Effect of microfield fluctuations on Coulomb collisions

The effect of plasma microfields on Coulomb collisions between the particles is considered. It is shown that perturbations from other particles insignificantly affect the frequency of short-range collisions. The results of calculating the pair correlation function of the particles in a plasma for distances much shorter than the interparticle distance agree well with predictions of the binary theory.     

Steady-state vortex structure in a plasma with a strong magnetic field

A study is made of nonquasineutral vortex structures in a plasma with a magnetic field B _z in which the charges separate on a spatial scale equal to the magnetic Debye radius r _B=B _z/4πen _e. The electric field arising due to charge separation leads to radial expansion of the ions, thereby destroying the initial electron vortex. It is shown that the ion pressure gradient stops ion expansion in a nonquasineutral electron vortex and gives rise to a steady structure with a characteristic scale on the order of r _B. With the electron inertia taken into account in the hydrodynamic approximation, the magnetic vortex structure in a hot plas mamanifests itself in the appearance of a “hole” in the plasma density.     

On fast solid-body rotation of the solar core and differential (liquid-like) rotation of the solar surface

On the basis of a two-component (two-fluid) hydrodynamic model, it is shown that the probable phenomenon of solar core rotation with a velocity higher than the average velocity of global rotation of the Sun, discovered by the SOHO mission, can be related to fast solid-body rotation of the light hydrogen component of the solar plasma, which is caused by thermonuclear fusion of hydrogen into helium inside the hot dense solar core. Thermonuclear fusion of four protons into a helium nucleus (α-particle) creates a large free specific volume per unit particle due to the large difference between the densities of the solar plasma and nuclear matter. As a result, an efficient volumetric sink of one of the components of the solar substance—hydrogen—forms inside the solar core. Therefore, a steady-state radial proton flux converging to the center should exist inside the Sun, which maintains a constant concentration of hydrogen as it burns out in the solar core. It is demonstrated that such a converging flux of hydrogen plasma with the radial velocity v _r (r) = ?βr creates a convective, v _r ?v _φ/?r, and a local Coriolis, v _r v _φ/r,φ nonlinear hydrodynamic forces in the solar plasma, rotating with the azimuthal velocity v _φ. In the absence of dissipation, these forces should cause an exponential growth of the solid-body rotation velocity of the hydrogen component inside the solar core. However, friction between the hydrogen and helium components of the solar plasma due to Coulomb collisions of protons with α-particles results in a steady-state regime of rotation of the hydrogen component in the solar core with an angular velocity substantially exceeding the global rotational velocity of the Sun. It is suggested that the observed differential (liquid-like) rotation of the visible surface of the Sun (photosphere) with the maximum angular velocity at the equator is caused by sold-body rotation of the solar plasma in the radiation zone and strong turbulence in the tachocline layer, where the turbulent viscosity reaches its maximum value at the equator. There, the tachocline layer exerts the most efficient drag on the less dense outer layers of the solar plasma, which are slowed down due to the interaction with the ambient space plasma (solar wind).     

Numerical modeling of the formation of steady-state nonequilibrium distributions of particles interacting through a power-law potential

The formation of a steady-state nonequilibrium distribution function of particles interacting through the repulsive potential U ~ α/r ^β(1≤β≤4), which operates at an infinite range, is studied numerically. The collisional particle dynamics in such a system is investigated using a spatially homogeneous nonlinear collision integral in the Landau-Fokker-Planck form, which is a model Boltzmann collision integral for arbitrary potentials of interaction accompanied by little momentum transfer between particles in collisions. Numerical modeling is based on completely conservative difference schemes. It is shown that the principal condition for the existence of steady-state nonequilibrium distributions is the presence of a particle or an energy flux oriented in the proper manner in momentum space. A steady-state local distribution exists inside the momentum interval between the energy source and sink and has the form of a gradually decreasing function. Since a radical change in the distribution function under nonequilibrium conditions leads to an anomalous enhancement of the conduction of a medium and its emission characteristics, the results obtained can be used, e.g., to predict the behavior of semiconductors with an intrinsic or extrinsic conductivity under the action of particle fluxes or electromagnetic radiation.     

