Relevant bibliographies by topics / Hamiltonian problems

Academic literature on the topic 'Hamiltonian problems'

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Published: 10 March 2023

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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 (May 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 communication between the prover and the verifier. We also show that $2$-local stoquastic LH-MIN is hard for the class \MA. With the additional promise of having a polynomial spectral gap, we show that stoquastic LH-MIN belongs to the class \POSTBPP=\BPPpath --- a generalization of \BPP{} in which a post-selective readout is allowed. This last result also shows that any problem solved by adiabatic quantum computation using stoquastic Hamiltonians is in PostBPP.
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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 method can be used for stable calculations of the oscillation numbers and finite eigenvalues of the Hamiltonian problems.
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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 (November 20, 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: see text] potential, for both of which the sl(2) expression is already known. It also appears that, by utilizing both the partner potential transformation and the formalism of the Lie-algebraic construction of quantum mechanics, it may be possible to construct part of a Hamiltonian’s spectrum from the quasi-solvability of its partner Hamiltonian.
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Iserles, A., J. M. Sanz-Serna, and M. P. Calvo. "Numerical Hamiltonian Problems." Mathematics of Computation 64, no. 211 (July 1995): 1346. http://dx.doi.org/10.2307/2153506.

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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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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 (May 19, 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 general criterion—a sufficient condition—under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer’s theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian’s interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.
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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 (June 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 protocols for both Hamiltonian simulation and gate synthesis.
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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 Hamiltonian simulation. We find that, contrary to our intuition, anti-commutative relations could also reduce the hardness of Hamiltonian simulation. Specifically, Hamiltonians with mutually anti-commutative terms are easy to simulate, as what happens with ones consisting of mutually commutative terms. Such a property is further utilized to reduce the algorithmic error or the gate complexity in the truncated Taylor series quantum algorithm for general problems. Moreover, we propose two modified linear combinations of unitaries methods tailored for Hamiltonians with different degrees of anti-commutation. We numerically verify that the proposed methods exploiting anti-commutative relations could significantly improve the simulation accuracy of electronic Hamiltonians. Our work sheds light on the roles of commutative and anti-commutative relations in simulating quantum systems.
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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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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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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 data assimilation schemes. In our 4d Var schemes we add a weak constraint that imposes the conservation of the Hamiltonian, the total energy, at the initial time. This is effectively imposing an energy constraint from one data assimilation window to the next. Our results imply that these weak constraints affect the underlying geometry of the resulting data assimilation solution. We also demonstrate that this constraint reduces the error on this solution and the forecast. By imposing this constraint we are including additional information to the system. Due to the additional term in the cost function gradient, the analysis can only change in such a way as to satisfy this weak constraint. This thesis therefore demonstrates that the inclusion of similar weak con-straints, perhaps using the conservation of potential vorticity, could improve the analysis and forecast for atmospheric models.
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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 properties of the solution graph $R(P)$ can give rise to interesting questions. The connectivity of $R(P)$ is the most prominent question in this research area. This is reasonable, since the main motivation for modelling combinatorial solutions as a graph is to be able to transform one into the other in a stepwise fashion, by following paths between solutions in the graph. Connectivity questions can be made binary, that is expressed as decision problems which accept a 'yes' or 'no' answer. For example, given two specific solutions, is there a path between them? Is the graph of solutions $R(P)$ connected? In this thesis, we first show that the diameter of the solution graph $R_{l}(G)$ of vertex $l$-colourings of k-colourable chordal and chordal bipartite graphs $G$ is $O(n^2)$, where $l > k$ and n is the number of vertices of $G$. Then, we formulate a decision problem on the connectivity of the graph colouring solution graph, where we allow extra colours to be used in order to enforce a path between two colourings with no path between them. We give some results for general instances and we also explore what kind of graphs pose a challenge to determine the complexity of the problem for general instances. Finally, we give a linear algorithm which decides whether there is a path between two solutions of the Hamiltonian Cycle Problem for graphs of maximum degree five, and thus providing insights towards the complexity classification of the decision problem.
