2,075 research outputs found
A Brownian Model for Crystal Nucleation
In this work a phenomenological stochastic differential equation is proposed
to model the time evolution of the radius of a pre-critical molecular cluster
during nucleation (the classical order parameter). Such a stochastic
differential equation constitutes the basis for the calculation of the
(nucleation) induction time under Kramers' theory of thermally activated escape
processes. Considering the nucleation stage as a Poisson rare-event, analytical
expressions for the induction time statistics are deduced for both steady and
unsteady conditions, the latter assuming the semiadiabatic limit. These
expressions can be used to identify the underlying mechanism of molecular
cluster formation (distinguishing between homogeneous or heterogeneous
nucleation from the nucleation statistics is possible) as well as to predict
induction times and induction time distributions. The predictions of this model
are in good agreement with experimentally measured induction times at constant
temperature, unlike the values obtained from the classical equation, but
agreement is not so good for induction time statistics. Stochastic simulations
truncated to the maximum waiting time of the experiments confirm that this fact
is due to the time constraints imposed by experiments. Correcting for this
effect, the experimental and predicted curves fit remarkably well. Thus, the
proposed model seems to be a versatile tool to predict cluster size
distributions, nucleation rates, (nucleation) induction time and induction time
statistics for a wide range of conditions (e.g. time-dependent temperature,
supersaturation, pH, etc.) where classical nucleation theory is of limited
applicability.Comment: 20 pages, 3 figure
Zero Order Estimates for Analytic Functions
The primary goal of this paper is to provide a general multiplicity estimate.
Our main theorem allows to reduce a proof of multiplicity lemma to the study of
ideals stable under some appropriate transformation of a polynomial ring. In
particular, this result leads to a new link between the theory of polarized
algebraic dynamical systems and transcendental number theory. On the other
hand, it allows to establish an improvement of Nesterenko's conditional result
on solutions of systems of differential equations. We also deduce, under some
condition on stable varieties, the optimal multiplicity estimate in the case of
generalized Mahler's functional equations, previously studied by Mahler,
Nishioka, Topfer and others. Further, analyzing stable ideals we prove the
unconditional optimal result in the case of linear functional systems of
generalized Mahler's type. The latter result generalizes a famous theorem of
Nishioka (1986) previously conjectured by Mahler (1969), and simultaneously it
gives a counterpart in the case of functional systems for an important
unconditional result of Nesterenko (1977) concerning linear differential
systems. In summary, we provide a new universal tool for transcendental number
theory, applicable with fields of any characteristic. It opens the way to new
results on algebraic independence, as shown in Zorin (2010).Comment: 42 page
Vibrations and fractional vibrations of rods, plates and Fresnel pseudo-processes
Different initial and boundary value problems for the equation of vibrations
of rods (also called Fresnel equation) are solved by exploiting the connection
with Brownian motion and the heat equation. The analysis of the fractional
version (of order ) of the Fresnel equation is also performed and, in
detail, some specific cases, like , 1/3, 2/3, are analyzed. By means
of the fundamental solution of the Fresnel equation, a pseudo-process ,
with real sign-varying density is constructed and some of its properties
examined. The equation of vibrations of plates is considered and the case of
circular vibrating disks is investigated by applying the methods of
planar orthogonally reflecting Brownian motion within . The composition of
F with reflecting Brownian motion yields the law of biquadratic heat
equation while the composition of with the first passage time of
produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure
Semiclassical theory of surface plasmons in spheroidal clusters
A microscopic theory of linear response based on the Vlasov equation is
extended to systems having spheroidal equilibrium shape. The solution of the
linearized Vlasov equation, which gives a semiclassical version of the random
phase approximation, is studied for electrons moving in a deformed equilibrium
mean field. The deformed field has been approximated by a cavity of spheroidal
shape, both prolate and oblate. Contrary to spherical systems, there is now a
coupling among excitations of different multipolarity induced by the
interaction among constituents. Explicit calculations are performed for the
dipole response of deformed clusters of different size. In all cases studied
here the photoabsorption strength for prolate clusters always displays a
typical double-peaked structure. For oblate clusters we find that the
high--frequency component of the plasmon doublet can get fragmented in the
medium size region (). This fragmentation is related to the
presence of two kinds of three-dimensional electron orbits in oblate cavities.