Competitive interactions of Persian oak coppice trees (<Emphasis Type="Italic">Quercus brantii</Emphasis> var. <Emphasis Type="Italic">persica</Emphasis>) in a pure dry woodland revealed through point pattern analysis

Understanding intraspecific interactions among Persian oaks is essential to predict the responses of Zagros dry woodlands purely covered by these coppice trees to environmental changes (such as drought) that have direct effects on the sustainability of these woodlands. This investigation attempted to explore the scale-dependent competition among Persian oaks and highlight the impacts of competitive interactions on their biophysical properties (i.e. tree height, diameter at root collar and crown attributes) via point pattern analysis. Structurally different summary statistics were implemented to analyse the spatial pattern of Persian oaks in a pure 9-ha study plot. Nearest neighbour distribution function D(r) indicated that these coppice trees had no nearest neighbours up to the spatial scale of 2 m, and they all had a nearest neighbour at distances shorter than 12 m. Furthermore, pair correlation function g(r) showed the significant dispersion of Persian oaks up to the scale of 5 m, which may be the outcome of intraspecific competition for resources such as soil nutrients and water. As explored by mark variograms γ _m (r), Persian oaks of the same size had significant spatial correlations that illustrated the competitive (not facilitative) interactions of these coppice trees in the study plot. Mark correlation function k _mm (r) additionally revealed negative correlations of height and radial growth up to large spatial scales. Consequently, the outcome of this study highlighted the significant effects of competitive intraspecific interactions among Persian oak coppice trees on their spatial pattern and biophysical properties.     

Spatial distribution of the RF power absorbed in a helicon plasma source

The spatial distributions of the RF power absorbed by plasma electrons in an ion source operating in the helicon mode (ω _ci < ω < ω _ce < ω _pe ) are studied numerically by using a simplified model of an RF plasma source in an external uniform magnetic field. The parameters of the source used in numerical simulations are determined by the necessity of the simultaneous excitation of two types of waves, helicons and Trivelpiece-Gould modes, for which the corresponding transparency diagrams are used. The numerical simulations are carried out for two values of the working gas (helium) pressure and two values of the discharge chamber length under the assumption that symmetric modes are excited. The parameters of the source correspond to those of the injector of the nuclear scanning microprobe operating at the Institute of Applied Physics, National Academy of Sciences of Ukraine. It is assumed that the mechanism of RF power absorption is based on the acceleration of plasma electrons in the field of a Trivelpiece-Gould mode, which is interrupted by pair collisions of plasma electrons with neutral atoms and ions of the working gas. The simulation results show that the total absorbed RF power at a fixed plasma density depends in a resonant manner on the magnetic field. The resonance is found to become smoother with increasing working gas pressure. The distributions of the absorbed RF power in the discharge chamber are presented. The achievable density of the extracted current is estimated using the Bohm criterion.     

Incoherent Scattering of Electromagnetic Waves by Langmuir Fluctuations Trapped in a Plasma Density Well

Incoherent scattering of a probing wave by Langmuir fluctuations trapped and enhanced near a local minimum of the electron density (plasma density well) in plasma with a parabolic density profile is considered. Steady-state amplitudes of fluctuations are calculated for arbitrary velocity distribution functions of plasma particles with allowance for electron collisions. It is shown that quasi-periodic oscillations with two characteristic scales can be present in the spectrum of the plasma line. The smaller scale is due to the wellknown effect of discretization of the spectrum of Langmuir fluctuations in a plasma density well. The larger scale is associated with the generation of scattered waves in two spatial regions and subsequent interference of these waves at the exit from the density well. Oscillations with this scale are more stable under unsteady plasma conditions and can be more often observed in experiments. The results of this work can be used to experimentally determine the plasma parameters, such as the electron collision frequency and the size and lifetime of the plasma density well.     

