Relevant bibliographies by topics / Hamiltonian problems

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Hamiltonian problems'

Author: Grafiati
Published: 10 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Hamiltonian problems"

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Bravyi, S., D. P. DiVincenzo, R. Oliveira, and B. M. Terhal. "The complexity of stoquastic local Hamiltonian problems." Quantum Information and Computation 8, no. 5 (2008): 361–85. http://dx.doi.org/10.26421/qic8.5-1.

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We study the complexity of the Local Hamiltonian Problem (denoted as LH-MIN) in the special case when a Hamiltonian obeys the condition that all off-diagonal matrix elements in the standard basis are real and non-positive. We will call such Hamiltonians, which are common in the natural world, stoquastic. An equivalent characterization of stoquastic Hamiltonians is that they have an entry-wise non-negative Gibbs density matrix for any temperature. We prove that LH-MIN for stoquastic Hamiltonians belongs to the complexity class \AM{}--- a probabilistic version of \NP{} with two rounds of communi
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Elyseeva, Julia. "The Oscillation Numbers and the Abramov Method of Spectral Counting for Linear Hamiltonian Systems." EPJ Web of Conferences 248 (2021): 01002. http://dx.doi.org/10.1051/epjconf/202124801002.

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In this paper we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. For the Hamiltonian problems we do not assume any controllability and strict normality assumptions which guarantee that the classical eigenvalues of the problems are isolated. We also omit the Legendre condition for their Hamiltonians. We show that the Abramov method of spectral counting can be modified for the more general case of finite eigenvalues of the Hamiltonian problems and then the constructive ideas of the Abramov meth
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Pannell, William H. "The intersection between dual potential and sl(2) algebraic spectral problems." International Journal of Modern Physics A 35, no. 32 (2020): 2050208. http://dx.doi.org/10.1142/s0217751x20502085.

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The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation [Formula: see text] has long been used as a method of simplifying spectral problems in quantum mechanics. This paper seeks to examine this further by expressing such Hamiltonians in terms of the generators of sl(2) algebra, which provides another method of solving spectral problems. It appears that doing so greatly restricts the set of allowable potentials, with the only nontrivial potentials allowed being the Coulomb [Formula: see text] potential and the harmonic oscillator [Formula: se
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Iserles, A., J. M. Sanz-Serna, and M. P. Calvo. "Numerical Hamiltonian Problems." Mathematics of Computation 64, no. 211 (1995): 1346. http://dx.doi.org/10.2307/2153506.

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Masanes, Ll, G. Vidal, and J. I. Latorre. "Time--optimal Hamiltonian simulation and gate synthesis using homogeneous local unitaries." Quantum Information and Computation 2, no. 4 (2002): 285–96. http://dx.doi.org/10.26421/qic2.4-2.

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Motivated by experimental limitations commonly met in the design of solid state quantum computers, we study the problems of non--local Hamiltonian simulation and non--local gate synthesis when only {\em homogeneous} local unitaries are performed in order to tailor the available interaction. Homogeneous (i.e. identical for all subsystems) local manipulation implies a more refined classification of interaction Hamiltonians than the inhomogeneous case, as well as the loss of universality in Hamiltonian simulation. For the case of symmetric two--qubit interactions, we provide time--optimal protoco
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Sattath, Or, Siddhardh C. Morampudi, Chris R. Laumann, and Roderich Moessner. "When a local Hamiltonian must be frustration-free." Proceedings of the National Academy of Sciences 113, no. 23 (2016): 6433–37. http://dx.doi.org/10.1073/pnas.1519833113.

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A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a gen
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Bassour, Mustapha. "Hamiltonian Polynomial Eigenvalue Problems." Journal of Applied Mathematics and Physics 08, no. 04 (2020): 609–19. http://dx.doi.org/10.4236/jamp.2020.84047.

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Zhao, Qi, and Xiao Yuan. "Exploiting anticommutation in Hamiltonian simulation." Quantum 5 (August 31, 2021): 534. http://dx.doi.org/10.22331/q-2021-08-31-534.

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Quantum computing can efficiently simulate Hamiltonian dynamics of many-body quantum physics, a task that is generally intractable with classical computers. The hardness lies at the ubiquitous anti-commutative relations of quantum operators, in corresponding with the notorious negative sign problem in classical simulation. Intuitively, Hamiltonians with more commutative terms are also easier to simulate on a quantum computer, and anti-commutative relations generally cause more errors, such as in the product formula method. Here, we theoretically explore the role of anti-commutative relation in
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Sanz-Serna, J. M. "Symplectic integrators for Hamiltonian problems: an overview." Acta Numerica 1 (January 1992): 243–86. http://dx.doi.org/10.1017/s0962492900002282.

