1,421 Results Found

In this paper, we present new Hamiltonian operators for the integrable couplings of the Ablowitz–Kaup–Newell–Segur hierarchy and the Kaup–Newell hierarchy. The corresponding Hamiltonians allow nontrivial degeneration. Multi-Ha...

In this paper, we report on recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs) by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In particular, we con...

The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles $C_0$ and $C_t$ of a graph G, whether there is a sequence of Hamiltonian cycles $C_0,C_1,\dots ,C_t$ such that $C_i$ can be obtaine...

Recently, the problem of counting Hamiltonian cycles in 2-tiled graphs was resolved by Vegi Kalamar, Bokal, and Žerak. In this paper, we continue our research on generalized tiled graphs. We extend algorithms on counting traversing Hamiltonian c...

In this paper, a symplectic algorithm is utilized to investigate constrained Hamiltonian systems. However, the symplectic method cannot be applied directly to the constrained Hamiltonian equations due to the non-canonicity. We firstly discuss the can...

A comprehensive overview of the irreversible port-Hamiltonian system’s formulation for finite and infinite dimensional systems defined on 1D spatial domains is provided in a unified manner. The irreversible port-Hamiltonian system formulation s...

The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory....

Here we describe eight new methods, arisen in the last 60 years, to study solutions of a Hamiltonian system with n degrees of freedom. The first six of them are intended for systems with small parameters or without them. The methods allow to find fam...

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadratu...

This paper proposes a change in the traditional epistemological paradigm and a look at classical thermodynamics from the point of view of control theory, with the aim of discovering energy state variables. The paper proposes a transition from “...

In this study, we investigate Hamiltonian cycles in the right-Cayley graphs of gyrogroups. More specifically, we give a gyrogroup version of the factor group lemma and show that some right-Cayley graphs of certain gyrogroups are Hamiltonian.

The aim of this paper is to develop a Hamilton–Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton–Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given Hamiltonian functio...

The symmetry of the spectrum and the completeness of the eigenfunction system of the Hamiltonian operator matrix have important applications in the symplectic Fourier expansion method in elasticity. However, the symplectic self-adjointness of Hamilto...

The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-ca...

Linear vector fields on Lie groups constitute a fundamental class of dynamical systems, as their flows are one-parameter subgroups of automorphisms and their infinitesimal behavior is entirely determined by derivations of the Lie algebra. When a Lie...

A novel approach to the Hamiltonian formulation of quantum field theory at finite temperature is presented. The temperature is introduced by compactification of a spatial dimension. The whole finite-temperature theory is encoded in the ground state o...

In the present paper, a role of Hamiltonian systems in mathematical and physical formalisms is considered with the help of skew-symmetric differential forms. In classical mechanics the Hamiltonian system is realized from the Euler–Lagrange equa...

The all-at-once technique has attracted many researchers’ interest in recent years. In this paper, we combine this technique with a classical symplectic and symmetric method for solving Hamiltonian systems. The solutions at all time steps are obtaine...

Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized....

Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. It then comes to discussing conjectures of whether all primary constraints correspond to...

This work aims to analyze a new system of two fractional Hamiltonian equations. We propose an effective method for transforming the established model into a system of two distinct equations. Two functionals that are connected to the converted system...

A diesel engine is a typical dynamic system. In this paper, a dynamics method is proposed to establish the Hamiltonian model of the diesel engine, which solves the main difficulty of constructing a Hamiltonian function under the multi-field coupling...

This study investigates the geometric linearization of constraint Hamiltonian systems using the Jacobi metric and the Eisenhart lift. We establish a connection between linearization and maximally symmetric spacetimes, focusing on the Noether symmetri...

It is known that corresponding to each Noether symmetry there is a conserved quantity. Another class of symmetries that corresponds to conserved quantities is the class of Mei symmetries. However, the two sets of symmetries may give different conserv...

In graph theory, Hamiltonian path refers to the path that visits each vertex exactly once. In this paper, we designed a method to generate random Hamiltonian path within digital images, which is equivalent to permutation in image encryption. By these...

The paper studies the construction of the Hamiltonian for circuits built from the (α,β) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to Σ-circuits, i.e., circuits built exc...

In 1930, Kuratowski showed that $K_{3,3}$ and $K_5$ are the only two minor-minimal nonplanar graphs. Robertson and Seymour extended finiteness of the set of forbidden minors for any surface. Širáň and Kochol showed that there are infinitely many k-crossing-c...

