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A mathematical framework for Continuous Time Finance based on operator algebraic methods offers a new direct and entirely constructive perspective on the field and leads to new numerical analysis techniques. This is partly a review paper as…
The use of energy functionals based on density as the basic variable is advocated for ab initio molecular dynamics. It is demonstrated that the constraint of positivity of density can be incorporated easily by using square root density for…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Suppressing undesired nonunitary effects is a major challenge in quantum computation and quantum control. In this work, by considering the adiabatic dynamics in presence of a surrounding environment, we theoretically and experimentally…
Metadynamics is a powerful method to accelerate molecular dynamics simulations, but its efficiency critically depends on the identification of collective variables that capture the slow modes of the process. Unfortunately, collective…
Optimal exploitation of supercomputing resources for the evaluation of electrostatic forces remains a challenge in molecular dynamics simulations of very large systems. The most efficient methods are currently based on particle-mesh Ewald…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
The thorough treatment of electron-lattice interactions from first principles is one of the main goals in condensed matter physics. While the commonly applied adiabatic Born-Oppenheimer approximation is sufficient for describing many…
We discuss statics and dynamics of condensation in a zero-range process with compartments of limited sizes. For the symmetric dynamics the stationary state has a factorized form. For the asymmetric dynamics the steady state factorizes only…
The dynamics of dissipative soft-sphere gases obeys Newton's equation of motion which are commonly solved numerically by (force-based) Molecular Dynamics schemes. With the assumption of instantaneous, pairwise collisions, the simulation can…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
We extend the concept of superadiabatic dynamics, or transitionless quantum driving, to quantum open systems whose evolution is governed by a master equation in the Lindblad form. We provide the general framework needed to determine the…
The role of gravity in human motor control is at the same time obvious and difficult to isolate. It can be assessed by performing experiments in variable gravity. We propose that adiabatic invariant theory may be used to reveal…
Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques…
Optimal control (OC) using inverse dynamics provides numerical benefits such as coarse optimization, cheaper computation of derivatives, and a high convergence rate. However, to take advantage of these benefits in model predictive control…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…