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In the sciences, situations where dissipation is not significant may invariably be modelled by Hamiltonian systems of ordinary, or partial, differential equations. Symplectic integrators are numerical methods specifically aimed at advancing in time the solution of Hamiltonian systems. Roughly speaking, ‘symplecticness’ is a characteristic property possessed by the solutions of Hamiltonian problems. A numerical method is called symplectic if, when applied to Hamiltonian problems, it generates numerical solutions which inherit the property of symplecticness.
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Amodio, P., F. Iavernaro, and D. Trigiante. "Symmetric schemes and Hamiltonian perturbations of linear Hamiltonian problems." Numerical Linear Algebra with Applications 12, no. 2-3 (2005): 171–79. http://dx.doi.org/10.1002/nla.408.

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Dissertations / Theses on the topic "Hamiltonian problems"

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Pester, Cornelia. "Hamiltonian eigenvalue symmetry for quadratic operator eigenvalue problems." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601470.

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When the eigenvalues of a given eigenvalue problem are symmetric with respect to the real and the imaginary axes, we speak about a Hamiltonian eigenvalue symmetry or a Hamiltonian structure of the spectrum. This property can be exploited for an efficient computation of the eigenvalues. For some elliptic boundary value problems it is known that the derived eigenvalue problems have this Hamiltonian symmetry. Without having a specific application in mind, we trace the question, under which assumptions the spectrum of a given quadratic eigenvalue problem possesses the Hamiltonian structure.
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Watkinson, Laura. "Four Dimensional Variational Data Assimilation for Hamiltonian Problems." Thesis, University of Reading, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485506.

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In this thesis we bring together two areas of mathematics; Hamiltonian dynamics and data assimilation. We construct a four dimensional variational (4d Var) data assimilation scheme for two Hamiltonian systems. This is to reflect the Hamiltonian behaviour observed in the atmosphere. We know, for example, that potential vorticity is conserved in atmospheric models. However, current data assimilation schemes do not explicitly include such physical relationships. In this thesis, by considering the two and three body problems, we demonstrate how such characteristic behaviour can be included in the
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Groves, Mark David. "Hamiltonian theory and its application to water-wave problems." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316842.

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Koch, Michael Conrad. "Inverse analysis in geomechanical problems using Hamiltonian Monte Carlo." Kyoto University, 2020. http://hdl.handle.net/2433/253350.

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Lignos, Ioannis. "Reconfigurations of combinatorial problems : graph colouring and Hamiltonian cycle." Thesis, Durham University, 2017. http://etheses.dur.ac.uk/12098/.

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We explore algorithmic aspects of two known combinatorial problems, Graph Colouring and Hamiltonian Cycle, by examining properties of their solution space. One can model the set of solutions of a combinatorial problem $P$ by the solution graph $R(P)$, where vertices are solutions of $P$ and there is an edge between two vertices, when the two corresponding solutions satisfy an adjacency reconfiguration rule. For example, we can define the reconfiguration rule for graph colouring to be that two solutions are adjacent when they differ in colour in exactly one vertex. The exploration of the proper
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Gu, Xiang. "Hamiltonian structures and Riemann-Hilbert problems of integrable systems." Scholar Commons, 2018. https://scholarcommons.usf.edu/etd/7677.

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We begin this dissertation by presenting a brief introduction to the theory of solitons and integrability (plus some classical methods applied in this field) in Chapter 1, mainly using the Korteweg-de Vries equation as a typical model. At the end of this Chapter a mathematical framework of notations and terminologies is established for the whole dissertation. In Chapter 2, we first introduce two specific matrix spectral problems (with 3 potentials) associated with matrix Lie algebras $\mbox{sl}(2;\mathbb{R})$ and $\mbox{so}(3;\mathbb{R})$, respectively; and then we engender two soliton hierarc
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Parodi, Emanuele. "Classification problems for Hamiltonian evolutionary equations and their discretizations". Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4704.

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In the present Thesis, we deal mainly with the subclass of Hamiltonian evolutionary PDEs and their Poisson brackets (PBs). We address the problem of classifying discrete differential-geometric PBs (dDGPBs) of any fixed order on target space of dimension 1 and describing their compatible pencils. Furthermore, we explain a new criterium about the existence of tri-Hamiltonian structures for nonlinear wave systems.
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Rudoy, Mikhail. "Hamiltonian cycle and related problems : vertex-breaking, grid graphs, and Rubik's Cubes." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/113112.