Estuarine morphometry governs optically active substances, K d(PAR) and beam attenuation: assessments from a tropical ria and a temperate coastal plain estuary

Data on optical properties such as diffuse attenuation coefficient K _d(PAR), beam attenuation coefficient (c _p) and the optically active constituents (OACs) CDOM, Chl-a and suspended particulate matter were obtained in a Danish temperate coastal plain estuary (56°N) and a Vietnamese tropical ria (12°N) at high discharges. The major difference was the spatial distribution of the optical properties against distance, best described by significant power functions in the ria, compared to significant linear functions in the coastal plain. It was hypothesized that estuarine morphometry could explain this spatial distribution. Partition and multiple regression analyses showed that Chl-a governed K _d(PAR) and beam attenuation coefficient in both estuaries. Significant, high correlations were obtained by multiple regression analyses in the estimation of K _d(PAR) and beam attenuation coefficients in the two estuaries using OACs as input parameters. It is concluded that there are no large differences in OAC concentrations between the two estuaries. The spatial distributions of OACs and optical properties were significantly different and governed by the estuary morphometry, i.e. a power distribution in the tropical ria and a linear function in the temperate coastal plain estuary, and applicable to similar estuary types.     

Soliton behaviour in a bistable reaction diffusion model

We analyze a generic reaction-diffusion model that contains the important features of Turing systems and that has been extensively used in the past to model biological interesting patterns. This model presents various fixed points. Analysis of this model has been made in the past only in the case when there is only a single fixed point, and a phase diagram of all the possible instabilities shows that there is a place where a Turing-Hopf bifurcation occurs producing oscillating Turing patterns. In here we focus on the interesting situation of having several fixed points, particularly when one unstable point is in between two equally stable points. We show that the solutions of this bistable system are traveling front waves, or solitons. The predictions and results are tested by performing extensive numerical calculations in one and two dimensions. The dynamics of these solitons is governed by a well defined spatial scale, and collisions and interactions between solitons depend on this scale. In certain regions of parameter space the wave fronts can be stationary, forming a pattern resembling spatial chaos. The patterns in two dimensions are particularly interesting because they can present a coherent dynamics with pseudo spiral rotations that simulate the myocardial beat quite closely. We show that our simple model can produce complicated spatial patterns with many different properties, and could be used in applications in many different fields.      

Determination of plasma density from data on the ion current to cylindrical and planar probes

To improve probe methods of plasma diagnostics, special probe measurements were performed and numerical models describing ion transport to a probe with allowance for collisions were developed. The current–voltage characteristics of cylindrical and planar probes were measured in an RF capacitive discharge in argon at a frequency of 81 MHz and plasma densities of 10¹⁰–10¹¹ cm^–3, typical of modern RF reactors. 1D and 2D numerical models based on the particle-in-cell method with Monte Carlo collisions for simulating ion motion and the Boltzmann equilibrium for electrons are developed to describe current collection by a probe. The models were used to find the plasma density from the ion part of the current–voltage characteristic, study the effect of ion collisions, and verify simplified approaches to determining the plasma density. A 1D hydrodynamic model of the ion current to a cylindrical probe with allowance for ion collisions is proposed. For a planar probe, a method to determine the plasma density from the averaged numerical results is developed. A comparative analysis of different approaches to calculating the plasma density from the ion current to a probe is performed.     

Optimum body size in aphids

Abstract.

• 1 Smallness in British plant-sucking bugs is associated with feeding on the contents of individual plant cells, especially phloem.
• 2 The sizes of species of aphids living in similar habitats and the rates of water loss from those that have and lack a filter chamber do not support the contention that small size in aphids is a means of maximizing the loss of water by cuticular transpiration.
• 3 An optimum energy partitioning model, previously developed for aphids, was used to predict the interspecifie relation between adult weight and birth weight that would maximize the population growth rate, r_m. Using the observed r_m/IRGR ratio (0.8–0.9) and that the gonads are smaller than the soma at birth the predicted relation between the logarithm of the adult weight and the logarithm of the birth weight is linear and has a slope of 1.
• 4 The relation between the logarithm of the adult weight and the logarithm of the birth weight for eighteen species of aphids is linear and has a slope of 1.
• 5 Birth size differs between species of aphids and in each species is assumed to be the minimum size necessary for feeding. Accepting this constraint then the optimum adult size for maximizing r_m is approximately 15 times the birth size.

