Model of fractal aggregates induced by shear

It is an undoubted fact that particle aggregates from marine, aerosol, and engineering systems have fractal structures. In this study, fractal geometry is used to describe the morphology of irregular aggregates. The mean-field theory is employed to solve coagulation kinetic equation of aggregates. The Taylor-expansion method of moments in conjunction with the self-similar fractal characteristics is used to represent the particulate field. The effect of the target fractal dimensions on zeroth-order moment, second-order moment, and geometric standard deviation of the aggregates is explored. Results show that the developed moment method is an efficient and powerful approach to solving such evolution equations.

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ON STRONGLY NONLINEAR AUTOREGRESSIVE MODELS: IMPLICATIONS FOR THE THEORY OF TRANSIENT AND STATIONARY RESPONSES OF MANY-BODY SYSTEMS

Fluctuation and Noise Letters ◽

10.1142/s0219477513500223 ◽

2013 ◽

Vol 12 (04) ◽

pp. 1350022 ◽

Cited By ~ 1

Author(s):

T. D. FRANK ◽

S. MONGKOLSAKULVONG

Keyword(s):

Evolution Equations ◽

Mean Field Theory ◽

Mean Field ◽

Ar Model ◽

Many Body ◽

Response Dynamics ◽

Process Mean ◽

Stationary Response ◽

Strongly Nonlinear ◽

Many Body Systems

Two widely used concepts in physics and the life sciences are combined: mean field theory and time-discrete time series modeling. They are merged within the framework of strongly nonlinear stochastic processes, which are processes whose stochastic evolution equations depend self-consistently on process expectation values. Explicitly, a generalized autoregressive (AR) model is presented for an AR process that depends on its process mean value. Criteria for stationarity are derived. The transient dynamics in terms of the relaxation of the first moment and the stationary response to fluctuations in terms of the autocorrelation function are discussed. It is shown that due to the stochastic feedback via the process mean, transient and stationary responses may exhibit qualitatively different temporal patterns. That is, the model offers a time-discrete description of many-body systems that in certain parameter domains feature qualitatively different transient and stationary response dynamics.

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Crackling noise and avalanches in minerals

Physics and Chemistry of Minerals ◽

10.1007/s00269-021-01138-6 ◽

2021 ◽

Vol 48 (5) ◽

Author(s):

Ekhard K. H. Salje ◽

Xiang Jiang

Keyword(s):

Electric Fields ◽

Power Law ◽

Mean Field Theory ◽

Mean Field ◽

Fractal Dimensions ◽

Similar Time ◽

Scaling Properties ◽

Pattern Formations ◽

Observation Method ◽

Great Complexity

AbstractThe non-smooth, jerky movements of microstructures under external forcing in minerals are explained by avalanche theory in this review. External stress or internal deformations by impurities and electric fields modify microstructures by typical pattern formations. Very common are the collapse of holes, the movement of twin boundaries and the crushing of biominerals. These three cases are used to demonstrate that they follow very similar time dependences, as predicted by avalanche theories. The experimental observation method described in this review is the acoustic emission spectroscopy (AE) although other methods are referenced. The overarching properties in these studies is that the probability to observe an avalanche jerk J is a power law distributed P(J) ~ J−ε where ε is the energy exponent (in simple mean field theory: ε = 1.33 or ε = 1.66). This power law implies that the dynamic pattern formation covers a large range (several decades) of energies, lengths and times. Other scaling properties are briefly discussed. The generated patterns have high fractal dimensions and display great complexity.

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Analysis of the susceptible-infected-susceptible epidemic dynamics in networks via the non-backtracking matrix

IMA Journal of Applied Mathematics ◽

10.1093/imamat/hxaa003 ◽

2020 ◽

Vol 85 (2) ◽

pp. 214-230 ◽

Cited By ~ 1

Author(s):

Naoki Masuda ◽

Victor M Preciado ◽

Masaki Ogura

Keyword(s):

Lower Bound ◽

Line Graph ◽

Mean Field Theory ◽

Mean Field ◽

Moment Closure ◽

Order Moment ◽

Epidemic Threshold ◽

Incidence Matrices ◽

Epidemic Dynamics ◽

The Given

Abstract We study the stochastic susceptible-infected-susceptible model of epidemic processes on finite directed and weighted networks with arbitrary structure. We present a new lower bound on the exponential rate at which the probabilities of nodes being infected decay over time. This bound is directly related to the leading eigenvalue of a matrix that depends on the non-backtracking and incidence matrices of the network. The dimension of this matrix is $N+M$, where $N$ and $M$ are the number of nodes and edges, respectively. We show that this new lower bound improves on an existing bound corresponding to the so-called quenched mean-field theory. Although the bound obtained from a recently developed second-order moment-closure technique requires the computation of the leading eigenvalue of an $N^2\times N^2$ matrix, we illustrate in our numerical simulations that the new bound is tighter, while being computationally less expensive for sparse networks. We also present the expression for the corresponding epidemic threshold in terms of the adjacency matrix of the line graph and the non-backtracking matrix of the given network.

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RECIPE FOR THE SOLUTION OF THE DIRAC EQUATION BY THE BASIS SET EXPANSION METHOD

Modern Physics Letters A ◽

10.1142/s0217732393000817 ◽

1993 ◽

Vol 08 (09) ◽

pp. 787-795 ◽

Cited By ~ 10

Author(s):

Y.K. GAMBHIR ◽

P. RING

Keyword(s):

Field Theory ◽

Dirac Equation ◽

Mean Field Theory ◽

Mean Field ◽

Expansion Method ◽

Finite Basis ◽

Basis Set ◽

Spherical Case ◽

Relativistic Mean Field ◽

Basis Set Expansion

The problem arising due to the use of finite basis set expansion method for the solution of the Dirac equation in the Relativistic Mean Field theory, is analyzed, particularly the appearance of the “Spurious” states. A satisfactory prescription (or remedy) for the avoidance of these “Spurious” states is proposed. Illustrative results for this are presented. The proposed prescription is critically analyzed and it is shown to be consistent with that encountered for the spherical case in the molecular and atomic physics problems.

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Mean field theory of n-layer unbinding

Journal de Physique II ◽

10.1051/jp2:1993100 ◽

1993 ◽

Vol 3 (3) ◽

pp. 385-393 ◽

Cited By ~ 13

Author(s):

W. Helfrich

Keyword(s):

Field Theory ◽

Mean Field Theory ◽

Mean Field

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Mean Field Theory of enhanced defect formation in AgCl and AgBr

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1980626 ◽

1980 ◽

Vol 41 (C6) ◽

pp. C6-97-C6-100 ◽

Cited By ~ 4

Author(s):

R. J. Friauf

Keyword(s):

Field Theory ◽

Defect Formation ◽

Mean Field Theory ◽

Mean Field

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Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i3.470 ◽

2015 ◽

Vol 11 (3) ◽

pp. 3134-3138 ◽

Cited By ~ 3

Author(s):

Mostafa Khater ◽

Mahmoud A.E. Abdelrahman

Keyword(s):

Elliptic Function ◽

Traveling Wave ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Traveling Wave Solutions ◽

Expansion Method ◽

Mathematical Physics ◽

Nonlinear Evolution Equations ◽

Jacobian Elliptic Function ◽

Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity andÂ reliability of the method are tested by its applications to the Couple Boiti-Leon-PempinelliÂ System which plays an important role in mathematical physics.

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