Measurement of minority-carrier drift mobility in solar cells using a modulated electron beam

A determination of diffusivity on solar cells is here reported which utilizes a one dimensional treatment of diffusion under sinusoidal excitation. An intensity-modulated beam of a scanning electron microscope was used as a source of excitation. The beam was injected into the rear of the cell, and the modulated component of the induced terminal current was recovered phase sensitively. A Faraday cup to measure the modulated component of beam current was mounted next to the sample, and connected to the same electronics. A step up transformer and preamplifier were mounted on the sample holder. Beam currents on the order of 400-pA were used in order to minimize effects of high injection. The beam voltage was 34-kV, and the cell bias was kept at 0-V

Damage coefficients in low resistivity silicon

Electron and proton damage coefficients are determined for low resistivity silicon based on minority-carrier lifetime measurements on bulk material and diffusion length measurements on solar cells. Irradiations were performed on bulk samples and cells fabricated from four types of boron-doped 0.1 ohm-cm silicon ingots, including the four possible combinations of high and low oxygen content and high and low dislocation density. Measurements were also made on higher resistivity boron-doped bulk samples and solar cells. Major observations and conclusions from the investigation are discussed

Non-homogeneous random walks, subdiffusive migration of cells and anomalous chemotaxis

This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the non-local in time master equation and fractional equation for the probability of cell position. We show the structural instability of fractional subdiffusive equation with respect to the partial variations of anomalous exponent. We find the criteria under which the anomalous aggregation of cells takes place in the semi-infinite domain.Comment: 18 pages, accepted for publicatio

From microscopic to macroscopic descriptions of cell\ud migration on growing domains

Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this paper, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs

Reaction mechanism of the direct gas phase synthesis of H2O2 catalyzed by Au3

The gas phase reaction of molecular oxygen and hydrogen catalyzed by a Au3cluster to yield H2O2 was investigated theoretically using second order Z-averaged perturbation theory, with the final energies obtained with the fully size extensive completely renormalized CR-CC(2,3) coupled clustertheory. The proposed reaction mechanism is initiated by adsorption and activation of O2 on the Au3cluster. Molecular hydrogen then binds to the Au3O2 global minimum without an energy barrier. The reaction between the activated oxygen and hydrogen molecules proceeds through formation of hydroperoxide (HO2) and a hydrogen atom, which subsequently react to form the product hydrogen peroxide. All reactants, intermediates, and product remain bound to the goldcluster throughout the course of the reaction. The steps in the proposed reaction mechanism have low activation energy barriers below 15kcal∕mol. The overall reaction is highly exothermic by ∼30kcal∕mol

Minimal speed of fronts of reaction-convection-diffusion equations

We study the minimal speed of propagating fronts of convection reaction diffusion equations of the form $u_t + \mu \phi(u) u_x = u_{xx} +f(u)$ for positive reaction terms with $f'(0 >0$. The function $\phi(u)$ is continuous and vanishes at $u=0$. A variational principle for the minimal speed of the waves is constructed from which upper and lower bounds are obtained. This permits the a priori assesment of the effect of the convective term on the minimal speed of the traveling fronts. If the convective term is not strong enough, it produces no effect on the minimal speed of the fronts. We show that if $f''(u)/\sqrt{f'(0)} + \mu \phi'(u) < 0$, then the minimal speed is given by the linear value $2 \sqrt{f'(0)}$, and the convective term has no effect on the minimal speed. The results are illustrated by applying them to the exactly solvable case $u_t + \mu u u_x = u_{xx} + u (1 -u)$. Results are also given for the density dependent diffusion case $u_t + \mu \phi(u) u_x = (D(u)u_x)_x +f(u)$.Comment: revised, new results adde

Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source

This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues. For the considered class of models, we establish existence of a new type of ultra-singular self-similar solutions. These solutions arise as limits of the solutions of the initial value problem with zero initial data and infinitely strong source at the boundary. We prove existence and uniqueness of such solutions in the suitable weighted energy spaces. Moreover, we prove that the obtained self-similar solutions are the long-time limits of the solutions of the initial value problem with zero initial data and a time-independent boundary source

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with {\em E. coli}. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion