11,198 research outputs found
On the future infimum of positive self-similar Markov processes
We establish integral tests and laws of the iterated logarithm for the upper
envelope of the future infimum of positive self-similar Markov processes and
for increasing self-similar Markov processes at 0 and infinity. Our proofs are
based on the Lamperti representation and time reversal arguments due to
Chaumont and Pardo [9]. These results extend laws of the iterated logarithm for
the future infimum of Bessel processes due to Khoshnevisan et al. [11]
Coarsening of Topological Defects in Oscillating Systems with Quenched Disorder
We use large scale simulations to study interacting particles in two
dimensions in the presence of both an ac drive and quenched disorder. As a
function of ac amplitude, there is a crossover from a low drive regime where
the colloid positions are highly disordered to a higher ac drive regime where
the system dynamically reorders. We examine the coarsening of topological
defects formed when the system is quenched from a disordered low ac amplitude
state to a high ac amplitude state. When the quench is performed close to the
disorder-order crossover, the defect density decays with time as a power law
with \alpha = 1/4 to 1/3. For deep quenches, in which the ac drive is increased
to high values such that the dynamical shaking temperature is strongly reduced,
we observe a logarithmic decay of the defect density into a grain boundary
dominated state. We find a similar logarithmic decay of defect density in
systems containing no pinning. We specifically demonstrate these effects for
vortices in thin film superconductors, and discuss implications for dynamical
reordering transition studies in these systems.Comment: 7 pages, 8 postscript figures; this extended version to appear in
Phys. Rev.
- and - Relaxation Dynamics of a fragile plastic crystal
We present a thorough dielectric investigation of the relaxation dynamics of
plastic crystalline Freon112, which exhibits freezing of the orientational
degrees of freedom into a glassy crystal below 90 K. Among other plastic
crystals, Freon112 stands out by being relatively fragile within Angell's
classification scheme and by showing an unusually strong -relaxation.
Comparing the results to those on Freon112a, having only a single molecular
conformation, points to the importance of the presence of two molecular
conformations in Freon112 for the explanation of its unusual properties.Comment: 17 pages, 6 figure
Distributional properties of exponential functionals of Levy processes
We study the distribution of the exponential functional
I(\xi,\eta)=\int_0^{\infty} \exp(\xi_{t-}) \d \eta_t, where and
are independent L\'evy processes. In the general setting using the theories of
Markov processes and Schwartz distributions we prove that the law of this
exponential functional satisfies an integral equation, which generalizes
Proposition 2.1 in Carmona et al "On the distribution and asymptotic results
for exponential functionals of Levy processes". In the special case when
is a Brownian motion with drift we show that this integral equation leads to an
important functional equation for the Mellin transform of , which
proves to be a very useful tool for studying the distributional properties of
this random variable. For general L\'evy process ( being Brownian
motion with drift) we prove that the exponential functional has a smooth
density on , but surprisingly the second derivative at zero
may fail to exist. Under the additional assumption that has some positive
exponential moments we establish an asymptotic behaviour of \p(I(\xi,\eta)>x)
as , and under similar assumptions on the negative exponential
moments of we obtain a precise asympotic expansion of the density of
as . Under further assumptions on the L\'evy process
one is able to prove much stronger results about the density of the
exponential functional and we illustrate some of the ideas and techniques for
the case when has hyper-exponential jumps.Comment: In this version we added a remark after Theorem 1 about extra
conditions required for validity of equation (2.3
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