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The conserved Swift-Hohenberg equation (or Phase-Field-Crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase transitions: at low temperature, the corresponding mean-field…
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…
We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…
We study the one dimensional three species monomer-monomer reaction model in the reaction controlled limit using mean-field theory and dynamic Monte Carlo simulations. The phase diagram consists of a reactive steady state bordered by three…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
Selective adsorption in a two-dimensional model of a binary hard-disk mixture on patterned adhesive surfaces is studied using grand canonical Monte Carlo simulations. The two species have equal diameters and equal bulk chemical potentials,…
The kinetics of the chiral phase transition is studied within a linear quark-meson-$\sigma$ model, using a Monte-Carlo approach to semiclassical particle-field dynamics. The meson fields are described on the mean-field level and quarks and…
The accuracy of the energy landscape of silicon systems obtained from various density functional methods, a tight binding scheme and force fields is studied. Quantum Monte Carlo results serve as quasi exact reference values. In addition to…
We study 2D fronts propagating up a co-moving reaction rate gradient in finite number reaction-diffusion systems. We show that in a 2D rectangular channel, planar solutions to the deterministic mean-field equation are stable with respect to…
The formation, growth, structure and cluster size distribution (CSD) properties in a two-dimensional system of particles interacting with Lennard-Jones (LJ) potential under controlled cooling condition have been studied using Monte-Carlo…
We introduce the concept of stationary metastable states (SMS's) in the presence of another more stable state. The stationary nature allows us to study SMS's by using a restricted partition function formalism as advocated by Penrose and…
The mass-based Maxwell-Stefan approach to one-phase multicomponent reactive mixtures is mathematically analyzed. It is shown that the resulting quasilinear, strongly coupled reaction-diffusion system is locally well-posed in an…
The behavior of strongly correlated Fermi systems is investigated beyond the onset of a phase transition where the single-particle spectrum $\xi({\bf p})$ becomes flat. The Landau-Migdal quasiparticle picture is shown to remain applicable…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
We use a mean-field-based transformer model to theoretically investigate how auxiliary variables, such as positional encoding, prevent mode collapse of self-attention mechanisms. The use of mean-field transformers to analyze the properties…
One-step generative modeling has emerged as a leading approach to amortize the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and…
We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result…
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent…