相关论文: Birkhoffian formulation of the dynamics of LC circ…

Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…

An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…

We consider nonlinear multibody systems and present a suitable set of coordinates for the internal dynamics which allow to decouple the internal dynamics without the need to compute the Byrnes-Isidori form. Furthermore, we derive sufficient…

We report the discovery of an envelope Hamiltonian describing the charged-particle dynamics in general linear coupled lattices.

We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…

In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…

Mixed quantum-classical models have been proposed in several contexts to overcome the computational challenges of fully quantum approaches. However, current models typically suffer from long-standing consistency issues, and, in some cases,…

We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity…

In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for…

This article presents a simple port-Hamiltonian formulation of the equations for an RLC electric circuit as a differential-algebraic equation system, and a proof that structural analysis always succeeds on it for a well-posed circuit, thus…

We prove lower bounds for the Dirichlet Laplacian on possibly unbounded domains in terms of natural geometric conditions. This is used to derive uncertainty principles for low energy functions of general elliptic second order divergence…

We propose a general framework for computing Retarded Green's Functions (RGFs) on quantum computers by recasting their evaluation as a problem of circuit differentiation. Our proposal is based on real-time evolution and specifically…

At the heart of quantum technology development is the control of quantum systems at the level of individual quanta. Mathematically, this is realised through the study of Hamiltonians and the use of methods to solve the dynamics of quantum…

Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable.…

Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…

A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…

In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…

In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…

A systematic procedure is proposed for deriving all the gauge symmetries of the general, not necessarily variational, equations of motion. For the variational equations, this procedure reduces to the Dirac-Bergmann algorithm for the…