Related papers: Differential-algebraic systems with dissipative Ha…
We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, fusions, and commuting traces are derived. Explicit…
In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature…
We study linear time-invariant dissipative Hamiltonian differential-algebraic systems. We characterize when the systems are robustly asymptotically stable and derive exact conditions and bounds when this property is lost under…
Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…
In this paper we prove that a large class of linear evolution PDEs defines a Stokes-Dirac structure over Hilbert spaces. To do so, the theory of boundary control system is employed. This definition encompasses problems from mechanics, that…
We consider linear first-order systems of ordinary differential equations (ODEs) in port-Hamiltonian (pH) form. Physical parameters are remodelled as random variables to conduct an uncertainty quantification. A stochastic Galerkin…
Differential graded (DG) algebras are powerful tools from rational homotopy theory. We survey some recent applications of these in the realm of homological commutative algebra.
We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson…
Discretization methods for differential-algebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE). This allows to make use of any discretization scheme…
The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper…
A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which…
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…
Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the observed quantities (outputs) and the inputs…
Hybrid numerical-experimental testing is a standard approach for complex dynamical structures that are, on the one hand, not easy to model due to complexity and parameter uncertainty and, on the other hand, too expensive for full-scale…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash…
A quantum statistical random system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble of random matrices. The eigenenergies of…
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of Hamiltonian vector…
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…