How Small a System is Too Small for Studying Liquid Behavior?

1992 ◽  
Vol 291 ◽  
Author(s):  
Marcia. H. Grabow
Keyword(s):  
Computer Simulations ◽  
Thermodynamic Limit ◽  
Small Systems ◽  
Small System ◽  
Liquid Behavior

ABSTRACTAlthough it is often convenient to perform computer simulations with small systems, in liquids the structure obtained using a small system may not be the same that would be obtained in the thermodynamic limit. In this paper we address the question specifically for the case of Stillinger-Weber silicon, identifying the region of density and temperature where small systems give different results from larger systems.

scholarly journals DIRECT SIMULATIONS OF SMALL MULTI-FERMION SYSTEMS

2003 ◽  
Vol 14 (08) ◽  
pp. 1027-1040
Author(s):  
MICHAEL CREUTZ
Keyword(s):  
Renormalization Group ◽  
Computer Simulations ◽  
Large Volume ◽  
Lattice Systems ◽  
Small Systems ◽  
Natural Mapping ◽  
Fermion Systems ◽  
Occupation Numbers ◽  
Computer Resources ◽  
System Volume

I explore computer simulations of the dynamics of small multi-fermion lattice systems. The method is more general, but I concentrate on Hubbard type models where the fermions hop between a small number of connected sites. I use the natural mapping of fermion occupation numbers onto computer bits. Signs from fermion interchange are reduced to bit counting. The technique inherently requires computer resources growing exponentially with the system volume; so, it restricted to modestly small systems. Large volume results would require combining these techniques with further approximations, perhaps in a recursive renormalization group manner.

scholarly journals On classes of null sets

1972 ◽  
Vol 14 (3) ◽  
pp. 317-328
Author(s):  
John Lloyd
Keyword(s):  
Small Systems ◽  
Small System

Results concerning classes of null sets have been obtained by various authors. See, for example, [3], [4], [6], [7]. This paper contains results concerning classes of null sets and the notion of a ‘small system’. The motivation for considering ‘small systems’ comes from a paper by Riečan (c.f. [2]).

Initial Assessment of Small Systems (MEMS and NEMS) Course Taught in an Undergraduate and Graduate Classroom

2002 ◽  
Author(s):  
Jason W. Paquette ◽  
K. J. Kim
Keyword(s):  
System Design ◽  
Molecular Motors ◽  
Scaling Laws ◽  
System Development ◽  
Initial Assessment ◽  
Micro Electro Mechanical Systems ◽  
Small Systems ◽  
Small System ◽  
Course Work ◽  
The University

Micro-electro-mechanical systems (MEMS) and nanotechnology are a fast developing technology which combines very small mechanical structures with microelectronics circuits. These devices range in scale from nanometers (10−9 m) to several millimeters, and they are fabricated using the established techniques of microelectronics construction. Due to the increasingly large size and opportunities in these fields, it is becoming necessary to offer course work with small systems for students at the undergraduate and graduate level. A course in MEMS/NEMS small systems was taught at the University of Nevada, Reno in the spring of 2002. The course used the text written by Hsu [1] along with supplementary material. Problems and examples of applying fundamental principles from mechanics, electromagnetism, thermodynamics and optics among others to problems in MEMS design, fabrication and actuation were considered. The course is primarily designed to introduce both engineering undergraduate and graduate students to the possibilities of this exciting new engineering field. Also, current MEMS, NEMS, and microfluidic applications, such as sensors, actuators, heat exchangers, and chemical/biological analysis systems, were discussed. The course introduced a broad spectrum of topics related to small system development including basic engineering science for small system design, engineering mechanics, thermofluid engineering, scaling laws, materials for small systems, fabrication technologies, small system design, advanced nano-materials (molecular motors, nanotubes, polymer nanocomposites), standard characterization techniques: SEM, TEM, AFM, and applications (MEMS, NEMS and microfluidics).

scholarly journals When Thermodynamic Properties of Adsorbed Films Depend on Size: Fundamental Theory and Case Study

Nanomaterials ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1691 ◽  
Author(s):  
Bjørn A. Strøm ◽  
Jianying He ◽  
Dick Bedeaux ◽  
Signe Kjelstrup
Keyword(s):  
Substantial Part ◽  
Small Systems ◽  
Small System ◽  
Spreading Pressure ◽  
Enthalpy Of Adsorption ◽  
Size And Shape ◽  
Adsorbed Films ◽  
Geometric Variables ◽  
System Properties ◽  
First Time

Small system properties are known to depend on geometric variables in ways that are insignificant for macroscopic systems. Small system considerations are therefore usually added to the conventional description as needed. This paper presents a thermodynamic analysis of adsorbed films of any size in a systematic and general way within the framework of Hill’s nanothermodynamics. Hill showed how to deal with size and shape as variables in a systematic manner. By doing this, the common thermodynamic equations for adsorption are changed. We derived the governing thermodynamic relations characteristic of adsorption in small systems, and point out the important distinctions between these and the corresponding conventional relations for macroscopic systems. We present operational versions of the relations specialized for adsorption of gas on colloid particles, and we applied them to analyze molecular simulation data. As an illustration of their use, we report results for CO2 adsorbed on graphite spheres. We focus on the spreading pressure, and the entropy and enthalpy of adsorption, and show how the intensive properties are affected by the size of the surface, a feature specific to small systems. The subdivision potential of the film is presented for the first time, as a measure of the film’s smallness. For the system chosen, it contributes with a substantial part to the film enthalpy. This work can be considered an extension and application of the nanothermodynamic theory developed by Hill. It provides a foundation for future thermodynamic analyses of size- and shape-dependent adsorbed film systems, alternative to that presented by Gibbs.

