scholarly journals On the scaling laws for low-temperature plasmas at macro and micro scales

2021 ◽  
Vol 2064 (1) ◽  
pp. 012037
Author(s):  
Y Fu ◽  
X Wang ◽  
B Zheng ◽  
P Zhang ◽  
Q H Fan ◽  
...  
Keyword(s):  
Electron Density ◽  
Scaling Laws ◽  
Similarity Theory ◽  
Ohmic Heating ◽  
Low Pressure ◽  
Theoretical Background ◽  
Driving Frequency ◽  
Practical Applications ◽  
Rf Discharges ◽  
Similarity Relations

Abstract The theoretical background and historical development of the similarity theory during the past decades are reviewed. We demonstrate similar discharges in local and nonlocal kinetic regimes, taking the low-pressure capacitive radio frequency (rf) discharges and microdischarges as examples. By using fully kinetic particle-in-cell simulations, we verify the similarity law (SL) and show a violation of frequency scaling (f-scaling) in the low-pressure capacitive rf plasmas. The similarity relations for electron density and electron power absorption are confirmed in similar rf discharges. With only the driving frequency varied, the f-scaling for electron density is also validated, showing almost the same trend as the similarity scaling, across most of the frequency regime. However, violations of the f-scaling are observed at lower frequencies, which are found to be relevant to the electron heating mode transition from stochastic to Ohmic heating. The scaling characteristics have also been comprehensively studied for microdischarges with dimensions from hundreds to several microns, with transition from secondary electron dominated regime to field emission regime. Finally, practical applications of the similarity and scaling laws are summarized.

Large qualitative models of complex chemical and bioengineering processes

1991 ◽  
Vol 56 (10) ◽  
pp. 2107-2141 ◽  
Author(s):  
Mirko Dohnal
Keyword(s):  
Case Studies ◽  
Chemical Process ◽  
Ad Hoc ◽  
Chemical Reactor ◽  
Theoretical Background ◽  
Qualitative Model ◽  
Complex Chemical ◽  
Practical Applications ◽  
Qualitative Models ◽  
Decomposition Principle

Qualitative model is a theoretical background of commonsense. Complex qualitative models can have prohibitively many solutions (qualitative states). Therefore a qualitative analogy of such classical quantitative tools as e.g. the decomposition is developed. Practical applications of decomposition principle is nearly always ad hoc. Therefore two case studies are presented in details, a chemical process (mixer, chemical reactor, separator) and an anaerobic fermentor.

Structural similitudes of stiffened cylinders

2017 ◽  
Vol 24 (3) ◽  
pp. 527-541 ◽  
Author(s):  
G Petrone ◽  
M Manfredonia ◽  
S De Rosa ◽  
F Franco
Keyword(s):  
Numerical Simulation ◽  
Structural Engineering ◽  
Scaling Laws ◽  
Similarity Theory ◽  
Design Tool ◽  
Engineering Science ◽  
The Finite Element Method ◽  
Engineering Problems ◽  
Incomplete Similarity ◽  
Scaled Models

Similarity theory is a branch of engineering science that deals with establishing conditions of similarity among phenomena and is applied to various fields, such as structural engineering problems, vibration and impact. Tests and numerical simulation of scaled models are still a valuable design tool, whose purpose is to accurately predict the behaviour of large or small prototypes through scaling laws applied to the experimental and numerical results. The aim of this paper is to predict the behaviour of the complete and incomplete similarity of stiffened cylinders by applying distorted scaling laws of the models in similitude. The investigation is performed using models based on the finite element method within commercial software. Two classes of cylinders scaled, with different laws, and, hence, reproducing replicas (exact similitude) and avatars (distorted similitude) are investigated.

