162 research outputs found
Equilibrium of anchored interfaces with quenched disordered growth
The roughening behavior of a one-dimensional interface fluctuating under
quenched disorder growth is examined while keeping an anchored boundary. The
latter introduces detailed balance conditions which allows for a thorough
analysis of equilibrium aspects at both macroscopic and microscopic scales. It
is found that the interface roughens linearly with the substrate size only in
the vicinity of special disorder realizations. Otherwise, it remains stiff and
tilted.Comment: 6 pages, 3 postscript figure
Non-perturbative phenomena in the three-dimensional random field Ising model
The systematic approach for the calculations of the non-perturbative
contributions to the free energy in the ferromagnetic phase of the random field
Ising model is developed. It is demonstrated that such contributions appear due
to localized in space instanton-like excitations. It is shown that away from
the critical region such instanton solutions are described by the set of the
mean-field saddle-point equations for the replica vector order parameter, and
these equations can be formally reduced to the only saddle-point equation of
the pure system in dimensions (D-2). In the marginal case, D=3, the
corresponding non-analytic contribution is computed explicitly. Nature of the
phase transition in the three-dimensional random field Ising model is
discussed.Comment: 12 page
Numerical Results for the Ground-State Interface in a Random Medium
The problem of determining the ground state of a -dimensional interface
embedded in a -dimensional random medium is treated numerically. Using a
minimum-cut algorithm, the exact ground states can be found for a number of
problems for which other numerical methods are inexact and slow. In particular,
results are presented for the roughness exponents and ground-state energy
fluctuations in a random bond Ising model. It is found that the roughness
exponent , with the related energy
exponent being , in ,
respectively. These results are compared with previous analytical and numerical
estimates.Comment: 10 pages, REVTEX3.0; 3 ps files (separate:tar/gzip/uuencoded) for
figure
Extremal statistics in the energetics of domain walls
We study at T=0 the minimum energy of a domain wall and its gap to the first
excited state concentrating on two-dimensional random-bond Ising magnets. The
average gap scales as , where , is the energy fluctuation exponent, length scale, and
the number of energy valleys. The logarithmic scaling is due to extremal
statistics, which is illustrated by mapping the problem into the
Kardar-Parisi-Zhang roughening process. It follows that the susceptibility of
domain walls has also a logarithmic dependence on system size.Comment: Accepted for publication in Phys. Rev.
Au-Ag template stripped pattern for scanning probe investigations of DNA arrays produced by Dip Pen Nanolithography
We report on DNA arrays produced by Dip Pen Nanolithography (DPN) on a novel
Au-Ag micro patterned template stripped surface. DNA arrays have been
investigated by atomic force microscopy (AFM) and scanning tunnelling
microscopy (STM) showing that the patterned template stripped substrate enables
easy retrieval of the DPN-functionalized zone with a standard optical
microscope permitting a multi-instrument and multi-technique local detection
and analysis. Moreover the smooth surface of the Au squares (abput 5-10
angstrom roughness) allows to be sensitive to the hybridization of the
oligonucleotide array with label-free target DNA. Our Au-Ag substrates,
combining the retrieving capabilities of the patterned surface with the
smoothness of the template stripped technique, are candidates for the
investigation of DPN nanostructures and for the development of label free
detection methods for DNA nanoarrays based on the use of scanning probes.Comment: Langmuir (accepted
Equilibrium roughening transition in a 1D modified sine-Gordon model
We present a modified version of the one-dimensional sine-Gordon that
exhibits a thermodynamic, roughening phase transition, in analogy with the 2D
usual sine-Gordon model. The model is suited to study the crystalline growth
over an impenetrable substrate and to describe the wetting transition of a
liquid that forms layers. We use the transfer integral technique to write down
the pseudo-Schr\"odinger equation for the model, which allows to obtain some
analytical insight, and to compute numerically the free energy from the exact
transfer operator. We compare the results with Monte Carlo simulations of the
model, finding a perfect agreement between both procedures. We thus establish
that the model shows a phase transition between a low temperature flat phase
and a high temperature rough one. The fact that the model is one dimensional
