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The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…
We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…
Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single-step and multi-step phase transitions to…
We study the steady state structure and dynamics of a 2-d Ising interface placed in an inhomogeneous external field with a sigmoidal profile which moves with velocity $v_{e}$. In the strong coupling limit the problem maps onto an…
In nature interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviours. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active…
A modified version of the Multicluster Dynamic Model of nuclei is proposed to construct completely antisymmetrized wave functions of multicluster systems. An overlap kernel operator is introduced to renormalize the total wave function after…
Molecular simulations employing empiric force fields have provided valuable knowledge about the ice growth process in the last decade. The development of novel computational techniques allows us to study this process, which requires long…
We present a phase field model for vesicle growth or shrinkage induced by an osmotic pressure due to a chemical potential gradient. The model consists of an Allen-Cahn equation describing the evolution of phase field and a Cahn-Hilliard…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals…
The Neural Tangent Kernel (NTK) offers a powerful tool to study the functional dynamics of neural networks. In the so-called lazy, or kernel regime, the NTK remains static during training and the network function is linear in the static…
We study the interplay between wetting and miscibility of a symmetric polymer mixture via MC simulations and SCF calculations. The film surfaces interact with the monomers via short ranged potentials and the wetting transition is of first…
We analyze the time evolution of quantum entanglement in a model consisting of two two-level atoms interacting with a two-mode electromagnetic field for a variety of initial states. We study two different coupling schemes motivated by the…
Snap-buckling is a rapid shape transition in slender structures, appearing as a fundamental switching mechanism of natural and man-made systems. Boundary conditions of structures are crucial to predict and control their snap-buckling…
Starting from a three-dimensional description of an active nematic layer, we employ an asymptotic theory to derive a series of low-dimensional continuum models that capture the coupled dynamics of flat and curved films, including variations…
Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the crystalline lattice. To investigate the kinetic anisotropy and velocity of different crystallographic faces we use the hyperbolic (modified) phase…
We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit a continuous phase transition from an…
The secretion of vesicles for intracellular transport often rely on the aggregation of specialized membrane-bound proteins into a coat able to curve cell membranes. The nucleation and growth of a protein coat is a kinetic process that…
We study pattern formation, fluctuations and scaling induced by a growth-promoting active walker on an otherwise static interface. Active particles on an interface define a simple model for energy consuming proteins embedded in the plasma…