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Journal articles on the topic 'Non-Convex Hamiltonian'

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

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

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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17

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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18

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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19

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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20

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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21

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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22

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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23

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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24

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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25

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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26

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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27

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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28

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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29

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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30

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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31

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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32

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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33

Tian, Yuzhou, Qiaoling Wei, and Meirong Zhang. "On the polynomial integrability of the critical systems for optimal eigenvalue gaps." Journal of Mathematical Physics 64, no. 9 (2023). http://dx.doi.org/10.1063/5.0140966.

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This exploration consists of two parts. First, we will deduce a family of critical systems consisting of nonlinear ordinary differential equations, indexed by the exponent p ∈ (1, ∞) of the Lebesgue spaces concerned. These systems can be used to obtain the optimal lower or upper bounds for eigenvalue gaps of Sturm–Liouville operators and are equivalent to non-convex Hamiltonian systems of two degrees of freedom. Second, with appropriate choices of exponents p, the critical systems are polynomial systems in four dimensions. These systems will be investigated from two aspects. The first one is t

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34

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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