The conductivity enhancement of n-doped Si due to strain has been calculated by solving the Boltzmann equation within the relaxation-time approximation. For T = 0, we determined the Fermi surface from first principles, whereas for T Ͼ 0, we modeled the Fermi surface using the effective-mass approximation. We explain the saturation of the conductivity enhancement with increasing strain in terms of the topology of the Fermi surface. We find in accordance with experiment a decreasing enhancement with increasing doping concentration.
Within the framework of random multiplicative energy cascade models of fully developed turbulence, finite-size-scaling expressions for two-point correlators and cumulants are derived, taking into account the observationally unavoidable conversion from an ultrametric to an Euclidean two-point distance. The comparison with two-point statistics of the surrogate energy dissipation, extracted from various wind tunnel and atmospheric boundary layer records, allows an accurate deduction of multiscaling exponents and cumulants, even at moderate Reynolds numbers for which simple power-law fits are not feasible. The extracted exponents serve as input for parametric estimates of the probabilistic cascade generator. Various cascade generators are evaluated.
In the context of random multiplicative energy cascade processes, we derive analytical expressions for translationally invariant one-and two-point cumulants in logarithmic field amplitudes. Such cumulants make it possible to distinguish between hitherto equally successful cascade generator models and hence supplement lowest-order multifractal scaling exponents and multiplier distributions.Although the underlying hydrodynamic equations are deterministic, the statistical description of fully developed turbulence has by now a long tradition [1]. Random multiplicative energy cascade models form a particularly simple and robust class of such statistical models. While different theoretical models can reproduce experimentally observed multifractal scaling exponents rather easily [2], observed multiplier distributions [3,4] eliminate many candidate cascade generators. Nevertheless, a number of competing generators remain, equally successful in reproducing both scaling exponents and multipliers. To make further progress in ferreting out the best cascade generator within this approximation, new observables are clearly called for.While most experiments have concentrated on measuring statistics in the energy dissipation density ε, we recently found a complete and analytical solution working in ln ε rather than ε itself [5]. In this letter, we show that cumulants in ln ε are analytically calculable even when restoring translational invariance to the solutions to emulate the spatial homogeneity of experimental turbulence statistics. Cumulants turn out to be powerful tools which for third and fourth
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.