Chaotic motion of space charge wavefronts in semiconductors under time-independent voltage bias

A standard drift-diffusion model of space charge wave propagation in semiconductors has been studied numerically and analytically under dc voltage bias. For sufficiently long samples, appropriate contact resistivity and applied voltage - such that the sample is biased in a regime of negative differential resistance - we find chaos in the propagation of nonlinear fronts (charge monopoles of alternating sign) of electric field. The chaos is always low-dimensional, but has a complex spatial structure; this behavior can be interpreted using a finite dimensional asymptotic model in which the front (charge monopole) positions and the electrical current are the only dynamical variables.Comment: 12 pages, 8 figure

Chaos in resonant-tunneling superlattices

Spatio-temporal chaos is predicted to occur in n-doped semiconductor superlattices with sequential resonant tunneling as their main charge transport mechanism. Under dc voltage bias, undamped time-dependent oscillations of the current (due to the motion and recycling of electric field domain walls) have been observed in recent experiments. Chaos is the result of forcing this natural oscillation by means of an appropriate external microwave signal.Comment: 3 pages, LaTex, RevTex, 3 uuencoded figures (1.2M) are available upon request from [email protected], to appear in Phys.Rev.

Universality of the Gunn effect: self-sustained oscillations mediated by solitary waves

The Gunn effect consists of time-periodic oscillations of the current flowing through an external purely resistive circuit mediated by solitary wave dynamics of the electric field on an attached appropriate semiconductor. By means of a new asymptotic analysis, it is argued that Gunn-like behavior occurs in specific classes of model equations. As an illustration, an example related to the constrained Cahn-Allen equation is analyzed.Comment: 4 pages,3 Post-Script figure

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly stablished.Comment: 10 pages, 6 Post-Script figure

Effects of noise on hysteresis and resonance width in graphene and nanotubes resonators

We investigate the role that noise plays in the hysteretic dynamics of a suspended nanotube or a graphene sheet subject to an oscillating force. We find that not only the size but also the position of the hysteresis region in these systems can be controlled by noise. We also find that nano-resonators act as noise rectifiers: by increasing the noise in the setup, the resonance width of the characteristic peak in these systems is reduced and, as a result, the quality factor is increased.Comment: 15 pages, 6 figures. Sent to PRB (in revision

Modelling the unfolding pathway of biomolecules: theoretical approach and experimental prospect

We analyse the unfolding pathway of biomolecules comprising several independent modules in pulling experiments. In a recently proposed model, a critical velocity $v_{c}$ has been predicted, such that for pulling speeds $v>v_{c}$ it is the module at the pulled end that opens first, whereas for $v<v_{c}$ it is the weakest. Here, we introduce a variant of the model that is closer to the experimental setup, and discuss the robustness of the emergence of the critical velocity and of its dependence on the model parameters. We also propose a possible experiment to test the theoretical predictions of the model, which seems feasible with state-of-art molecular engineering techniques.Comment: Accepted contribution for the Springer Book "Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications" (proceedings of the BIRS CMM16 Workshop held in Banff, Canada, August 2016), 16 pages, 6 figure

Dynamics of Electric Field Domains and Oscillations of the Photocurrent in a Simple Superlattice Model

A discrete model is introduced to account for the time-periodic oscillations of the photocurrent in a superlattice observed by Kwok et al, in an undoped 40 period AlAs/GaAs superlattice. Basic ingredients are an effective negative differential resistance due to the sequential resonant tunneling of the photoexcited carriers through the potential barriers, and a rate equation for the holes that incorporates photogeneration and recombination. The photoexciting laser acts as a damping factor ending the oscillations when its power is large enough. The model explains: (i) the known oscillatory static I-V characteristic curve through the formation of a domain wall connecting high and low electric field domains, and (ii) the photocurrent and photoluminescence time-dependent oscillations after the domain wall is formed. In our model, they arise from the combined motion of the wall and the shift of the values of the electric field at the domains. Up to a certain value of the photoexcitation, the non-uniform field profile with two domains turns out to be metastable: after the photocurrent oscillations have ceased, the field profile slowly relaxes toward the uniform stationary solution (which is reached on a much longer time scale). Multiple stability of stationary states and hysteresis are also found. An interpretation of the oscillations in the photoluminescence spectrum is also given.Comment: 34 pages, REVTeX 3.0, 10 figures upon request, MA/UC3M/07/9

