Non-Linear Damping of Surface Alfvén Waves Due to Uniturbulence

This investigation is concerned with uniturbulence associated with surface Alfvén waves that exist in a Cartesian equilibrium model with a constant magnetic field and a piece-wise constant density. The surface where the equilibrium density changes in a discontinuous manner are the source of surface Alfvén waves. These surface Alfvén waves create uniturbulence because of the variation of the density across the background magnetic field. The damping of the surface Alfvén waves due to uniturbulence is determined using the Elsässer formulation. Analytical expressions for the wave energy density, the energy cascade, and the damping time are derived. The study of uniturbulence due to surface Alfvén waves is inspired by the observation that (the fundamental radial mode of) kink waves behave similarly to surface Alfvén waves. The results for this relatively simple case of surface Alfvén waves can help us understand the more complicated case of kink waves in cylinders. We perform a series of 3D ideal MHD simulations for a numerical demonstration of the non-linearly self-cascading model of unidirectional surface Alfvén waves using the code MPI-AMRVAC. We show that surface Alfvén waves damping time in the numerical simulations follows well our analytical prediction for that quantity. Analytical theory and the simulations show that the damping time is inversely proportional to the amplitude of the surface Alfvén waves and the density contrast. This unidirectional cascade may play a role in heating the coronal plasma.

Analytical RS-GBSM-Based Nonstationary Low-Altitude Air-to-Air Channel Modeling over Open Area

Aerial communication is very flexible due to almost no restrictions on geographical conditions. In recent years, with the development and application of the unmanned aerial vehicle, the air-to-air communication attracts dense interests from the researchers. More accurate and precise channel modeling for air-to-air communication is a new hot topic because of its essential role in the performance evaluation of the systems. This paper presents an analytical nonstationary regular-shaped geometry-based statistical model for low-altitude air-to-air communication over an open area with considerations on ground scattering. Analytical expressions of the channel impulse response and the autocorrelation functions based on the three-ray model are derived. Based on the assumption of uniform distribution of the ground scatterers, the distributions of the channel coefficients such as time delay and path attenuation are derived, simulated, compared, and fitted. The nonstationary characteristics of the channel are observed through the time-variant distributions of the channel coefficients as well as the time-variant autocorrelated functions and time-variant Doppler power spectrum density.

Linear bounded potential model for semiconductor band bending

We propose a simple but unexplored model for the semiconductor band bending with the aim to obtain a relatively simple expression to calculate the energy spectrum for the confined levels and the analytical expressions for wave-functions. This model consists of a linear potential but it is bounded or trimmed in energy unlike the well known wedge potential model. We present exact solutions for this potential in the frame of the effective mass approximation and they are valid for electron or hole confinement potential. This model provides a more adequate physical scenario than the wedge potential since it takes into account the charge balance involved in the band bending potential. These results allow to treat confined potential problems as in the case of a two-dimensional electron gas (2DEG) in a simplified way. We discuss the application of this approximation to the recombination time of electrons an holes and for the Franz-Keldysh effect.

Linkage disequilibrium between rare mutations

The statistical associations between mutations, collectively known as linkage disequilibrium (LD), encode important information about the evolutionary forces acting within a population. Yet in contrast to single-site analogues like the site frequency spectrum, our theoretical understanding of linkage disequilibrium remains limited. In particular, little is currently known about how mutations with different ages and fitness costs contribute to expected patterns of LD, even in simple settings where recombination and genetic drift are the major evolutionary forces. Here, I introduce a forward-time framework for predicting linkage disequilibrium between pairs of neutral and deleterious mutations as a function of their present-day frequencies. I show that the dynamics of linkage disequilibrium become much simpler in the limit that mutations are rare, where they admit a simple heuristic picture based on the trajectories of the underlying lineages. I use this approach to derive analytical expressions for a family of frequency-weighted LD statistics as a function of the recombination rate, the frequency scale, and the additive and epistatic fitness costs of the mutations. I find that the frequency scale can have a dramatic impact on the shapes of the resulting LD curves, reflecting the broad range of time scales over which these correlations arise. I also show that the differences between neutral and deleterious LD are not purely driven by differences in their mutation frequencies, and can instead display qualitative features that are reminiscent of epistasis. I conclude by discussing the implications of these results for recent LD measurements in bacteria. This forward-time approach may provide a useful framework for predicting linkage disequilibrium across a range of evolutionary scenarios.

Optimal experimental designs for estimating genetic and non-genetic effects underlying infectious disease transmission

