1,219 research outputs found
Microscopic theory for the glass transition in a system without static correlations
We study the orientational dynamics of infinitely thin hard rods of length L,
with the centers-of-mass fixed on a simple cubic lattice with lattice constant
a.We approximate the influence of the surrounding rods onto dynamics of a pair
of rods by introducing an effective rotational diffusion constant D(l),l=L/a.
We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a
time-dependent torque-torque correlator of an isolated pair of rods. A glass
transition occurs at l_c, if v(l_c)=1. We present a variational and a
numerically exact evaluation of v(l).Close to l_c the diffusion constant
decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a
glass transition in the absence of any static correlations, in contrast to
present form of mode coupling theory.Comment: 6 pages, 3 figure
Short Time Behavior in De Gennes' Reptation Model
To establish a standard for the distinction of reptation from other modes of
polymer diffusion, we analytically and numerically study the displacement of
the central bead of a chain diffusing through an ordered obstacle array for
times . Our theory and simulations agree quantitatively and show
that the second moment approaches the often viewed as signature of
reptation only after a very long transient and only for long chains (N > 100).
Our analytically solvable model furthermore predicts a very short transient for
the fourth moment. This is verified by computer experiment.Comment: 4 pages, revtex, 4 ps file
Critical behaviour of the Rouse model for gelling polymers
It is shown that the traditionally accepted "Rouse values" for the critical
exponents at the gelation transition do not arise from the Rouse model for
gelling polymers. The true critical behaviour of the Rouse model for gelling
polymers is obtained from spectral properties of the connectivity matrix of the
fractal clusters that are formed by the molecules. The required spectral
properties are related to the return probability of a "blind ant"-random walk
on the critical percolating cluster. The resulting scaling relations express
the critical exponents of the shear-stress-relaxation function, and hence those
of the shear viscosity and of the first normal stress coefficient, in terms of
the spectral dimension of the critical percolating cluster and the
exponents and of the cluster-size distribution.Comment: 9 pages, slightly extended version, to appear in J. Phys.
Dynamics of gelling liquids: a short survey
The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a
Zimm-type model with crosslink statistics taken either from bond percolation or
Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of
the random connectivity on the dynamics of molecular clusters, the Zimm-type
model also accounts for hydrodynamic interactions on a preaveraged level. The
incoherent intermediate scattering function is computed in thermal equilibrium,
its critical behaviour near the sol-gel transition is analysed and related to
the scaling of cluster diffusion constants at the critical point. Second,
non-equilibrium dynamics is studied by looking at stress relaxation in a simple
shear flow. Anomalous stress relaxation and critical rheological properties are
derived. Some of the results contradict long-standing scaling arguments, which
are shown to be flawed by inconsistencies.Comment: 21 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of
his 60th birthday; Changes: added comments on the gel phase and some
reference
Prophet Inequalities for IID Random Variables from an Unknown Distribution
A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: given a sequence of random variables X1, . . . , Xn drawn independently from a distribution F , the goal is to choose a stopping time Ï so as to maximize α such that for all distributions F we have E[XÏ ] ℠α · E[maxt Xt ]. What makes this problem challenging is that the decision whether Ï = t may only depend on the values of the random variables X1, . . . , Xt and on the distribution F . For a long time the best known bound for the problem had been α â„ 1 â 1/e â 0.632, but quite recently a tight bound of α â 0.745 was obtained. The case where F is unknown, such that the decision whether Ï = t may depend only on the values of the random variables X1, . . . , Xt , is equally well motivated but has received much less attention. A straightforward guarantee for this case of α â„ 1/e â 0.368 can be derived from the solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F , and show that even with o(n) samples α †1/e. On the other hand, n samples allow for a significant improvement, while O(n2) samples are equivalent to knowledge of the distribution: specifically, with n samples α â„ 1 â 1/e â 0.632 and α †ln(2) â 0.693, and with O(n2) samples α â„ 0.745 â Δ for any Δ > 0
Effects of differential mobility on biased diffusion of two species
Using simulations and a simple mean-field theory, we investigate jamming
transitions in a two-species lattice gas under non-equilibrium steady-state
conditions. The two types of particles diffuse with different mobilities on a
square lattice, subject to an excluded volume constraint and biased in opposite
directions. Varying filling fraction, differential mobility, and drive, we map
out the phase diagram, identifying first order and continuous transitions
between a free-flowing disordered and a spatially inhomogeneous jammed phase.