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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 hierarchies. The computation and analysis of their Hamiltonian structures based on the trace identity affirms that the obtained hierarchies are Liouville integrable. This chapter shows the entire process of how a soliton hierarchy is engendered by starting from a proper matrix spectral problem. In Chapter 3, at first we elucidate the Gauge equivalence among three types $u$-linear Hamiltonian operators, and construct then the corresponding B\"acklund transformations among them explicitly. Next we derive the if-and-only-if conditions under which the linear coupling of the discussed u-linear operators and matrix differential operators with constant coefficients is still Hamiltonian. Very amazingly, the derived conditions show that the resulting Hamiltonian operators is truncated only up to the 3rd differential order. Finally, a few relevant examples of integrable hierarchies are illustrated. In Chapter, 4 we first present a generalized modified Korteweg-de Vries hierarchy. Then for one of the equations in this hierarchy, we build the associated Riemann-Hilbert problems with some equivalent spectral problems. Next, computation of soliton solutions is performed by reducing the Riemann-Hilbert problems to those with identity jump matrix, i.e., those correspond to reflectionless inverse scattering problems. Finally a special reduction of the original matrix spectral problem will be briefly discussed.
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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.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 123-124).
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). Given a multigraph G some of whose vertices are marked "breakable," TRVB asks whether it is possible to convert G into a tree via a sequence of applications of the vertex-breaking operation: disconnecting the edges at a degree-G breakable vertex by replacing that vertex with G degree-1 vertices. We consider the special cases of TRVB with any combination of the following additional constraints: G must be planar, G must be a simple graph, the degree of every breakable vertex must belong to an allowed list G, and the degree of every unbreakable vertex must belong to an allowed list G. We fully characterize these variants of TRVB as polynomially solvable or NP-complete. The TRVB problem is useful when analyzing the complexity of what could be called single-traversal problems, where some space (i.e., a configuration graph or a grid) must be traversed in a single path or cycle subject to local constraints. When proving such a problem NP-hard, a reduction from TRVB can often be used as a simpler alternative to reducing from a hard variant of Hamiltonian Cycle. Next, we analyze several variants of the Hamiltonian Cycle problem whose complexity was left open in a 2007 paper by Arkin et al [3]. That paper is a systematic study of the complexity of the Hamiltonian Cycle problem on square, triangular, or hexagonal grid graphs, restricted to polygonal, thin, super-thin, degree-bounded, or solid grid graphs. The authors solved many combinations of these problems, proving them either polynomially solvable or NP-complete, but left three combinations open. We prove two of these unsolved combinations to be NP-complete: Hamiltonian Cycle in Square Polygonal Grid Graphs and Hamiltonian Cycle in Hexagonal Thin Grid Graphs. We also consider a new restriction, where the grid graph is both thin and polygonal, and prove that the Hamiltonian Cycle problem then becomes polynomially solvable for square, triangular, and hexagonal grid graphs. Several of these results are shown by application of the TRVB results, demonstrating the usefulness of that problem. Finally, we apply the Square Grid Graph Hamiltonian Cycle problem to close a longstanding open problem: we prove that optimally solving an n x n x n Rubik's Cube is NP-complete. This improves the previous result that optimally solving an n x n x n Rubik's Cube with missing stickers is NP-complete. We prove this result first for the simpler case of the Rubik's Square -- an n x n x 1 generalization of the Rubik's Cube -- and then proceed with a similar but more complicated proof for the Rubik's Cube case.
by Mikhail Rudoy.
M. Eng.
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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
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 systems of ODEs, whose exact solution is even harder to nd; then the role played by numerical integrators for ODEs is fundamental to many applied scientists. It is probably impossible to count all the scienti c papers that made use of numerical integrators during the last century and this is enough to recognize the importance of them in the progress of modern science. Moreover, in modern research, models keep getting more complicated, in order to catch more and more peculiarities of the physical systems they describe, thus it is crucial to keep improving numerical integrator's e ciency and accuracy. The rst, simpler and most famous numerical integrator was introduced by Euler in 1768 and it is nowadays still used very often in many situations, especially in educational settings because of its immediacy, but also in the practical integration of simple and well-behaved systems of ODEs. Since that time, many mathematicians and applied scientists devoted their time to the research of new and more e cient methods (in terms of accuracy and computational cost). The development of numerical integrators followed both the scienti c interests and the technological progress of the ages during whom they were developed. In XIX century, when most of the calculations were executed by hand or at most with mechanical calculators, Adams and Bashfort introduced the rst linear multistep methods (1855) and the rst Runge- Kutta methods appeared (1895-1905) due to the early works of Carl Runge and Martin Kutta. Both multistep and Runge-Kutta methods generated an incredible amount of research and of great results, providing a great understanding of them and making them very reliable in the numerical integration of a large number of practical problems. It was only with the advent of the rst electronic computers that the computational cost started to be a less crucial problem and the research e orts started to move towards the development of problem-oriented methods. It is probably possible to say that the rst class of problems that needed an ad-hoc numerical treatment was that of sti problems. These problems require highly stable numerical integrators (see Section ??) or, in the worst cases, a reformulation of the problem itself. Crucial contributions to the theory of numerical integrators for ODEs were given in the XX century by J.C. Butcher, who developed a theory of order for Runge-Kutta methods based on rooted trees and introduced the family of General Linear Methods together with K. Burrage, that uni ed all the known families of methods for rst order ODEs under a single formulation. General Linear Methods are multistagemultivalue methods that combine the characteristics of Runge-Kutta and Linear Multistep integrators... [edited by Author]
XIII n.s.
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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], and to introduce the Kleinman-Newton method at the end of the chapter. In Chapter 2 we will demonstrate the proof. In Chapter 3 we will show the related numerical work and results.
Ph. D.
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Attia, Ahmed Mohamed Mohamed. "Advanced Sampling Methods for Solving Large-Scale Inverse Problems." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/73683.

