2,207 research outputs found
Exact Lyapunov Exponent for Infinite Products of Random Matrices
In this work, we give a rigorous explicit formula for the Lyapunov exponent
for some binary infinite products of random real matrices. All
these products are constructed using only two types of matrices, and ,
which are chosen according to a stochastic process. The matrix is singular,
namely its determinant is zero. This formula is derived by using a particular
decomposition for the matrix , which allows us to write the Lyapunov
exponent as a sum of convergent series. Finally, we show with an example that
the Lyapunov exponent is a discontinuous function of the given parameter.Comment: 1 pages, CPT-93/P.2974,late
Scaling Behaviour and Complexity of the Portevin-Le Chatelier Effect
The plastic deformation of dilute alloys is often accompanied by plastic
instabilities due to dynamic strain aging and dislocation interaction. The
repeated breakaway of dislocations from and their recapture by solute atoms
leads to stress serrations and localized strain in the strain controlled
tensile tests, known as the Portevin-Le Chatelier (PLC) effect. In this present
work, we analyse the stress time series data of the observed PLC effect in the
constant strain rate tensile tests on Al-2.5%Mg alloy for a wide range of
strain rates at room temperature. The scaling behaviour of the PLC effect was
studied using two complementary scaling analysis methods: the finite variance
scaling method and the diffusion entropy analysis. From these analyses we could
establish that in the entire span of strain rates, PLC effect showed Levy walk
property. Moreover, the multiscale entropy analysis is carried out on the
stress time series data observed during the PLC effect to quantify the
complexity of the distinct spatiotemporal dynamical regimes. It is shown that
for the static type C band, the entropy is very low for all the scales compared
to the hopping type B and the propagating type A bands. The results are
interpreted considering the time and length scales relevant to the effect.Comment: 35 pages, 6 figure
Charge-Fluctuation-Induced Non-analytic Bending Rigidity
In this Letter, we consider a neutral system of mobile positive and negative
charges confined on the surface of curved films. This may be an appropriate
model for: i) a highly charged membrane whose counterions are confined to a
sheath near its surface; ii) a membrane composed of an equimolar mixture of
anionic and cationic surfactants in aqueous solution. We find that the charge
fluctuations contribute a non-analytic term to the bending rigidity that varies
logarithmically with the radius of curvature. This may lead to spontaneous
vesicle formation, which is indeed observed in similar systems.Comment: Revtex, 9 pages, no figures, submitted to PR
Fluctuations of a driven membrane in an electrolyte
We develop a model for a driven cell- or artificial membrane in an
electrolyte. The system is kept far from equilibrium by the application of a DC
electric field or by concentration gradients, which causes ions to flow through
specific ion-conducting units (representing pumps, channels or natural pores).
We consider the case of planar geometry and Debye-H\"{u}ckel regime, and obtain
the membrane equation of motion within Stokes hydrodynamics. At steady state,
the applied field causes an accumulation of charges close to the membrane,
which, similarly to the equilibrium case, can be described with renormalized
membrane tension and bending modulus. However, as opposed to the equilibrium
situation, we find new terms in the membrane equation of motion, which arise
specifically in the out-of-equilibrium case. We show that these terms lead in
certain conditions to instabilities.Comment: 7 pages, 2 figures. submitted to Europhys. Let
Screening by symmetry of long-range hydrodynamic interactions of polymers confined in sheets
Hydrodynamic forces may significantly affect the motion of polymers. In
sheet-like cavities, such as the cell's cytoplasm and microfluidic channels,
the hydrodynamic forces are long-range. It is therefore expected that that
hydrodynamic interactions will dominate the motion of polymers in sheets and
will be manifested by Zimm-like scaling. Quite the opposite, we note here that
although the hydrodynamic forces are long-range their overall effect on the
motion of polymers vanishes due to the symmetry of the two-dimensional flow. As
a result, the predicted scaling of experimental observables such as the
diffusion coefficient or the rotational diffusion time is Rouse-like, in accord
with recent experiments. The effective screening validates the use of the
non-interacting blobs picture for polymers confined in a sheet.Comment: http://www.weizmann.ac.il/complex/tlusty/papers/Macromolecules2006.pdf
http://pubs.acs.org/doi/abs/10.1021/ma060251
Long-Ranged Orientational Order in Dipolar Fluids
Recently Groh and Dietrich claimed the thermodynamic state of a dipolar fluid
depends on the shape of the fluid's container. For example, a homogeneous fluid
in a short fat container would phase separate when transferred to a tall skinny
container of identical volume and temperature. Their calculation thus lacks a
thermodynamic limit. We show that removal of demagnetizing fields restores the
true, shape independent, thermodynamic limit. As a consequence, spontaneously
magnetized liquids display inhomogeneous magnetization textures.Comment: 3 pages, LaTex, no figures. Submitted as comment to PRL, May 199
Charge Fluctuations on Membrane Surfaces in Water
We generalize the predictions for attractions between over-all neutral
surfaces induced by charge fluctuations/correlations to non-uniform systems
that include dielectric discontinuities, as is the case for mixed charged lipid
membranes in an aqueous solution. We show that the induced interactions depend
in a non-trivial way on the dielectric constants of membrane and water and show
different scaling with distance depending on these properties. The generality
of the calculations also allows us to predict under which dielectric conditions
the interaction will change sign and become repulsive
Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation
The fractal structure of directed percolation clusters, grown at the
percolation threshold inside parabolic-like systems, is studied in two
dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a
dynamical exponent z, the surface shape is a relevant perturbation when k<1/z
and the fractal dimensions of the anisotropic clusters vary continuously with
k. Analytic expressions for these variations are obtained using a blob picture
approach.Comment: 6 pages, Plain TeX file, epsf, 3 postscript-figure
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