20,290 research outputs found
Dynamical transition for a particle in a squared Gaussian potential
We study the problem of a Brownian particle diffusing in finite dimensions in
a potential given by where is Gaussian random field.
Exact results for the diffusion constant in the high temperature phase are
given in one and two dimensions and it is shown to vanish in a power-law
fashion at the dynamical transition temperature. Our results are confronted
with numerical simulations where the Gaussian field is constructed, in a
standard way, as a sum over random Fourier modes. We show that when the number
of Fourier modes is finite the low temperature diffusion constant becomes
non-zero and has an Arrhenius form. Thus we have a simple model with a fully
understood finite size scaling theory for the dynamical transition. In addition
we analyse the nature of the anomalous diffusion in the low temperature regime
and show that the anomalous exponent agrees with that predicted by a trap
model.Comment: 18 pages, 4 figures .eps, JPA styl
Poissonian bursts in e-mail correspondence
Recent work has shown that the distribution of inter-event times for e-mail
communication exhibits a heavy tail which is statistically consistent with a
cascading Poisson process. In this work we extend the analysis to higher-order
statistics, using the Fano and Allan factors to quantify the extent to which
the empirical data depart from the known correlations of Poissonian statistics.
The analysis shows that the higher-order statistics from the empirical data is
indistinguishable from that of randomly reordered time series, thus
demonstrating that e-mail correspondence is no more bursty or correlated than a
Poisson process. Furthermore synthetic data sets generated by a cascading
Poisson process replicate the burstiness and correlations observed in the
empirical data. Finally, a simple rescaling analysis using the best-estimate
rate of activity, confirms that the empirically observed correlations arise
from a non-homogeneus Poisson process
Diffusion of active tracers in fluctuating fields
The problem of a particle diffusion in a fluctuating scalar field is studied.
In contrast to most studies of advection diffusion in random fields we analyze
the case where the particle position is also coupled to the dynamics of the
field. Physical realizations of this problem are numerous and range from the
diffusion of proteins in fluctuating membranes and the diffusion of localized
magnetic fields in spin systems. We present exact results for the diffusion
constant of particles diffusing in dynamical Gaussian fields in the adiabatic
limit where the field evolution is much faster than the particle diffusion. In
addition we compute the diffusion constant perturbatively, in the weak coupling
limit where the interaction of the particle with the field is small, using a
Kubo-type relation. Finally we construct a simple toy model which can be solved
exactly.Comment: 13 pages, 1 figur
Perturbation theory for the effective diffusion constant in a medium of random scatterer
We develop perturbation theory and physically motivated resummations of the
perturbation theory for the problem of a tracer particle diffusing in a random
media. The random media contains point scatterers of density uniformly
distributed through out the material. The tracer is a Langevin particle
subjected to the quenched random force generated by the scatterers. Via our
perturbative analysis we determine when the random potential can be
approximated by a Gaussian random potential. We also develop a self-similar
renormalisation group approach based on thinning out the scatterers, this
scheme is similar to that used with success for diffusion in Gaussian random
potentials and agrees with known exact results. To assess the accuracy of this
approximation scheme its predictions are confronted with results obtained by
numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style
Childhood maltreatment and amygdala connectivity in methamphetamine dependence: a pilot study.
IntroductionChildhood maltreatment, a well-known risk factor for the development of substance abuse disorders, is associated with functional and structural abnormalities in the adult brain, particularly in the limbic system. However, almost no research has examined the relationship between childhood maltreatment and brain function in individuals with drug abuse disorders.MethodsWe conducted a pilot study of the relationship between childhood maltreatment (evaluated with the Childhood Trauma Questionnaire; Bernstein and Fink 1998) and resting-state functional connectivity of the amygdala (bilateral region of interest) with functional magnetic resonance imaging in 15 abstinent, methamphetamine-dependent research participants. Within regions that showed connectivity with the amygdala as a function of maltreatment, we also evaluated whether amygdala connectivity was associated positively with negative affect and negatively with healthy emotional processing.ResultsThe results indicated that childhood maltreatment was positively associated with resting-state connectivity between the amygdala and right hippocampus, right parahippocampal gyrus, right inferior temporal gyrus, right orbitofrontal cortex, cerebellum, and brainstem. Furthermore, connectivity between the amygdala and hippocampus was positively related to measures of depression, trait anxiety, and emotion dysregulation, and negatively related to self-compassion and dispositional mindfulness.ConclusionsThese findings suggest that childhood maltreatment may contribute to increased limbic connectivity and maladaptive emotional processing in methamphetamine-dependent adults, and that healthy emotion regulation strategies may serve as a therapeutic target to ameliorate the associated behavioral phenotype. Childhood maltreatment warrants further investigation as a potentially important etiological factor in the neurobiology and treatment of substance use disorders
Shell Model Monte Carlo method in the -formalism and applications to the Zr and Mo isotopes
We report on the development of a new shell-model Monte Carlo algorithm which
uses the proton-neutron formalism. Shell model Monte Carlo methods, within the
isospin formulation, have been successfully used in large-scale shell-model
calculations. Motivation for this work is to extend the feasibility of these
methods to shell-model studies involving non-identical proton and neutron
valence spaces. We show the viability of the new approach with some test
results. Finally, we use a realistic nucleon-nucleon interaction in the model
space described by (1p_1/2,0g_9/2) proton and
(1d_5/2,2s_1/2,1d_3/2,0g_7/2,0h_11/2) neutron orbitals above the Sr-88 core to
calculate ground-state energies, binding energies, B(E2) strengths, and to
study pairing properties of the even-even 90-104 Zr and 92-106 Mo isotope
chains
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