Computer simulation study of a two-dimensional dipolar lattice

Summary The present work reports Monte Carlo calculations on a classical square lattice, consisting of purely dipolar plane rotators with identical dipole moments. Dipolar interactions are known not be essential for nematic ordering, but they can play a significant role in some specific cases; along the lines of the lattice model approximation already used in simulation work on liquid crystals, our system can be considered as an extreme case of nematogenic potential model. The system possesses an antiferroelectric ground state and, at higher temperature, it undergoes a transition to an orientationally disordered phase; comparison with the mean-field treatment of the transition is also reported. The structural properties were investigated by calculating orientational correlation functions, and found to exhibit some qualitative differences with respect to other potential models previously investigated for nematics. Simulation results indicate a close qualitative similarity with a three-dimensional analogue investigated in our previous work.

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Riassunto Il presente lavoro riporta calcoli Monte Carlo per un reticolo classico quadrato, costituito da rotatori piani puramente dipolari, con identici momenti. è noto che le interazioni dipolari non sono essenziali per l'ordinamento nematico, ma esse possono avere un ruolo significativo in alcuni casi specifici; lungo le linee dell'approssimazione a modello reticolare già applicata in lavori di simulazione per cristalli liquidi, il nostro sistema può pertanto venire considerato come un caso estremo di modello di potenziale nematogenico. Il sistema possiede stato fondamentale antiferroelettrico ed, a temperatura piú elevata, transisce ad una fase orientazionalmente disordinata; si riportano per confronto i risultati della trattazione a campo medio per tale transizione. Le proprietà strutturali furono investigate calcolando funzioni di correlazione orientazionale, e si è trovato che esse mostrano qualche differenza qualitativa rispetto ad altri modelli di potenziale previamente studiati per nematici. I risultati di simulazione indicano una stretta somiglianza qualitativa con un analogo tridimensionale investigato in nostri precedenti lavori.

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Резюме В этой работе предлагаются вычисления по методу Монте-Карло для классической квадратичной решетки, состоящей нз чнсто дипольных плоских ротаторов с тождественными дипольными моментами. Известно, что дипольные взаимодействия не являются существенными для нематического упорядочения, но они могут играть существенную роль в некоторых специфических случаях: в частности, в приближении модельной решетки, уже использованном при моделировании на жидких кристаллах, наша система может рассматриваться как предельный случай модели немтическочо потенциала. Рассмотренная система обладает антиферромагнитным основным состоянием и при высоких температурах она претерпевает переход в ориентационно разупорядоченную фазу; также проводится сравнение с рассмотрением этого перехода с помощью среднего поля. Исследуются структурные свойства, вычисляя ориентационные корреляционные функции. Обнаружено существование некоторых качественных различий по сравнению с моделями потенциалов, ранее использованных для нематиков. Результаты моделирования обнаруживают качественное подобие с трехмерным аналогом, исследованным в нашей предыдущей работе.

     

Fracture analysis of concrete using singular fractal functions with lattice beam network and confirmation with acoustic emission study

In the present study singular fractal functions (SFF) were used to generate stress-strain plots for quasi-brittle material like concrete and cement mortar and subsequently stress-strain plot of cement mortar obtained using SFF was used for modeling fracture process in concrete. The fracture surface of concrete is rough and irregular. The fracture surface of concrete is affected by the concrete’s microstructure that is influenced by water cement ratio, grade of cement and type of aggregate [1], [2], [3] and [4]. Also the macrostructural properties such as the size and shape of the specimen, the initial notch length and the rate of loading contribute to the shape of the fracture surface of concrete. It is known that concrete is a heterogeneous and quasi-brittle material containing micro-defects and its mechanical properties strongly relate to the presence of micro-pores and micro-cracks in concrete [1], [2], [3] and [4]. The damage in concrete is believed to be mainly due to initiation and development of micro-defects with irregularity and fractal characteristics. However, repeated observations at various magnifications also reveal a variety of additional structures that fall between the ‘micro’ and the ‘macro’ and have not yet been described satisfactorily in a systematic manner [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [15], [16] and [17]. The concept of singular fractal functions by Mosolov was used to generate stress-strain plot of cement concrete, cement mortar and subsequently the stress-strain plot of cement mortar was used in two-dimensional lattice model [28]. A two-dimensional lattice model was used to study concrete fracture by considering softening of matrix (cement mortar). The results obtained from simulations with lattice model show softening behavior of concrete and fairly agrees with the experimental results. The number of fractured elements are compared with the acoustic emission (AE) hits. The trend in the cumulative fractured beam elements in the lattice fracture simulation reasonably reflected the trend in the recorded AE measurements. In other words, the pattern in which AE hits were distributed around the notch has the same trend as that of the fractured elements around the notch which is in support of lattice model.     

Passive heat transfer in a turbulent channel flow simulation using large eddy simulation based on the lattice Boltzmann method framework

In this paper, a large eddy simulation based on the lattice Boltzmann framework is carried out to simulate the heat transfer in a turbulent channel flow, in which the temperature can be regarded as a passive scalar. A double multiple relaxation time (DMRT) thermal lattice Boltzmann model is employed. While applying DMRT, a multiple relaxation time D3Q19 model is used to simulate the flow field, and a multiple relaxation time D3Q7 model is used to simulate the temperature field. The dynamic subgrid stress model, in which the turbulent eddy viscosity and the turbulent Prandtl number are dynamically computed, is integrated to describe the subgrid effect. Not only the strain rate but also the temperature gradient is calculated locally by the non-equilibrium moments. The Reynolds number based on the shear velocity and channel half height is 180. The molecular Prandtl numbers are set to be 0.025 and 0.71. Statistical quantities, such as the average velocity, average temperature, Reynolds stress, root mean square (RMS) velocity fluctuations, RMS temperature and turbulent heat flux are obtained and compared with the available data. The results demonstrate great reliability of DMRT–LES in studying turbulence.     

