Related papers: The mixed convolved action
A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approach is offered that effectively propagates the statistics in time. Loss of sensitivity to an…
In the present work, by taking advantage of a so-called practical limitation of fractional derivatives, namely, the absence of a simple chain and Leibniz's rules, we proposed a generalized fractional calculus of variation where the…
This paper presents a modular framework for motion planning using movement primitives. Central to the approach is Contraction Theory, a modular stability tool for nonlinear dynamical systems. The approach extends prior methods by achieving…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
We develop a non-anticipating calculus of variations for functionals on a space of laws of continuous semi-martingales, which extends the classical one. We extend Hamilton's least action principle and Noether's theorem to this generalized…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to…
We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, leading to coupled nonlinear systems of ordinary differential equations. Recent work in scalar auxiliary variable…
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for…
Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
Connections between the principle of stationary action and optimal control, and between established notions of minimax and viscosity solutions, are combined to describe trajectories of energy conserving systems as solutions of corresponding…
We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…