scholarly journals Finite-size integral equations in the theory of liquids and the thermodynamic limit in computer simulations

2018 ◽  
Vol 116 (21-22) ◽  
pp. 3301-3310 ◽  
Author(s):  
M. Heidari ◽  
K. Kremer ◽  
R. Potestio ◽  
R. Cortes-Huerto
Keyword(s):  
Integral Equations ◽  
Computer Simulations ◽  
Thermodynamic Limit ◽  
Finite Size ◽  
Theory Of Liquids

scholarly journals Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method

Entropy ◽  
2018 ◽  
Vol 20 (4) ◽  
pp. 222 ◽  
Author(s):  
Maziar Heidari ◽  
Kurt Kremer ◽  
Raffaello Potestio ◽  
Robinson Cortes-Huerto
Keyword(s):  
Computer Simulations ◽  
Thermodynamic Limit ◽  
Size Effects ◽  
Finite Size ◽  
Analysis Method ◽  
Finite Size Effects

Tunnelling resistance of a one-dimensional random lattice

1987 ◽  
Vol 65 (7) ◽  
pp. 760-766
Author(s):  
Robert Barrie ◽  
I. C. D. S. Carvalho
Keyword(s):  
Computer Simulations ◽  
Thermodynamic Limit ◽  
Linear Chain ◽  
Filling Fraction ◽  
Random Lattice ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Finite Systems ◽  
The Third ◽  
A Site

The resistivity of a one-dimensional lattice consisting of randomly distributed conducting and insulating sites is considered. Tunnelling resistance of the form R0iebi is assumed for a cluster of i adjacent insulating sites. Three different ensembles are considered and compared. In the first ensemble, the number of insulating "atoms" is fixed and distributed in a linear chain; in the second one, there exists a fixed probability p of having an insulator "atom" occupying a site in a linear chain; and finally in the third one, a line is bent into a circle and the probability p is considered. It is observed that in the thermodynamic limit, the average ensemble resistance per site diverges at the critical filling fraction pc = e−b, while the variance of the resistance diverges at the lower filling fraction [Formula: see text]. Computer simulations of large but finite systems, however, exhibit a much weaker divergence of the resistance per site at pc and no divergence of the variance at pc1.

A High Resolution Study of G.P. Zones in Aluminum - 4.2 at % Silver

1982 ◽  
Vol 40 ◽  
pp. 722-723 ◽  
Author(s):  
R. Gronsky
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
High Resolution ◽  
Computer Simulations ◽  
Structural Characteristics ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Resolution Study

The phenomenon of clustering in Al-Ag alloys has been extensively studied since the early work of Guinierl, wherein the pre-precipitation state was characterized as an assembly of spherical, ordered, silver-rich G.P. zones. Subsequent x-ray and TEM investigations yielded results in general agreement with this model. However, serious discrepancies were later revealed by the detailed x-ray diffraction - based computer simulations of Gragg and Cohen, i.e., the silver-rich clusters were instead octahedral in shape and fully disordered, atleast below 170°C. The object of the present investigation is to examine directly the structural characteristics of G.P. zones in Al-Ag by high resolution transmission electron microscopy.

Multislice calculations for quasi-periodic and non-periodic objects

1990 ◽  
Vol 48 (4) ◽  
pp. 138-139
Author(s):  
R. Herrera ◽  
A. Gómez
Keyword(s):  
Electron Diffraction ◽  
Computer Simulations ◽  
Periodic Table ◽  
Amorphous Materials ◽  
Space Group ◽  
Essential Step ◽  
Shape Effects ◽  
Atomic Scattering ◽  
Diffraction Patterns ◽  
Periodic Continuation

Computer simulations of electron diffraction patterns and images are an essential step in the process of structure and/or defect elucidation. So far most programs are designed to deal specifically with crystals, requiring frequently the space group as imput parameter. In such programs the deviations from perfect periodicity are dealt with by means of “periodic continuation”.However, for many applications involving amorphous materials, quasiperiodic materials or simply crystals with defects (including finite shape effects) it is convenient to have an algorithm capable of handling non-periodicity. Our program “HeGo” is an implementation of the well known multislice equations in which no periodicity assumption is made whatsoever. The salient features of our implementation are: 1) We made Gaussian fits to the atomic scattering factors for electrons covering the whole periodic table and the ranges [0-2]Å−1 and [2-6]Å−1.

Computer simulations for the TEM bend contour technique

1996 ◽  
Vol 54 ◽  
pp. 134-135
Author(s):  
Vladimir Yu. Kolosov ◽  
Anders R. Thölén
Keyword(s):  
Computer Simulations ◽  
Real Space ◽  
Advantages And Disadvantages ◽  
Short Overview ◽  
Diffraction Contrast ◽  
Beam Method ◽  
Convergent Beam ◽  
Contour Technique

In this paper we give a short overview of two TEM applications utilizing the extinction bend contour technique (BC) giving the advantages and disadvantages; especially we consider two areas in which the BC technique remains unique. Special attention is given to an approach including computer simulations of TEM micrographs.BC patterns are often observed in TEM studies but are rarely exploited in a serious way. However, this type of diffraction contrast was one of the first to be used for analysis of imperfections in crystalline foils, but since then only some groups have utilized the BC technique. The most extensive studies were performed by Steeds, Eades and colleagues. They were the first to demonstrate the unique possibilities of the BC method and named it real space crystallography, which developed later into the somewhat similar but more powerful convergent beam method. Maybe, due to the difficulties in analysis, BCs have seldom been used in TEM, and then mainly to visualize different imperfections and transformations.

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