Static lattice simulation of structure and transport in superionic conductors

We describe the scope, methodology and achievements of static lattice simulation methods in the study of fast-ion conductors. We discuss first the type of conduction mechanism to which simulations may be applied; we contrast the information available from static with that from dynamics simulations. The techniques and potentials used by the calculations are then described. Applications to β-Al₂O₃, Li₃N and fluorite structured compounds are then considered.     

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.

     

Computer simulation study of a simple cubic dipolar lattice

Summary The present work reports Monte Carlo calculations on a classical simple cubic lattice, consisting of point dipoles with identical dipole moments. Dipolar interactions are known not to 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 thus 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 mean-field and spherical-model treatments 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.

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Riassunto Il presente lavoro riporta calcoli Monte Carlo per un reticolo classico cubico semplice, costituito da dipoli puntiformi con identico momento dipolare. è noto che le interazioni dipolari non sono essenziali per l’ordinamento nematico, ma esse possono avere un ruolo significantivo 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 essere considerato come un caso estremo di modello di potenziale nematogenico. Il sistema possiede stato fondamentale antiferroelectrico ed, a temperature piú elevata, transisce ad una fase orientazionalmente disordinata; sono riportati per confronto i risultati delle trattazioni a campo medio, ed a modello sferico 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.

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Резюме В работе предлагается моделирование по методу Монте-Карло классической простой кубической решетки, образованной точечными диполями с тождественными дипольными моментами. Известно, что дипольные взаимодействия не являются существенными для нематическояо упорядочения, но они игроют существенную роль в некоторых специфических случаях. Рассматриваемая система обладает антиферроэлектрическим основным состоянием и, при высокой темлературе, претерпевает переход в ориентационно упорядоченную фазу. Проводится сравнение с приближ=yeнием среднего поля и рассмотрением в рамках сферической модели этого перехода. Псследуутся структурные свойства, посредством вычисления ориентационных корреляционных функций. Обнаружены нектторые ксчественные различия по сравнению с другими потенциалыми моделями, ранее рассмотренными для описания нематики.

     

Computer simulation of defects and oxygen transport in yttria-stabilized zirconia

We have used molecular dynamics simulations and energy minimization calculations to examine defect energetics and oxygen diffusion in yttria-stabilized zirconia (YSZ). Oxygen vacancies prefer to be second nearest neighbors to yttrium dopants. The oxygen diffusion coefficient shows a peak at 8 mol% yttria consistent with experimental findings. The activation energy for oxygen diffusion varies from 0.6 to 1.0 eV depending on the yttria content. The Y_Zr′–V_O^··–Y_Zr′ complex with a binding energy of − 0.85 eV may play an important role in any conductivity degradation of YSZ.     

Semiclassical and quantum transport in the two-dimensional electron gas in a hard-wall antidot lattice

Commensurate peaks of magnetoresistance and Shubnikov-de Haas and Aharonov-Bohm oscillations in the two-dimensional electron gas (2DEG) in a lattice of antidots with hard potential walls have been experimentally studied. The behavior of both classical magnetoresistance peaks and quantum oscillations has been shown to fundamentally depend on the lattice period and the antidot size, as well as on the smoothness of the potential at the 2DEG-antidot interface. This result indicates the necessity of revising the interpretation of all numerous experiments with antidot lattices, since this effect has been explicitly or implicitly neglected in them.     

Computer simulation study of the statistics of self-avoiding-walks on a dilute lattice

A computer simulation study of the statistics of linear polymers in a random medium, described by self-avoiding-walks (SAW) on a randomly (bond) dilute square lattice has been made. The “phase diagram”, giving the critical value of the average connective constant (average inverse fugacity associated with a monomer in an infinite polymer) as a function of the bond concentration, has been obtained enumerating exactly (and extrapolating) the number of (finite step) SAWs on randomly dilute (Monte Carlo sample) lattices. The “phase diagram”, so obtained, has been compared with those obtained using the Cayley tree approximation and the real space renormalization group technique.     

Computer simulation of topological effects in lattice theories: A model study

The quantum pendulum as a model is put on a lattice, producing a straightforward definition of topological charge. It is used to single out non-perturbative effects in a Monte Carlo calculation and compare them with a semiclassical picture. The method of subtracting perturbative contributions from numerical results recently used for the gluon condensate is tested.     

