230 research outputs found
Numerical Method for Accessing the Universal Scaling Function for a Multi-Particle Discrete Time Asymmetric Exclusion Process
In the universality class of the one dimensional Kardar-Parisi-Zhang surface
growth, Derrida and Lebowitz conjectured the universality of not only the
scaling exponents, but of an entire scaling function. Since Derrida and
Lebowitz's original publication [PRL 80 209 (1998)] this universality has been
verified for a variety of continuous time, periodic boundary systems in the KPZ
universality class. Here, we present a numerical method for directly examining
the entire particle flux of the asymmetric exclusion process (ASEP), thus
providing an alternative to more difficult cumulant ratios studies. Using this
method, we find that the Derrida-Lebowitz scaling function (DLSF) properly
characterizes the large system size limit (N-->infty) of a single particle
discrete time system, even in the case of very small system sizes (N <= 22).
This fact allows us to not only verify that the DLSF properly characterizes
multiple particle discrete-time asymmetric exclusion processes, but also
provides a way to numerically solve for quantities of interest, such as the
particle hopping flux. This method can thus serve to further increase the ease
and accessibility of studies involving even more challenging dynamics, such as
the open boundary ASEP
Analytical description of finite size effects for RNA secondary structures
The ensemble of RNA secondary structures of uniform sequences is studied
analytically. We calculate the partition function for very long sequences and
discuss how the cross-over length, beyond which asymptotic scaling laws apply,
depends on thermodynamic parameters. For realistic choices of parameters this
length can be much longer than natural RNA molecules. This has to be taken into
account when applying asymptotic theory to interpret experiments or numerical
results.Comment: 10 pages, 13 figures, published in Phys. Rev.
Arsenic in the Iberoamerican region. The IBEROARSEN Network and a possible economic solution for arsenic removal in isolated rural zones
In this work, a short description of the problematic of arsenic in Iberoamerica will be given, indicating the affected geographical regions and their incidence on the quality of life of the populations. In Argentina, Chile, Bolivia, Peru, Ecuador and Mexico, at least 4 million people depend on water sources with toxic concentrations of arsenic. While in these countries the problem is known since decades, in Uruguay, Brazil, Nicaragua, Honduras and El Salvador, the problem has been detected or investigated only in last years, and, in other Latinamerican countries, the studies began only recently. In Spain and Portugal the problem of As is becoming increasingly important. The presence of As in drinking waters, together with poverty and malnutrition, causes the incidence of CERHA (chronic endemic regional hydroarsenicism, HACRE in Spanish), an illness that provokes serious problems like skin lesions and even cancer. The activities of the IBEROARSEN Network of the CYTED Program, an Iberoamerican project that aims at the interconnection of groups devoted to arsenic R&D, trying to find solutions to this problem in the region, will be described. In addition, results of evaluation of the efficiency of two very simple low-cost methods for As removal in plastic bottles using solar light, one of them using heterogeneous photocatalysis with TiO2 immobilized on the walls followed by iron addition, and another one based on the use of zerovalent iron, which employs very cheap materials, are presented. The study was performed with synthetic and natural waters of rural, isolated, poor populations, not connected to the drinking water network of the provinces of Tucumán and Santiago del Estero, Argentina. For HP tests, synthetic as well as natural samples containing arsenic placed in bottles internally covered by a TiO2 layer and exposed to solar or artificial UV light followed by an addition of an iron source resulted in As concentration well below the national standards. For ZVI tests, iron wool demonstrated to be a better iron source than packing wire for As removal. Solar irradiation, in synthetic as well as in natural samples, seems to definitively improve As removal, avoiding the use of high amounts of iron. Although both HP and ZVI gave similar results, the use of the first one could be superior due to the ability of removing simultaneously As, organic matter, toxic metals and microbiological contamination
Statistical mechanics of RNA folding: a lattice approach
We propose a lattice model for RNA based on a self-interacting two-tolerant
trail. Self-avoidance and elements of tertiary structure are taken into
account. We investigate a simple version of the model in which the native state
of RNA consists of just one hairpin. Using exact arguments and Monte Carlo
simulations we determine the phase diagram for this case. We show that the
denaturation transition is first order and can either occur directly or through
an intermediate molten phase.Comment: 8 pages, 9 figure
Statistical mechanics of RNA folding: importance of alphabet size
We construct a minimalist model of RNA secondary-structure formation and use
it to study the mapping from sequence to structure. There are strong,
qualitative differences between two-letter and four or six-letter alphabets.
With only two kinds of bases, there are many alternate folding configurations,
yielding thermodynamically stable ground-states only for a small set of
structures of high designability, i.e., total number of associated sequences.
