6,781 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
Critical properties of the unconventional spin-Peierls system TiOBr
We have performed detailed x-ray scattering measurements on single crystals
of the spin-Peierls compound TiOBr in order to study the critical properties of
the transition between the incommensurate spin-Peierls state and the
paramagnetic state at Tc2 ~ 48 K. We have determined a value of the critical
exponent beta which is consistent with the conventional 3D universality
classes, in contrast with earlier results reported for TiOBr and TiOCl. Using a
simple power law fit function we demonstrate that the asymptotic critical
regime in TiOBr is quite narrow, and obtain a value of beta_{asy} = 0.32 +/-
0.03 in the asymptotic limit. A power law fit function which includes the first
order correction-to-scaling confluent singularity term can be used to account
for data outside the asymptotic regime, yielding a more robust value of
beta_{avg} = 0.39 +/- 0.05. We observe no evidence of commensurate fluctuations
above Tc1 in TiOBr, unlike its isostructural sister compound TiOCl. In
addition, we find that the incommensurate structure between Tc1 and Tc2 is
shifted in Q-space relative to the commensurate structure below Tc1.Comment: 12 pages, 8 figures. Submitted to Physical Review
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.
The Effects of Prices and Policies on the Demand for Marijuana: Evidence from the National Household Surveys on Drug Abuse
Recent studies have shown that efforts to curb alcohol use by increasing the price of alcohol and limiting youth's access have succeeded, but they may have had the unintended consequencce of increasing marijuana use. This possibility is troubling in light of a recent government report that shows that marijuana use among teens more than doubled between 1990 and 1997. What impact will the proposed large increase in cigarette prices have on the demand for other substances such as marijuana? To better understand how the demand for marijuana responds to changes in the policies and prices that affect its use, we explore the National Household Survy on Drug Abuse (NHSDA). Overall, we find that marijuana, alcohol, and tobacco are complements, sot that increasing the price of any one will decrease the demand for marijuana. The results of this paper will help guide the creation of comprehensive policies that curb the use of marijuana in two ways: first, they quantify the effects of policies aimed at curbing the use of each substance, allowing policymakers to evaluate alternative policy options; and second, they clarify the dynamics and interactions between alcohol, tobacco, and marijuana use in response to government policies.
Commensurate Fluctuations in the Pseudogap and Incommensurate spin-Peierls Phases of TiOCl
X-ray scattering measurements on single crystals of TiOCl reveal the presence
of commensurate dimerization peaks within both the incommensurate spin-Peierls
phase and the so-called pseudogap phase above T_c2. This scattering is
relatively narrow in Q-space indicating long correlation lengths exceeding ~
100 A below T* ~ 130 K. It is also slightly shifted in Q relative to that of
the commensurate long range ordered state at the lowest temperatures, and it
coexists with the incommensurate Bragg peaks below T_c2. The integrated
scattering over both commensurate and incommensurate positions evolves
continuously with decreasing temperature for all temperatures below T* ~ 130 K.Comment: To appear in Physical Review B: Rapid Communications. 5 page
Evidence for the droplet/scaling picture of spin glasses
We have studied the Parisi overlap distribution for the three dimensional
Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T
around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the
full Parisi replica symmetry breaking, just as was also observed in recent
Monte Carlo simulations on a cubic lattice. However, for lower temperatures our
data agree with predictions from the droplet or scaling picture. The failure to
see droplet model behaviour in Monte Carlo simulations is due to the fact that
all existing simulations have been done at temperatures too close to the
transition temperature so that sytem sizes larger than the correlation length
have not been achieved.Comment: 4 pages, 6 figure
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
Suppression of the commensurate spin-Peierls state in Sc-doped TiOCl
We have performed x-ray scattering measurements on single crystals of the
doped spin-Peierls compound Ti(1-x)Sc(x)OCl (x = 0, 0.01, 0.03). These
measurements reveal that the presence of non-magnetic dopants has a profound
effect on the unconventional spin-Peierls behavior of this system, even at
concentrations as low as 1%. Sc-doping suppresses commensurate fluctuations in
the pseudogap and incommensurate spin-Peierls phases of TiOCl, and prevents the
formation of a long-range ordered spin-Peierls state. Broad incommensurate
scattering develops in the doped compounds near Tc2 ~ 93 K, and persists down
to base temperature (~ 7 K) with no evidence of a lock-in transition. The width
of the incommensurate dimerization peaks indicates short correlation lengths on
the order of ~ 12 angstroms below Tc2. The intensity of the incommensurate
scattering is significantly reduced at higher Sc concentrations, indicating
that the size of the associated lattice displacement decreases rapidly as a
function of doping.Comment: 7 pages, 5 figure
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
- …