6,857 research outputs found
Survival of a diffusing particle in an expanding cage
We consider a Brownian particle, with diffusion constant D, moving inside an
expanding d-dimensional sphere whose surface is an absorbing boundary for the
particle. The sphere has initial radius L_0 and expands at a constant rate c.
We calculate the joint probability density, p(r,t|r_0), that the particle
survives until time t, and is at a distance r from the centre of the sphere,
given that it started at a distance r_0 from the centre.Comment: 5 page
Spin glasses in the limit of an infinite number of spin components
We consider the spin glass model in which the number of spin components, m,
is infinite. In the formulation of the problem appropriate for numerical
calculations proposed by several authors, we show that the order parameter
defined by the long-distance limit of the correlation functions is actually
zero and there is only "quasi long range order" below the transition
temperature. We also show that the spin glass transition temperature is zero in
three dimensions.Comment: 9 pages, 13 figure
Phase-ordering of conserved vectorial systems with field-dependent mobility
The dynamics of phase-separation in conserved systems with an O(N) continuous
symmetry is investigated in the presence of an order parameter dependent
mobility M(\phi)=1-a \phi^2. The model is studied analytically in the framework
of the large-N approximation and by numerical simulations of the N=2, N=3 and
N=4 cases in d=2, for both critical and off-critical quenches. We show the
existence of a new universality class for a=1 characterized by a growth law of
the typical length L(t) ~ t^{1/z} with dynamical exponent z=6 as opposed to the
usual value z=4 which is recovered for a<1.Comment: RevTeX, 8 pages, 13 figures, to be published in Phys. Rev.
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Publication rates on the topic of racial and ethnic diversity in dermatology versus other specialties
Background: The population of the U.S. is becoming more diverse every year. The field of dermatology is not following the same trend. Objective: To assess the promotion of diversity in the field of dermatology by analyzing publications focused on diversity, compared to other specialties. Methods: The PubMed database was systematically searched to identify publications focused on diversity from January 2008 to July 2019. The search criteria were as follows: dermatology/radiology/ophthalmology/ anesthesiology/orthopedic surgery/family medicine/ internal medicine/general surgery AND diversity/ diverse/racial/race/ethnic/ethnicity/cultural/culture/competency/competence. Comparisons were made using single-factor ANOVA and two-group t-tests. A qualitative analysis was performed for publications in the field of dermatology. Results: From January 2016 to July 2019, there were 25 publications focused on diversity in dermatology (Mean=6.25, SD=2.06), compared to 6 in radiology (Mean=1.50, SD=1.29, P=0.01), two in ophthalmology (Mean=0.50, SD=0.58, P=0.01), two in anesthesiology (Mean=0.50, SD=1.00, P=0.01), 12 in orthopedic surgery (Mean=3.00, SD=1.41, P=0.04), 23 in family medicine (Mean=5.75, SD=2.22, P=0.75), 9 in internal medicine (Mean=2.25, SD=1.71, P=0.02), and 7 in general surgery (Mean=1.75, SD=0.50, P=0.02). Conclusions: Although the field of dermatology has suffered from a lack of racial/ethnic diversity, efforts to promote diversity via increased publications in the last four years have been stronger in dermatology compared to many other fields
On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
Finite-size scaling (FSS) is a standard technique for measuring scaling
exponents in spin glasses. Here we present a critique of this approach,
emphasizing the need for all length scales to be large compared to microscopic
scales. In particular we show that the replacement, in FSS analyses, of the
correlation length by its asymptotic scaling form can lead to apparently good
scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page
The Stability of the Replica Symmetric State in Finite Dimensional Spin Glasses
According to the droplet picture of spin glasses, the low-temperature phase
of spin glasses should be replica symmetric. However, analysis of the stability
of this state suggested that it was unstable and this instability lends support
to the Parisi replica symmetry breaking picture of spin glasses. The
finite-size scaling functions in the critical region of spin glasses below T_c
in dimensions greater than 6 can be determined and for them the replica
symmetric solution is unstable order by order in perturbation theory.
Nevertheless the exact solution can be shown to be replica-symmetric. It is
suggested that a similar mechanism might apply in the low-temperature phase of
spin glasses in less than six dimensions, but that a replica symmetry broken
state might exist in more than six dimensions.Comment: 5 pages. Modified to include a paragraph on the relation of this work
to that of Newman and Stei
Mean-field theory for a spin-glass model of neural networks: TAP free energy and paramagnetic to spin-glass transition
An approach is proposed to the Hopfield model where the mean-field treatment
is made for a given set of stored patterns (sample) and then the statistical
average over samples is taken. This corresponds to the approach made by
Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin
glasses. Taking into account the fact that in the Hopfield model there exist
correlations between different elements of the interaction matrix, we obtain
its TAP free energy explicitly, which consists of a series of terms exhibiting
the cluster effect. Nature of the spin-glass transition in the model is also
examined and compared with those given by the replica method as well as the
cavity method.Comment: 12 pages, LaTex, 1 PostScript figur
Growth Laws for Phase Ordering
We determine the characteristic length scale, , in phase ordering
kinetics for both scalar and vector fields, with either short- or long-range
interactions, and with or without conservation laws. We obtain
consistently by comparing the global rate of energy change to the energy
dissipation from the local evolution of the order parameter. We derive growth
laws for O(n) models, and our results can be applied to other systems with
similar defect structures.Comment: 12 pages, LaTeX, second tr
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