scholarly journals Third-Order Correlation Functions for a Coulomb Pair

2019 ◽  
Vol 64 (6) ◽  
pp. 477
Author(s):  
V. I. Vaskivskyi
Keyword(s):  
Explicit Form ◽  
Electrostatic Interaction ◽  
Interaction Potential ◽  
Correlation Functions ◽  
Algebraic Method ◽  
Third Order ◽  
Interaction Operator ◽  
First Time

Third-order correlation functions for two particles with the electrostatic interaction have been obtained for the first time using the direct algebraic method. The main relations for the correlation functions that do not depend on the explicit form of the interaction potential between particles, as well as the relations that appear for four specific forms of the interaction operator, are considered.

scholarly journals Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Liu Yang ◽  
Chunfang Shen ◽  
Dapeng Xie
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Type Theorem ◽  
Third Order ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems ◽  
First Time ◽  
Multipoint Boundary Value Problem

Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O’Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper.

Measurement and modelling of homogeneous axisymmetric turbulence

1998 ◽  
Vol 374 ◽  
pp. 59-90 ◽  
Author(s):  
TORBJÖRN SJÖGREN ◽  
ARNE V. JOHANSSON
Keyword(s):  
Transport Equation ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Theoretical Description ◽  
Wind Tunnel Experiments ◽  
Third Order ◽  
Point Velocity ◽  
First Time ◽  
Rapid Pressure

A new method for determining the slow and rapid pressure-strain rate terms directly from wind-tunnel experiments has been developed with the aid of a newly developed theoretical description of the kinematics of homogeneous axisymmetric turbulence. Both the straining and the return-to-isotropy process of homogeneous axisymmetric turbulence are studied with the aim of improving Reynolds stress closures. Direct experimental determination of the different terms in the transport equation for the Reynolds stress tensor plays a major role in the validation and development of turbulence models. For the first time it is shown that the pressure{strain correlation can be determined with good accuracy without balancing it out from the Reynolds stress transport equation (and without measuring the pressure). Instead it is determined through evaluation of integrals containing second- and third-order two-point velocity correlations. All the terms in the Reynolds stress equations are measured directly and balance is achieved.

scholarly journals Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

2015 ◽  
Vol 471 (2177) ◽  
pp. 20150060 ◽  
Author(s):  
A. Gillman ◽  
G. Amadio ◽  
K. Matouš ◽  
T. L. Jackson
Keyword(s):  
Mechanical Properties ◽  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Three Dimensional ◽  
Adaptive Methods ◽  
Shape Effect ◽  
Third Order ◽  
Recent Letter ◽  
Penetrable Spheres ◽  
First Time

Obtaining an accurate higher order statistical description of heterogeneous materials and using this information to predict effective material behaviour with high fidelity has remained an outstanding problem for many years. In a recent letter, Gillman & Matouš (2014 Phys. Lett. A 378, 3070–3073. ()) accurately evaluated the three-point microstructural parameter that arises in third-order theories and predicted with high accuracy the effective thermal conductivity of highly packed material systems. Expanding this work here, we predict for the first time effective thermo-mechanical properties of granular Platonic solid packs using third-order statistical micromechanics. Systems of impenetrable and penetrable spheres are considered to verify adaptive methods for computing n -point probability functions directly from three-dimensional microstructures, and excellent agreement is shown with simulation. Moreover, a significant shape effect is discovered for the effective thermal conductivity of highly packed composites, whereas a moderate shape effect is exhibited for the elastic constants.

scholarly journals Model of Close Packing for Determination of the Major Characteristics of the Liquid Dispersions Components

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Kiril Hristov Kolikov ◽  
Dimo Donchev Hristozov ◽  
Radka Paskova Koleva ◽  
Georgi Aleksandrov Krustev
Keyword(s):  
Dispersion Medium ◽  
Algebraic Method ◽  
Close Packing ◽  
Pure Substance ◽  
Sedimentation Stability ◽  
Dispersion Phase ◽  
Liquid Dispersion ◽  
The Masses ◽  
First Time

We introduce a close packing model of the particles from the disperse phase of a liquid dispersion. With this model, we find the sediment volumes, the emergent, and the bound dispersion medium. We formulate a new approach for determining the equivalent radii of the particles from the sediment and the emergent (different from the Stokes method). We also describe an easy manner to apply algebraic method for determining the average volumetric mass densities of the ultimate sediment and emergent, as well as the free dispersion medium (without using any pycnometers or densitometers). The masses of the different components and the density of the dispersion phase in the investigated liquid dispersion are also determined by means of the established densities. We introduce for the first time a dimensionless scale for numeric characterization and therefore an index for predicting the sedimentation stability of liquid dispersions in case of straight and/or reverse sedimentation. We also find the quantity of the pure substance (without pouring out or drying) in the dispersion phase of the liquid dispersions.