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Ensemble and variational techniques have gained wide popularity as the two main approaches for solving data assimilation and inverse problems. The majority of the methods in these two approaches are derived (at least implicitly) under the assumption that the underlying probability distributions are Gaussian. It is well accepted, however, that the Gaussianity assumption is too restrictive when applied to large nonlinear models, nonlinear observation operators, and large levels of uncertainty. This work develops a family of fully non-Gaussian data assimilation algorithms that work by directly sampling the posterior distribution. The sampling strategy is based on a Hybrid/Hamiltonian Monte Carlo (HMC) approach that can handle non-normal probability distributions. The first algorithm proposed in this work is the "HMC sampling filter", an ensemble-based data assimilation algorithm for solving the sequential filtering problem. Unlike traditional ensemble-based filters, such as the ensemble Kalman filter and the maximum likelihood ensemble filter, the proposed sampling filter naturally accommodates non-Gaussian errors and nonlinear model dynamics, as well as nonlinear observations. To test the capabilities of the HMC sampling filter numerical experiments are carried out using the Lorenz-96 model and observation operators with different levels of nonlinearity and differentiability. The filter is also tested with shallow water model on the sphere with linear observation operator. Numerical results show that the sampling filter performs well even in highly nonlinear situations where the traditional filters diverge. Next, the HMC sampling approach is extended to the four-dimensional case, where several observations are assimilated simultaneously, resulting in the second member of the proposed family of algorithms. The new algorithm, named "HMC sampling smoother", is an ensemble-based smoother for four-dimensional data assimilation that works by sampling from the posterior probability density of the solution at the initial time. The sampling smoother naturally accommodates non-Gaussian errors and nonlinear model dynamics and observation operators, and provides a full description of the posterior distribution. Numerical experiments for this algorithm are carried out using a shallow water model on the sphere with observation operators of different levels of nonlinearity. The numerical results demonstrate the advantages of the proposed method compared to the traditional variational and ensemble-based smoothing methods. The HMC sampling smoother, in its original formulation, is computationally expensive due to the innate requirement of running the forward and adjoint models repeatedly. The proposed family of algorithms proceeds by developing computationally efficient versions of the HMC sampling smoother based on reduced-order approximations of the underlying model dynamics. The reduced-order HMC sampling smoothers, developed as extensions to the original HMC smoother, are tested numerically using the shallow-water equations model in Cartesian coordinates. The results reveal that the reduced-order versions of the smoother are capable of accurately capturing the posterior probability density, while being significantly faster than the original full order formulation. In the presence of nonlinear model dynamics, nonlinear observation operator, or non-Gaussian errors, the prior distribution in the sequential data assimilation framework is not analytically tractable. In the original formulation of the HMC sampling filter, the prior distribution is approximated by a Gaussian distribution whose parameters are inferred from the ensemble of forecasts. The Gaussian prior assumption in the original HMC filter is relaxed. Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a Gaussian Mixture Model (GMM) to the prior ensemble. The base filter developed following this strategy is named cluster HMC sampling filter (ClHMC ). A multi-chain version of the ClHMC filter, namely MC-ClHMC , is also proposed to guarantee that samples are taken from the vicinities of all probability modes of the formulated posterior. These methodologies are tested using a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption in the HMC filtering paradigm. To provide a unified platform for data assimilation research, a flexible and a highly-extensible testing suite, named DATeS , is developed and described in this work. The core of DATeS is implemented in Python to enable for Object-Oriented capabilities. The main components, such as the models, the data assimilation algorithms, the linear algebra solvers, and the time discretization routines are independent of each other, such as to offer maximum flexibility to configure data assimilation studies.
Ph. D.
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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. Boston, MA: 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. London: Chapman & Hall, 1994.

