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Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the…
The self-diffusion coefficient of a granular gas in the homogeneous cooling state is analyzed near the shearing instability. Using mode-coupling theory, it is shown that the coefficient diverges logarithmically as the instability is…
In particle-based stochastic reaction-diffusion models, reaction rate and placement kernels are used to decide the probability per time a reaction can occur between reactant particles, and to decide where product particles should be placed.…
A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
We present a first-principles formalism for studying dynamical heterogeneities in glass forming liquids. Based on the Non-Equilibrium Self-Consistent Generalized Langevin Equation theory, we were able to describe the time-dependent local…
Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible…
We consider the quantum reaction-diffusion dynamics in $d$ spatial dimensions of a Fermi gas subject to binary annihilation reactions $A+A \to \emptyset$. These systems display collective nonequilibrium long-time behavior, which is…
The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schr\"odinger equation. In many cases the Hamiltonian obtained is that of an integrable quantum chain. Within this approach…
This article considers the generative modeling of the (mixed) states of quantum systems, and an approach based on denoising diffusion model is proposed. The key contribution is an algorithmic innovation that respects the physical nature of…
We prove a priori bounds for solutions of stochastic reaction diffusion equations with super-linear damping in the reaction term. These bounds provide a control on the supremum of solutions on any compact space-time set which only depends…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
We present a new method to solve the dynamics of disordered spin systems on finite time-scales. It involves a closed driven diffusion equation for the joint spin-field distribution, with time-dependent coefficients described by a dynamical…
Mesoscopic density functional theory for inhomogeneous mixtures of sperical particles is developed in terms of mesoscopic volume fractions by a systematic coarse-graining procedure starting form microscopic theory. Approximate expressions…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
In this thesis, we investigate the emergence of kinetic processes in finite quantum systems. We first generalize the Redfield theory to describe the dynamics of a small quantum system weakly interacting with an environment of finite heat…
The change from the diffusion-limited to the reaction-limited cooperative behaviour in reaction-diffusion systems is analysed by comparing the universal long-time behaviour of the coagulation-diffusion process on a chain and on the Bethe…