Some Positone Problems Suggested by Nonlinear Heat Generation

There is much current interest in boundary value problems containing positive linear differential operators and monotone functions of the dependent variable, see for example, M.A. Krasnosel'ski [1] and H. H. Schaefer [2]. We call such problems "positone" and shall examine here a particular class of them (which have been called non-linear eigenvalue problems in [2])

Thermopower of gapped bilayer graphene

We calculate thermopower of clean and impure bilayer graphene systems. Opening a band gap through the application of an external electric field is shown to greatly enhance the thermopower of bilayer graphene, which is more than four times that of the monolayer graphene and gapless bilayer graphene at room temperature. The effect of scattering by dilute charged impurities is discussed in terms of the self-consistent Born approximation. Temperature dependence of the thermopower is also analyzed.Comment: 8 pages, 5 figures; An inconsistency in the definitions of Eq.(17) and (18) in version 1 is found and correcte

On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String Vacua

Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the pdf is not yet known. As a first result of this work, an explicit analytic expression for the density of the sum of two gamma random variables is derived. Then a computationally efficient algorithm to numerically calculate the linear combination of chi square random variables is developed. An explicit expression for the error bound is obtained. The proposed technique is shown to be computationally efficient, i.e. only polynomial in growth in the number of terms compared to the exponential growth of most other methods. It provides a vast improvement in accuracy and shows only logarithmic growth in the required precision. In addition, it is applicable to a much greater number of terms and currently the only way of computing the distribution for hundreds of terms. As an application, the exponential dependence of the eigenvalue fluctuation probability of a random matrix model for 4d supergravity with N scalar fields is found to be of the asymptotic form exp(-0.35N).Comment: 21 pages, 19 figures. 3rd versio

Measurement and simulation of anisotropic magnetoresistance in single GaAs/MnAs core/shell nanowires

We report four probe measurements of the low field magnetoresistance in single core/shell GaAs/MnAs nanowires synthesized by molecular beam epitaxy, demonstrating clear signatures of anisotropic magnetoresistance that track the field-dependent magnetization. A comparison with micromagnetic simulations reveals that the principal characteristics of the magnetoresistance data can be unambiguously attributed to the nanowire segments with a zinc blende GaAs core. The direct correlation between magnetoresistance, magnetization and crystal structure provides a powerful means of characterizing individual hybrid ferromagnet/semiconductor nanostructures.Comment: Submitted to Applied Physics Letters; some typos corrected and a defective figure replace

Analytic approach to the evolutionary effects of genetic exchange

We present an approximate analytic study of our previously introduced model of evolution including the effects of genetic exchange. This model is motivated by the process of bacterial transformation. We solve for the velocity, the rate of increase of fitness, as a function of the fixed population size, $N$. We find the velocity increases with $\ln N$, eventually saturated at an $N$ which depends on the strength of the recombination process. The analytical treatment is seen to agree well with direct numerical simulations of our model equations