3,069 research outputs found
Short-time scaling behavior of growing interfaces
The short-time evolution of a growing interface is studied within the
framework of the dynamic renormalization group approach for the
Kadar-Parisi-Zhang (KPZ) equation and for an idealized continuum model of
molecular beam epitaxy (MBE). The scaling behavior of response and correlation
functions is reminiscent of the ``initial slip'' behavior found in purely
dissipative critical relaxation (model A) and critical relaxation with
conserved order parameter (model B), respectively. Unlike model A the initial
slip exponent for the KPZ equation can be expressed by the dynamical exponent
z. In 1+1 dimensions, for which z is known exactly, the analytical theory for
the KPZ equation is confirmed by a Monte-Carlo simulation of a simple ballistic
deposition model. In 2+1 dimensions z is estimated from the short-time
evolution of the correlation function.Comment: 27 pages LaTeX with epsf style, 4 figures in eps format, submitted to
Phys. Rev.
Dynamic Scaling in a 2+1 Dimensional Limited Mobility Model of Epitaxial Growth
We study statistical scale invariance and dynamic scaling in a simple
solid-on-solid 2+1 - dimensional limited mobility discrete model of
nonequilibrium surface growth, which we believe should describe the low
temperature kinetic roughening properties of molecular beam epitaxy. The model
exhibits long-lived ``transient'' anomalous and multiaffine dynamic scaling
properties similar to that found in the corresponding 1+1 - dimensional
problem. Using large-scale simulations we obtain the relevant scaling
exponents, and compare with continuum theories.Comment: 5 pages, 4 ps figures included, RevTe
Kinetic roughening of surfaces: Derivation, solution and application of linear growth equations
We present a comprehensive analysis of a linear growth model, which combines
the characteristic features of the Edwards--Wilkinson and noisy Mullins
equations. This model can be derived from microscopics and it describes the
relaxation and growth of surfaces under conditions where the nonlinearities can
be neglected. We calculate in detail the surface width and various correlation
functions characterizing the model. In particular, we study the crossover
scaling of these functions between the two limits described by the combined
equation. Also, we study the effect of colored and conserved noise on the
growth exponents, and the effect of different initial conditions. The
contribution of a rough substrate to the surface width is shown to decay
universally as , where is
the time--dependent correlation length associated with the growth process,
is the initial roughness and the correlation length of the
substrate roughness, and is the surface dimensionality. As a second
application, we compute the large distance asymptotics of the height
correlation function and show that it differs qualitatively from the functional
forms commonly used in the intepretation of scattering experiments.Comment: 28 pages with 4 PostScript figures, uses titlepage.sty; to appear in
Phys. Rev.
Linear theory of unstable growth on rough surfaces
Unstable homoepitaxy on rough substrates is treated within a linear continuum
theory. The time dependence of the surface width is governed by three
length scales: The characteristic scale of the substrate roughness, the
terrace size and the Ehrlich-Schwoebel length . If (weak step edge barriers) and ,
then displays a minimum at a coverage , where the initial surface width is reduced by a factor
. The r\^{o}le of deposition and diffusion noise is analyzed. The
results are applied to recent experiments on the growth of InAs buffer layers
[M.F. Gyure {\em et al.}, Phys. Rev. Lett. {\bf 81}, 4931 (1998)]. The overall
features of the observed roughness evolution are captured by the linear theory,
but the detailed time dependence shows distinct deviations which suggest a
significant influence of nonlinearities
Structural, magnetic, electric, dielectric, and thermodynamic properties of multiferroic GeV4S8
The lacunar spinel GeV4S8 undergoes orbital and ferroelectric ordering at the
Jahn-Teller transition around 30 K and exhibits antiferromagnetic order below
about 14 K. In addition to this orbitally driven ferroelectricity, lacunar
spinels are an interesting material class, as the vanadium ions form V4
clusters representing stable molecular entities with a common electron
distribution and a well-defined level scheme of molecular states resulting in a
unique spin state per V4 molecule. Here we report detailed x-ray, magnetic
susceptibility, electrical resistivity, heat capacity, thermal expansion, and
dielectric results to characterize the structural, electric, dielectric,
