On the Dynamic Response of Disordered Composites

1973 ◽  
Vol 40 (2) ◽  
pp. 511-517 ◽  
Author(s):  
J. J. McCoy
Keyword(s):  
Material Properties ◽  
Mass Density ◽  
Mean Field ◽  
Low Frequency ◽  
Temporal Variations ◽  
Spatial Variations ◽  
Inertia Effects ◽  
Long Wavelength ◽  
The Mean ◽  
Statistical Sample

A formulation is obtained that is to be satisfied by the mean (i.e., statistical averaged) field quantities in a statistical sample of heterogeneous, linearly elastic solids. Inertia effects are included in the analysis. A low frequency-long wavelength theory is extracted from the general formulation as an approximation to be used when spatial variations of the mean field quantities are slow relative to spatial variations of the material properties of the inhomogeneous solids. The temporal variations are restricted to slow variations on a time scale defined by the spatial variations of material properties and a characteristic wave speed. The predictions of the low frequency-long wavelength theory can be given a purely deterministic interpretation. Some aspects of the latter formulation are investigated. In particular, it is shown that the infinite wavelength limit reduces to an effective modulus theory. The effective elastic moduli tensor is identical to one that is obtained on ignoring inertia effects from the outset; the mass density to be used is the “averaged” mass density. By retaining correction terms it is then shown that elastic wave propagation will always exhibit both dispersion and decay over large enough propagation distances.

scholarly journals Temporal Variations of the Turbulence Profiles at the Sayan Solar Observatory Site

Atmosphere ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 499 ◽  
Author(s):  
Artem Shikhovtsev ◽  
Pavel Kovadlo ◽  
Vladimir Lukin
Keyword(s):  
Atmospheric Turbulence ◽  
Temporal Variability ◽  
Low Frequency ◽  
Temporal Variations ◽  
Solar Observatory ◽  
Vertical Profiles ◽  
Spatial And Temporal Scales ◽  
Atmospheric Disturbances ◽  
Wide Range ◽  
The Mean

The paper focuses on the development of the method to estimate the mean characteristics of the atmospheric turbulence. Using an approach based on the shape of the energy spectrum of atmospheric turbulence over a wide range of spatial and temporal scales, the vertical profiles of optical turbulence are calculated. The temporal variability of the vertical profiles of turbulence under different low-frequency atmospheric disturbances is considered.

scholarly journals On the Validity of Neural Mass Models

2021 ◽  
Vol 14 ◽  
Author(s):  
Nicolás Deschle ◽  
Juan Ignacio Gossn ◽  
Prejaas Tewarie ◽  
Björn Schelter ◽  
Andreas Daffertshofer
Keyword(s):  
Mean Field ◽  
Low Frequency ◽  
Inhibitory Neuron ◽  
Inhibitory Neurons ◽  
Neural Population ◽  
Mass Model ◽  
Time Scale Separation ◽  
Neural Mass ◽  
The Mean ◽  
Parameter Ranges

Modeling the dynamics of neural masses is a common approach in the study of neural populations. Various models have been proven useful to describe a plenitude of empirical observations including self-sustained local oscillations and patterns of distant synchronization. We discuss the extent to which mass models really resemble the mean dynamics of a neural population. In particular, we question the validity of neural mass models if the population under study comprises a mixture of excitatory and inhibitory neurons that are densely (inter-)connected. Starting from a network of noisy leaky integrate-and-fire neurons, we formulated two different population dynamics that both fall into the category of seminal Freeman neural mass models. The derivations contained several mean-field assumptions and time scale separation(s) between membrane and synapse dynamics. Our comparison of these neural mass models with the averaged dynamics of the population reveals bounds in the fraction of excitatory/inhibitory neuron as well as overall network degree for a mass model to provide adequate estimates. For substantial parameter ranges, our models fail to mimic the neural network's dynamics proper, be that in de-synchronized or in (high-frequency) synchronized states. Only around the onset of low-frequency synchronization our models provide proper estimates of the mean potential dynamics. While this shows their potential for, e.g., studying resting state dynamics obtained by encephalography with focus on the transition region, we must accept that predicting the more general dynamic outcome of a neural network via its mass dynamics requires great care.

A Dynamical Systems Approach to Stability Tracking of Treadmill Running

2008 ◽  
Author(s):  
Christopher S. Adam ◽  
Ian R. Berry ◽  
Kevin M. Short ◽  
Diana I. Saly
Keyword(s):  
Dynamical Systems ◽  
Nearest Neighbor ◽  
Systems Approach ◽  
Three Dimensional ◽  
Low Frequency ◽  
Temporal Variations ◽  
Gait Pattern ◽  
Treadmill Running ◽  
Reference Orbit ◽  
The Mean