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Gignoux, Claude, and Bernard Silvestre-Brac. Solved Problems in Lagrangian and Hamiltonian Mechanics. Dordrecht: 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. Dordrecht: Springer Netherlands, 2009.

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Classical mechanics: Systems of particles and Hamiltonian dynamics. New York: Springer, 2003.

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

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Classical mechanics: Systems of particles and Hamiltonian dynamics. 2nd ed. Heidelberg [Germany]: Springer, 2010.

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

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Lagrangian and Hamiltonian mechanics: Solutions to the exercises. Singapore: World Scientific, 1999.

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

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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, 1–14. Boston, MA: 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, 129–41. Boston, MA: 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, 143–53. Boston, MA: 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, 155–64. Boston, MA: 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, 165–77. Boston, MA: 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, 179–88. Boston, MA: 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, 15–23. Boston, MA: 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, 25–39. Boston, MA: 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, 41–52. Boston, MA: 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, 53–68. Boston, MA: 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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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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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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Brugnano, Luigi, Gianluca Frasca Caccia, and Felice Iavernaro. "Efficient implementation of geometric integrators for separable Hamiltonian problems." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825598.

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Huffman, Emilie F. "Solution to new sign problems with Hamiltonian Lattice Fermions." In The 32nd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2015. http://dx.doi.org/10.22323/1.214.0058.

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Chen, X. S., M. H. Lim, and D. C. Wunsch. "A Memetic Algorithm configured via a problem solving environment for the Hamiltonian Cycle problems." In 2007 IEEE Congress on Evolutionary Computation. IEEE, 2007. http://dx.doi.org/10.1109/cec.2007.4424821.

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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. Fort Belvoir, VA: Defense Technical Information Center, April 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), February 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. Fort Belvoir, VA: Defense Technical Information Center, March 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), November 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), November 1992. http://dx.doi.org/10.2172/6789042.

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