The possible scaling of our semiclassical equations with the valence electron
number and density is investigated.Comment: 23 pages, 8 figures, revised version, includes discussion of scalin
Holographic Superconductor/Insulator Transition at Zero Temperature
We analyze the five-dimensional AdS gravity coupled to a gauge field and a
charged scalar field. Under a Scherk-Schwarz compactification, we show that the
system undergoes a superconductor/insulator transition at zero temperature in
2+1 dimensions as we change the chemical potential. By taking into account a
confinement/deconfinement transition, the phase diagram turns out to have a
rich structure. We will observe that it has a similarity with the RVB
(resonating valence bond) approach to high-Tc superconductors via an emergent
gauge symmetry.Comment: 25 pages, 23 figures; A new subsection on a concrete string theory
embedding added, references added (v2); Typos corrected, references added
(v3
Nonperturbative aspects of ABJM theory
Using the matrix model which calculates the exact free energy of ABJM theory
on S^3 we study non-perturbative effects in the large N expansion of this
model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We
propose a general prescription to extract spacetime instanton actions from
general matrix models, in terms of period integrals of the spectral curve, and
we use it to determine them explicitly in the ABJM matrix model, as exact
functions of the 't Hooft coupling. We confirm numerically that these
instantons control the asymptotic growth of the genus expansion. Furthermore,
we find that the dominant instanton action at strong coupling determined in
this way exactly matches the action of an Euclidean D2-brane instanton wrapping
RP^3.Comment: 26 pages, 14 figures. v2: small corrections, final version published
in JHE
Capillary pressure of van der Waals liquid nanodrops
The dependence of the surface tension on a nanodrop radius is important for
the new-phase formation process. It is demonstrated that the famous Tolman
formula is not unique and the size-dependence of the surface tension can
distinct for different systems. The analysis is based on a relationship between
the surface tension and disjoining pressure in nanodrops. It is shown that the
van der Waals interactions do not affect the new-phase formation thermodynamics
since the effect of the disjoining pressure and size-dependent component of the
surface tension cancel each other.Comment: The paper is dedicated to the 80th anniversary of A.I. Rusano
Entanglement Entropy and Wilson Loop in St\"{u}ckelberg Holographic Insulator/Superconductor Model
We study the behaviors of entanglement entropy and vacuum expectation value
of Wilson loop in the St\"{u}ckelberg holographic insulator/superconductor
model. This model has rich phase structures depending on model parameters. Both
the entanglement entropy for a strip geometry and the heavy quark potential
from the Wilson loop show that there exists a "confinement/deconfinement" phase
transition. In addition, we find that the non-monotonic behavior of the
entanglement entropy with respect to chemical potential is universal in this
model. The pseudo potential from the spatial Wilson loop also has a similar
non-monotonic behavior. It turns out that the entanglement entropy and Wilson
loop are good probes to study the properties of the holographic superconductor
phase transition.Comment: 23 pages,12 figures. v2: typos corrected, accepted in JHE
The gravity duals of SO/USp superconformal quivers
We study the gravity duals of SO/USp superconformal quiver gauge theories
realized by M5-branes wrapping on a Riemann surface ("G-curve") together with a
Z_2-quotient. When the G-curve has no punctures, the gravity solutions are
classified by the genus g of the G-curve and the torsion part of the four-form
flux G_4. We also find that there is an interesting relation between anomaly
contributions from two mysterious theories: T_{SO(2N)} theory with SO(2N)^3
flavor symmetry and \tilde{T}_{SO(2N)} theory with SO(2N) x USp(2N-2)^2 flavor
symmetry. The dual gravity solutions for various SO/USp-type tails are also
studied.Comment: 27 pages, 13 figures; v2 minor corrections, typos corrected, Figure
13 replaced, references adde
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