In the theory of open quantum systems, the Markovian approximation is very widespread. Usually, it assumes the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation for density matrix dynamics and quantum regression formulae for mul...

Galilean Monte Carlo (GMC) allows exploration in a big space along systematic trajectories, thus evading the square-root inefficiency of independent steps. Galilean Monte Carlo has greater generality and power than its historical precursor Hamiltonia...

Let $G=(V,E)$ be a graph. The first Zagreb index of a graph G is defined as ${\sum }_{u\in V}{d}_G^2\left(u\right)$, where $d_G\left(u\right)$ is the degree of vertex u in G. A graph G is called Hamiltonian (resp. traceable) if G has a cycle (resp. path) containing all the vertices of...

In this paper, we mainly consider the Hamiltonian indices of three classes of graphs obtained from Petersen graph, that is, the minimum integer m of m-time iterated line graph $L^m\left(G\right)$ of these three classes of graphs such that $L^m\left(G\right)$ is Hamiltonian. We...

The hypercube $Q_n$ is a well-known and efficient interconnection network. Ruskey and Savage posed the following question: does every matching in a hypercube $Q_n$ for $n\ge 2$ extend to a Hamiltonian cycle? Fink addressed this by proving that every perfect...

Inthis paper, we consider the reducibility of a class of nonlinear almost periodic Hamiltonian systems. Under suitable hypothesis of analyticity, non-resonant conditions and non-degeneracy conditions, by using KAM iteration, it is shown that the cons...

The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms, have received a lot of attention in the literature. However, a full unde...

Hamiltonian mechanics plays an important role in the development of nonlinear science. This paper aims for a fractional Hamiltonian system of variable order. Several issues are discussed, including differential equation of motion, Noether symmetry, a...

Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie...

In this review work, we outline a conceptual path that, starting from the numerical investigation of the transition between weak chaos and strong chaos in Hamiltonian systems with many degrees of freedom, comes to highlight how, at the basis of equil...

A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations using the conservation for energy and potential enstrophy is presented. Different mechanisms, such as vortical flows and emission of gravity waves, emerge fr...

Finding a Hamiltonian cycle in a graph G = (V, E) is a well-known problem. The challenge of finding a Hamiltonian cycle that avoids these faults when faulty vertices or edges are present has been extensively studied. When the edge set of G is partiti...

A family of explicit symplectic partitioned Runge-Kutta methods are derived with effective order 3 for the numerical integration of separable Hamiltonian systems. The proposed explicit methods are more efficient than existing symplectic implicit Rung...

This paper presents a nonlinear velocity observer of tether deployment using the immersion and invariance technique, and the velocity observer design problem is recast as a problem of designing an attractive and invariant manifold inside the Hamilton...

The present work applies and extends the previously developed Quantitative Geometrical Thermodynamics (QGT) formalism to the derivation of a Hamiltonian for the damped harmonic oscillator (DHO) across all damping regimes. By introducing complex time,...

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motion...

This paper studies the number of small limit cycles produced around an elementary center for Hamiltonian differential systems with the elliptic Hamiltonian function $H=\frac{1}{2}{y}^2+\frac{1}{2}{x}^2-\frac{2}{3}{x}^3+\frac{a}{4}{x}^4(a\ne 0)$ under two types of polynomial perturbations of de...

It is well known that Einstein’s equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that time evolution of the gravitatio...

Shape registration, finding the correct alignment of two sets of data, plays a significant role in computer vision such as objection recognition and image analysis. The iterative closest point (ICP) algorithm is one of well known and widely used algo...

In this paper, we construct a highly simplified mathematical model for studying the problem of conjugate heat transfer in gas turbine blades and their cooling ducts. Our simple model focuses on the relevant coupling structures and aims to reduce the...

In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM) and generalized Kudryashov method (GKM) are applied to find several exact soluti...

Dirac’s Generalized Hamiltonian Dynamics (GHD) is a purely classical formalism for systems having constraints: it incorporates the constraints into the Hamiltonian. Dirac designed the GHD specifically for applications to quantum field theory. I...

In this paper, we analyse the classical action as a tool to reveal the phase space structure of Hamiltonian systems simply and intuitively. We construct a scalar field using the values of the action along the trajectories to analyse the phase space....