Irregular Lattice Research Articles

The heterogeneous gas with singular interaction: generalized circular law and heterogeneous renormalized energy

We introduce and analyze d-dimensional Coulomb gases with random charge distribution and general external confining potential. We show that these gases satisfy a large-deviation principle. The analysis of the minima of the rate function (which is the leading term of the energy) reveals that, at equilibrium, the particle distribution is a generalized circular law (i.e. with spherical support but not necessarily uniform distribution). In the classical electrostatic external potential, there are infinitely many minimizers of the rate function. The most likely macroscopic configuration is a disordered distribution in which particles are uniformly distributed (for d = 2, the circular law), and charges are independent of the positions of the particles. General charge-dependent confining potentials unfold this degenerate situation: in contrast, the particle density is not uniform, and particles spontaneously organize according to their charge. In this picture the classical electrostatic potential appears as a transition at which order is lost. Sub-leading terms of the energy are derived: we show that these are related to an operator, generalizing the Coulomb renormalized energy, which incorporates the heterogeneous nature of the charges. This heterogeneous renormalized energy informs us about the microscopic arrangements of the particles, which are non-standard, strongly dependent on the charges, and include progressive and irregular lattices.

On the question of the Wilson fermion doubling phenomenon on an irregular lattice

It is shown that the Wilson fermion doubling phenomenon on irregular lattices (simplicial complexes) does exist. This means that the irregular (not smooth) zero or soft modes exist. The statement is proved on four-dimensional lattice by means of the Atiyah-Singer index theorem.

A Laplace type problem for irregular lattice with cell composed by four isoscele triangles

A Laplace type problem for irregular lattice with cell composed by four isoscele triangles

A Laplace type problem for irregular lattice with fundamental cell composed by three triangles and a trapetium

In the previous papers, [1], [2], [3], [4],[5], [6], [7], [8], [9], [10], [11], [12], [13] and [14] the authors studies some Laplace problem for different lattices. In this paper paper we determine the probability that a random segment of constant length intersects a side of the lattice with fundamental cell represented in fig. 1. Let < (a) the lattice with fundamental cell C0 represented in fig. 1 1608 D. Barilla and F. Grasso

Laplace type problem for an irregular lattice

Laplace type problem for an irregular lattice

A Laplace type problem for an irregular lattice with cell composed by two isoscele triangles and an isoscele trapezium

A Laplace type problem for an irregular lattice with cell composed by two isoscele triangles and an isoscele trapezium

A Buffon-Laplace type problem for an irregular lattice with cell composed by pentagon+triangle with obstacles

A Buffon-Laplace type problem for an irregular lattice with cell composed by pentagon+triangle with obstacles

A Buffon-Laplace type problem for an irregular lattice and different obstacles

A Buffon-Laplace type problem for an irregular lattice and different obstacles

Dynamical and geometrical exponents of self-affine rough surfaces on regular and random lattices

In this paper, a wide range of rough surfaces, such as random deposition (RD) and incorporating with relaxation (RDR), ballistic deposition (BD) and restricted solid-on-solid model (RSOS), in (2 + 1)-dimension, on the regular (square, triangular, honeycomb) and random (Voronoi) lattices is simulated. We numerically show that the dynamical (growth and roughness) and geometrical (fractal dimension, loop correlation and the length distribution) exponents of these rough surfaces are independent of the underlying regular or irregular lattices. Also the universality holds at the level of statistical properties of the iso-height lines (contours) on different lattices. Finally, we indicate that the hyperscaling relations are valid for the contours of all the studied Gaussian and non-Gaussian self-affine rough surfaces.