     

Additive partitioning of plant diversity with respect to grassland management regime,fertilisation and abiotic factors

Understanding patterns of vascular plant diversity in managed temperate grasslands and the processes that determine them requires analyses at multiple spatial scales. In this study, we applied additive partitioning to plant species richness data of two contrasting management regimes (meadow vs. pasture) collected from a nested sampling design that consisted of two hierarchical scales. At the local scale, we quantified additive diversity components in 180 vegetation plots, and at the regional scale in 60 grassland parcels. Total observed regional species richness (γ_r) was partitioned into its additive components within (α_l) and among vegetation plots (β_l) and among grassland parcels (β_r). We used the same approach in a comparison of common and infrequent plant species. Partitioning analyses revealed that the relative contributions of diversity components to total observed regional species richness changed as a function of spatial scale. We found that species richness among grassland parcels (β_r) of both meadows and pastures contributed most to total observed regional species richness (γ_r) of all and infrequent plant species (up to 81% and 96%, respectively), whereas for common species only up to 51% of γ_r were attributable to species richness among grassland parcels (β_r). To gain insight into the processes that may affect local patterns of species richness in grasslands, we analysed the observed local species diversity components with respect to management regime, nitrogen fertilisation and abiotic environmental factors (slope angle and soil quality). Our results show that grazing at a low-to-moderate stocking density promotes the β-diversity of all plant species at the local scale due to increased within-habitat heterogeneity. Low application rates of nitrogen fertilisers and abiotic environmental conditions such as steep slopes and soils with a low nutrient status generally benefited local species diversity components. We conclude that the observed patterns of plant species diversity are shaped by processes at multiple spatial scales.     

Determination of flumazenil in plasma by gas chromatography-negative ion chemical ionization mass spectrometry

A gas chromatographic-negative ion chemical ionization mass spectrometric (GC-NCI-MS) method for the determination of flumazenil in plasma is described. The GC of flumazenil (M_r 303) is considered to be difficult as it is readily adsorbed in the GC column. Therefore, preconditioning the GC column with reconstituted extract from plasma and Silyl-8 was required to cover the active sites on the column. Monitoring the maximum mass peak (m/z 275) of the flumazenil resulted in a tenfold enhancement of sensitivity and signal-to-noise ratio (concentration = 1 ng/ml). Isotopically labeled flumazenil-d₃ (M_r 306, m/z 278) was used as the internal standard. The detection limit for flumazenil was found to be 0.1 ng/ml with an injection volume of 2 μl. The signal-to-noise ratio was about 10. The routine quantification limit was set at 2 ng/ml for dog plasma and 1 ng/ml for human plasma. The sample volumes in both instances were 1 ml.     

Simulations of the Ion Current to a Probe in Plasma with Allowance for Ionization and Ion–Neutral Collisions: II. Cylindrical Probe

The ion current to a cylindrical probe is considered with allowance for volume ionization, ion–neutral collisions, and the ion orbital moment. A model based on the molecular dynamics method and applicable in a wide range of plasma parameters (r_p/λ_D= 0.01–100, r_i/λ_D= 0.002–200, ν_i/ω_0i= 0.01–0.05, and T_i/T_e = 0?0.01) is proposed A convenient representation of the dependence of the relative ion current density on the Langmuir coefficient β² and a technique for determining the plasma density from simulation results are offered.     

A theoretical study of the distribution of substances around roots resulting from simultaneous diffusion and mass flow

Summary The change in concentration of a solute in soil, moving near the surface of a root by both mass flow and diffusion, has been calculated by a numerical method with a computer. The effect of change in the plant controlled variables v₀ (the solvent flux at the root surface) and k (the root absorbing power), and the soil variables b (the buffer power) and D (the diffusion coefficient) are described in turn.The concentration at the root surface, relative to the undisturbed soil solution, approaches a limiting value v₀/k. As v₀ is increased, the limiting value is approached more rapidly, and the zone of disturbance is more compressed. A steady state is reached if r₀v₀/bD>2, but if r₀v₀/bD<2 the disturbance continues to spread outwards even though the concentration at the root surface has nearly attained its limiting value.As k is increased, other factors being constant, the limiting relative concentration at the root surface is approached more rapidly, but the spread of the disturbance away from the root is little affected.As Db is decreased, corresponding to a decrease in soil moisture, the concentration at the root surface reaches its limit more rapidly and the zone of disturbance is compressed.If, because of increase in the concentration at the root surface, the efficiency of root absorption declines, the relative concentration will exceed v₀/k, and may reach no limit — at least until the assumptions of the model used break down.     

