相关论文: Perturbative density functional methods for choles…
We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…
Building a general theoretical framework to describe the microscopic origin of macroscopic chirality in (colloidal) liquid crystals is a long-standing challenge. Here, we combine classical density functional theory with Monte Carlo…
Predicting the macroscopic chiral behaviour of cholesteric liquid crystals from the microscopic chirality of the particles is highly non-trivial, even when the chiral interactions are purely entropic in nature. Here we introduce a novel…
We study the crystalline phase of the $O(2N)$ Gross--Neveu model with a chemical potential for $a \leq N-2$ of the fermions. We analyze the problem in three independent ways: using perturbative QFT methods, a semiclassical large $N$…
We construct the complete liquid crystal phase diagram of hard plate-like cylinders for variable aspect ratio using Onsager's second virial theory with the Parsons-Lee decoupling approximation to account for higher-body interactions in the…
We establish a complete picture of condensation in the inclusion process in the thermodynamic limit with vanishing diffusion, covering all scaling regimes of the diffusion parameter and including large deviation results for the maximum…
We model a cholesteric liquid crystal as a planar uniaxial multilayer system, where the orientation of each layer differs slightly from that of the adjacent one. This allows us to analytically simplify the otherwise acutely complicated…
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…
We carry out Monte Carlo simulations to investigate the effect of molecular shape on liquid-crystal order. In our approach, each model mesogen consists of several soft spheres bonded rigidly together. The arrangement of the spheres may be…
Existence and local-uniqueness theorems for weak solutions of a system consisting of the drift-diffusion-Poisson equations and the Poisson-Boltzmann equation, all with stochastic coefficients, are presented. For the numerical approximation…
We propose a fully mixed virtual element method for the numerical approximation of the coupling between stress-altered diffusion and linear elasticity equations with strong symmetry of total poroelastic stress (using the Hellinger--Reissner…
We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of…
We develop numerical tools for Diagrammatic Monte-Carlo simulations of non-Abelian lattice field theories in the t'Hooft large-N limit based on the weak-coupling expansion. First we note that the path integral measure of such theories…
We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly…
We test the performance of a recently proposed fundamental measure density functional of aligned hard cylinders by calculating the phase diagram of a monodisperse fluid of these particles. We consider all possible liquid crystalline…
Covariance estimation for high-dimensional datasets is a fundamental problem in modern day statistics with numerous applications. In these high dimensional datasets, the number of variables p is typically larger than the sample size n. A…
In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…
This paper focuses on exploring the sparsity of the inverse covariance matrix $\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky…
Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized many-body wave functions, especially with modern neural-network quantum states. In practice, however, the stochastic estimators…
We study swelling and structural properties of ionic microgel suspensions within a comprehensive coarse-grained model that combines the polymeric and colloidal natures of microgels as permeable, compressible, charged spheres governed by…