1,706 research outputs found
Fractional time random walk subdiffusion and anomalous transport with finite mean residence times: faster, not slower
Continuous time random walk (CTRW) subdiffusion along with the associated
fractional Fokker-Planck equation (FFPE) is traditionally based on the premise
of random clock with divergent mean period. This work considers an alternative
CTRW and FFPE description which is featured by finite mean residence times
(MRTs) in any spatial domain of finite size. Transient subdiffusive transport
can occur on a very large time scale which can greatly exceed mean
residence time in any trap, , and even not being related to
it. Asymptotically, on a macroscale transport becomes normal for .
However, mesoscopic transport is anomalous. Differently from viscoelastic
subdiffusion no long-range anti-correlations among position increments are
required. Moreover, our study makes it obvious that the transient subdiffusion
and transport are faster than one expects from their normal asymptotic limit on
a macroscale. This observation has profound implications for anomalous
mesoscopic transport processes in biological cells because of macroscopic
viscosity of cytoplasm is finite
Distinguishing fractional and white noise in one and two dimensions
We discuss the link between uncorrelated noise and Hurst exponent for one and
two-dimensional interfaces. We show that long range correlations cannot be
observed using one-dimensional cuts through two-dimensional self-affine
surfaces whose height distributions are characterized by a Hurst exponent lower
than -1/2. In this domain, fractional and white noise are not distinguishable.
A method analysing the correlations in two dimensions is necessary. For Hurst
exponents larger than -1/2, a crossover regime leads to a systematic over
estimate of the Hurst exponent.Comment: 3 pages RevTeX, 4 Postscript figure
Self-consistent fragmented excited states of trapped condensates
Self-consistent excited states of condensates are solutions of the
Gross-Pitaevskii (GP) equation and have been amply discussed in the literature
and related to experiments. By introducing a more general mean-field which
includes the GP one as a special case, we find a new class of self-consistent
excited states. In these states macroscopic numbers of bosons reside in
different one-particle functions, i.e., the states are fragmented. Still, a
single chemical potential is associated with the condensate. A numerical
example is presented, illustrating that the energies of the new, fragmented,
states are much lower than those of the GP excited states, and that they are
stable to variations of the particle number and shape of the trap potential.Comment: (11 pages 2 figures, submitted to PRL
Rotation of an atomic Bose-Einstein condensate with and without a quantized vortex
We theoretically examine the rotation of an atomic Bose-Einstein condensate
in an elliptical trap, both in the absence and presence of a quantized vortex.
Two methods of introducing the rotating potential are considered -
adiabatically increasing the rotation frequency at fixed ellipticity, and
adiabatically increasing the trap ellipticity at fixed rotation frequency.
Extensive simulations of the Gross-Pitaevskii equation are employed to map out
the points where the condensate becomes unstable and ultimately forms a vortex
lattice. We highlight the key features of having a quantized vortex in the
initial condensate. In particular, we find that the presence of the vortex
causes the instabilities to shift to lower or higher rotation frequencies,
depending on the direction of the vortex relative to the trap rotation.Comment: 15 pages, 8 figure
Double-Slit Interferometry with a Bose-Einstein Condensate
A Bose-Einstein "double-slit" interferometer has been recently realized
experimentally by (Y. Shin et. al., Phys. Rev. Lett. 92 50405 (2004)). We
analyze the interferometric steps by solving numerically the time-dependent
Gross-Pitaevski equation in three-dimensional space. We focus on the
adiabaticity time scales of the problem and on the creation of spurious
collective excitations as a possible source of the strong dephasing observed
experimentally. The role of quantum fluctuations is discussed.Comment: 4 pages, 3 figure
Scale-free network topology and multifractality in weighted planar stochastic lattice
We propose a weighted planar stochastic lattice (WPSL) formed by the random
sequential partition of a plane into contiguous and non-overlapping blocks and
find that it evolves following several non-trivial conservation laws, namely
is independent of time , where
and are the length and width of the th block. Its dual on the
other hand, obtained by replacing each block with a node at its center and
common border between blocks with an edge joining the two vertices, emerges as
a network with a power-law degree distribution where
revealing scale-free coordination number disorder since
also describes the fraction of blocks having neighbours. To quantify the
size disorder, we show that if the th block is populated with then its distribution in the WPSL exhibits multifractality.Comment: 7 pages, 8 figures, To appear in New Journal of Physics (NJP
Critical scaling in standard biased random walks
The spatial coverage produced by a single discrete-time random walk, with
asymmetric jump probability and non-uniform steps, moving on an
infinite one-dimensional lattice is investigated. Analytical calculations are
complemented with Monte Carlo simulations. We show that, for appropriate step
sizes, the model displays a critical phenomenon, at . Its scaling
properties as well as the main features of the fragmented coverage occurring in
the vicinity of the critical point are shown. In particular, in the limit , the distribution of fragment lengths is scale-free, with nontrivial
exponents. Moreover, the spatial distribution of cracks (unvisited sites)
defines a fractal set over the spanned interval. Thus, from the perspective of
the covered territory, a very rich critical phenomenology is revealed in a
simple one-dimensional standard model.Comment: 4 pages, 4 figure
Twin boundaries in d-wave superconductors
Twin boundaries in orthorhombic d-wave superconductors are investigated
numerically using the Bogoliubov-deGennes formalism within the context of an
extended Hubbard model. The twin boundaries are represented by tetragonal
regions of variable width, with a reduced chemical potential. For sufficiently
large twin boundary width and change in chemical potential, an induced s-wave
component may break time-reversal symmetry at a low temperature. This
temperature, and the magnitude of the complex component, are found to depend
strongly on electron density. The results are compared with recent tunneling
measurements.Comment: ReVTeX, 4 pages, 4 postscript figure
Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model
Suspensions of self-propelled particles are studied in the framework of
two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the
effective viscosity of such suspensions in the limit of small concentrations.
This formula includes the two terms that are found in the 2D version of
Einstein's classical result for passive suspensions. To this, the main result
of the paper is added, an additional term due to self-propulsion which depends
on the physical and geometric properties of the active suspension. This term
explains the experimental observation of a decrease in effective viscosity in
active suspensions.Comment: 15 pages, 3 figures, submitted to Physical Biolog
Adsorption of colloidal particles in the presence of external field
We present a new class of sequential adsorption models in which the adsorbing
particles reach the surface following an inclined direction (shadow models).
Capillary electrophoresis, adsorption in the presence of a shear or on an
inclined substrate are physical manifestations of these models. Numerical
simulations are carried out to show how the new adsorption mechanisms are
responsible for the formation of more ordered adsorbed layers and have
important implications in the kinetics, in particular modifying the jamming
limit.Comment: LaTex file, 3 figures available upon request, to appear in
Phys.Rev.Let
- …