J. C. Cressoni

Amnestically induced persistence in random walks.

We study how the Hurst exponent alpha depends on the fraction f of the total time t remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walkers position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimers disease and other dementias.

Universal aspects of photocurrent-voltage characteristics in dye-sensitized nanocrystalline TiO2 photoelectrochemical cells

We propose a linearizable model for the nonlinear photocurrent-voltage characteristics of dye-sensitized nanocrystalline

Multifractality of one electron eigen states in 1D disordered long range models

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THE NATURE OF ELECTRONIC STATES IN A DISORDERED CHAIN WITH LONG-RANGED HOPPING AMPLITUDES

photoelectrochemical solar cells. We solve the model and report theoretically predicted values for fill factors. A single free parameter of the model controls the fill factor. Upon renormalization, diverse experimental current-voltage data collapse onto a single universal function. The theoretical underpinning provides insight into physical mechanisms responsible for the large fill factors as well as their known dependence on the open circuit voltage. These advances allow the estimation of the complete current-voltage curve and fill factor from any three experimental data points, e.g., the open circuit voltage, the short circuit current, and one other intermediate measurement.

Stochastic modeling approach to the incubation time of prionic diseases.

One investigates the spatial structure of one-electron eigenstates for the one-dimensional Anderson model with long-range off-diagonal disorder hn,m=[−1,+1]/|n−m|δ where [a,b] means a uniform random distribution between a and b. Two cases are considered according to the choices for the on-site energy en, namely, en=0 and en=[0,1]. For δ=1 all states are critical and the multifractal spectra f(α) is computed for the states near the center of the band. The level-spacing distribution function is also obtained and its behavior for both small and large separations are studied.

Thermo-kinetic model for Prion diseases

In this work we investigate the nature of the electronic states in a one-dimensional tight-binding model with on-site energetic disorder and long-ranged hopping amplitudes. These are assumed to follow a power-law decay behavior with distance in the form h(r)∝1/rα, with α>1. Direct numerical diagonalization, finite-size scaling and a spectral statistics analysis show that as α→1 the localization length exhibits an exponential growth as the upper band edge is approached. Strong finite-size corrections are present in this regime near the upper band edge with the one-electron states displaying a strong level repulsion even at large, although finite, chains.

Spontaneous symmetry breaking in amnestically induced persistence

Transmissible spongiform encephalopathies are neurodegenerative diseases for which prions are the attributed pathogenic agents. A widely accepted theory assumes that prion replication is due to a direct interaction between the pathologic (PrP(Sc)) form and the host-encoded (PrP(C)) conformation, in a kind of autocatalytic process. Here we show that the overall features of the incubation time of prion diseases are readily obtained if the prion reaction is described by a simple mean-field model. An analytical expression for the incubation time distribution then follows by associating the rate constant to a stochastic variable log normally distributed. The incubation time distribution is then also shown to be log normal and fits the observed BSE (bovine spongiform encephalopathy) data very well. Computer simulation results also yield the correct BSE incubation time distribution at low PrP(C) densities.

Thermodynamics of an alternate σ=1 and S=32 Ising chain mapped onto an effective BEG model

A mean field theory of the auto catalytic Prions conversion reaction is developed under a conservation law for Prions density. These reactions take place in the brain where a normally folded Prion protein (PrPc) is converted into a misfolded, more stable, form (PrPSc). The results reproduce most of the known facts observed in Prion diseases such as: very long incubation time, rapid death after the first symptoms manifestation, dependence of the incubation and death times on the concentration of the initial contamination dose and the existence of a minimum contamination dose for the detection of the disease. Results of computing simulations are also presented.

Narrow log-periodic modulations in non-Markovian random walks

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of four phases, for this system: (i) classical nonpersistence, (ii) classical persistence, (iii) log-periodic nonpersistence, and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however, log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.

Discrete-time non-Markovian random walks: The effect of memory limitations on scaling

A linear chain of alternate Ising spins σ=1 and S=32, with bi-linear, bi-quadratic, single-ion and Zeeman interactions is studied. It is shown that this system can be mapped onto an effective BEG model, by the use of an extended decoration transformation. Exact results are obtained for the ground-state phase diagram and thermodynamical responses such as specific heat and magnetic susceptibility are shown.