19,208 research outputs found
Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem
We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise
correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho
and the spatial dimension d. By means of a stochastic Cole-Hopf transformation,
the critical and correction-to-scaling exponents at the roughening transition
are determined to all orders in a (d - d_c) expansion. We also argue that there
is a intriguing possibility that the rough phases above and below the lower
critical dimension d_c = 2 (1 + \rho) are genuinely different which could lead
to a re-interpretation of results in the literature.Comment: Latex, 7 pages, eps files for two figures as well as Europhys. Lett.
style files included; slightly expanded reincarnatio
Correlation of eigenstates in the critical regime of quantum Hall systems
We extend the multifractal analysis of the statistics of critical wave
functions in quantum Hall systems by calculating numerically the correlations
of local amplitudes corresponding to eigenstates at two different energies. Our
results confirm multifractal scaling relations which are different from those
occurring in conventional critical phenomena. The critical exponent
corresponding to the typical amplitude, , gives an almost
complete characterization of the critical behavior of eigenstates, including
correlations. Our results support the interpretation of the local density of
states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure
On Critical Exponents and the Renormalization of the Coupling Constant in Growth Models with Surface Diffusion
It is shown by the method of renormalized field theory that in contrast to a
statement based on a mathematically ill-defined invariance transformation and
found in most of the recent publications on growth models with surface
diffusion, the coupling constant of these models renormalizes nontrivially.
This implies that the widely accepted supposedly exact scaling exponents are to
be corrected. A two-loop calculation shows that the corrections are small and
these exponents seem to be very good approximations.Comment: 4 pages, revtex, 2 postscript figures, to appear in Phys.Rev.Let
Finite-size scaling of directed percolation above the upper critical dimension
We consider analytically as well as numerically the finite-size scaling
behavior in the stationary state near the non-equilibrium phase transition of
directed percolation within the mean field regime, i.e., above the upper
critical dimension. Analogous to equilibrium, usual finite-size scaling is
valid below the upper critical dimension, whereas it fails above. Performing a
momentum analysis of associated path integrals we derive modified finite-size
scaling forms of the order parameter and its higher moments. The results are
confirmed by numerical simulations of corresponding high-dimensional lattice
models.Comment: 4 pages, one figur
Canonical phase space approach to the noisy Burgers equation
Presenting a general phase approach to stochastic processes we analyze in
particular the Fokker-Planck equation for the noisy Burgers equation and
discuss the time dependent and stationary probability distributions. In one
dimension we derive the long-time skew distribution approaching the symmetric
stationary Gaussian distribution. In the short time regime we discuss
heuristically the nonlinear soliton contributions and derive an expression for
the distribution in accordance with the directed polymer-replica model and
asymmetric exclusion model results.Comment: 4 pages, Revtex file, submitted to Phys. Rev. Lett. a reference has
been added and a few typos correcte
Risk factors for ischemic stroke and transient ischemic attack in patients under age 50
To analyze risk factors for ischemic stroke and transient ischemic attack (TIA) in young adults under the age of 50. To make recommendations for additional research and practical consequences. From 97 patients with ischemic stroke or TIA under the age of 50, classical cardiovascular risk factors, coagulation disorders, history of migraine, use of oral contraceptives, cardiac abnormalities on ECG and echocardiography, and the results of duplex ultrasound were retrospectively analyzed. Literature was reviewed and compared to the results. 56.4% of the patients had hypertension, 12.1% increased total cholesterol, 20% hypertriglyceridemia, 31.5% an increased LDL-level, 32.6% a decreased HDL-level and 7.2% a disturbed glucose tolerance. Thrombophilia investigation was abnormal in 21 patients and auto-immune serology was abnormal in 15 patients. Ten of these patients were already known with a systemic disease associated with an increased risk for ischemic stroke (i.e. systemic lupus erythematosus). The ECG was abnormal in 16.7% of the cases, the echocardiography in 12.1% and duplex ultrasound of the carotid arteries was in 31.8% of the cases abnormal. Conventional cardiovascular risk factors are not only important in patients over the age of 50 with ischemic stroke or TIA, but also in this younger population under the age of 50. Thrombophilia investigation and/ or autoimmune serology should be restricted to patients without conventional cardiovascular risk factors and a history or other clinical symptoms associated with hypercoagulability and/ or autoimmune diseases
Spreading with immunization in high dimensions
We investigate a model of epidemic spreading with partial immunization which
is controlled by two probabilities, namely, for first infections, , and
reinfections, . When the two probabilities are equal, the model reduces to
directed percolation, while for perfect immunization one obtains the general
epidemic process belonging to the universality class of dynamical percolation.
We focus on the critical behavior in the vicinity of the directed percolation
point, especially in high dimensions . It is argued that the clusters of
immune sites are compact for . This observation implies that a
recently introduced scaling argument, suggesting a stretched exponential decay
of the survival probability for , in one spatial dimension,
where denotes the critical threshold for directed percolation, should
apply in any dimension and maybe for as well. Moreover, we
show that the phase transition line, connecting the critical points of directed
percolation and of dynamical percolation, terminates in the critical point of
directed percolation with vanishing slope for and with finite slope for
. Furthermore, an exponent is identified for the temporal correlation
length for the case of and , , which
is different from the exponent of directed percolation. We also
improve numerical estimates of several critical parameters and exponents,
especially for dynamical percolation in .Comment: LaTeX, IOP-style, 18 pages, 9 eps figures, minor changes, additional
reference
Quasiperiodic Modulated-Spring Model
We study the classical vibration problem of a chain with spring constants
which are modulated in a quasiperiodic manner, {\it i. e.}, a model in which
the elastic energy is , where and is an irrational number. For
, it is shown analytically that the spectrum is absolutely
continuous, {\it i.e.}, all the eigen modes are extended. For ,
numerical scaling analysis shows that the spectrum is purely singular
continuous, {\it i.e.}, all the modes are critical.Comment: REV TeX fil
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