Related papers: The mixed convolved action
A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
The design of adaptive structures is one method to improve sustainability of buildings. Adaptive structures are able to adapt to different loading and environmental conditions or to changing requirements by either small or large shape…
We derive a consistent differential representation for the dynamics of a self-financing portfolio for different hedging strategies. In the basis of the derivation there is the so called "retarded action principle", which represents the…
Recently it has been reported that biased range-measurements among neighboring agents in the gradient distance-based formation control can lead to predictable collective motion. In this paper we take advantage of this effect and by…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We comment on the method of Dreisigmeyer and Young [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems with fractional derivatives. It was previously hoped that using fractional…
In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…
This paper proposes a new model for individuals movement in ecology. The movement process is defined as a solution to a stochastic differential equation whose drift is the gradient of a multimodal potential surface. This offers a new…
The two most commonly used methods to model the behaviour of granular flows are discrete element and continuum mechanics simulations. These approaches concentrate on the deterministic description of particle or bulk material motion. Unlike…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…
In this paper, we investigate specific least action principles for laws of stochastic processes within a framework which stands on filtrations preserving variations. The associated Euler-Lagrange conditions, which we obtain, exhibit a…