Traditional analysis of running gait utilizes averaged biomechanical data from several strides to generate a mean curve. This curve is then used to define the average picture of a runners gait. However, such measures are frequently accompanied by time normalization, which results in a loss of temporal variations in the gait patterns. An examination of stability requires analysis of both time and position, therefore loss of such information makes stability analysis difficult. On the contrary, the use of a dynamical systems approach for gait analysis allows for a better understanding of how variations in gait pattern change over time. In the current study runners ran on a treadmill, with both a flat and uneven surface, at a self selected speed. Three-dimensional position data was captured for 11 different anatomical locations at a frequency of 120 Hz using a Qualysis motion capture system. The data was first shifted to a lumbar coordinate system to account for low frequency drift attributed to the subjects’ drift on the treadmill. Since all of the markers were rigidly connected, via the subject, the movements and variations of certain components of the 33-dimensional measurements were not independent. As a result, it was possible to reduce the dimensionality of the transformed data using singular value decomposition techniques. The primary components were then analyzed using the method of delay embeddings to extract geometric information, revealing the natural structure found in the data as a result of the periodicity of each running stride. A nearest neighbor mean stride orbit was then computed to create a reference orbit, so that deviations from the mean stride orbit can be measured. The expectation was that a more stable running configuration would lead to smaller deviations from the mean stride orbit. On-going work that will be reported includes: (i) analysis of running stability related to the reference stride comparator, (ii) compensation of lumbar centroid dynamics, (iii) reconstructions using one dimension from the lumbar centroid transformed data, and (iv) consideration of transients, fatigue, adaptation, etc.

A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

2009 ◽  
Vol 623 ◽  
pp. 283-316 ◽  
Author(s):  
DIRK M. LUCHTENBURG ◽  
BERT GÜNTHER ◽  
BERND R. NOACK ◽  
RUDIBERT KING ◽  
GILEAD TADMOR
Keyword(s):  
High Frequency ◽  
Field Model ◽  
Mean Field ◽  
Low Frequency ◽  
Navier Stokes ◽  
Mean Field Model ◽  
High Lift ◽  
The Mean ◽  
Generalized Mean ◽  
Low Dimensional

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier–Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

scholarly journals UNIFIED TREATMENT OF A+B→0 AND A+A→0 CHEMICAL REACTIONS THROUGH THOMPSON'S APPROACH

1999 ◽  
Vol 13 (22n23) ◽  
pp. 829-836 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Chemical Reactions ◽  
Mean Field ◽  
Reaction Rates ◽  
Rigorous Results ◽  
Critical Dimensions ◽  
Long Wavelength ◽  
Diffusion Limited ◽  
First Case ◽  
Long Time ◽  
The Mean

In this work we propose an action to describe diffusion limited chemical reactions belonging to various classes of universality. This action is treated through Thompson's approach and can encompass both cases where we have segregation as in the A + B →0 reaction, as well as the simplest one, namely the A + A →0 reaction. Our results for long-time and long-wavelength behaviors of the species concentrations and reaction rates agree with exact results of Peliti for A + A →0 reaction and rigorous results of Bramson and Lebowitz for A + B →0 reaction, with equal initial concentrations. The different classes of universality are reflected by the obtained upper critical dimensions varying continuously from d c =2 in the first case to d c =4 in the last one. Just as at the upper critical dimensions, we find universal logarithmic corrections to the mean field behavior.

BOSE-FERMI TRANSMUTATION 2+1 DIMENSIONS: EFFECT OF SELF-INTERACTIONS AND THE MAXWELL TERM

1991 ◽  
Vol 06 (26) ◽  
pp. 2379-2387 ◽  
Author(s):  
R. SHANKAR ◽  
M. SIVAKUMAR
Keyword(s):  
Mean Field ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Abelian Gauge ◽  
Charged Scalar ◽  
Long Wavelength ◽  
Wavelength Approximation ◽  
The Mean ◽  
Chern Simons ◽  
Fermion Current

We show the partition function of self-interacting charged scalar fields coupled with Abelian gauge fields governed by Maxwell-Chern-Simons action is equivalent in the long-wavelength approximation to that of a massive four-Fermi theory. The coupling constants and mass of the fermionic theory is explicitly related to those of the bosonic theory. The gauge invariant charged scalar current is shown to be transmuted to fermion current. The physical mass of the fermion is computed at the mean field level and shown to be finite at large self-coupling.

GAUGE THEORY OF ANTIFERROMAGNETISM IN TWO DIMENSIONS FOR LARGE RANK SYMMETRY GROUP

1990 ◽  
Vol 04 (01) ◽  
pp. 17-28 ◽  
Author(s):  
D. V. KHVESHCHENKO ◽  
P. B. WIEGMANN
Keyword(s):  
Gauge Theory ◽  
Symmetry Group ◽  
Mean Field ◽  
Two Dimensions ◽  
Magnetic Systems ◽  
Large Rank ◽  
Long Wavelength ◽  
The Mean ◽  
Chern Simons ◽  
Spin And Statistics

We examine long wavelength fluctuations in two-dimensional magnetic systems with the symmetry group of a large rank N. The mean field solution is obtained and the existence of the parity-violating ground state is established. On the basis of the 1/N expansion, an effective gauge theory containing the Chern-Simons term is derived, which allows one to obtain a spectrum, spin and statistics of long wavelength excitations.

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

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