2,555 research outputs found
Emergence of fractal behavior in condensation-driven aggregation
We investigate a model in which an ensemble of chemically identical Brownian
particles are continuously growing by condensation and at the same time undergo
irreversible aggregation whenever two particles come into contact upon
collision. We solved the model exactly by using scaling theory for the case
whereby a particle, say of size , grows by an amount over the
time it takes to collide with another particle of any size. It is shown that
the particle size spectra of such system exhibit transition to dynamic scaling
accompanied by the emergence of fractal of
dimension . One of the remarkable feature of this
model is that it is governed by a non-trivial conservation law, namely, the
moment of is time invariant regardless of the choice of the
initial conditions. The reason why it remains conserved is explained by using a
simple dimensional analysis. We show that the scaling exponents and
are locked with the fractal dimension via a generalized scaling relation
.Comment: 8 pages, 6 figures, to appear in Phys. Rev.
Diamagnetic Susceptibility and Current Distributions in Granular Superconductors at Percolation
Comments: 4 pages RevTeX, 4 Postscript figures. References added. We study a
two-dimensional granular superconducting network at the percolation threshold
under the influence of an external perpendicular magnetic field. By numerical
simulations on the full nonlinear problem, we determine the scaling exponent
for the magnetic susceptibility. Further, we report on the scaling properties
of the current distribution. The scaling of the current is found to be
independent of the value of the magnetic field. Our results are in
contradiction with previous numerical results based on linearized equations. We
find a value for the susceptibility exponent which does not agree with existing
theoretical suggestions, but agrees perfectly with renormalization group
calculations
Analytical results for a trapped, weakly-interacting Bose-Einstein condensate under rotation
We examine the problem of a repulsive, weakly-interacting and harmonically
trapped Bose-Einstein condensate under rotation. We derive a simple analytic
expression for the energy incorporating the interactions when the angular
momentum per particle is between zero and one and find that the interaction
energy decreases linearly as a function of the angular momentum in agreement
with previous numerical and limiting analytical studies.Comment: 3 pages, RevTe
The Stable Roommates problem with short lists
We consider two variants of the classical Stable Roommates problem with
Incomplete (but strictly ordered) preference lists SRI that are degree
constrained, i.e., preference lists are of bounded length. The first variant,
EGAL d-SRI, involves finding an egalitarian stable matching in solvable
instances of SRI with preference lists of length at most d. We show that this
problem is NP-hard even if d=3. On the positive side we give a
(2d+3)/7-approximation algorithm for d={3,4,5} which improves on the known
bound of 2 for the unbounded preference list case. In the second variant of
SRI, called d-SRTI, preference lists can include ties and are of length at most
d. We show that the problem of deciding whether an instance of d-SRTI admits a
stable matching is NP-complete even if d=3. We also consider the "most stable"
version of this problem and prove a strong inapproximability bound for the d=3
case. However for d=2 we show that the latter problem can be solved in
polynomial time.Comment: short version appeared at SAGT 201
Weakly Interacting Bose-Einstein Condensates Under Rotation: Mean-field versus Exact Solutions
We consider a weakly-interacting, harmonically-trapped Bose-Einstein
condensed gas under rotation and investigate the connection between the
energies obtained from mean-field calculations and from exact diagonalizations
in a subspace of degenerate states. From the latter we derive an approximation
scheme valid in the thermodynamic limit of many particles. Mean-field results
are shown to emerge as the correct leading-order approximation to exact
calculations in the same subspace.Comment: 4 pages, RevTex, submitted to PR
Volatility of Linear and Nonlinear Time Series
Previous studies indicate that nonlinear properties of Gaussian time series
with long-range correlations, , can be detected and quantified by studying
the correlations in the magnitude series , i.e., the ``volatility''.
However, the origin for this empirical observation still remains unclear, and
the exact relation between the correlations in and the correlations in
is still unknown. Here we find analytical relations between the scaling
exponent of linear series and its magnitude series . Moreover, we
find that nonlinear time series exhibit stronger (or the same) correlations in
the magnitude time series compared to linear time series with the same
two-point correlations. Based on these results we propose a simple model that
generates multifractal time series by explicitly inserting long range
correlations in the magnitude series; the nonlinear multifractal time series is
generated by multiplying a long-range correlated time series (that represents
the magnitude series) with uncorrelated time series [that represents the sign
series ]. Our results of magnitude series correlations may help to
identify linear and nonlinear processes in experimental records.Comment: 7 pages, 5 figure
Dynamic instability of a rotating Bose-Einstein condensate
We consider a Bose-Einstein condensate subject to a rotating harmonic
potential, in connection with recent experiments leading to the formation of
vortices. We use the classical hydrodynamic approximation to the non-linear
Schr\"odinger equation to determine almost analytically the evolution of the
condensate. We predict that this evolution can exhibit dynamical instabilities,
for the stirring procedure previously demonstrated at ENS and for a new
stirring procedure that we put forward. These instabilities take place within
the range of stirring frequency and amplitude for which vortices are produced
experimentally. They provide therefore an initiating mechanism for vortex
nucleation.Comment: 4 pages, 3 figures, last version including comparison with
experiment
Stable marriage and roommates problems with restricted edges: complexity and approximability
In the Stable Marriage and Roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually acceptable agents. If any two agents mutually prefer each other to their partner, then they block the matching, otherwise, the matching is said to be stable. We investigate the complexity of finding a solution satisfying additional constraints on restricted pairs of agents. Restricted pairs can be either forced or forbidden. A stable solution must contain all of the forced pairs, while it must contain none of the forbidden pairs.
Dias et al. (2003) gave a polynomial-time algorithm to decide whether such a solution exists in the presence of restricted edges. If the answer is no, one might look for a solution close to optimal. Since optimality in this context means that the matching is stable and satisfies all constraints on restricted pairs, there are two ways of relaxing the constraints by permitting a solution to: (1) be blocked by as few as possible pairs, or (2) violate as few as possible constraints n restricted pairs.
Our main theorems prove that for the (bipartite) Stable Marriage problem, case (1) leads to View the MathML source-hardness and inapproximability results, whilst case (2) can be solved in polynomial time. For non-bipartite Stable Roommates instances, case (2) yields an View the MathML source-hard but (under some cardinality assumptions) 2-approximable problem. In the case of View the MathML source-hard problems, we also discuss polynomially solvable special cases, arising from restrictions on the lengths of the preference lists, or upper bounds on the numbers of restricted pairs
Shape deformations and angular momentum transfer in trapped Bose-Einstein condensates
Angular momentum can be transferred to a trapped Bose-Einstein condensate by
distorting its shape with an external rotating field, provided the rotational
frequency is larger than a critical frequency fixed by the energy and angular
momentum of the excited states of the system. By using the Gross-Pitaevskii
equation and sum rules, we explore the dependence of such a critical frequency
on the multipolarity of the excitations and the asymmetry of the confining
potential. We also discuss its possible relevance for vortex nucleation in
rotating traps.Comment: 4 pages revtex, 2 figures include
Structure of plastically compacting granular packings
The developing structure in systems of compacting ductile grains were studied
experimentally in two and three dimensions. In both dimensions, the peaks of
the radial distribution function were reduced, broadened, and shifted compared
with those observed in hard disk- and sphere systems. The geometrical
three--grain configurations contributing to the second peak in the radial
distribution function showed few but interesting differences between the
initial and final stages of the two dimensional compaction. The evolution of
the average coordination number as function of packing fraction is compared
with other experimental and numerical results from the literature. We conclude
that compaction history is important for the evolution of the structure of
compacting granular systems.Comment: 12 pages, 12 figure
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