Surface waves in plasma waveguides with a smooth transverse inhomogeneity

A theory of cylindrical surface waves in a circular waveguide filled with a smoothly inhomogeneous plasma is presented. For a special radial profile of the plasma density, dispersion relations for the complex frequencies of surface waves are derived analytically. The dispersion relations are solved numerically (in the long-wavelength limit) and numerically. It is shown that there are two types of surface waves. When passing to the case of a sharply bounded plasma, one of the waves becomes an ordinary surface wave, while the other becomes strongly damped.     

Unidirectional electrostatic waves in an inhomogeneous cold magnetized plasma in plane and cylindrical waveguides

Waves in a cold electron plasma with a nonuniform density profile in a weak uniform magnetic field are considered in the electrostatic limit. Plane and cylindrical waveguides filled with plasmas having different density profiles are investigated. The dispersion curves and eigenfunctions for the waves are obtained, and the asymmetry of the waves with respect to their propagation direction is discussed.     

Theory of nonlinear space charge waves in neutralized electron flows: Gas-dynamic approach

The problem of the structure and dynamics of nonlinear longitudinal space charge waves in an electron flow that is treated as a gas and is described by an adiabatic equation of state with an arbitrary adiabatic index is solved exactly, and the solution obtained is examined in detail. The isothermal case is considered separately. It is shown that the waves in question can occur in the form of a fast or a slow space charge wave. The boundary values of the velocity and amplitude of these waves are obtained. The effect of the finite transverse dimensions of the electron flow on the structure of the wave and its dynamics is investigated.     

Ladder network prediction of transients in linear spatially inhomogeneous cables

A numerical method is described for finding steady state and transient responses in electrically linear, spatially inhomogeneous cables. Spatial inhomogeneities are incorporated by representing the cable by a number of finite length uniform cylindrical segments, each having the radius and electrical characteristics of a small region along the cable. Input waveforms are approximated by truncated Fourier series of sinusoidal components. Output waveforms are produced by multiplying the input Fourier series sinusoids by their respective transfer functions between input and output points on the cable and summing the resultant output point sinusoids. The transfer functions, representing attenuation and phase shift for each input sinusoid, are obtained by numerical analysis of an electrical ladder network derived from the cylindrical segment model of the cable. Results are shown for application of this method to both cylindrical and expanding radius cable geometries.     

Kin in space: social viscosity in a spatially and genetically substructured network

Population substructuring is a fundamental aspect of animal societies. A growing number of theoretical studies recognize that who-meets-whom is not random, but rather determined by spatial relationships or illustrated by social networks. Structural properties of large highly dynamic social systems are notoriously difficult to unravel. Network approaches provide powerful ways to analyse the intricate relationships between social behaviour, dispersal strategies and genetic structure. Applying network analytical tools to a colony of the highly gregarious Galápagos sea lion (Zalophus wollebaeki), we find several genetic clusters that correspond to spatially determined 'network communities'. Overall relatedness was low, and genetic structure in the network can be interpreted as an emergent property of philopatry and seems not to be primarily driven by targeted interactions among highly related individuals in family groups. Nevertheless, social relationships between directly adjacent individuals in the network were stronger among genetically more similar individuals. Taken together, these results suggest that even small differences in the degree of relatedness can influence behavioural decisions. This raises the fascinating prospect that kin selection may also apply to low levels of relatedness within densely packed animal groups where less obvious co-operative interactions such as increased tolerance and stress reduction are important.     

Surface charge of plasma lipoproteins from the data of potentiometric studies

The method of potentiometric titration is used to measure a surface very low, low- and high-density charge of the human blood plasma lipoproteins. Density of the surface charges is -0.5 X 10(-2); -0.2 X 10(-2); -3.4 X 10(-2) K/m2, respectively. The surface area of the lipoproteins determined by the method of radiation-free energy transfer between fluorescent probes amounts to 185.9; 241.7 and 426.8 m2 per 1 g of lipoprotein, respectively. Results of the experiments satisfactorily coincide with the data, obtained by other methods.     

Investigation of the charge and potential of a dust grain in a low-pressure plasma with allowance for ionization in the intergrain space

The formation of the ion flow to a dust grain and the distribution of the electric potential in a low-pressure dusty plasma are investigated theoretically with allowance for ionization in the intergrain space. Poisson’s equation similar to the Langmuir plasma-sheath equation is solved numerically with the use of partial analytic solutions at the boundary of the Seitz-Wigner cell and in thin layers in the intergrain space. The charge and potential of a dust grain are found as functions of the grain radius and cell size. The grain potential and the total cell potential energy as functions of the cell size display weak minima, whose positions correspond to the observed intergrain distance in dusty crystals.     

Conversion of normal waves in the electron-cyclotron frequency range at the critical surface in a cold anisotropic plasma inhomogeneous in two dimensions

Linear O-X conversion in the vicinity of a critical-density magnetic surface in a cold anisotropic plasma is studied using the model of a plasma inhomogeneous in two dimensions. Analytic expressions for the conversion and reflection coefficients are derived.     