Lattice Boltzmann model for thermal free surface flows with liquid-solid phase transition

Purpose

The main objective of this work is to develop an algorithm to use the Lattice Boltzmann method for solving free surface thermal flow problems with solid/liquid phase changes.

Approach

A multi-distribution function model is applied to simulate hydrodynamic flow and the coupled thermal diffusion-convection problem.

Findings

The free surface problem, i.e. the reconstruction of the missing distribution functions at the interface, can be solved by applying a physical transparent momentum and heat flux based methodology. The developed method is subsequently applied to some test cases in order to assess its computational potentials.

Practical implications

Many industrial processes involve problems where non-isothermal motion and simultaneous solidification of fluids with free surface is important. Examples are all castings processes and especially foaming processes which are characterized by a huge and strongly changing surface.

Value

A reconstruction algorithm to treat a thermal hydrodynamic problem with free surfaces is presented which is physically transparent and easy to implement.     

Lattice Boltzmann simulation of flows in bifurcate channel at rotating inflow boundary conditions and resulted different outflow fluxes

The Lattice Boltzmann method(LBM) is used to simulate the flow field in a bifurcate channel which is a simplified model of the draft tube of hydraulic turbine machine.According to the simulation results,some qualitative conclusions can be deduced.The reason of uneven flux in different branches of draft tube is given.Not only the vortex rope itself,but also the attenuation of the rotation strength is important in bringing on the uneven flux.The later leads to adverse pressure gradient,and changes the velocity profile.If the outlet contains more than one exit,the one that contains the vortex rope will lose flux because of this adverse pressure gradient.Several possible methods can be used to minimize the adverse pressure gradient domain in order to improve the efficiency of turbine machine.     

Equivariant Ehrhart theory

Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of numerous classical results, and give applications to the Ehrhart theory of rational polytopes and centrally symmetric polytopes. We also recover a character formula of Procesi, Dolgachev, Lunts and Stembridge for the action of a Weyl group on the cohomology of a toric variety associated to a root system.     

Crystal chemistry peculiarities of Cs2Te4O12

The Raman and IR-absorption spectra of the Cs₂Te₄O₁₂ lattice are first recorded and interpreted. Extraordinary features observed in the structure and Raman spectra of Cs₂Te₄O₁₂ are analyzed by using ab initio and lattice-dynamical model calculations. This compound is specified as a caesium-tellurium tellurate Cs₂Te^IV(Te^VIO₄)₃ in which Te^IV atoms transfer their 5p electrons to [Te^VIO₄]₃⁶⁻ tellurate anions, thus fulfilling (jointly with Cs atoms) the role of cations. The Te^VI-O-Te^VI bridge vibration Raman intensity is found abnormally weak, which is reproduced by model treatment including the Cs⁺ ion polarizability properties in consideration.     

The number of extreme points of tropical polyhedra

The celebrated upper bound theorem of McMullen determines the maximal number of extreme points of a polyhedron in terms of its dimension and the number of constraints which define it, showing that the maximum is attained by the polar of the cyclic polytope. We show that the same bound is valid in the tropical setting, up to a trivial modification. Then, we study the tropical analogues of the polars of a family of cyclic polytopes equipped with a sign pattern. We construct bijections between the extreme points of these polars and lattice paths depending on the sign pattern, from which we deduce explicit bounds for the number of extreme points, showing in particular that the upper bound is asymptotically tight as the dimension tends to infinity, keeping the number of constraints fixed. When transposed to the classical case, the previous constructions yield some lattice path generalizations of Gale's evenness criterion.     

Weak sense of direction labelings and graph embeddings

An edge-labeling λ for a directed graph G has a weak sense of direction (WSD) if there is a function f that satisfies the condition that for any node u and for any two label sequences α and α^′ generated by non-trivial walks on G starting at u, f(α)=f(α^′) if and only if the two walks end at the same node. The function f is referred to as a coding function of λ. The weak sense of direction number of G, WSD(G), is the smallest integer k so that G has a WSD-labeling that uses k labels. It is known that WSD(G)≥Δ⁺(G), where Δ⁺(G) is the maximum outdegree of G.Let us say that a function τ:V(G)→V(H) is an embedding from G onto H if τ demonstrates that G is isomorphic to a subgraph of H. We show that there are deep connections between WSD-labelings and graph embeddings. First, we prove that when f_H is the coding function that naturally accompanies a Cayley graph H and G has a node that can reach every other node in the graph, then G has a WSD-labeling that has f_H as a coding function if and only if G can be embedded onto H. Additionally, we show that the problem “Given G, does G have a WSD-labeling that uses a particular coding function f?” is NP-complete even when G and f are fairly simple.Second, when D is a distributive lattice, H(D) is its Hasse diagram and G(D) is its cover graph, then WSD(H(D))=Δ⁺(H(D))=d^∗, where d^∗ is the smallest integer d so that H(D) can be embedded onto the d-dimensional mesh. Along the way, we also prove that the isometric dimension of G(D) is its diameter, and the lattice dimension of G(D) is Δ⁺(H(D)). Our WSD-labelings are poset-based, making use of Birkhoff’s characterization of distributive lattices and Dilworth’s theorem for posets.