相关论文: Wulff construction in statistical mechanics and in…
We present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the…
We apply the geometric construction of solutions of some variational problems of combinatorics to estimate the number of partitions and of plane partitions of an integer.
Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of…
Geometrical constructions, such as the tangent construction on the molar free energy for determining whether a particular composition of a solution, is stable, are related to similar tangent constructions on the orientation-dependent…
In this introductory review, we give an overview of the computational chemistry methods commonly used in the field of metal-organic frameworks (MOFs), to describe or predict the structures themselves and characterize their various…
We present a computational study for the equilibrium shape of gold nanoparticles. By linking extensive quantum-mechanical calculations, based on Density-Functional Theory (DFT) to Wulff construction, we predict equilibrium shapes that are…
The present work revisits the classical Wulff problem restricted to crystalline integrands, a class of surface energies that gives rise to finitely faceted crystals. The general proof of the Wulff theorem was given by J.E. Taylor (1978) by…
A domain in a Langmuir monolayer can be expected to have a shape that reflects the textural anisotropy of the material it contains. This paper explores the consequences of XY-like ordering. It is found that an extension of the Wulff…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
The equilibrium shape of crystals is a fundamental property of both aesthetic appeal and practical import. It is also a visible macro-manifestation of the underlying atomic-scale forces and chemical makeup, most conspicuous in…
Predicting and characterizing the crystal structure of materials is a key problem in materials research and development. It is typically addressed with highly accurate quantum mechanical computations on a small set of candidate structures,…
Predicting quasicrystal structures is a multifaceted problem that can involve predicting a previously unknown phase, predicting the structure of an experimentally observed phase, or predicting the thermodynamic stability of a given…
In this study, we present a novel approach along with the needed computational strategies for efficient and scalable feature engineering of the crystal structure in compounds of different chemical compositions. This approach utilizes a…
We give a realization of crystal graphs for basic representations of the quantum affine algebra U_q(C_n^{(1)}) using combinatorics of Young walls. The notion of splitting blocks plays a crucial role in the construction of crystal graphs.
The prediction of material structure from chemical composition has been a long-standing challenge in natural science. Although there have been various methodological developments and successes with computer simulations, the prediction of…
We use surface tension to distinguish between phases with isotropic internal structure from phases which are microscopically anisotropic. There are many interesting open problems, especially in two dimensions, and in phase coexistence.
The expectation of the descent number of a random Young tableau of a fixed shape is given, and concentration around the mean is shown. This result is generalized to the major index and to other descent functions. The proof combines…
It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
For any polynomial representation of the special linear group, the nodes of the corresponding crystal may be indexed by semi-standard Young tableaux. Under certain conditions, the standard Young tableaux occur, and do so with weight 0.…