Potential of a test charge in a dust-electron plasma

The potential of a slowly moving test charge in a positive-dust-electron plasma is calculated taking into account dust grain charge fluctuations, as well as collisions between neutral atoms and electrons and dust grains. The results should be useful for understanding the shielding in a dusty plasma sheath with levitated grains.     

Roots in space: a spatially explicit model for below-ground competition in plants

Game theory provides an untapped framework for predicting how below-ground competition will influence root proliferation in a spatially explicit environment. We model root competition for space as an evolutionary game. In response to nutrient competition between plants, an individual's optimal strategy (the spatial distribution of root proliferation) depends on the rooting strategies of neighbouring plants. The model defines and predicts the fundamental (in the absence of competition) and realized (in the presence of competition) root space of an individual plant. Overlapping fundamental root spaces guarantee smaller, yet still overlapping, realized root spaces as individuals concede some but not all space to a neighbour's roots. Root overlap becomes an intentional consequence of the neighbouring plants playing a nutrient foraging game. Root proliferation and regions of root overlap should increase with soil fertility, decline with the distance cost of root production (e.g. soil compactness) and shift with competitive asymmetries. Seemingly erratic patterns of root proliferation and root overlap become the expected outcome of nutrient foraging games played in soils with small-scale heterogeneities in nutrient availability.     

Drift of large-core spiral waves in inhomogeneous excitable media

Spiral waves in excitable media may drift due to interaction with medium inhomogeneities. We describe this drift asymptotically, within the kinematic (eikonal) approximation.     

Estimating equations for spatially correlated data in multi-dimensional space

We use the quasilikelihood concept to propose an estimatingequation for spatial data with correlation across the studyregion in a multi-dimensional space. With appropriate mixingconditions, we develop a central limit theorem for a randomfield under various L_p metrics. The consistency and asymptoticnormality of quasilikelihood estimators can then be derived.We also conduct simulations to evaluate the performance of theproposed estimating equation, and a dataset from East LansingWoods is used to illustrate the method.     

Nonlinear isothermal waves in a degenerate electron plasma

A nonlinear differential equation describing oscillations of the chemical potential in a one-dimensional steady-state wave propagating in a degenerate electron gas against an immobile neutralizing ion background is derived, investigated, and solved exactly. It is found that the wave phase velocity is bounded below by a critical velocity, whose exact value is obtained.     

Langmuir wave in weakly inhomogeneous relativistic plasma

The evolution of a Langmuir wave in a weakly inhomogeneous relativistic plasma with a positive density gradient is considered. It is shown that, at relativistic phase velocities, the wave evolution even at the tail of the electron distribution, where it is close to linear in the nonrelativistic case, results in the wave transformation into a hybrid of two waves with different spatial periods. Nonlinear dispersion relations for different stages of the wave evolution are derived.     

Trapping of high-energy electrons into regime of surfatron acceleration by electromagnetic waves in space plasma

The phenomenon of trapping of weakly relativistic charged particles (with kinetic energies on the order of mc ²) into a regime of surfatron acceleration by an electromagnetic wave that propagates in plasma across a weak external magnetic field has been studied using nonlinear numerical calculations based on a solution of the relativistic equations of motion. Analysis showed that, for the wave amplitude above a certain threshold value and the initial wave phase outside the interval favorable for the surfing regime, the trajectory of a charged particle initially corresponds to its cyclotron rotation in the external magnetic field. For the initial particle energies studied, the period of this rotation is relatively short. After a certain number (from several dozen to several thousand and above) of periods of rotation, the wave phase takes a value that is favorable for trapping of the charged particle on its trajectory by the electromagnetic wave, provided the Cherenkov resonance conditions are satisfied. As a result, the wave traps the charged particle and imparts it an ultrarelativistic acceleration. In momentum space, the region of trapping into the regime of surfing on an electromagnetic wave turns out to be rather large.     

Regular and stochastic decays of waves in a plasma cavity

The regular and stochastic decays of fast high-frequency waves in a cavity filled with a low-density magnetoactive plasma are studied both theoretically and experimentally. The conditions for the transformation of the regular regime into the stochastic one are determined. The theoretical and experimental results are in a good agreement. Possible applications of stochastic decay are discussed.     

Dissipative surface waves in plasma

Debatable aspects of the theory of nonpotential surface waves propagating along the boundary of a dissipative medium with frequency dispersion are discussed. On the basis of the known theoretical results and theoretical analysis carried out in this work, a theory of surface waves that is valid for any dissipation of the perturbation energy in the medium is developed. It is shown that, if dissipation is sufficiently strong, there can be surface waves the physical nature and dispersion law of which differ radically from those of ordinary surface waves. The damping rate of such waves is low even at large dissipation in the medium, and their group and phase velocities exceed the speed of light. In particular, surface waves on the interface between vacuum and cold collisional electron plasma are considered. The existence of such surface waves for different media of laboratory and natural origin is discussed.