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The dynamics of the interaction of a system of two thin volatile liquid droplets resting on a soft viscoelastic solid substrate are investigated theoretically. The developed model fully considers the effect of evaporative cooling and the…
An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and…
Phase separation has recently emerged as an important organizational principle in the dense and heterogeneous environment within living cells. Here, we use a synthetic system to show that compressive stresses in a polymer network suppress…
The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an $N$-particle…
We consider the problem of a cylindrical (quasi-two-dimensional) droplet impacting on a hard surface. Cylindrical droplet impact can be engineered in the laboratory, and a theoretical model of the system can also be used to shed light on…
The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent…
In many macroscopic dynamic wetting problems, it is assumed that the macroscopic interface is quasistatic, and the dissipation appears only in the region close to the contact line. When approaching the moving contact line, a microscopic…
We present a general description of two mixed branes interactions. For this we consider two mixed branes with dimensions p_1 and p_2, in external field B_{\mu\nu} and arbitrary gauge fields A^1_{\alpha_1} and A^2_{\alpha_2} on the world…
We consider the curvature driven dynamics of a domain wall separating two equivalent states in systems displaying a modulational instability of a flat front. We derive an amplitude equation for the dynamics of the curvature close to the…
The pair contact process with diffusion is studied by means of multispin Monte Carlo simulations and density matrix renormalization group calculations. Effective critical exponents are found to behave nonmonotonically as functions of time…
In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
Motivated by recent experiments on multi-component membranes, the growth kinetics of domains on vesicles is theoretically studied. It is known that the steady-state rate of coalescence cannot be obtained by taking the long-time limit of the…
This paper presents an averaging method for nonlinear systems defined on Riemannian manifolds. We extend closeness of solutions results for ordinary differential equations on $R^{n}$ to dynamical systems defined on Riemannian manifolds by…
We describe a numerical model for the interaction of light with large raindrops using realistic nonspherical drop shapes. We apply geometrical optics and a Monte Carlo technique to perform ray traces through the drops. We solve the problem…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
We study entanglement dynamics in dispersive optomechanical systems consisting of two optical modes and a mechanical oscillator inside an optical cavity. The two optical modes interact with the mechanical oscillator, but not directly with…
To understand the non-equilibrium relaxation dynamics of a liquid droplet on a switchable substrate the interplay of different length- and time-scales needs to be understood. We present a method to map the microscopic information, resulting…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
Recently Biskup et al. [Europhys. Lett. 60 (2002) 21] studied the behaviour of d-dimensional finite-volume liquid-vapour systems at a fixed excess $\delta N$ of particles above the ambient gas density. They identify a dimensionless…