A Centered Bivariate Spatial Regression Model for Binary Data with an Application to Presettlement Vegetation Data in the Midwestern United States

Spatially structured discrete data arise in diverse areas of application, such as forestry, epidemiology, or soil sciences. Data from several binary variables are often collected at each location. Variation in distributional properties across the spatial domain is of interest. The specific application that motivates our work involves characterizing historical distributions of two species of Oak in the Driftless Area in the Midwestern United States. Scientists are interested in understanding the patterns of interaction between species, as well as their relationships to spatial covariates. Accounting for spatial dependence is not only of inherent interest but also reduces prediction mean squared error, and is necessary for obtaining appropriate measures of uncertainty (i.e., standard errors and confidence intervals). To address the needs of the application, we introduce a centered bivariate autologistic model, which accounts for the statistical dependence in two response variables simultaneously, for the association between them and for the effect of spatial covariates. The model proposed here offers a relatively stable large-scale model structure, with model parameters which can be interpreted in the usual sense across levels of dependence. Since the model allows for separate dependence parameters for each variable, it offers, in essence, the equivalent of a model with a non-separable covariance function. The flexible model framework permits straightforward generalizations to structures with more than two variables, a temporal component, or an irregular lattice domain. Supplementary materials accompanying this paper appear on-line.

Partial long-range order in antiferromagnetic Potts models

The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered. This situation may arise from frustration of the interactions, but also from an irregular but unfrustrated lattice structure. We study partial long-range order in a range of antiferromagnetic $q$-state Potts models on different two-dimensional lattices and for all relevant values of $q$. We exploit the power of tensor-based numerical methods to evaluate the partition function of these models and hence to extract the key thermodynamic properties -- entropy, specific heat, magnetization, and susceptibility -- giving deep insight into the phase transitions and ordered states of each system. Our calculations reveal a range of phenomena related to partial ordering, including different types of entropy-driven phase transition, the role of lattice irregularity, very large values of the critical $q_c$, and double phase transitions.

Crystal Structure and Hydration Characteristics of Tricalcium Silicate Doped with Magnesium Oxide

The research investigates various methods to identify magnesium oxide influences on the crystal structure and hydration properties of tricalcium silicate. The f-CaO content of the clinkers were analyzed by chemical analysis. The complex disordered superstructure of the tricalcium silicate has been studied by a joint XRD, NMR and TEM. The results show that MgO exerts a remarkable influence on the polymorphisms of C3S. Mg is not only substitutional atom but also interstitial atom in the crystal lattice of tricalcium silicate. The HRTEM pattern of C3S doped with MgO is covered by the various irregular lattice. The addition of appropriate amount of MgO in raw meal can change the formation kinetic of C3S, slightly perturb the environment of SiO44- tetrahedral, modify the crystal structure of C3S and affect the hydration activity. Doped with MgO in the raw meal can slow down the hydration rate of alite slightly in early stage.

Quantum mechanical NMR simulation algorithm for protein-size spin systems

Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling quantum mechanical simulation methods have not so far been available. In this communication we adapt the restricted state space approximation to protein NMR spectroscopy and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of relaxation processes using Bloch–Redfield–Wangsness theory) on isotopically enriched human ubiquitin – a protein containing over a thousand nuclear spins forming an irregular polycyclic three-dimensional coupling lattice. The algorithm uses careful tailoring of the density operator space to only include nuclear spin states that are populated to a significant extent. The reduced state space is generated by analysing spin connectivity and decoherence properties: rapidly relaxing states as well as correlations between topologically remote spins are dropped from the basis set.

Sparse 2-D Array Placement for Arbitrary Pattern Mask and With Excitation Constraints: A Simple Deterministic Approach

We present a novel algorithm for the synthesis of planar (2-D) arrays subject to arbitrary pattern masks and excitation constraints (e.g., dynamic range). The algorithm is simple and deterministic, and considers the radiating element pattern. The procedure starts with a conventional constrained fixed-grid synthesis on a regular lattice, yielding a goal radiated field. Next, element locations are selected sequentially by maximizing projection on field difference to goal, while excitation amplitudes are computed using fixed-grid constrained synthesis for irregular lattices. The final result is the sparse layout and constrained excitation coefficients. The proposed method is validated against literature results; application examples are given for circular flat-top, isoflux and triangular flat-top shaped beam patterns, with constraints on excitation coefficients dynamic range, both for isotropic and patch-type element patterns.