Ordered structures are observed to drift, with a characteristic velocity, in
the direction of the more mobile species.Comment: 15 pages, 4 figure
Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy
Inertial-range scaling behavior of high-order (up to order N=51) structure
functions of a passively advected vector field has been analyzed in the
framework of the rapid-change model with strong small-scale anisotropy with the
aid of the renormalization group and the operator-product expansion. It has
been shown that in inertial range the leading terms of the structure functions
are coordinate independent, but powerlike corrections appear with the same
anomalous scaling exponents as for the passively advected scalar field. These
exponents depend on anisotropy parameters in such a way that a specific
hierarchy related to the degree of anisotropy is observed. Deviations from
power-law behavior like oscillations or logarithmic behavior in the corrections
to structure functions have not been found.Comment: 15 pages, 18 figure
Biofeedback fixation training method for improving eccentric vision in patients with loss of foveal function secondary to different maculopathies
© 2019, The Author(s). Purpose: Fixation stability (FS) of the preferred retinal locus (PRL) may be improved by biofeedback fixation training (BFT) with microperimetry. Such training can be done on the patientâs PRL or in different retinal loci with better functional characteristics. We studied both options and compared the outcomes. Methods: Sixty-seven consecutive patients with bilateral central vision loss, poor FS and visual acuity (VA) lower than 0.3 LogMAR were recruited for BFT with microperimeter. Patients were assigned into 2 groups. In group A, BFT was performed on the patientâs spontaneous PRL. In group B, PRL was located between 2 adjacent loci with the highest light sensitivity and the lowest distance from the fovea. Two sets of 12 weekly BFT sessions were performed. Primary outcomes were: FS, VA and reading speed. Results: Outcomes were statistically significantly better in group B. Mean percentage of FS at therapy end improved from 32 to 35% for group A and from 40 to 55% in group B. Mean VA improved from 1 to 0.86 in group A and from 1 to 0.84 in group B. Reading speed (wpm) improved from 56 to 58 in group A and from 63 to 89 in group B. Conclusions: This study describes a reliable methodology of improving eccentric fixation stability using BFT in microperimetry, when the fixation training locus is individualized as the retinal area with best functional characteristics. Further studies are needed to validate its value in a larger scale of patients, at different stages of the disease, and its persistence over time
Gel-Electrophoresis and Diffusion of Ring-Shaped DNA
A model for the motion of ring-shaped DNA in a gel is introduced and studied
by numerical simulations and a mean-field approximation. The ring motion is
mediated by finger-shaped loops (hernias) that move in an amoeba-like fashion
around the gel obstructions. This constitutes an extension of previous
reptation tube treatments. It is shown that tension is essential for describing
the dynamics in the presence of hernias. It is included in the model as long
range interactions over stretched DNA regions. The mobility of ring-shaped DNA
is found to saturate much as in the well-studied case of linear DNA.
Experiments in polymer gels, however, show that the mobility drops
exponentially with the DNA ring size. This is commonly attributed to
dangling-ends in the gel that can impale the ring. The predictions of the
present model are expected to apply to artificial 2D obstacle arrays (W.D.
Volkmuth, R.H. Austin, Nature 358,600 (1992)) which have no dangling-ends. In
the zero-field case an exact solution of the model steady-state is obtained,
and quantities such as the average ring size are calculated. An approximate
treatment of the ring dynamics is given, and the diffusion coefficient is
derived. The model is also discussed in the context of spontaneous symmetry
breaking in one dimension.Comment: 8 figures, LaTeX, Phys. Rev. E - in pres
Sand in the wheels, or oiling the wheels, of international finance? : New Labour's appeal to a 'new Bretton Woods'
Tony Blairâs political instinct typically is to associate himself only with the future. As such, his explicit appeal to âthe pastâ in his references to New Labourâs desire to establish a ânew Bretton Woodsâ is sufficient in itself to arouse some degree of analytical curiosity (see Blair 1998a). The fact that this appeal was made specifically in relation to Bretton Woods is even more interesting. The resonant image of the international economic context established by the original Bretton Woods agreements invokes a style and content of policy-making which Tony Blair typically dismisses as neither economically nor politically consistent with his preferred vision of the future (see Blair 2000c, 2001b)
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