scholarly journals Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain

2019 ◽  
Vol 52 (33) ◽  
pp. 334001 ◽  
Author(s):  
Elisabeth Agoritsas ◽  
Thibaud Maimbourg ◽  
Francesco Zamponi
Keyword(s):  
Shear Strain ◽  
Particle Systems ◽  
Dynamical Equations ◽  
Infinite Dimensional ◽  
Anisotropic Case

NONLINEAR PROBLEMS IN INFINITE INTERACTING PARTICLE SYSTEMS

2008 ◽  
Vol 11 (02) ◽  
pp. 179-211 ◽  
Author(s):  
ROBERT OLKIEWICZ ◽  
LIHU XU ◽  
BOGUSŁAW ZEGARLIŃSKI
Keyword(s):  
Configuration Space ◽  
Interacting Particle Systems ◽  
Nonlinear Problems ◽  
Particle Systems ◽  
Markov Semigroups ◽  
Infinite Dimensional ◽  
Interacting Particle

We introduce and study a class of nonlinear jump type Markov semigroups for systems with infinite dimensional configuration space.

Infinite-dimensional stochastic difference equations for particle systems and network flows

1989 ◽  
Vol 26 (02) ◽  
pp. 325-344
Author(s):  
R. W. R. Darling
Keyword(s):  
Neural Network ◽  
Flow Model ◽  
Network Flows ◽  
Particle Systems ◽  
Stochastic Flow ◽  
Random Vectors ◽  
Infinite Dimensional ◽  
Countably Infinite ◽  
Infinite Set ◽  
Number Of Births

Let V be a countably infinite set, and let {Xn, n = 0, 1, ·· ·} be random vectors in which satisfy Xn = AnXn – 1 + ζ n , for i.i.d. random matrices {An } and i.i.d. random vectors {ζ n }. Interpretation: site x in V is occupied by Xn (x) particles at time n; An describes random transport of existing particles, and ζ n (x) is the number of ‘births' at x. We give conditions for (1) convergence of the sequence {Xn } to equilibrium, and (2) a central limit theorem for n–1/2(X 1 + · ·· + Xn ), respectively. When the matrices {An } consist of 0's and 1's, these conditions are checked in two classes of examples: the ‘drip, stick and flow model' (a stochastic flow with births), and a neural network model.

Infinite-dimensional stochastic difference equations for particle systems and network flows

1989 ◽  
Vol 26 (2) ◽  
pp. 325-344 ◽  
Author(s):  
R. W. R. Darling
Keyword(s):  
Neural Network ◽  
Flow Model ◽  
Network Flows ◽  
Particle Systems ◽  
Stochastic Flow ◽  
Random Vectors ◽  
Infinite Dimensional ◽  
Countably Infinite ◽  
Infinite Set ◽  
Number Of Births

Let V be a countably infinite set, and let {Xn, n = 0, 1, ·· ·} be random vectors in which satisfy Xn = AnXn– 1 + ζn, for i.i.d. random matrices {An} and i.i.d. random vectors {ζ n}. Interpretation: site x in V is occupied by Xn(x) particles at time n; An describes random transport of existing particles, and ζ n(x) is the number of ‘births' at x. We give conditions for (1) convergence of the sequence {Xn} to equilibrium, and (2) a central limit theorem for n–1/2(X1 + · ·· + Xn), respectively. When the matrices {An} consist of 0's and 1's, these conditions are checked in two classes of examples: the ‘drip, stick and flow model' (a stochastic flow with births), and a neural network model.

Application of Modified Bloch Waves to Image Analysis of Extended Linear Defects

1974 ◽  
Vol 32 ◽  
pp. 402-403
Author(s):  
S. Nakahara ◽  
D. M. Maher
Keyword(s):  
Image Analysis ◽  
Computational Approach ◽  
Dislocation Loops ◽  
Plane Wave Expansion ◽  
Dynamical Equations ◽  
Bloch Waves ◽  
Linear Defects ◽  
Imperfect Crystal ◽  
Localized Defects ◽  
Defective Crystals

Since Head first demonstrated the advantages of computer displayed theoretical intensities from defective crystals, computer display techniques have become important in image analysis. However the computational methods employed resort largely to numerical integration of the dynamical equations of electron diffraction. As a consequence, the interpretation of the results in terms of the defect displacement field and diffracting variables is difficult to follow in detail. In contrast to this type of computational approach which is based on a plane-wave expansion of the excited waves within the crystal (i.e. Darwin representation ), Wilkens assumed scattering of modified Bloch waves by an imperfect crystal. For localized defects, the wave amplitudes can be described analytically and this formulation has been used successfully to predict the black-white symmetry of images arising from small dislocation loops.

Analysis of magneto rheological elastomers for energy harvesting systems

2020 ◽  
Vol 64 (1-4) ◽  
pp. 439-446
Author(s):  
Gildas Diguet ◽  
Gael Sebald ◽  
Masami Nakano ◽  
Mickaël Lallart ◽  
Jean-Yves Cavaillé
Keyword(s):  
Magnetic Field ◽  
Energy Harvesting ◽  
Shear Strain ◽  
Magnetic Induction ◽  
Magnetic Particles ◽  
Homogeneous Magnetic Field ◽  
Electrical Signal ◽  
Harvesting Systems ◽  
Dc Bias ◽  
Magneto Rheological

Magneto Rheological Elastomers (MREs) are composite materials based on an elastomer filled by magnetic particles. Anisotropic MRE can be easily manufactured by curing the material under homogeneous magnetic field which creates column of particles. The magnetic and elastic properties are actually coupled making these MREs suitable for energy conversion. From these remarkable properties, an energy harvesting device is considered through the application of a DC bias magnetic induction on two MREs as a metal piece is applying an AC shear strain on them. Such strain therefore changes the permeabilities of the elastomers, hence generating an AC magnetic induction which can be converted into AC electrical signal with the help of a coil. The device is simulated with a Finite Element Method software to examine the effect of the MRE parameters, the DC bias magnetic induction and applied shear strain (amplitude and frequency) on the resulting electrical signal.

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

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