Bayesian hierarchical modelling of noisy spatial rates on a modestly large and discontinuous irregular lattice

We present Bayesian hierarchical spatial model development motivated from a recent analysis of noisy small area response rate data, named the Booster data. The Booster data are postcode-level aggregates from a recent mail-out recruitment for a physical exercise intervention in deprived urban neighbourhoods in Sheffield, UK. Bayesian hierarchical Bernoulli-binomial spatial mixture zero-inflated Binomial models were developed for modelling overdispersion and for separation of systematic and random variations in the noisy and mostly low crude response rates. We present methods that enabled us to explore the underlying spatial rate variation, clustering of low or high response rate areas and neighbourhood characteristics that were associated with variations and patterns of invitation mail-outs, zero-response and response rates. Three spatial prior formulations, the intrinsic conditional autoregressive or (iCAR), the Besag-York-Mollié (BYM) and the modified BYM models, were explored for their performance on modelling sparse data on a modestly large and discontinuous irregular lattice. An in-depth Bayesian analysis of the Booster data is presented, with the resulting posterior estimation and inference implemented via Markov chain Monte Carlo simulation in WinBUGS. With increasing availability of spatial data referenced at fine spatial scales such as the postcode, the sparse-data situation and the Bayesian models and methods discussed herein should have considerable relevance to small area disease and health mapping and to spatial regression.

A Buffon-Laplace type problem for an irregular lattice and "body test" rectangle

A Buffon-Laplace type problem for an irregular lattice and "body test" rectangle

A Buffon-Laplace type problems for an irregular lattice and with maximum probability

A Buffon-Laplace type problems for an irregular lattice and with maximum probability

Natural-fibre-reinforced plastics in actively bent structures

This joint venture research brings together three different fields of research which have led to novel findings: these relate to single-motion erection of irregular lattice gridshells using geometric optimisation techniques for the application of natural fibre-reinforced composites within the context of actively bent elements for curved load-bearing structures. Fabrication tests are carried out for pultruded flat test specimens and tubular sections made from environmentally advantageous composites with flax or sisal fibres and a partially bio-based resin. The flat test specimens with flax fibres exhibit excellent tensile and bending strength properties but the sisal yarns prove more successful for pultrusion. Fibre-reinforced composites (including natural fibre-reinforced plastics) compare favourably to timber and steel for application in actively bent structures where low weight, bending-stress reserves and large curvatures are required. The pultrusion tests also identify serious manufacturing challenges (such as the twisting of sisal fibres), which lead to inconsistent properties and subsequently highlight the need for further investigation. The experimental realisation of a 10 m span irregular lattice gridshell using glass fibre-reinforced plastic was completed as a proof of concept for the suitability of active bending for pultruded fibre-reinforced profiles and also to validate newly developed computational optimisation and construction procedures for irregular gridshell lattices.

О возможности применения сетчатых оболочек с несимметрично уложенными нитями в качестве приводов управляемой упругой деформации

О возможности применения сетчатых оболочек с несимметрично уложенными нитями в качестве приводов управляемой упругой деформации

Effective tight-binding models for excitons in branched conjugated molecules

Effective tight-binding models have been introduced to describe vertical electronic excitations in branched conjugated molecules. The excited-state electronic structure is characterized by quantum particles (excitons) that reside on an irregular lattice (graph) that reflects the molecular structure. The methodology allows for the exciton spectra and energy-dependent exciton scattering matrices to be described in terms of a small number of lattice parameters which can be obtained from quantum-chemical computations using the exciton scattering approach as a tool. We illustrate the tight-binding model approach using the time-dependent Hartree-Fock computations in phenylacetylene oligomers. The on-site energies and hopping constants have been identified from the exciton dispersion and scattering matrices. In particular, resonant, as well as bound states, are reproduced for a symmetric quadruple branching center. The capability of the tight-binding model approach to describe the exciton-phonon coupling and energetic disorder in large branched conjugated molecules is briefly discussed.