Related papers: A de Broglie-Bohm Model of Pure Shape Dynamics: $N…
We investigate the dynamical coupling between the motion and the deformation of a single self-propelled domain based on two different model systems in two dimensions. One is represented by the set of ordinary differential equations for the…
We propose an example of smooth autonomous system governed by differential delay equation manifesting chaotic dynamics apparently associated with hyperbolic attractor of Smale - Williams type. The general idea is to depart from a system…
There exist methods to reformulate in an exact way the many-body problem of interacting bosons in terms of the stochastic evolution of single particle wave functions. For one such reformulation, the so-called simple Fock scheme, we present…
We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the…
The state of a classical point-particle system may often be specified by giving the position and momentum for each constituent particle. For non-pointlike particles, the center-of-mass position may be augmented by an additional coordinate…
Modeling and simulating how oxygen supply shapes neuronal excitability is crucial for advancing the understanding of brain function in pathological scenarios, such as ischemia. This condition is caused by a reduced blood supply, leading to…
Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow…
In this work a finite element simulation of the motion of a rigid body in a fluid, with free surface, is described. A completely general referential description (of which both Lagrangian and Eulerian descriptions are special cases) of an…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
We present a geometrical inspired study of the dynamics of $Dp$-branes. We focus on the usual nonpolynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
We consider an electrodiffusion model describing the evolution of $N$ ionic species in a three-dimensional fluid flowing through a porous medium and forced by added body charges. We address the global well-posedness and long-time dynamics…
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle…
In this work the root to macroscopic quantum effects is revealed based on the quasiparticle model of collective excitations in an arbitrary degenerate electron gas. The $N$-electron quantum system is considered as $N$ streams coupled,…
Properties of the yrast states of a system of $N$ bosons confined to a one-dimensional ring and interacting via contact forces is examined both variationally and by numerical diagonalizations. The latter allow for obtaining numerical…
Bohmian mechanics is an interpretation of quantum mechanics that describes the motion of quantum particles with an ensemble of deterministic trajectories. Several attempts have been made to utilize Bohmian trajectories as a computational…
We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a 3-body problem in the complex plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on…
Astrophysical systems differ often in two points from classical thermodynamical systems: 1.) They are open and 2.) gravity is a dominant factor. Both modifies the homogeneous equilibrium structure, known from classical thermodynamics. In…
We present a perturbative treatment of the evolution under their mutual self-gravity of particles displaced off an infinite perfect lattice, both for a static space and for a homogeneously expanding space as in cosmological N-body…
Applications of active particles require a method for controlling their dynamics. While this is typically achieved via direct interventions, indirect interventions based, e.g., on an orientation-dependent self-propulsion speed of the…