Asymptotic solution of a model for bilayer organic diodes and solar cells

Organic diodes and solar cells are constructed by placing together two organic semiconducting materials with dissimilar electron affinities and ionization potentials. The electrical behavior of such devices has been successfully modeled numerically using conventional drift diffusion together with recombination (which is usually assumed to be bimolecular) and thermal generation. Here a particular model is considered and the dark current-voltage curve and the spatial structure of the solution across the device is extracted analytically using asymptotic methods. We concentrate on the case of Shockley-Read-Hall recombination but note the extension to other recombination mechanisms. We find that there are three regimes of behavior, dependent on the total current. For small currents-i.e., at reverse bias or moderate forward bias-the structure of the solution is independent of the total current. For large currents-i.e., at strong forward bias-the current varies linearly with the voltage and is primarily controlled by drift of charges in the organic layers. There is then a narrow range of currents where the behavior undergoes a transition between the two regimes. The magnitude of the parameter that quantifies the interfacial recombination rate is critical in determining where the transition occurs. The extension of the theory to organic solar cells generating current under illumination is discussed as is the analogous current-voltage curves derived where the photo current is small. Finally, by comparing the analytic results to real experimental data, we show how the model parameters can be extracted from the shape of current-voltage curves measured in the dark. © 2012 Society for Industrial and Applied Mathematics

Application of the quantum spin glass theory to image restoration

Quantum fluctuation is introduced into the Markov random fields (MRF's) model for image restoration in the context of Bayesian approach. We investigate the dependence of the quantum fluctuation on the quality of BW image restoration by making use of statistical mechanics. We find that the maximum posterior marginal (MPM) estimate based on the quantum fluctuation gives a fine restoration in comparison with the maximum a posterior (MAP) estimate or the thermal fluctuation based MPM estimate.Comment: 19 pages, 9 figures, 1 table, RevTe

Dynamics of fluctuations in a fluid below the onset of Rayleigh-B\'enard convection

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-B\'enard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing-down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.Comment: 13 pages, 10 figures, 52 reference

Dynamics and thermodynamics of the spherical frustrated Blume-Emery-Griffiths model

We introduce a spherical version of the frustrated Blume-Emery-Griffiths model and solve exactly the statics and the Langevin dynamics for zero particle-particle coupling (K=0). In this case the model exhibits an equilibrium transition from a disordered to a spin glass phase which is always continuous for nonzero temperature. The same phase diagram results from the study of the dynamics. Furthermore, we notice the existence of a nonequilibrium time regime in a region of the disordered phase, characterized by aging as occurs in the spin glass phase. Due to a finite equilibration time, the system displays in this region the pattern of interrupted aging.Comment: 19 pages, 8 figure

Hydrodynamics of Spatially Ordered Superfluids

We derive the hydrodynamic equations for the supersolid and superhexatic phases of a neutral two-dimensional Bose fluid. We find, assuming that the normal part of the fluid is clamped to an underlying substrate, that both phases can sustain third-sound modes and that in the supersolid phase there are additional modes due to the superfluid motion of point defects (vacancies and interstitials).Comment: 24 pages of ReVTeX and 7 uuencoded figures. Submitted for publication in Phys. Rev.

Long-Ranged Correlations in Sheared Fluids

The presence of long-ranged correlations in a fluid undergoing uniform shear flow is investigated. An exact relation between the density autocorrelation function and the density-mometum correlation function implies that the former must decay more rapidly than $1/r$, in contrast to predictions of simple mode coupling theory. Analytic and numerical evaluation of a non-perturbative mode-coupling model confirms a crossover from $1/r$ behavior at ''small'' $r$ to a stronger asymptotic power-law decay. The characteristic length scale is $\ell \approx \sqrt{\lambda_{0}/a}$ where $$ is the sound damping constant and $a$ is the shear rate.Comment: 15 pages, 2 figures. Submitted to PR

Noise sensitivity of sub- and supercritically bifurcating patterns with group velocities close to the convective-absolute instability

The influence of small additive noise on structure formation near a forwards and near an inverted bifurcation as described by a cubic and quintic Ginzburg Landau amplitude equation, respectively, is studied numerically for group velocities in the vicinity of the convective-absolute instability where the deterministic front dynamics would empty the system.Comment: 16 pages, 7 Postscript figure

A model for the atomic-scale structure of a dense, nonequilibrium fluid: the homogeneous cooling state of granular fluids

It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the two-body distribution function. The model is applied to the homogeneous cooling state of granular fluids and upon comparison to molecular dynamics simulations is found to provide an accurate picture of the pair distribution function.Comment: 29 pages, 11 figures Revision corrects formatting of the figure

Anomalous Quantum Diffusion at the Superfluid-Insulator Transition

We consider the problem of the superconductor-insulator transition in the presence of disorder, assuming that the fermionic degrees of freedom can be ignored so that the problem reduces to one of Cooper pair localization. Weak disorder drives the critical behavior away from the pure critical point, initially towards a diffusive fixed point. We consider the effects of Coulomb interactions and quantum interference at this diffusive fixed point. Coulomb interactions enhance the conductivity, in contrast to the situation for fermions, essentially because the exchange interaction is opposite in sign. The interaction-driven enhancement of the conductivity is larger than the weak-localization suppression, so the system scales to a perfect conductor. Thus, it is a consistent possibility for the critical resistivity at the superconductor-insulator transition to be zero, but this value is only approached logarithmically. We determine the values of the critical exponents $\eta,z,\nu$ and comment on possible implications for the interpretation of experiments

Transport in rough self-affine fractures

Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium approximation predicts the right scaling behavior of the permeability and of the velocity fluctuations, in terms of the aperture of the fracture, the roughness exponent and the characteristic length of the fracture surfaces, in the limit of small separation between surfaces. The permeability of the fractures is also investigated as a function of the normal and lateral relative displacements between surfaces, and is shown that it can be bounded by the permeability of two-dimensional fractures. The development of channel-like structures in the velocity field is also numerically investigated for different relative displacements between surfaces. Finally, the dispersion of tracer particles in the velocity field of the fractures is investigated by analytic and numerical methods. The asymptotic dominant role of the geometric dispersion, due to velocity fluctuations and their spatial correlations, is shown in the limit of very small separation between fracture surfaces.Comment: submitted to PR