scipostphys.13.4.082.

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In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven (1+1)(1+1) dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble non-equilibrium quantum dynamics. The sequence of driving Hamiltonians is drawn from an independent and identically distributed random ensemble. At each driving step, the deformed Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength and therefore induces a Möbius transformation on the complex coordinates. The non-equilibrium dynamics is then determi

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Madouri, Fethi, Abdeldjalil Merdaci, and Tarek Sbeouelji. "Collapse-revival of entanglement in a non-commutative harmonic oscillator revealed via coherent states and path integral." Zeitschrift für Naturforschung A, November 18, 2022. http://dx.doi.org/10.1515/zna-2022-0160.

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Abstract We develop an approach using coherent states and path integral to investigate the dynamics of entanglement in a simple two-dimensional non-commutative harmonic oscillator. We start by employing a Bopp shift to convert the Hamiltonian describing the system into a commutative equivalent one. This allows us to construct coherent states and calculate the propagator in standard way. By deriving the explicit expression of the time-dependent coherent states and considering its connection with the number states, we provide exact results for evaluating the degree of entanglement between the gr

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Aliyev, Nicat, Volker Mehrmann, and Emre Mengi. "Approximation of stability radii for large-scale dissipative Hamiltonian systems." Advances in Computational Mathematics 46, no. 1 (2020). http://dx.doi.org/10.1007/s10444-020-09763-5.

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Abstract A linear time-invariant dissipative Hamiltonian (DH) system $\dot x = (J-R)Q x$ẋ=(J−R)Qx, with a skew-Hermitian J, a Hermitian positive semidefinite R, and a Hermitian positive definite Q, is always Lyapunov stable and under further weak conditions even asymptotically stable. By exploiting the characterizations from Mehl et al. (SIAM J. Matrix Anal. Appl. 37(4), 1625–1654, 2016), we focus on the estimation of two stability radii for large-scale DH systems, one with respect to non-Hermitian perturbations of R in the form R + BΔCH for given matrices B, C, and another with respect to He

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Bounemoura, Abed, and Jacques Féjoz. "Hamiltonian perturbation theory for ultra-differentiable functions." Memoirs of the American Mathematical Society 270, no. 1319 (2021). http://dx.doi.org/10.1090/memo/1319.

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Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard implicit function theorems. They comprise Gevrey functions and thus, as a limiting case, analytic functions. Using majorizing series, we manage to characterize them in terms of a real sequence M M bounding the growth of derivatives. In this functional setting, we prove two fundamental results of Hamiltonian perturbation theory: the invariant torus t

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Keller, Chaya, and Yael Stein. "Blockers for Triangulations of a Convex Polygon and a Geometric Maker-Breaker Game." Electronic Journal of Combinatorics 27, no. 4 (2020). http://dx.doi.org/10.37236/7205.

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Let $G$ be a complete convex geometric graph whose vertex set $P$ forms a convex polygon $C$, and let $\mathcal{F}$ be a family of subgraphs of $G$. A blocker for $\mathcal{F}$ is a set of diagonals of $C$, of smallest possible size, that contains a common edge with every element of $\mathcal{F}$. Previous works determined the blockers for various families $\mathcal{F}$ of non-crossing subgraphs, including the families of all perfect matchings, all spanning trees, all Hamiltonian paths, etc. In this paper we present a complete characterization of the family $\mathcal{B}$ of blockers for

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