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In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling…
We examine the symmetry-breaking effect of fixed constellations of particles on the surface-directed spinodal decomposition of binary blends in the presence of particles whose surfaces have a preferential affinity for one of the components.…
In this study, we present a comprehensive exploration of formation of different phases in lipid molecules using a coarse-grained implicit solvent model, where each lipid molecule is represented as a rigid, three-bead rod-like structure. Our…
As one kind important phase field equations, Cahn-Hilliard equations contain spatial high order derivatives, strong nonlinearities, and even singularities. When using the physics informed neural network (PINN) to simulate the long time…
Many materials containing colloids or polymers are polydisperse: They comprise particles with properties (such as particle diameter, charge, or polymer chain length) that depend continuously on one or several parameters. This review…
In this paper we present a mathematical model to describe the phenomenon of phase separation, which is modelled as space regions where an order parameter changes smoothly. The model proposed, including thermal and mixing effects, is deduced…
Liquid-liquid phase separation of charge/aromatic-enriched intrinsically disordered proteins (IDPs) is critical in the biological function of membraneless organelles. Much of the physics of this recent discovery remains to be elucidated.…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…
We investigate the phase behavior of symmetric AB diblock copolymers confined into a thin film. The film boundaries are parallel, impenetrable and attract the A component of the diblock copolymer. Using a self-consistent field technique…
We study the kinetics of two-temperature induced phase separation (2-TIPS) in dilute binary mixtures of active ("hot") and passive ("cold") particles using molecular dynamics simulations and a coarse-grained hydrodynamic model. Following a…
A one-dimensional model of a dispersive medium with intrinsic loss, compensated by a parametric drive, is proposed. It is a combination of the well-known parametrically driven nonlinear Schr\"{o}dinger (NLS) and complex cubic…
We provide a general convergence theorem of an idealized stochastic Polyak step size called SPS$^*$. Besides convexity, we only assume a local expected gradient bound, that includes locally smooth and locally Lipschitz losses as special…
We use specialized Monte Carlo simulation methods and moment free energy calculations to provide conclusive evidence that dense polydisperse spheres at equilibrium demix into coexisting fcc phases, with more phases appearing as the spread…
Physics-Informed Neural Networks present a novel approach in SciML that integrates physical laws in the form of partial differential equations directly into the NN through soft constraints in the loss function. This work studies the…
We develop an innovative technique for studying inhomogeneous phases with a spontaneous broken symmetry. The method relies on the knowledge of the exact form of the free energy in the homogeneous phase and on a specific gradient expansion…
In this letter we show that the late-time scaling state in spinodal decomposition is not unique. We performed lattice Boltzmann simulations of the phase-ordering of a 50%-50% binary mixture using as initial conditions for the phase-ordering…
Aqueous two-phase systems (ATPSs), that is, phase-separating solutions of water soluble but mutually immiscible molecular species, offer fascinating prospects for selective partitioning, purification, and extraction. Here, we formulate a…
A simple expression for the composition dependence of the Flory-Huggins interaction parameter of polymer/solvent systems reported earlier is used to model the demixing of polymer solutions into two liquid phases. To this end the system…
Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To…
We describe a simple coarse-grained model which is suited to study lipid layers and their phase transitions. Lipids are modeled by short semiflexible chains of beads with a solvophilic head and a solvophobic tail component. They are forced…