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Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
The recent success of large foundation models in artificial intelligence has prompted the emergence of chemical pre-trained models. Despite the growing interest in large molecular pre-trained models that provide informative representations…
The Ornstein-Uhlenbeck (OU) process describes the dynamics of Brownian particles in a confining harmonic potential, thereby constituting the paradigmatic model of overdamped, mean-reverting Langevin dynamics. Despite its widespread…
The charge distribution of the heaviest fragment detected in the decay of quasi-projectiles produced in intermediate energy heavy-ion collisions has been observed to be bimodal. This feature is expected as a generic signal of phase…
It was recently argued that one-dimensional systems of several strongly interacting fermions of different mass undergo critical transitions between different spatial orderings when the external confinement adiabatically changes its shape.…
We extend and apply a recently developed approach to the study of dynamic bifurcations in PDEs based on the geometric blow-up method. We show that this approach, which has so far only been applied to study a dynamic Turing bifurcation in a…
A two-mode Bose-Einstein condensate coupled by a high-frequency modulation field is found to display rich features. An effective stationary Hamiltonian approach reveals the emergence of additional degenerate eigenstates as well as new…
Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the…
We consider a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractional Brownian motion. For such process we specify mean and…
This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
Complex Ornstein-Uhlenbeck (OU) processes have various applications in statistical modelling. They play role e.g. in the description of the motion of a charged test particle in a constant magnetic field or in the study of rotating waves in…
Systems of active particles can show a large variety of collective behavior. In theory, two aspects determine the collective behavior: the model at the particle level and the parameter regime. While many studies consider a single model and…
Transport models of growth hormones can be used to reproduce the hormone accumulations that occur in plant organs. Mostly, these accumulation patterns are calculated using time step methods, even though only the resulting steady state…
In this article we present the modeling of bi-stability view problems described by the activity or firing rates of two interacting population of neurons. Starting from the study of a complex system, the sys-tem of stochastic differential…
Stochastic reaction-diffusion processes may be presented in terms of integrable quantum chains and can be used to describe various biological and chemical systems. Exploiting the integrability of the models one finds in some cases good…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the…
We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of…
This work presents a methodology for modeling and predicting human behavior in settings with N humans interacting in highly multimodal scenarios (i.e. where there are many possible highly-distinct futures). A motivating example includes…