Related papers: Mass-Zero constrained dynamics and statistics for …
Multiscale dynamics are frequently present in real-world processes, such as the atmosphere-ocean and climate science. Because of time scale separation between a small set of slowly evolving variables and much larger set of rapidly changing…
This paper developes a data-driven magnetostatic finite-element (FE) solver which directly exploits measured material data instead of a material curve constructed from it. The distances between the field solution and the measurement points…
A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
This paper investigates a class of Lagrangian control systems with $n$ degrees-of-freedom (DOF) and n-1 actuators, assuming that $n-1$ virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds.…
This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with…
A new formulation of time-dependent Relaxed Magnetohydrodynamics (RxMHD) is derived variationally from Hamilton's Action Principle using microscopic conservation of mass, and macroscopic conservation of total magnetic helicity, cross…
We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family…
A new Markov Chain Monte Carlo method for simulating the dynamics of molecular systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is…
The unconstrained ensemble describes completely open systems whose control parameters are chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of…
We consider a nonlinear system, affine with respect to an unbounded control $u$ which is allowed to range in a closed cone. To this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to…
The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative…
This paper presents a coordinate-free formulation of virtual holonomic constraints for underactuated Lagrangian control systems on Riemannian manifolds. It is shown that when a virtual constraint enjoys a regularity property, the…
This paper presents a Lagrangian approach to simulating multibody dynamics in a tensegrity framework with an ability to tackle holonomic constraint violations in an energy-preserving scheme. Governing equations are described using…
Simulations of magnetization dynamics in a multiscale environment enable rapid evaluation of the Landau-Lifshitz-Gilbert equation in a mesoscopic sample with nanoscopic accuracy in areas where such accuracy is required. We have developed a…
We consider a classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the…
The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of non-trivial viable dynamic modes for the Poincar\'e gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The…
Many living and physical systems such as cell aggregates, tissues or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these…
A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…