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]).

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.

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.

Operator Evaluation of Small Systems

1990 ◽  
Vol 82 (8) ◽  
pp. 40-45 ◽  
Author(s):  
William D. Gollnitz ◽  
Barbara Kittle
Keyword(s):  
Small Systems

Precipitation in small systems—II. Mean field equations more effective than population balance

1996 ◽  
Vol 51 (19) ◽  
pp. 4423-4436 ◽  
Author(s):  
S. Manjunath ◽  
K.S. Gandhi ◽  
R. Kumar ◽  
Doraiswami Ramkrishna
Keyword(s):  
Mean Field ◽  
Population Balance ◽  
Field Equations ◽  
Small Systems ◽  
Mean Field Equations

Institutional Alternatives for Small Systems in the 21st Century

2002 ◽  
Vol 94 (4) ◽  
pp. 59-61
Author(s):  
Peter E. Shanaghan ◽  
Janice A. Beecher
Keyword(s):  
21St Century ◽  
Small Systems

Study on Key Problems at Power System Black Start

2012 ◽  
Vol 614-615 ◽  
pp. 1958-1961
Author(s):  
Pei Ying Guo ◽  
Jian Biao Yang ◽  
Cheng Zhe Li ◽  
Tian Yuan
Keyword(s):  
Power System ◽  
Theoretical Research ◽  
Small System ◽  
Rapid Restoration ◽  
The Impact

Developing effective black start plans is significant to the rapid restoration from the power system blackout. This paper makes theoretical research in some key concerns of self-excitation, over-voltage, the impact of starting loads on the voltage and frequency, and stability of the initial small system. The paper also presents countermeasures against these problems. This overview should be very useful to utility operators involved in the development of black start plans.

A High-Density Bipolar Logic Masterslice for Small Systems

1981 ◽  
Vol 25 (3) ◽  
pp. 142-151 ◽  
Author(s):  
J. Z. Chen ◽  
W. B. Chin ◽  
T.-S. Jen ◽  
J. Hutt
Keyword(s):  
High Density ◽  
Small Systems
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