Related papers: A compact, structural analysis amenable, port-Hami…
Hamiltonian systems are one of the most important class of dynamical systems with a geometric structure called symplecticity and the numerical algorithms which can preserve such geometric structure are of interest. In this article we study…
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics…
This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a…
Digital circuits, despite having been studied for nearly a century and used at scale for about half that time, have until recently evaded a fully compositional theoretical in which arbitrary circuits may be freely composed together without…
In this work we exploit Dirac's Constraint Analysis (DCA) in Hamiltonian formalism to study different types of Superconducting Quantum Circuits (SQC) in a {\it{unified}} way. The Lagrangian of a SQC reveals the constraints, that are…
The central problem in electronic structure theory is the computation of the eigenvalues of the electronic Hamiltonian -- an unbounded, self-adjoint operator acting on a Hilbert space of antisymmetric functions. Coupled cluster (CC)…
Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…
A generic data-assisted control architecture within the port-Hamiltonian framework is proposed, introducing a physically meaningful observable that links conservative dynamics to all actuation, dissipation, and disturbance channels. A…
One promising application of near-term quantum devices is to prepare trial wavefunctions using short circuits for solving different problems via variational algorithms. For this purpose, we introduce a new circuit design that combines…
An elliptic relative equilibrium (ERE) is a special solution of the planar $N$-body problem generated by a central configuration. Its linear stability depends on the eccentricity $e$ and the masses of the bodies. However, for $e>0$, the…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
In a previous article, the authors developed two conversion methods to improve the $\Sigma$-method for structural analysis (SA) of differential-algebraic equations (DAEs). These methods reformulate a DAE on which the $\Sigma$-method fails…
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…
This paper studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Specifically we develop scalable techniques for constructing the attraction regions associated with a particular stable equilibrium,…
In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry…
It is well known that any port-Hamiltonian (pH) system is passive, and conversely, any minimal and stable passive system has a pH representation. Nevertheless, this equivalence is only concerned with the input-output mapping but not with…
Harmonic stator-rotor coupling offers a promising approach for the interconnection of rotating subsystems in the simulation of electric machines. This paper studies the stability of discretization schemes based on harmonic coupling in the…
Singular charge sources in terms of Dirac delta functions present a well-known numerical challenge for solving Poisson's equation. For a sharp interface between inhomogeneous media, singular charges could be analytically treated by…
One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the…
Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is…