scholarly journals Modeling Dendrimers Charge Interaction in Solution: Relevance in Biosystems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Domenico Lombardo
Keyword(s):  
Structural Properties ◽  
Electrostatic Interaction ◽  
Interaction Potential ◽  
Biomedical Application ◽  
Specific Interaction ◽  
Great Part ◽  
Molecular Organization ◽  
Suitable Model ◽  
Wide Range ◽  
Charge Interaction

Dendrimers are highly branched macromolecules obtained by stepwise controlled, reaction sequences. The ability to be designed for specific applications makes dendrimers unprecedented components to control the structural organization of matter during the bottom-up synthesis of functional nanostructures. For their applications in the field of biotechnology the determination of dendrimer structural properties as well as the investigation of the specific interaction with guest components are needed. We show how the analysis of the scattering structure factorS(q), in the framework of current models for charged systems in solution, allows for obtaining important information of the interdendrimers electrostatic interaction potential. The finding of the presented results outlines the important role of the dendrimer charge and the solvent conditions in regulating, through the modulation of the electrostatic interaction potential, great part of the main structural properties. This charge interaction has been indicated by many studies as a crucial factor for a wide range of structural processes involving their biomedical application. Due to their easily controllable properties dendrimers can be considered at the crossroad between traditional colloids, associating polymers, and biological systems and represent then an interesting new technological approach and a suitable model system of molecular organization in biochemistry and related fields.

Investigation on the growth, structural, HOMO–LUMO and optical studies of 1-ethyl-2-[2-(4-hydroxy-phenyl)-vinyl]-pyridinium iodide (HSPI) – a new stilbazolium derivative for third-order NLO applications

RSC Advances ◽  
2016 ◽  
Vol 6 (42) ◽  
pp. 35977-35990 ◽  
Author(s):  
K. Nivetha ◽  
S. Kalainathan ◽  
Manabu Yamada ◽  
Yoshihiko Kondo ◽  
Fumio Hamada
Keyword(s):  
Optical Quality ◽  
Slow Evaporation ◽  
Optical Studies ◽  
Third Order ◽  
Slow Evaporation Technique ◽  
Evaporation Technique ◽  
Optical Crystal ◽  
First Time ◽  
Homo Lumo ◽  
Phenyl Vinyl

The organic third-order non-linear optical crystal HSPI, a new derivative of the stilbazolium family, was successfully synthesized and the optical quality single crystal was grown by a slow evaporation technique for the first time.

scholarly journals Искажения прямоугольного радиоимпульса с хаотической несущей, распространяющегося в диспергирующей резонансно-поглощающей газовой среде

2019 ◽  
Vol 45 (8) ◽  
pp. 43
Author(s):  
Г.М. Стрелков ◽  
Ю.С. Худышев
Keyword(s):  
Correlation Functions ◽  
Dispersive Medium ◽  
Rectangular Pulse ◽  
Third Order ◽  
Wide Region ◽  
Frequency Correlation ◽  
The Third ◽  
Chebyshev Map ◽  
Gas Medium ◽  
Chaotic Carrier

AbstractWe briefly describe the possible character and peculiarities of dispersion-induced distortions of a rectangular pulse with chaotic carrier modeled using the third-order Chebyshev map of the first kind propagating in a resonantly absorbing gas medium. It is established that, as the pulse goes away from the radiator, its envelope exhibits transformation toward a noiselike shape. In a rather wide region of parameters of the dispersive medium, distortions of the envelope are not accompanied by breakage or principal changes of its autocorrelation and frequency correlation functions.

scholarly journals Space gravity spectroscopy: the benefits of Taylor-Karman structured criterion matrices

2003 ◽  
Vol 1 ◽  
pp. 113-120 ◽  
Author(s):  
P. Marinkovice ◽  
E. Grafarend ◽  
T. Reubelt
Keyword(s):  
Correlation Functions ◽  
Random Function ◽  
Homogeneous Distribution ◽  
Data Validation ◽  
Third Order ◽  
Order Tensor ◽  
Correlation Tensor ◽  
The Third ◽  
Leo Satellite

Abstract. As soon as a space gravity spectroscopy was successfully performed, for instance by means of semicontinuous ephemeris of LEO - GPS tracked satellites, the problem of data validation appeared. It is for this purpose that a stochastic model for the homogeneous and isotropic analysis of measurements, obtained as “directly" measured values in LEO satellite missions (CHAMP, GRACE, GOCE), is studied. An isotropic analysis is represented by the homogeneous distribution of measured values and the statistical properties of the model are calculated. In particular, a correlation structure function is defined by the third order tensor (Taylor-Karman tensor) for the ensemble average of a set of incremental differences in measured components. Specifically, Taylor-Karman correlation tensor is calculated with the assumption that the analyzed random function is of a “potential type". The special class of homogeneous and isotropic correlation functions is introduced. Finally, a successful application of the concept is presented in the case study CHAMP and a comparison between modeled and estimated correlations is performed.Key words. data validation, 3D correlation tensor, homogeneous and isotropic correlation functions, Taylor-Karman structure, CHAMP

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