scholarly journals Extreme Poisson’s Ratios of Honeycomb, Re-Entrant, and Zig-Zag Crystals of Binary Hard Discs

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1127
Author(s):  
Mikołaj Bilski ◽  
Paweł M. Pigłowski ◽  
Krzysztof W. Wojciechowski
Keyword(s):  
High Pressures ◽  
Symmetry Axis ◽  
Analytic Formula ◽  
2D Systems ◽  
Two Dimensional ◽  
A Value ◽  
Upper Limit ◽  
The Monte Carlo Method ◽  
Isotropic Pressure ◽  
Different Diameters

Two-dimensional (2D) crystalline structures based on a honeycomb geometry are analyzed by computer simulations using the Monte Carlo method in the isobaric-isothermal ensemble. The considered crystals are formed by hard discs (HD) of two different diameters which are very close to each other. In contrast to equidiameter HD, which crystallize into a homogeneous solid which is elastically isotropic due to its six-fold symmetry axis, the systems studied in this work contain artificial patterns and can be either isotropic or anisotropic. It turns out that the symmetry of the patterns obtained by the appropriate arrangement of two types of discs strongly influences their elastic properties. The Poisson’s ratio (PR) of each of the considered structures was studied in two aspects: (a) its dependence on the external isotropic pressure and (b) in the function of the direction angle, in which the deformation of the system takes place, since some of the structures are anisotropic. In order to accomplish the latter, the general analytic formula for the orientational dependence of PR in 2D systems was used. The PR analysis at extremely high pressures has shown that for the vast majority of the considered structures it is approximately direction independent (isotropic) and tends to the upper limit for isotropic 2D systems, which is equal to +1. This is in contrast to systems of equidiameter discs for which it tends to 0.13, i.e., a value almost eight times smaller.

scholarly journals Extremely Non-Auxetic Behavior of a Typical Auxetic Microstructure Due to Its Material Properties

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7837
Author(s):  
Mikołaj Bilski ◽  
Krzysztof W. Wojciechowski ◽  
Tomasz Stręk ◽  
Przemysław Kędziora ◽  
James N. Grima-Cornish ◽  
...  
Keyword(s):  
Symmetry Axis ◽  
Common Belief ◽  
Two Dimensional ◽  
Upper Limit ◽  
The Monte Carlo Method ◽  
Isotropic Media ◽  
Thermodynamic Conditions ◽  
The Common ◽  
Auxetic Structure ◽  
The Ideal

The re-entrant honeycomb microstructure is one of the most famous, typical examples of an auxetic structure. The re-entrant geometries also include other members as, among others, the star re-entrant geometries with various symmetries. In this paper, we focus on one of them, having a 6-fold symmetry axis. The investigated systems consist of binary hard discs (two-dimensional particles with two slightly different sizes, interacting through infinitely repulsive pairwise potential), from which different structures, based on the mentioned geometry, were formed. To study the elastic properties of the systems, computer simulations using the Monte Carlo method in isobaric-isothermal ensemble with varying shape of the periodic box were performed. The results show that all the considered systems are isotropic and not auxetic—their Poisson’s ratio is positive in each case. Moreover, Poisson’s ratios of the majority of examined structures tend to +1 with increasing pressure, which is the upper limit for two-dimensional isotropic media, thus they can be recognized as the ideal non-auxetics in appropriate thermodynamic conditions. The results obtained contradict the common belief that the unique properties of metamaterials result solely from their microstructure and indicate that the material itself can be crucial.

scholarly journals Two-Dimensional Materials with Giant Optical Nonlinearities near the Theoretical Upper Limit

ACS Nano ◽  
2021 ◽  
Vol 15 (4) ◽  
pp. 7155-7167
Author(s):  
Alireza Taghizadeh ◽  
Kristian S. Thygesen ◽  
Thomas G. Pedersen
Keyword(s):  
Optical Nonlinearities ◽  
Two Dimensional ◽  
Upper Limit ◽  
Two Dimensional Materials

Interpretation and use of standard atomic weights (IUPAC Technical Report)

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Adriaan M. H. van der Veen ◽  
Juris Meija ◽  
Antonio Possolo ◽  
David Brynn Hibbert
Keyword(s):  
Monte Carlo ◽  
Atomic Weight ◽  
Standard Uncertainty ◽  
Uncertainty In Measurement ◽  
Propagation Of Uncertainty ◽  
A Value ◽  
The Monte Carlo Method ◽  
Technical Report ◽  
Molecular Masses ◽  
Expression Of Uncertainty

Abstract Many calculations for science or trade require the evaluation and propagation of measurement uncertainty. Although relative atomic masses (standard atomic weights) of elements in normal terrestrial materials and chemicals are widely used in science, the uncertainties associated with these values are not well understood. In this technical report, guidelines for the use of standard atomic weights are given. This use involves the derivation of a value and a standard uncertainty from a standard atomic weight, which is explained in accordance with the requirements of the Guide to the Expression of Uncertainty in Measurement. Both the use of standard atomic weights with the law of propagation of uncertainty and the Monte Carlo method are described. Furthermore, methods are provided for calculating uncertainties of relative molecular masses of substances and their mixtures. Methods are also outlined to compute material-specific atomic weights whose associated uncertainty may be smaller than the uncertainty associated with the standard atomic weights.

scholarly journals Entropy, Information, and Symmetry: Ordered is Symmetrical

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 11 ◽  
Author(s):  
Edward Bormashenko
Keyword(s):  
Binary System ◽  
Physical System ◽  
Quantitative Measure ◽  
2D Systems ◽  
Two Dimensional ◽  
One Dimensional ◽  
Entropy Information

Entropy is usually understood as the quantitative measure of “chaos” or “disorder”. However, the notions of “chaos” and “disorder” are definitely obscure. This leads to numerous misinterpretations of entropy. We propose to see the disorder as an absence of symmetry and to identify “ordering” with symmetrizing of a physical system; in other words, introducing the elements of symmetry into an initially disordered physical system. We demonstrate with the binary system of elementary magnets that introducing elements of symmetry necessarily diminishes its entropy. This is true for one-dimensional (1D) and two-dimensional (2D) systems of elementary magnets. Imposing symmetry does not influence the Landauer principle valid for the addressed systems. Imposing the symmetry restrictions onto the system built of particles contained within the chamber divided by the permeable partition also diminishes its entropy.