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Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 123-124).<br>In this thesis, we analyze the computational complexity of several problems related to the Hamiltonian Cycle problem. We begin by introducing a new problem, which we call Tree-Residue Vertex-Breaking (TRVB). Giv
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De, Martino Giuseppe. "Multi-Value Numerical Modeling for Special Di erential Problems." Doctoral thesis, Universita degli studi di Salerno, 2015. http://hdl.handle.net/10556/1982.

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2013 - 2014<br>The subject of this thesis is the analysis and development of new numerical methods for Ordinary Di erential Equations (ODEs). This studies are motivated by the fundamental role that ODEs play in applied mathematics and applied sciences in general. In particular, as is well known, ODEs are successfully used to describe phenomena evolving in time, but it is often very di cult or even impossible to nd a solution in closed form, since a general formula for the exact solution has never been found, apart from special cases. The most important cases in the applications are sys
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Kang, Jinghong. "The Computational Kleinman-Newton Method in Solving Nonlinear Nonquadratic Control Problems." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30435.

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This thesis deals with non-linear non-quadratic optimal control problems in an autonomous system and a related iterative numerical method, the Kleinman-Newton method, for solving the problem. The thesis proves the local convergence of Kleinman-Newton method using the contraction mapping theorem and then describes how this Kleinman-Newton method may be used to numerically solve for the optimal control and the corresponding solution. In order to show the proof and the related numerical work, it is necessary to review some of earlier work in the beginning of Chapter 1 [Zhang], an
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Books on the topic "Hamiltonian problems"

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Sanz-Serna, J. M., and M. P. Calvo. Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4.

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P, Calvo M., ed. Numerical Hamiltonian problems. Chapman & Hall, 1994.

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Gignoux, Claude, and Bernard Silvestre-Brac. Solved Problems in Lagrangian and Hamiltonian Mechanics. Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2393-3.

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Bernard, Silvestre-Brac, and SpringerLink (Online service), eds. Solved Problems in Lagrangian and Hamiltonian Mechanics. Springer Netherlands, 2009.

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Greiner, Walter. Classical mechanics: Systems of particles and Hamiltonian dynamics. Springer, 2003.

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Ning, Xuanxi. The blocking flow theory and its application to Hamiltonian graph problems. Shaker Verlag, 2006.

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Mielke, Alexander. Hamiltonian and Lagrangian flows on center manifolds: With applications to elliptic variational problems. Springer-Verlag, 1991.

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Riahi, Hasna. Study of the critical points at infinity arising from the failure of the Palais-Smale condition for n-body type problems. American Mathematical Society, 1999.

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Borkar, Vivek S., Vladimir Ejov, Jerzy A. Filar, and Giang T. Nguyen. Hamiltonian Cycle Problem and Markov Chains. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3232-6.

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Goncharov, V. P. Problemy gidrodinamiki v gamilʹtonovom opisanii. Izd-vo Moskovskogo universiteta, 1993.

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Book chapters on the topic "Hamiltonian problems"

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Sanz-Serna, J. M., and M. P. Calvo. "Hamiltonian systems." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_1.

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Sanz-Serna, J. M., and M. P. Calvo. "Properties of symplectic integrators." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_10.

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Sanz-Serna, J. M., and M. P. Calvo. "Generating functions." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_11.

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Sanz-Serna, J. M., and M. P. Calvo. "Lie formalism." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_12.

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Sanz-Serna, J. M., and M. P. Calvo. "High-order methods." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_13.

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Sanz-Serna, J. M., and M. P. Calvo. "Extensions." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_14.

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Sanz-Serna, J. M., and M. P. Calvo. "Symplecticness." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_2.

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Sanz-Serna, J. M., and M. P. Calvo. "Numerical methods." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_3.

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Sanz-Serna, J. M., and M. P. Calvo. "Order conditions." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_4.

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Sanz-Serna, J. M., and M. P. Calvo. "Implementation." In Numerical Hamiltonian Problems. Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3093-4_5.

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Conference papers on the topic "Hamiltonian problems"

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Langfitt, Quinn, Reuben Tate, and Stephan Eidenbenz. "Phantom Edges in the Problem Hamiltonian: A Method for Increasing Performance and Graph Visibility for QAOA." In 2025 International Conference on Quantum Communications, Networking, and Computing (QCNC). IEEE, 2025. https://doi.org/10.1109/qcnc64685.2025.00016.