Edge dislocations in crystal structures considered as traveling waves of discrete models

The static stress needed to depin a 2D edge dislocation, the lower dynamic stress needed to keep it moving, its velocity and displacement vector profile are calculated from first principles. We use a simplified discrete model whose far field distortion tensor decays algebraically with distance as in the usual elasticity. An analytical description of dislocation depinning in the strongly overdamped case (including the effect of fluctuations) is also given. A set of $N$ parallel edge dislocations whose centers are far from each other can depin a given one provided $N=O(L)$, where $L$ is the average inter-dislocation distance divided by the Burgers vector of a single dislocation. Then a limiting dislocation density can be defined and calculated in simple cases.Comment: 10 pages, 3 eps figures, Revtex 4. Final version, corrected minor error

Discrete models of dislocations and their motion in cubic crystals

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the Peierls stress. Explicit expressions are given for crystals with cubic symmetry: sc, fcc and bcc. Numerical simulations of this model with conservative or damped dynamics illustrate static and moving edge and screw dislocations and describe their cores and profiles. Dislocation loops and dipoles are also numerically observed. Cracks can be created and propagated by applying a sufficient load to a dipole formed by two edge dislocations.Comment: 23 pages, 15 figures, to appear in Phys. Rev.

May anomalous X chromosome methylation be responsible for the spontaneous abortion of a male foetus?

Pregnancy loss is an important reproductive problem which appears to be highly associated with genetic factors. A spontaneous abortion occurred before prenatal diagnosis could be performed, in a woman who carried a fragile X full mutation. DNA extracted from formalin-fixed para ffin-embedded chorionic villi preparations indicated that it was a male embryo with an apparently methylated X chromosome. The previous analysis of the family showed that her daughter, who also carried a full mutation, exhibited an extremely skewed X inactivation of the normal allele (100%) and a severe fragile X phenotype. Thus, we speculate that the aberrant pattern of X chromosome methylation in this family may provoke the spontaneous miscarriage of this pregnancy that could be explained by at least partial inactivation of the unique X chromosome in a male foetus. Spontaneous abortion occurs quite frequently in humans, and recurrent pregnancy loss is a significant problem in women’s health (Christiansen 2006). Many cases of spontaneous abortion defy diagnosis and genetic factors have been proposed as a major contribution (Lanasa and Hogge 2000; Sierra and Stephenson 2006). The X chromosome inactiva tion (XCI) is the process in which one of the two X chromosomes present in each cell of female mammals is inactivated during early embryogenesis, to achieve dosage compensation with males (Avner and Heard 2001; Heard 2004). Initial steps of XCI involve a ‘counting process’, which senses the X chromosome/autosome ratio that restricts XCI to female embryos and, thereafter, the choice of which chromosome is inactivated (Morey et al . 2004).Skewed XCI leads to an expression of X-linked recessive disorders in females (Plenge et al. 2002; Mart´ınez et al. 2005; Renault et al. 2007). Another form of X-inactivation called meiotic sex chromosome inactivation (MSCI), takes place in males, during spermatogenesis and is a manifestation of the general meiotic-silencing mechanism (Turner 2007). In this study, we report the spontaneous abortion of a male foetus with an apparently methylated X chromosome, and propose that anomalous inactivation of its uniqueX chromosome could explain nonviability of the embryo and pregnancy loss. Therefore, we strongly suggest, as a follow up, that the methylation status of the X chromosome be tested in early spontaneous abortion of males in the absence of any other known genetic or nongenetic cause