Related papers: Scaling equations for mode-coupling theories with …
Within the mode-coupling theory for structural relaxation in simple systems the asymptotic laws and their leading-asymptotic correction formulas are derived for the motion of a tagged particle near a glass-transition singularity. These…
Upon cooling, glass-forming liquids experience a two-step relaxation associated to the cage rattling and the escape from the cage, and the following decoupling between the \b{eta}- and the {\alpha}-relaxations. The found decoupling…
We present mesoscale numerical simulations based on the coupling of the fluctuating lattice Boltzmann method (FLBM) for multicomponent systems with a wetted finite-size particle model. This newly coupled methodologies are used to study the…
In the mode coupling theory of the liquid to glass transition the long time structural relaxation follows from equations solely determined by equilibrium structural parameters. The present extension of these structural relaxation equations…
$\beta$ and $\alpha$ relaxation processes are dynamical scaling regimes of glassy systems occurring on two separate time scales which both diverge as the glass state is approached. We study here the crossover scaling from $\beta$- to…
We study the asymptotic dynamics of multi-bubble solutions to the focusing energy-critical wave equation in five dimensions. Assuming that the solution asymptotically decomposes into a finite superposition of spatially separated bubbles…
The many-body physics at quantum phase transitions shows a subtle interplay between quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we first give a pedagogical introduction to the equilibrium…
Wave kinetic theory for rapidly rotating flows is developed in this paper using a rigorous application of multiple scales perturbation theory. The governing equations are an asymptotically reduced set of equations that are derived from the…
The multichannel scattering problem in an adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-trivial constant asymptotic behavior at large internuclear separations. The asymptotic solutions at…
We discuss a novel approach, the point-to-set correlation functions, that allows to determine relevant static and dynamic length scales in glass-forming liquids. We find that static length scales increase monotonically when the temperature…
We present a study of diffusion of small tagged particles in a solvent, using mode coupling theory (MCT) analysis and computer simulations. The study is carried out for various interaction potentials. For the first time, using MCT, it is…
To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of the dynamics that is…
The time-convolutionless mode-coupling (TMCT) equation for the intermediate scattering function $f_{\alpha}(q,t)$ derived recently by the present author is transformed into a simple nonlinear recursion formula for a generating function…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
Nonlocal MEMS equations exhibit finite-time quenching, or touchdown, which is difficult to capture numerically. We study a stagewise rescaling algorithm for a two-dimensional nonlocal MEMS equation in an asymptotically constant-feedback…
We reveal several distinct regimes of the relaxation dynamics of a small quantum system coupled to an environment within the plane of the dissipation strength and the reservoir temperature. This is achieved by discriminating between…
We present a theoretical analysis of the dynamic structure factor (DSF) of a liquid at and below the mode coupling critical temperature $T_c$, by developing a self-consistent theoretical treatment which includes the contributions both from…
Idealized glass transitions are discussed within a novel mode-coupling theory (TMCT) proposed by Tokuyama(Physica A 395,31(2014)). This is done in order to identify common grounds with and differences to the conventional mode-coupling…
In this paper, we develop an asymptotic-preserving dynamical low-rank method for the multiscale linear kinetic transport equation. The proposed scheme is unconditionally stable in the diffusive regime while preserving the correct asymptotic…
In polymers melts and supercooled liquids, the glassy dynamics is characterized by the rattling of monomers or particles in the cage formed by their neighbors. Recently, a direct correlation in such systems, described by a universal scaling…