Related papers: Unified criteria for crystallization in hard-core …
In this paper, we apply the Taylor--Wiles--Kisin patching method to the coherent cohomology of modular curves at minimal level. We establish a multiplicity-one result for the patched module by the $q$-expansion principle and show that a…
The main purpose of the present paper is to solve the thermodynamic inconsistencies that result when deriving equivalent micropolar models of periodic beam-lattice materials through standard continualization schemes. In fact, this technique…
We propose and analyze a combined finite volume--nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is…
We introduce rigid syntomic cohomology for strictly semistable log schemes over a complete discrete valuation ring of mixed characteristic (0,p). In case a good compactification exists, we compare this cohomology theory to…
We investigate two-fluid BGK kinetic methods for binary fluids. The developed theory works for asymmetric as well as symmetric systems. For symmetric systems it recovers Sirovich's theory and is summarized in models A and B. For asymmetric…
We study properties that allow first-order theories to be disjointly combined, including stable infiniteness, shininess, strong politeness, and gentleness. Specifically, we describe a Galois connection between sets of decidable theories,…
We develop a novel Hybrid High-Order method for the simulation of Darcy flows in fractured porous media. The discretization hinges on a mixed formulation in the bulk region and on a primal formulation inside the fracture. Salient features…
This paper presents a simple weak Galerkin (WG) finite element method for the Reissner-Mindlin plate model that partially eliminates the need for traditionally employed stabilizers. The proposed approach accommodates general, including…
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…
Finite-size criteria have emerged as an effective tool for deriving spectral gaps in higher-dimensional frustration-free quantum spin systems. We quantitatively improve the existing finite-size criteria by introducing a novel subsystem…
We perform a rigorous study of the Gibbs statistics of high-density hard-core random configurations on a unit triangular lattice $\mathbb{A}_2$ and a unit honeycomb graph $\mathbb{H}_2$, for any value of the (Euclidean) repulsion diameter…
A previously proposed [X. Shan and H. Chen, Phys. Rev. E {\bf 47}, 1815, (1993)] lattice Boltzmann model for simulating fluids with multiple components and interparticle forces is described in detail. Macroscopic equations governing the…
The scaled particle theory is applied to a description of thermodynamic properties of one-dimensional hard rod fluid in disordered porous media. To this end, we extended the SPT2 approach, which had been developed previously. Analytical…
We present a thermodynamically consistent theoretical framework for lyotropic liquid crystals (LCs) based on the GENERIC (General Equation for the Non-Equilibrium Reversible-Irreversible Coupling) formalism. This formalism ensures…
We present a phase field theory for binary crystal nucleation. In the one-component limit, quantitative agreement is achieved with computer simulations (Lennard-Jones system) and experiments (ice-water system) using model parameters…
We study the joint variability of structural information in a hard sphere fluid biased to avoid crystallisation and form fivefold symmetric geometric motifs. We show that the structural covariance matrix approach, originally proposed for…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
We derive a microscopic criterion for the stability of hard sphere configurations, and we show empirically that this criterion is marginally satisfied in the glass. This observation supports a geometric interpretation for the initial rapid…
We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not…
We prove an analogue of the Oppenheim conjecture for a system comprising an inhomogeneous quadratic form and a linear form in $3$ variables using dynamics on the space of affine lattices.