558 research outputs found
Dynamical Renormalization Group Study for a Class of Non-local Interface Equations
We provide a detailed Dynamic Renormalization Group study for a class of
stochastic equations that describe non-conserved interface growth mediated by
non-local interactions. We consider explicitly both the morphologically stable
case, and the less studied case in which pattern formation occurs, for which
flat surfaces are linearly unstable to periodic perturbations. We show that the
latter leads to non-trivial scaling behavior in an appropriate parameter range
when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that
nevertheless does not correspond to the KPZ universality class. This novel
asymptotic behavior is characterized by two scaling laws that fix the critical
exponents to dimension-independent values, that agree with previous reports
from numerical simulations and experimental systems. We show that the precise
form of the linear stabilizing terms does not modify the hydrodynamic behavior
of these equations. One of the scaling laws, usually associated with Galilean
invariance, is shown to derive from a vertex cancellation that occurs (at least
to one loop order) for any choice of linear terms in the equation of motion and
is independent on the morphological stability of the surface, hence
generalizing this well-known property of the KPZ equation. Moreover, the
argument carries over to other systems like the Lai-Das Sarma-Villain equation,
in which vertex cancellation is known {\em not to} imply an associated symmetry
of the equation.Comment: 34 pages, 9 figures. Journal of Statistical Mechanics: Theory and
Experiments (in press
Self-tuning of the cosmological constant
Here, I discuss the cosmological constant (CC) problems, in particular paying
attention to the vanishing cosmological constant. There are three cosmological
constant problems in particle physics. Hawking's idea of calculating the
probability amplitude for our Universe is peaked at CC = 0 which I try to
obtain after the initial inflationary period using a self-tuning model. I
review what has been discussed on the Hawking type calculation, and present a
(probably) correct way to calculate the amplitude, and show that the
Kim-Kyae-Lee self-tuning model allows a finite range of parameters for the CC =
0 to have a singularly large probability, approached from the AdS side.Comment: 12 pages with 8 figure
Strong anisotropy in surface kinetic roughening: analysis and experiments
We report an experimental assessment of surface kinetic roughening properties
that are anisotropic in space. Working for two specific instances of silicon
surfaces irradiated by ion-beam sputtering under diverse conditions (with and
without concurrent metallic impurity codeposition), we verify the predictions
and consistency of a recently proposed scaling Ansatz for surface observables
like the two-dimensional (2D) height Power Spectral Density (PSD). In contrast
with other formulations, this Ansatz is naturally tailored to the study of
two-dimensional surfaces, and allows to readily explore the implications of
anisotropic scaling for other observables, such as real-space correlation
functions and PSD functions for 1D profiles of the surface. Our results confirm
that there are indeed actual experimental systems whose kinetic roughening is
strongly anisotropic, as consistently described by this scaling analysis. In
the light of our work, some types of experimental measurements are seen to be
more affected by issues like finite space resolution effects, etc. that may
hinder a clear-cut assessment of strongly anisotropic scaling in the present
and other practical contexts
Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models
Among systems that display generic scale invariance, those whose asymptotic
properties are anisotropic in space (strong anisotropy, SA) have received a
relatively smaller attention, specially in the context of kinetic roughening
for two-dimensional surfaces. This is in contrast with their experimental
ubiquity, e.g. in the context of thin film production by diverse techniques.
Based on exact results for integrable (linear) cases, here we formulate a SA
Ansatz that, albeit equivalent to existing ones borrowed from equilibrium
critical phenomena, is more naturally adapted to the type of observables that
are measured in experiments on the dynamics of thin films, such as one and
two-dimensional height structure factors. We test our Ansatz on a paradigmatic
nonlinear stochastic equation displaying strong anisotropy like the Hwa-Kardar
equation [Phys. Rev. Lett. 62, 1813 (1989)], that was initially proposed to
describe the interface dynamics of running sand piles. A very important role to
elucidate its SA properties is played by an accurate (Gaussian) approximation
through a non-local linear equation that shares the same asymptotic properties
Tensorial mobilities for accurate solution of transport problems in models with diffuse interfaces
The general problem of two-phase transport in phase-field models is analyzed:
the flux of a conserved quantity is driven by the gradient of a potential
through a medium that consists of domains of two distinct phases which are
separated by diffuse interfaces. It is shown that the finite thickness of the
interfaces induces two effects that are not present in the analogous
sharp-interface problem: a surface excess current and a potential jump at the
interfaces. It is shown that both effects can be eliminated simultaneously only
if the coefficient of proportionality between flux and potential gradient
(mobility) is allowed to become a tensor in the interfaces. This opens the
possibility for precise and efficient simulations of transport problems with
finite interface thickness.Comment: 14 pages, 4 figure
High-temperature oxidation evaluation usingcrystal microbalance
High-temperature oxidising environments are frequently encountered but the limited number of in
situ techniques that can be implemented has hindered the monitoring possibilities and a better
comprehension of the oxidation phenomenon. In this paper, the high-temperature oxidation
behaviours of three alloys (AISI 316L, AISI 310 and HAYNES\uae HR-120\uae) were studied by using crystal
microbalances. Two types of crystal were tested: quartz or gallium orthophosphate crystals. First
the behaviour of thin sputtered deposited alloys on quartz slides was studied at 400 and 700\ub0C
under air oxidising conditions and compared to bulk samples. Kinetics measurements were
performed on the three alloy films deposited on the resonators at 400 or 700\ub0C: it was possible to
measure very small mass variations associated with thin oxide formation between 5 and 180 nm of
thickness. The crystal microbalance technique gives promising perspectives in understanding the
high-temperature corrosion and scaling mechanisms and also for in situ monitoring
Bloch oscillations of magnetic solitons in anisotropic spin-1/2 chains
We study the quantum dynamics of soliton-like domain walls in anisotropic
spin-1/2 chains in the presence of magnetic fields. In the absence of fields,
domain walls form a Bloch band of delocalized quantum states while a static
field applied along the easy axis localizes them into Wannier wave packets and
causes them to execute Bloch oscillations, i.e. the domain walls oscillate
along the chain with a finite Bloch frequency and amplitude. In the presence of
the field, the Bloch band, with a continuum of extended states, breaks up into
the Wannier-Zeeman ladder -- a discrete set of equally spaced energy levels. We
calculate the dynamical structure factor in the one-soliton sector at finite
frequency, wave vector, and temperature, and find sharp peaks at frequencies
which are integer multiples of the Bloch frequency. We further calculate the
uniform magnetic susceptibility and find that it too exhibits peaks at the
Bloch frequency. We identify several candidate materials where these Bloch
oscillations should be observable, for example, via neutron scattering
measurements. For the particular compound CoCl_2.2H_2O we estimate the Bloch
amplitude to be on the order of a few lattice constants, and the Bloch
frequency on the order of 100 GHz for magnetic fields in the Tesla range and at
temperatures of about 18 Kelvin.Comment: 31 single-spaced REVTeX pages, including 7 figures embedded with eps
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