Associations between field characteristics and soybean plant performance using canonical correlation analysis

The main objective of this study is to find associations between site characteristics (topographic, and soil physical and chemical properties) and soybean [Glycine max (L.) Merr.] plant performance (e.g. yield, canopy development) occurring at a field scale. The study took place in an Illinois production field in the 2000 and 2001 seasons. These associations were studied with canonical correlation analysis (CCA) followed by a spatial analysis of the resulting canonical variables with semivariography. The CCA discovered several significant associations between site characteristics. The first pair of canonical variables had a correlation coefficient of 0.76. The site characteristics most consistently correlated with the first pair of canonical variables were organic matter (OM) (r = 0.64 and 0.51 for the 2000 and 2001 seasons, respectively), pH (r = 0.39 and 0.51 for the 2000 and 2001 seasons, respectively), and deep electrical conductivity (EC_D) (r = 0.53 and 0.49 for the 2000 and 2001 seasons, respectively). Site variables soil phosphorous (P) and soil potassium (K) were inconsistently correlated with the site characteristics canonical variable. These results indicate that site variables related to soil water retention are more consistently associated with soybean performance than site variables related to soil fertility. The plant performance characteristic most correlated with the soybean performance canonical variable were NDVI_N (r = 0.76 and 0.72 for the 2000 and 2001 seasons, respectively), SPAD (r = 0.70 and 0.47 for the 2000 and 2001 seasons, respectively), and yield (r= 0.44 and 0.58 for the 2000 and 2001 seasons, respectively). The variables NDVI_N, yield, EC_D are obtained with sensors and thus they can be easily used at a production field scale. The common spatial structures in pairs of the canonical variables confirm the relationship between site properties and soybean performance, proving their potential in the demarcation of uniform areas within production fields. This approach can be used to explore soil plant relationships in other field studies.     

Analysis of the dependence of surfatron acceleration of electrons by an electromagnetic wave in space plasma on the particle momentum along the wave front

Based on the numerical solution of the nonlinear nonstationary second-order equation for the wave phase on the particle trajectory, the dynamics of surfatron acceleration of electrons by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed as a function of the electron momentum along the wave front. Numerical calculations show that, for strongly relativistic initial values of the electron momentum component along the wave front g _y (0) (the other parameters of the problem being the same), electrons are trapped into the regime of ultrarelativistic surfatron acceleration within a certain interval of the initial wave phase Ψ(0) on the particle trajectory. It is assumed in the calculations that |Ψ(0)| ≤ π. For strongly relativistic values of g _y (0), electrons are immediately trapped by the wave for 19% of the initial values of the phase Ψ(0) (favorable phases). For the rest of the values of Ψ(0), trapping does not occur even at long times. This circumstance substantially simplifies estimations of the wave damping due to particle acceleration in subsequent calculations. The dynamics of the relativistic factor and the components of the electron velocity and momentum under surfatron acceleration is also analyzed. The obtained results are of interest for the development of modern concepts of possible mechanisms of generation of ultrarelativistic particle fluxes in relatively calm space plasma, as well as for correct interpretation of observational data on the fluxes of such particles and explanation of possible reasons for the deviation of ultrarelativistic particle spectra detected in the heliosphere from the standard power-law scalings and the relation of these variations to space weather and large-scale atmospheric processes similar to tropical cyclones.     