Computer simulation of some dynamical properties of the Lorentz gas

We carried out molecular dynamics simulations of a Lorentz gas, consisting of a lone hydrogen molecule moving in a sea of stationary argon atoms. A Lennard-Jones form was assumed for the H₂-Ar potential. The calculations were performed at a reduced temperatureK ^* =kT/_{H 2–Ar} = 4.64 and at reduced densities ^*= _{Ar Ar} ³ in the range 0.074–0.414. The placement of Ar atoms was assumed to be random rather than dictated by equilibrium considerations. We followed the trajectories of many H₂ molecules, each of which is assigned in turn a velocity given by the Maxwell-Boltzmann distribution at the temperature of the simulation. Solving the equations of motion classically, we obtained the translational part of the incoherent dynamic structure factor for the H₂ molecule,S _tr(q, ). This was convoluted with the rotational structure factorS _rot(q, ) calculated assuming unhindered rotation to obtain the total structure factorS(q, ). Our results agree well with experimental data on this function obtained by Egelstaffet al. At the highest density ( ^*=0.414) we studied the dependence ofS(q, ) on system size (number of Ar atoms), number of H₂ molecules for which trajectories are generated, and the length of time over which these trajectories are followed.     

Computer simulation of the frustrated antiferromagnetic Heisenberg model on a layered triangle lattice

Critical properties of the 3D frustrated Heisenberg model on a triangle latticeare investigated using a replica Monte-Carlo method that considers the interaction between next nearest neighbors. Static magnetic and chiral critical indices for heat capacity α, susceptibility γ, γ _k , magnetization β, β _k , and correlation radius ν are calculated using the theory of finite-size scaling.     

页岩气在粗糙纳米孔中吸附和输运的分子模拟

从微观上理解固气表面的吸附和注气驱替原理,有助于完善页岩气开采理论.本文通过运用蒙特卡洛和分子动力学方法,模拟了甲烷在粗糙壁面结构孔隙中的吸附和流动行为.研究结果显示粗糙结构对甲烷的吸附量有显著影响,压力小于20 MPa时,粗糙模型中的吸附量更大.注气驱替时,粗糙模型中二氧化碳的突破时间和甲烷的采收率,相比光滑壁面模型明显增加.这是由于粗糙结构模型的页岩壁面表面积更大,在低压下气体吸附能力更强.矩形粗糙结构页岩模型的选择吸附性强于三角粗糙结构模型和光滑模型.研究阐明了甲烷吸附和驱替的微观机理,为提高页岩气采收率提供了指导.     

Monte Carlo simulation of a lattice gas model of multilayer adsorption

A lattice gas model of physical adsorption of atoms on a periodic substrate has been studied using Monte Carlo simulations. Adsorption isotherms and layer coverage isotherms are determined and from these we find distinct phase boundaries for transitions on successive layers. In contrast to mean field results our data suggests that the critical temperature increases only slowly with increasing layer number, and appears to approach the roughening temperature for infinite layer number.     

Strongly inhibited transport of a degenerate 1D Bose gas in a lattice

We report the observation of strongly damped dipole oscillations of a quantum degenerate 1D atomic Bose gas in a combined harmonic and optical lattice potential. Damping is significant for very shallow axial lattices (0.25 photon recoil energies), and increases dramatically with increasing lattice depth, such that the gas becomes nearly immobile for times an order of magnitude longer than the single-particle tunneling time. Surprisingly, we see no broadening of the atomic quasimomentum distribution after damped motion. Recent theoretical work suggests that quantum fluctuations can strongly damp dipole oscillations of a 1D atomic Bose gas, providing a possible explanation for our observations.     

Negative thermal expansion coefficient in the Kondo lattice

The thermal expansion coefficient is calculated for a two bands Fermi liquid : it is shown that the interband electronic transfer can give a large contribution. The calculation is applied to the Kondo lattice: the thermal expansion coefficient α can be negative for a certain range of values of the Kondo temperature, and a pseudo-gap is necessary. The experimental results about CeAl₃ are correctly interpreted by our model.     

Computer simulation of random sequential adsorption of two interacting species on a lattice

A computer-simulation model is introduced to study the variation in the coverage and porosity in a binary system by random sequential adsorption on a periodic square lattice. We study the effects of the range of the repulsive interaction between unlike species and of the probability of deposition of each particle type. For all choices of the interaction range there is a minimum in the total coverage of the lattice which occurs for equal deposition probability of the two species. The saturation coverage decreases on increasing the range of the interaction. For proper choices of the parameters of the model, regimes exist in which either pores or particles of one type form an infinite percolating network.