BACKGROUND: Infectious disease spread in populations is controlled by individuals' susceptibility (propensity to acquire infection), infectivity (propensity to pass on infection to others) and recoverability (propensity to recover/die). Estimating the effects of genetic risk factors on these host epidemiological traits can help reduce disease spread through genetic control strategies. However, the effects of previously identified "disease resistance SNPs" on these epidemiological traits are usually unknown. Recent advances in computational statistics make it now possible to estimate the effects of single nucleotide polymorphisms (SNPs) on these traits from longitudinal epidemic data (e.g. infection and/or recovery times of individuals or diagnostic test results). However, little is known how to optimally design disease transmission experiments or field studies to maximise the precision at which pleiotropic SNP effects estimates for susceptibility, infectivity and recoverability can be estimated. RESULTS: We develop and validate analytical expressions for the precision of SNP effects estimates on the three host traits assuming a disease transmission experiment with one or more non-interacting contact groups. Maximising these leads to three distinct "experimental" designs, each specifying a different set of ideal SNP genotype compositions across groups: a) appropriate for a single contact-group, b) a multi-group design termed "pure", and c) a multi-group design termed "mixed", where "pure" and "mixed" refer to contact groups consisting of individuals with the same or different SNP genotypes, respectively. Precision estimates for susceptibility and recoverability were found to be less sensitive to the experimental design than infectivity. Data from multiple groups were found more informative about infectivity effects than from a single group containing the same number of individuals. Whilst the analytical expressions suggest that the multi-group pure and mixed designs estimate SNP effects with similar precision, the mixed design is preferable because it uses information from naturally occurring infections rather than those artificially induced. The same optimal design principles apply to estimating other categorical fixed effects, such as vaccinations status, helping to more effectively quantify their epidemiological impact. An online software tool SIRE-PC has been developed which calculates the precision of estimated substitution and dominance effects of a single SNP (or vaccine status) associated with all three traits depending on experimental design parameters. CONCLUSIONS: The developed methodology and software tool can be used to aid the design of disease transmission experiments for estimating the effect of individual SNPs and other categorical variables underlying host susceptibility, infectivity and recoverability.

Fixation dynamics of beneficial alleles in prokaryotic polyploid chromosomes and plasmids

Theoretical population genetics has been mostly developed for sexually reproducing diploid and for monoploid (haploid) organisms, focusing on eukaryotes. The evolution of bacteria and archaea is often studied by models for the allele dynamics in monoploid populations. However, many prokaryotic organisms harbor multicopy replicons -- chromosomes and plasmids -- and theory for the allele dynamics in populations of polyploid prokaryotes remains lacking. Here we present a population genetics model for replicons with multiple copies in the cell. Using this model, we characterize the fixation process of a dominant beneficial mutation at two levels: the phenotype and the genotype. Our results show that, depending on the mode of replication and segregation, the fixation time of mutant phenotypes may precede the genotypic fixation time by many generations; we term this time interval the heterozygosity window. We furthermore derive concise analytical expressions for the occurrence and length of the heterozygosity window, showing that it emerges if the copy number is high and selection strong. Replicon ploidy thus allows for the maintenance of genetic variation following phenotypic adaptation and consequently for reversibility in adaptation to fluctuating environmental conditions.

Analysis of Dynamic Magnetoelastic Coupling in Mechanically Driven Magnetoelectric Antennas

Mechanically driven magnetoelectric antennas are a promising new technology that enable a reduction in antenna size by many orders of magnitude, as compared to conventional antennas. The magnetoelastic coupling in these antennas, a phenomenon playing a direct role in determining performance, has been modeled using approaches that are severely lacking in both accuracy and tractability. In response to this problem, we take a physics-based approach to the analysis of magnetoelastic coupling. We find that certain directions of applied stress will maximize the coupling and we derive general expressions to quantify it. Our results are applied in comprehensive simulations that demonstrate the dynamic nature of the coupling as well as the impact of various operating conditions and material properties. Our work contributes analytical expressions and associated insight that can serve not only as guidelines for the design of mechanically driven magnetoelectric antennas, but also as stepping stones towards the development of more accurate models.

Postbuckling analysis of ultra-low rigidity serpentine structures

Serpentine structures are of growing interest due to its unique mechanical and physical properties for applications in stretchable electronics, mechanical sensing, biomedical devices. Mechanics-guided, deterministic three-dimensional (3D) assembly provide routes to form remarkable 3D structures, which in turn significantly improve its potential for applications. Therefore, an accurate postbuckling analysis is essential to the complex 3D serpentine structures with arbitrary geometry/material parameters. Here, simple, analytical expressions are obtained for the displacement and effective rigidity of serpentine structures during postbuckling. By tuning geometry parameters, the amplitude of assembled 3D serpentine structures can span a very broad range from zero to that of a straight ribbon. The analytical model can be used in design, fabrication, and application of versatile 3D serpentine structures to ensure their compatibility with the ultra-low rigidity biological tissues. A hierarchical 3D serpentine structure with ultra-low rigidity is presented to demonstrate the application of the analytical model.

The determination of induction motor losses in steel taking into account its saturation

Purpose This paper aims to work out a method for calculating losses in induction motor steel taking into account its saturation. Design/methodology/approach The theory of electric machines is applied during the analysis of induction motor equivalent circuits. The theory of Fourier series is used to determine the harmonic components of voltage, current and power. Instantaneous power theory and trigonometric transformations are used to solve algebraic and differential equations and their systems. The methods of approximation and interpolation are applied to obtain analytical expressions from the experimental data. Experimental research was carried out to verify the reliability of theoretical provisions and research results. Findings A method for assessing an induction machine steel as a function of the generalized electromotive force has been proposed. It allows taking into account higher harmonics of the current, which are caused by the presence of nonlinearity of an induction motor magnetic circuit. Practical implications The obtained results can be used in calculating the energy characteristics and operating modes of an induction motor, as well as in the construction of control systems. Originality/value A method for determining the losses in the stator steel of an induction motor, using a generalized electromotive force, has been proposed for the first time. It enables taking into account the currents flowing both in the stator circuit and in the rotor circuit.