2,628 research outputs found
ON THE SPECTRAL THEORY OF SINGULAR INTEGRAL OPERATORS
A complete spectral representation is given for a class of singular integral operators. The influence of spectral multiplicity is partially taken into account. (T.F.H.
Analysis of electroencephalograms in Alzheimer's disease patients with multiscale entropy
The aim of this study was to analyse the electroencephalogram (EEG) background activity of Alzheimer’s disease (AD) patients using the Multiscale Entropy (MSE). The MSE is a recently developed method that quantifies the regularity of a signal on different time scales. These time scales are inspected by means of several coarse-grained sequences formed from the analysed signals. We recorded the EEGs from 19 scalp electrodes in 11 AD patients and 11 age-matched controls and estimated the MSE profile for each epoch of the EEG recordings. The shape of the MSE profiles reveals the EEG complexity, and it suggests that the EEG contains information in deeper scales than the smallest one. Moreover, the results showed that the EEG background activity is less complex in AD patients than control subjects. We found significant difference
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
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
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
Universal reduction of pressure between charged surfaces by long-wavelength surface charge modulation
We predict theoretically that long-wavelength surface charge modulations
universally reduce the pressure between the charged surfaces with counterions
compared with the case of uniformly charged surfaces with the same average
surface charge density. The physical origin of this effect is the fact that
surface charge modulations always lead to enhanced counterion localization near
the surfaces, and hence, fewer charges at the midplane. We confirm the last
prediction with Monte Carlo simulations.Comment: 8 pages 1 figure, Europhys. Lett., in pres
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
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
A formally exact field theory for classical systems at equilibrium
We propose a formally exact statistical field theory for describing classical
fluids with ingredients similar to those introduced in quantum field theory. We
consider the following essential and related problems : i) how to find the
correct field functional (Hamiltonian) which determines the partition function,
ii) how to introduce in a field theory the equivalent of the indiscernibility
of particles, iii) how to test the validity of this approach. We can use a
simple Hamiltonian in which a local functional transposes, in terms of fields,
the equivalent of the indiscernibility of particles. The diagrammatic expansion
and the renormalization of this term is presented. This corresponds to a non
standard problem in Feynman expansion and requires a careful investigation.
Then a non-local term associated with an interaction pair potential is
introduced in the Hamiltonian. It has been shown that there exists a mapping
between this approach and the standard statistical mechanics given in terms of
Mayer function expansion. We show on three properties (the chemical potential,
the so-called contact theorem and the interfacial properties) that in the field
theory the correlations are shifted on non usual quantities. Some perspectives
of the theory are given.Comment: 20 pages, 8 figure
Electrolytic depletion interactions
We consider the interactions between two uncharged planar macroscopic
surfaces immersed in an electrolyte solution which are induced by interfacial
selectivity. These forces are taken into account by introducing a depletion
free-energy density functional, in addition to the usual mean-field
Poisson-Boltzmann functional. The minimization of the total free-energy
functional yields the density profiles of the microions and the electrostatic
potential. The disjoining pressure is obtained by differentiation of the total
free energy with respect to the separation of the surfaces, holding the range
and strength of the depletion forces constant. We find that the induced
interaction between the two surfaces is always repulsive for sufficiently large
separations, and becomes attractive at shorter separations. The nature of the
induced interactions changes from attractive to repulsive at a distance
corresponding to the range of the depletion forces.Comment: 17 pages, 4 Postscript figures, submitted to Physical Review
- …