Related papers: An improved integration scheme for Mode-coupling-t…
Understanding the physics of glass formation remains one of the major unsolved challenges of condensed matter science. As a material solidifies into a glass, it exhibits a spectacular slowdown of the dynamics upon cooling or compression,…
The standard field-theoretical procedure to study the effect of long wavelength fluctuations on a genuine second-order phase transition is applied to the Mode-Coupling-Theory (MCT) dynamical singularity at $T_c$ in the $\beta$ regime.…
Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…
Generalized mode-coupling theory (GMCT) has recently emerged as a promising first-principles theory to study the poorly understood dynamics of glass-forming materials. Formulated as a hierarchical extension of standard mode-coupling theory…
A new iterative method for non-LTE multilevel polarized radiative transfer in hydrogen lines is presented. Iterative methods (such as the Jacobi method) tend to damp out high-frequency components of the error fast, but converges poorly due…
We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a proper choice of the slow variables corresponding to the conservation laws. The…
The mode-coupling theory of the glass transition (MCT) has been at the forefront of fundamental glass research for decades, yet the theory's underlying approximations remain obscure. Here we quantify and critically assess the effect of each…
We show that the glass transition predicted by the Mode-Coupling Theory (MCT) is a critical phenomenon with a diverging length and time scale associated to the cooperativity of the dynamics. We obtain the scaling exponents nu and z that…
We numerically benchmark methods for computing harmonic maps into the unit sphere, with particular focus on harmonic maps with singularities. For the discretization we compare two different approaches, both based on Lagrange finite…
We derive the Mode Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value. This sheds light on…
Generalized mode-coupling theory (GMCT) constitutes a systematically correctable, first-principles theory to study the dynamics of supercooled liquids and the glass transition. It is a hierarchical framework that, through the incorporation…
We report recent progress on the test of mode coupling theory for molecular liquids (MMCT) for molecules of arbitrary shape. The MMCT equations in the long time limit are solved for supercooled water including all molecular degrees of…
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…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
We study the dynamics of a one-component liquid constrained on a spherical substrate, a 2-sphere, and investigate how the mode-coupling theory (MCT) can describe the new features brought by the presence of curvature. To this end we have…
Coupled-mode theory (CMT) is a powerful tool for simulating near-harmonic systems. In telecommunications, variations of the theory have been used extensively to study waveguides, both analytically and through numerical modelling. Analogous…
Extending mode-coupling theory, we elaborate a microscopic theory for the glass transition of liquids confined between two parallel flat hard walls. The theory contains the standard MCT equations in bulk and in two dimensions as limiting…
We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…
A new grid system on a sphere is proposed that allows for straight-forward implementation of both spherical-harmonics-based spectral methods and gridpoint-based multigrid methods. The latitudinal gridpoints in the new grid are equidistant…