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Schwab, David, Roshan Eapen, and Puneet Singla. "Defining Admissible Maneuvers and Resulting Reachability Sets in the Three-Body Problem using Hamiltonian Normal Form Methods." In IAF Astrodynamics Symposium, Held at the 75th International Astronautical Congress (IAC 2024). International Astronautical Federation (IAF), 2024. https://doi.org/10.52202/078368-0141.

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Cubitt, Toby S., and Ashley Montanaro. "Complexity Classification of Local Hamiltonian Problems." In 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2014. http://dx.doi.org/10.1109/focs.2014.21.

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D’Ambrosio, Raffaele, Giuseppe Giordano, and Beatrice Paternoster. "Numerical conservation issues for stochastic Hamiltonian problems." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0081459.

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Olmos, Ivan, Jesus A. Gonzalez, and Mauricio Osorio. "Reductions between the Subgraph Isomorphism Problem and Hamiltonian and SAT Problems." In 17th International Conference on Electronics, Communications and Computers (CONIELECOMP'07). IEEE, 2007. http://dx.doi.org/10.1109/conielecomp.2007.30.

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Brugnano, Luigi, Felice Iavernaro, Donato Trigiante, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Hamiltonian BVMs (HBVMs): A Family of “Drift Free” Methods for Integrating polynomial Hamiltonian problems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241566.

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Fedorova, A., M. Zeitlin, and Z. Parsa. "Symmetry, Hamiltonian problems and wavelets in accelerator physics." In The sixteenth advanced international committee on future accelerators beam dynamics workshop on nonlinear and collective phenomena in beam physics. AIP, 1999. http://dx.doi.org/10.1063/1.58428.

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Brugnano, Luigi, Felice Iavernaro, Donato Trigiante, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Numerical Comparisons among Some Methods for Hamiltonian Problems." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498391.

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Pavel, Marilena. "Hamiltonian and Port-Hamiltonian Mechanics as A Possible Alternative for Helicopter Flight Dynamics Representation." In Vertical Flight Society 79th Annual Forum & Technology Display. The Vertical Flight Society, 2023. http://dx.doi.org/10.4050/f-0079-2023-18124.

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In the case of complicated, non-linear problems where simulations in the time-domain are needed to understand systems' behavior, Hamiltonian formulation can be used to obtain insight into system evolution in time. Hamiltonian dynamics has two advantages: 1) there is no need to write down the complete equations of motion explicity and thus help to solve the problem much quicker and 2) it can help understanding and designing controllers using the energy flow, Hamiltonian phase space and port-Hamiltonian representation for system evolution. The present paper highlights the importance of using the
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Zhang, WX. "Study on Complex Geometric Boundary Problems in Hamiltonian system." In 2020 3rd International Conference on Electron Device and Mechanical Engineering (ICEDME). IEEE, 2020. http://dx.doi.org/10.1109/icedme50972.2020.00146.

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Reports on the topic "Hamiltonian problems"

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Libura, Marek. Sensitivity Analysis for Shortest Hamiltonian Path and Traveling Salesman Problems. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada197167.

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Tessarotto, M., Lin Jin Zheng, and J. L. Johnson. Hamiltonian approach to the magnetostatic equilibrium problem. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/10115867.

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Kyuldjiev, Assen, Vladimir Gerdjikov, and Giuseppe Marmo. On Superintegrability of The Manev Problem and its Real Hamiltonian Form. GIQ, 2012. http://dx.doi.org/10.7546/giq-6-2005-262-275.

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Kyuldjiev, Assen, Vladimir Gerdjikov, and Giuseppe Marmo. On the Symmetries of the Manev Problem and Its Real Hamiltonian Form. GIQ, 2012. http://dx.doi.org/10.7546/giq-8-2007-221-233.

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Miller, D. L., J. F. Pekny, and G. L. Thompson. AN Exact Algorithm for Finding Undirected Hamiltonian Cycles Based on a Two-Matching Problem Relaxation. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada237241.

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Kandrup, H. E., and P. J. Morrison. Hamiltonian structure of the Vlasov-Einstein system and the problem of stability for spherical relativistic star clusters. Office of Scientific and Technical Information (OSTI), 1992. http://dx.doi.org/10.2172/10120708.

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Kandrup, H. E., and P. J. Morrison. Hamiltonian structure of the Vlasov-Einstein system and the problem of stability for spherical relativistic star clusters. Office of Scientific and Technical Information (OSTI), 1992. http://dx.doi.org/10.2172/6789042.

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