Electron density in low‐pressure Na‐Ne discharges deduced from laser absorption experiments

1986 ◽  
Vol 59 (7) ◽  
pp. 2324-2331 ◽  
Author(s):  
H. J. Cornelissen ◽  
H. J. H. Merks‐Eppingbroek
Keyword(s):  
Electron Density ◽  
Low Pressure ◽  
Laser Absorption

scholarly journals The International School of Crystallography: an example of continuing education

2014 ◽  
Vol 70 (a1) ◽  
pp. C1274-C1274
Author(s):  
Annalisa Guerri ◽  
Giovanna Scapin ◽  
Paola Spadon
Keyword(s):  
Interpersonal Relationships ◽  
Public Awareness ◽  
International School ◽  
Theoretical Background ◽  
Great Success ◽  
Practical Applications ◽  
Local Staff ◽  
School Teaching ◽  
Traditional Lectures ◽  
High Level

2014 has been declared by UNESCO the International Year of Crystallography. Following the declaration, many initiatives have flourished with the intent of spreading the science and culture of crystallography, since among the major objectives of the IYCr2014 are increase of public awareness on the science of crystallography, promotion of education and research in all fields of crystallography and fostering of international collaborations. The International School of Crystallography is an internationally recognized meeting that was started in 1974 by Prof. Riva di Sanseverino, with the similar goals of promoting high level crystallographic education, scientific exchanges and collaborations. In 2014 the school celebrates its 40th year of activity. During these forty years, courses have been held on many different topics addressing all aspects of crystallography, from crystal growth theory to practical applications in drug discovery to the use of cutting edge technologies; students and teachers have been brought together in an environment that fostered high level scientific discussions as well as unique interpersonal relationships. Many of the students moved on to become well known personality in the crystallographic community, while retaining collaborations and friendships started during the School. Through these years the School teaching methods have also evolved, taking advantage of the fast technological progress of the past 10 years or so. The School offers both traditional lectures and practical computer-based workshops, to guarantee the students not only a theoretical background, but also hands-on experiences on applied crystallography. The dedication of the organizers and lecturers, the unconditioned support of the local staff, and the unique location of the School have made it a great success and a very popular meeting for generations of crystallographers.

scholarly journals Diagnostics of low-pressure capacitively coupled RF discharge argon plasma

2019 ◽  
Vol 13 (27) ◽  
pp. 76-82
Author(s):  
Kadhim A. Aadim
Keyword(s):  
Electron Temperature ◽  
Electron Density ◽  
Langmuir Probe ◽  
Gas Flow ◽  
Low Pressure ◽  
Gas Pressure ◽  
Rf Discharge ◽  
Electrode Gap ◽  
Probe Characteristic ◽  
Capacitively Coupled

Low-pressure capacitively coupled RF discharge Ar plasma has been studied using Langmuir probe. The electron temperature, electron density and Debay length were calculated under different pressures and electrode gap. In this work the RF Langmuir probe is designed using 4MHz filter as compensation circuit and I-V probe characteristic have been investigated. The pressure varied from 0.07 mbar to 0.1 mbar while electrode gap varied from 2-5 cm. The plasma was generated using power supply at 4MHz frequency with power 300 W. The flowmeter is used to control Argon gas flow in the range of 600 standard cubic centimeters per minute (sccm). The electron temperature drops slowly with pressure and it's gradually decreased when expanding the electrode gap. As the gas pressure increases, the plasma density rises slightly at low gas pressure while it drops little at higher gas pressure. The electron density decreases rapidly with expand distances between electrodes.

scholarly journals Scaling laws and warning signs for bifurcations of SPDEs

2018 ◽  
Vol 30 (5) ◽  
pp. 853-868
Author(s):  
CHRISTIAN KUEHN ◽  
FRANCESCO ROMANO
Keyword(s):  
Differential Equations ◽  
Scaling Laws ◽  
Scaling Law ◽  
Warning Signs ◽  
Covariance Operator ◽  
Large Classes ◽  
Practical Applications ◽  
Critical Transitions ◽  
Degenerate Eigenvalues ◽  
Adjoint Operators

Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated with systems, which drift slowly towards a bifurcation point. In the context of stochastic ordinary differential equations, there are results on growth of variance and autocorrelation before a transition, which can be used as possible warning signs in applications. A similar theory has recently been developed in the simplest setting for stochastic partial differential equations (SPDEs) for self-adjoint operators in the drift term. This setting leads to real discrete spectrum and growth of the covariance operator via a certain scaling law. In this paper, we develop this theory substantially further. We cover the cases of complex eigenvalues, degenerate eigenvalues as well as continuous spectrum. This provides a fairly comprehensive theory for most practical applications of warning signs for SPDE bifurcations.

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