In contrast, sequences made from four bases, as found in nature, or six bases
have far fewer competing folding configurations, resulting in a much greater
average stability of the ground state.Comment: 7 figures; uses revtex
Localization-delocalization transition of disordered d-wave superconductors in class CI
A lattice model for disordered d-wave superconductors in class CI is
reconsidered. Near the band-center, the lattice model can be described by Dirac
fermions with several species, each of which yields WZW term for an effective
action of the Goldstone mode. The WZW terms cancel out each other because of
the four-fold symmetry of the model, which suggests that the quasiparticle
states are localized. If the lattice model has, however, symmetry breaking
terms which generate mass for any species of the Dirac fermions, remaining WZW
term which avoids the cancellation can derive the system to a delocalized
strong-coupling fixed point.Comment: 4 pages, revte
RNA denaturation: excluded volume, pseudoknots and transition scenarios
A lattice model of RNA denaturation which fully accounts for the excluded
volume effects among nucleotides is proposed. A numerical study shows that
interactions forming pseudoknots must be included in order to get a sharp
continuous transition. Otherwise a smooth crossover occurs from the swollen
linear polymer behavior to highly ramified, almost compact conformations with
secondary structures. In the latter scenario, which is appropriate when these
structures are much more stable than pseudoknot links, probability
distributions for the lengths of both loops and main branches obey scaling with
nonclassical exponents.Comment: 4 pages 3 figure
Superconductors with Magnetic Impurities: Instantons and Sub-gap States
When subject to a weak magnetic impurity potential, the order parameter and
quasi-particle energy gap of a bulk singlet superconductor are suppressed.
According to the conventional mean-field theory of Abrikosov and Gor'kov, the
integrity of the energy gap is maintained up to a critical concentration of
magnetic impurities. In this paper, a field theoretic approach is developed to
critically analyze the validity of the mean field theory. Using the
supersymmetry technique we find a spatially homogeneous saddle-point that
reproduces the Abrikosov-Gor'kov theory, and identify instanton contributions
to the density of states that render the quasi-particle energy gap soft at any
non-zero magnetic impurity concentration. The sub-gap states are associated
with supersymmetry broken field configurations of the action. An analysis of
fluctuations around these configurations shows how the underlying supersymmetry
of the action is restored by zero modes. An estimate of the density of states
is given for all dimensionalities. To illustrate the universality of the
present scheme we apply the same method to study `gap fluctuations' in a normal
quantum dot coupled to a superconducting terminal. Using the same instanton
approach, we recover the universal result recently proposed by Vavilov et al.
Finally, we emphasize the universality of the present scheme for the
description of gap fluctuations in d-dimensional superconducting/normal
structures.Comment: 18 pages, 9 eps figure
Statistical mechanics of secondary structures formed by random RNA sequences
The formation of secondary structures by a random RNA sequence is studied as
a model system for the sequence-structure problem omnipresent in biopolymers.
Several toy energy models are introduced to allow detailed analytical and
numerical studies. First, a two-replica calculation is performed. By mapping
the two-replica problem to the denaturation of a single homogeneous RNA in
6-dimensional embedding space, we show that sequence disorder is perturbatively
irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten
phase where many secondary structures with comparable total energy coexist. A
numerical study of various models at high temperature reproduces behaviors
characteristic of the molten phase. On the other hand, a scaling argument based
on the extremal statistics of rare regions can be constructed to show that the
low temperature phase is unstable to sequence disorder. We performed a detailed
numerical study of the low temperature phase using the droplet theory as a
guide, and characterized the statistics of large-scale, low-energy excitations
of the secondary structures from the ground state structure. We find the
excitation energy to grow very slowly (i.e., logarithmically) with the length
scale of the excitation, suggesting the existence of a marginal glass phase.
The transition between the low temperature glass phase and the high temperature
molten phase is also characterized numerically. It is revealed by a change in
the coefficient of the logarithmic excitation energy, from being disorder
dominated to entropy dominated.Comment: 24 pages, 16 figure
Localization and delocalization in dirty superconducting wires
We present Fokker-Planck equations that describe transport of heat and spin
in dirty unconventional superconducting quantum wires. Four symmetry classes
are distinguished, depending on the presence or absence of time-reversal and
spin rotation invariance. In the absence of spin-rotation symmetry, heat
transport is anomalous in that the mean conductance decays like
instead of exponentially fast for large enough length of the wire. The
Fokker-Planck equations in the presence of time-reversal symmetry are solved
exactly and the mean conductance for quasiparticle transport is calculated for
the crossover from the diffusive to the localized regime.Comment: 4 pages, RevTe
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