Methods to Accelerate Ray Tracing in the Monte Carlo Method for Surface-to-Surface Radiation Transport

2006 ◽  
Vol 128 (9) ◽  
pp. 945-952 ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Ray Tracing ◽  
Radiation Transport ◽  
Three Dimensional ◽  
Intersection Point ◽  
Surface Radiation ◽  
Computational Domain ◽  
Two Dimensional ◽  
Spatial Partitioning ◽  
The Monte Carlo Method

Two different algorithms to accelerate ray tracing in surface-to-surface radiation Monte Carlo calculations are investigated. The first algorithm is the well-known binary spatial partitioning (BSP) algorithm, which recursively bisects the computational domain into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The second algorithm is the volume-by-volume advancement (VVA) algorithm. This algorithm is new and employs the volumetric mesh to advance the ray through the computational domain until a legitimate intersection point is found. The algorithms are tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes. Both algorithms are found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. For three-dimensional geometries, the VVA algorithm is found to be clearly superior to BSP, particularly for cases with obstructions within the computational domain. For two-dimensional geometries, the VVA algorithm is found to be superior to the BSP algorithm only when obstructions are present and are densely packed.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

Equilibrium and nonequilibrium models on solomon networks with two square lattices

2017 ◽  
Vol 28 (08) ◽  
pp. 1750099
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Exponent ◽  
Critical Points ◽  
Majority Vote ◽  
Universality Class ◽  
2D Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
Regular Lattices

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios [Formula: see text], [Formula: see text], and [Formula: see text]. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

scholarly journals Análise dos Riscos em Projetos: Uma Aplicação do Método de Monte Carlo em uma Empresa do Setor Moveleiro

2018 ◽  
Vol 10 (2) ◽  
pp. 332-357
Author(s):  
Fernando Rodrigues de Amorim ◽  
Pedro Henrique Camargo de Abreu ◽  
Marco Tulio Ospina Patino ◽  
Leonardo Augusto Amaral Terra
Keyword(s):  
Monte Carlo ◽  
Investment Project ◽  
Modern Society ◽  
Exploratory Research ◽  
Investment Projects ◽  
A Value ◽  
The Monte Carlo Method ◽  
Monte Carlo Em ◽  
A Company

Globalization is a phenomenon that is present in modern society and, with its expansion, it is essential that companies can meet the constant demands of the market, but for this, it is necessary to make the best decisions and deal with various adversities related to the economy, competition, management, among others. The success of investment projects is determined by a set of techniques that must be applied so as not to compromise the viability of the project. When this viability is surrounded by uncertainties, a useful alternative to knowing the risks is the use of the Monte Carlo method. The present work aims to address the risk factors in a company of the furniture sector, using the Monte Carlo simulation to analyze the viability of this project. The methodology adopted was developed from a case study, through an exploratory research. The results showed that the investment project is viable, estimating a return between the 4th and 5th year of the project, in addition, the balance after the 10 years of investment would be around R$ 4,128,211.63, a value that represents 161.25% of the initial investment.

Optical properties of two-dimensional materials with tilted anisotropic Dirac cones: theoretical modelling with application to doped 8-Pmmn borophene

2021 ◽  
Author(s):  
Vl A Margulis ◽  
E E Muryumin
Keyword(s):  
Electronic Band Structure ◽  
Grazing Incidence ◽  
Dielectric Substrate ◽  
Incident Radiation ◽  
Brewster Angle ◽  
Theoretical Modelling ◽  
Two Dimensional ◽  
Electronic Band ◽  
A Value ◽  
Transmission And Absorption

Abstract The optical reflection, transmission and absorption properties of borophene, a newly discovered two-dimensional material with tilted anisotropic Dirac cones, are explored within a simple electronic band structure model of 8-Pmmn borophene, proposed by Zabolotskiy and Lozovik (2016 Phys. Rev. B 94 165403). It is assumed that the borophene layer is deposited on a dielectric substrate, such as Al2O3, and that the borophene's electron density is controlled by an external gate voltage. The reflectance, transmittance and absorbance of the borophene layer, the conduction band of which is filled with electrons up to the Fermi level, are calculated against the frequency of the incident radiation, as well as on the angle of its incidence on the layer. Considered are the two principal cases of the incident radiation polarization either parallel to or normal to the plane of incidence. We reveal that the optical characteristics of 8-Pmmn borophene are distinctly different for the above two cases at all angles of radiation incidence, excepting the grazing incidence, for which the borophene layer is found to behave like a mirror regardless of the wave polarization. The results obtained indicate the possibility of visualizing the borophene layer deposited on a dielectric substrate by observing the minimum reflectivity of this layer at a certain angle incidence (called the quasi-Brewster angle) of the p-polarized radiation, which may differ by a value of about ten degrees from the Brewster angle of the substrate.

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