A systematic comparison of summary characteristics for quantifying point patterns in ecology

Many functional summary characteristics such as Ripley's K function have been used in ecology to describe the spatial structure of point patterns to aid understanding of the underlying processes. However, their use is poorly guided in ecology because little is understood how well single summary characteristics, or a combination of them, capture the spatial structure of real world patterns. Here, we systematically tested the performance of combinations of eight summary characteristics [i.e. pair correlation function g(r), K‐function K(r), the proportion E(r) of points with no neighbor at distance r, the nearest neighbor distribution function D(r), the spherical contact distribution H_s(r), the kth nearest‐neighbor distribution functions D_k(r), the mean distance nn(k) to the kth neighbor, and the intensity function λ( x )]. To this end we used point pattern data covering a wide range of spatial structures including simulated (stationary) as well as real, possibly non‐stationary, patterns on tree species in a tropical forest in Panamá. To measure the information contained in a given combination of summary characteristics we used simulated annealing to reconstruct the observed patterns based only on the limited information provided by this combination and assessed how well other characteristics of the observed pattern were recovered. We found that the number of summary characteristics required to capture the spatial structure of stationary patterns varied between one (for patterns with near random structures) and three (for patterns with complex cluster and superposition structures), but with a robust ranking g(r), D_k(r), and H_s(r) that was largely independent on pattern idiosyncrasies. Stationary summary characteristics [with ranking g(r), D_k(r), H_s(r), E(r)] captured small‐ to intermediate scale properties of non‐stationary patterns, but for describing large‐scale spatial structures the intensity function was required. Our finding revealed that the current practice in ecology of using only one or two summary characteristics bears danger that essential characteristics of more complex patterns would not be detected. The technique of pattern reconstruction presented here has wide applications in ecology.     

Simulations of the ion current to a probe in plasma with allowance for ionization and ion-neutral collisions: I. Spherical probe

The ion current to a spherical probe is considered with allowance for volume ionization, ion-neutral collisions, and the ion orbital moment. A model based on the molecular dynamics method and applicable for a wide range of plasma parameters is proposed: r _p/λ_D = 0.001–100, λ _i /λ_D = 0.001–100, ${{\nu _i \lambda _D } \mathord{\left/ {\vphantom {{\nu _i \lambda _D } {\sqrt {{{kT_e } \mathord{\left/ {\vphantom {{kT_e } M}} \right. \kern-0em} M}} }}} \right. \kern-0em} {\sqrt {{{kT_e } \mathord{\left/ {\vphantom {{kT_e } M}} \right. \kern-0em} M}} }} = 0.01 - 1$ , and T _i /T _e = 0.01. A convenient representation of the dependences of the relative ion current density on the Langmuir coefficient α² and a technique for determining the plasma density from simulation results are offered.     

Nonlocal nature of the electron energy spectrum in a glow discharge in pure O2: I. Nonlocal character of the electron distribution function

Abstrac A study is made of the nonlocal nature of the electron energy distribution function in the positive column of a glow discharge in a tube filled with pure oxygen. The distribution function and the axial (E _z) and radial (E _r) electric fields as functions of radius are measured using an array of mobile probes. The experimentally obtained spatial profiles of the distribution function are used to test the applicability of the two-term approximation to the distribution function of the electrons with a nonlocal energy spectrum. The distribution function in a specified electric field E=E _z +E _r (where E _z ⊥ E _r) is calculated by solving the coordinate-dependent Boltzmann equation in the two-term approximation and by directly integrating the equations of electron motion using the Monte Carlo method. A comparison between the experimental data and the results of simulations carried out for a broad parameter range shows that, in the case of a highly nonlocal electron energy spectrum, the two-term approximation makes it possible to calculate the electron distribution function with a fairly good accuracy, in which case, however, in imposing the boundary conditions, the electron losses at the plasma surface should be treated in the kinetic approximation. It is shown that using the reflection coefficient of the plasma surface for electrons instead of the loss cone in space makes it possible to accurately calculate the electron energy distribution function over the entire parameter range under consideration, including the transient region in which the electron-energy relaxation length is comparable to the characteristic plasma dimension. __________ Translated from Fizika Plazmy, Vol. 26, No. 11, 2000, pp. 1038–1045. Original Russian Text Copyright ? 2000 by Ivanov, Klopovskii, Lopaev, Rakhimov, Rakhimova.