and that it has a true phase transition makes it an ideal framework for further
studies of roughening phase transitions.Comment: 11 pages, 13 figures. Accepted for publication in Physical Review
Roughness Scaling in Cyclical Surface Growth
The scaling behavior of cyclical growth (e.g. cycles of alternating
deposition and desorption primary processes) is investigated theoretically and
probed experimentally. The scaling approach to kinetic roughening is
generalized to cyclical processes by substituting the time by the number of
cycles . The roughness is predicted to grow as where is
the cyclical growth exponent. The roughness saturates to a value which scales
with the system size as , where is the cyclical
roughness exponent. The relations between the cyclical exponents and the
corresponding exponents of the primary processes are studied. Exact relations
are found for cycles composed of primary linear processes. An approximate
renormalization group approach is introduced to analyze non-linear effects in
the primary processes. The analytical results are backed by extensive numerical
simulations of different pairs of primary processes, both linear and
non-linear. Experimentally, silver surfaces are grown by a cyclical process
composed of electrodeposition followed by 50% electrodissolution. The roughness
is found to increase as a power-law of , consistent with the scaling
behavior anticipated theoretically. Potential applications of cyclical scaling
include accelerated testing of rechargeable batteries, and improved
chemotherapeutic treatment of cancerous tumors
Scaling Behavior of Cyclical Surface Growth
The scaling behavior of cyclical surface growth (e.g. deposition/desorption),
with the number of cycles n, is investigated. The roughness of surfaces grown
by two linear primary processes follows a scaling behavior with asymptotic
exponents inherited from the dominant process while the effective amplitudes
are determined by both. Relevant non-linear effects in the primary processes
may remain so or be rendered irrelevant. Numerical simulations for several
pairs of generic primary processes confirm these conclusions. Experimental
results for the surface roughness during cyclical electrodeposition/dissolution
of silver show a power-law dependence on n, consistent with the scaling
description.Comment: 2 figures adde
Magneto-Conductance Anisotropy and Interference Effects in Variable Range Hopping
We investigate the magneto-conductance (MC) anisotropy in the variable range
hopping regime, caused by quantum interference effects in three dimensions.
When no spin-orbit scattering is included, there is an increase in the
localization length (as in two dimensions), producing a large positive MC. By
contrast, with spin-orbit scattering present, there is no change in the
localization length, and only a small increase in the overall tunneling
amplitude. The numerical data for small magnetic fields , and hopping
lengths , can be collapsed by using scaling variables , and
in the perpendicular and parallel field orientations
respectively. This is in agreement with the flux through a `cigar'--shaped
region with a diffusive transverse dimension proportional to . If a
single hop dominates the conductivity of the sample, this leads to a
characteristic orientational `finger print' for the MC anisotropy. However, we
estimate that many hops contribute to conductivity of typical samples, and thus
averaging over critical hop orientations renders the bulk sample isotropic, as
seen experimentally. Anisotropy appears for thin films, when the length of the
hop is comparable to the thickness. The hops are then restricted to align with
the sample plane, leading to different MC behaviors parallel and perpendicular
to it, even after averaging over many hops. We predict the variations of such
anisotropy with both the hop size and the magnetic field strength. An
orientational bias produced by strong electric fields will also lead to MC
anisotropy.Comment: 24 pages, RevTex, 9 postscript figures uuencoded Submitted to PR
Energy landscapes in random systems, driven interfaces and wetting
We discuss the zero-temperature susceptibility of elastic manifolds with
quenched randomness. It diverges with system size due to low-lying local
minima. The distribution of energy gaps is deduced to be constant in the limit
of vanishing gaps by comparing numerics with a probabilistic argument. The
typical manifold response arises from a level-crossing phenomenon and implies
that wetting in random systems begins with a discrete transition. The
associated ``jump field'' scales as and for
(1+1) and (2+1) dimensional manifolds with random bond disorder.Comment: Accepted for publication in Phys. Rev. Let
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