magnetic, and thermodynamic properties of this interesting material, which also
exhibits strong electronic correlations. From the magnetic susceptibility, we
determine a negative Curie-Weiss temperature, indicative for antiferromagnetic
exchange and a paramagnetic moment close to a spin S = 1 of the V4 molecular
clusters. The low-temperature heat capacity provides experimental evidence for
gapped magnon excitations. From the entropy release, we conclude about strong
correlations between magnetic order and lattice distortions. In addition, the
observed anomalies at the phase transitions also indicate strong coupling
between structural and electronic degrees of freedom. Utilizing dielectric
spectroscopy, we find the onset of significant dispersion effects at the polar
Jahn-Teller transition. The dispersion becomes fully suppressed again with the
onset of spin order. In addition, the temperature dependencies of dielectric
constant and specific heat possibly indicate a sequential appearance of orbital
and polar order.Comment: 15 pages, 9 figure
Level Crossing Analysis of Growing surfaces
We investigate the average frequency of positive slope ,
crossing the height in the surface growing processes. The
exact level crossing analysis of the random deposition model and the
Kardar-Parisi-Zhang equation in the strong coupling limit before creation of
singularities are given.Comment: 5 pages, two column, latex, three figure
Quasispecies evolution in general mean-field landscapes
I consider a class of fitness landscapes, in which the fitness is a function
of a finite number of phenotypic "traits", which are themselves linear
functions of the genotype. I show that the stationary trait distribution in
such a landscape can be explicitly evaluated in a suitably defined
"thermodynamic limit", which is a combination of infinite-genome and strong
selection limits. These considerations can be applied in particular to identify
relevant features of the evolution of promoter binding sites, in spite of the
shortness of the corresponding sequences.Comment: 6 pages, 2 figures, Europhysics Letters style (included) Finite-size
scaling analysis sketched. To appear in Europhysics Letter
Spin wave resonances in antiferromagnets
Spin wave resonances with enormously large wave numbers corresponding to wave
vectors 10^5-10^6 cm^{-1} are observed in thin plates of FeBO3. The study of
spin wave resonances allows one to obtain information about the spin wave
spectrum. The temperature dependence of a non-uniform exchange constant is
determined for FeBO3. Considerable softening of the magnon spectrum resulting
from the interaction of magnons, is observed at temperatures above 1/3 of the
Neel temperature. The excitation level of spin wave resonances is found to
depend significantly on the inhomogeneous elastic distortions artificially
created in the sample. A theoretical model to describe the observed effects is
proposed.Comment: 6 pages, 6 figure
Coarsening of Sand Ripples in Mass Transfer Models with Extinction
Coarsening of sand ripples is studied in a one-dimensional stochastic model,
where neighboring ripples exchange mass with algebraic rates, , and ripples of zero mass are removed from the system. For ripples vanish through rare fluctuations and the average ripples mass grows
as \avem(t) \sim -\gamma^{-1} \ln (t). Temporal correlations decay as
or depending on the symmetry of the mass transfer, and
asymptotically the system is characterized by a product measure. The stationary
ripple mass distribution is obtained exactly. For ripple evolution
is linearly unstable, and the noise in the dynamics is irrelevant. For the problem is solved on the mean field level, but the mean-field theory
does not adequately describe the full behavior of the coarsening. In
particular, it fails to account for the numerically observed universality with
respect to the initial ripple size distribution. The results are not restricted
to sand ripple evolution since the model can be mapped to zero range processes,
urn models, exclusion processes, and cluster-cluster aggregation.Comment: 10 pages, 8 figures, RevTeX4, submitted to Phys. Rev.
Records and sequences of records from random variables with a linear trend
We consider records and sequences of records drawn from discrete time series
of the form , where the are independent and identically
distributed random variables and is a constant drift. For very small and
very large drift velocities, we investigate the asymptotic behavior of the
probability of a record occurring in the th step and the
probability that all entries are records, i.e. that . Our work is motivated by the analysis of temperature time series in
climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure
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