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An investigation of the quantum phase transition in both discrete and continuum field Dicke models is presented. A series of anticrossing features following the criticality is revealed in the band of the field modes. Critical exponents are…
We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field,…
In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The…
Even though our theoretical understanding of dendritic solidification is relatively well developed, our current ability to model this process quantitatively remains extremely limited. This is due to the fact that the morphological…
We report on a linear Langevin model that describes the evolution of the roughness of two interfaces that move towards each other and are coupled by a diffusion field. This model aims at describing the closing of the gap between two…
Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this…
The construction of a network of cell-to-cell contacts makes it possible to characterize the patterns and spatial organisation of tissues. Such networks are highly dynamic, depending on the changes of the tissue architecture caused by cell…
We study the dynamic properties of a model for wetting with two competing adsorbates on a planar substrate. The two species of particles have identical properties and repel each other. Starting with a flat interface one observes the…
Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature…
We present a model for cell growth, division and packing under soft constraints that arise from the deformability of the cells as well as of a membrane that encloses them. Our treatment falls within the framework of diffuse interface…
We provide a quantitative picture of non-conserved interface growth from a diffusive field making special emphasis on two main issues, the range of validity of the effective small-slopes (interfacial) theories and the interplay between the…
Motivated by the drying pattern experiment by Yamazaki and Mizuguchi[J. Phys. Soc. Jpn. {\bf 69} (2000) 2387], we propose the dynamics of sweeping interface, in which material distributed over a region is swept by a moving interface. A…
A molecular-dynamics type simulation method, which is suitable for investigating the dewetting dynamics of thin and viscous liquid layers, is discussed. The efficiency of the method is exemplified by studying a two-parameter depinning-like…
Recent observations of the growth of protein crystals have identified two different growth regimes. At low supersaturation, the surface of the crystal is smooth and increasing in size due to the nucleation of steps at defects and the…
A family of nonequilibrium kinetic Ising models, introduced earlier, evolving under the competing effect of spin flips at {\it zero temperature} and nearest neighbour random spin exchanges is further investigated here. By increasing the…
For cellular functions like division and polarization, protein pattern formation driven by NTPase cycles is a central spatial control strategy. Operating far from equilibrium, no general theory links microscopic reaction networks and…
The emergent dynamics in phase-separated mixtures of isometric active and passive Brownian particles is studied numerically in two dimensions. A novel steady-state of well-defined traveling fronts is observed, where the interface between…
The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-phase coupling. In this work, we develop a physics-informed…
The basic physics of nucleation in solid \hl{single-crystal} nanoparticles is revealed by a phase-field theory that includes surface energy, chemical reactions and coherency strain. In contrast to binary fluids, which form arbitrary contact…
To model mechanically-driven phase transformations using the phase-field theory, suitable models are needed for describing the mechanical fields related to individual phase-fields in the interfacial regions. They play a crucial role in…