Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Dust-acoustic supersolitons in a three-species dusty plasma with kappa distributions

Supersolitons are a form of soliton characterised, inter alia, by additional local extrema superimposed on the usual bipolar electric field signature. Previous studies of supersolitons supported by three-component plasmas have dealt with ion-acoustic structures. An analogous problem is now considered, namely, dust-acoustic supersolitons in a plasma composed of fluid negative dust grains and two kappa-distributed positive ion species. Calculations illustrating some supersoliton characteristics are presented. © Cambridge University Press 2013.

The Dynamics of Rapid Redshifted and Blueshifted Excursions in the Solar Hα Line

We analyze high temporal and spatial resolution time-series of spectralscans of the Hα line obtained with the CRisp Imaging SpectroPolarimeter instrument mounted on the Swedish Solar Telescope.The data reveal highly dynamic, dark, short-lived structures known asRapid Redshifted and Blueshifted Excursions (RREs, RBEs) that areon-disk absorption features observed in the red and blue wings ofspectral lines formed in the chromosphere. We study the dynamics of RREsand RBEs by tracking their evolution in space and time, measuring thespeed of the apparent motion, line of sight (LOS) Doppler velocity, andtransverse velocity of individual structures. A statistical study oftheir measured properties shows that RREs and RBEs have similaroccurrence rates, lifetimes, lengths, and widths. They also displaynon-periodic, nonlinear transverse motions perpendicular to their axesat speeds of 4-31 km s-1. Furthermore, both typesof structures either appear as high speed jets and blobs that aredirected outwardly from a magnetic bright point with speeds of50-150 km s-1, or emerge within a few seconds. Astudy of the different velocity components suggests that the transversemotions along the LOS of the chromospheric flux tubes are responsiblefor the formation and appearance of these redshifted/blueshiftedstructures. The short lifetime and fast disappearance of the RREs/RBEssuggests that, similar to type II spicules, they are rapidly heated totransition region or even coronal temperatures. We speculate that theKelvin-Helmholtz instability triggered by observed transversemotions of these structures may be a viable mechanism for their heating.

A new statistical framework for the quantification of covariate associations with species distributions

Identifying processes that shape species geographical ranges is a prerequisite for understanding environmental change. Currently, species distribution modelling methods do not offer credible statistical tests of the relative influence of climate factors and typically ignore other processes (e.g. biotic interactions and dispersal limitation). We use a hierarchical model fitted with Markov Chain Monte Carlo to combine ecologically plausible niche structures using regression splines to describe unimodal but potentially skewed response terms. We apply spatially explicit error terms that account for (and may help identify) missing variables. Using three example distributions of European bird species, we map model results to show sensitivity to change in each covariate. We show that the overall strength of climatic association differs between species and that each species has considerable spatial variation in both the strength of the climatic association and the sensitivity to climate change. Our methods are widely applicable to many species distribution modelling problems and enable accurate assessment of the statistical importance of biotic and abiotic influences on distributions.

Fractal species distributions do not produce power-law species-area relationships

We derive the species-area relationship (SAR) expected from an assemblage of fractally distributed species. If species have truly fractal spatial distributions with different fractal dimensions, we show that the expected SAR is not the classical power-law function, as suggested recently in the literature. This analytically derived SAR has a distinctive shape that is not commonly observed in nature: upward-accelerating richness with increasing area (when plotted on log-log axes). This suggests that, in reality, most species depart from true fractal spatial structure. We demonstrate the fitting of a fractal SAR using two plant assemblages (Alaskan trees and British grasses). We show that in both cases, when modelled as fractal patterns, the modelled SAR departs from the observed SAR in the same way, in accord with the theory developed here. The challenge is to identify how species depart from fractality, either individually or within assemblages, and more importantly to suggest reasons why species distributions are not self-similar and what, if anything, this can tell us about the spatial processes involved in their generation.

The geographical structure of British bird distributions:diversity, spatial turnover and scale

1. Using data on the spatial distribution of the British avifauna, we address three basic questions about the spatial structure of assemblages: (i) Is there a relationship between species richness (alpha diversity) and spatial turnover of species (beta diversity)? (ii) Do high richness locations have fewer species in common with neighbouring areas than low richness locations?, and (iii) Are any such relationships contingent on spatial scale (resolution or quadrat area), and do they reflect the operation of a particular kind of species-area relationship (SAR)?

2. For all measures of spatial turnover, we found a negative relationship with species richness. This held across all scales, with the exception of turnover measured as beta (sim).

3. Higher richness areas were found to have more species in common with neighbouring areas.

4. The logarithmic SAR fitted better than the power SAR overall, and fitted significantly better in areas with low richness and high turnover.

5. Spatial patterns of both turnover and richness vary with scale. The finest scale richness pattern (10 km) and the coarse scale richness pattern (90 km) are statistically unrelated. The same is true of the turnover patterns.

6. With coarsening scale, locations of the most species-rich quadrats move north. This observed sensitivity of richness 'hotspot' location to spatial scale has implications for conservation biology, e.g. the location of a reserve selected on the basis of maximum richness may change considerably with reserve size or scale of analysis.

7. Average turnover measured using indices declined with coarsening scale, but the average number of species gained or lost between neighbouring quadrats was essentially scale invariant at 10-13 species, despite mean richness rising from 80 to 146 species (across an 81-fold area increase). We show that this kind of scale invariance is consistent with the logarithmic SAR.

Particle-in-cell simulation study of the interaction between a relativistically moving leptonic micro-cloud and ambient electrons

Context. The jets of compact accreting objects are composed of electrons and a mixture of positrons and ions. These outflows impinge on the interstellar or intergalactic medium and both plasmas interact via collisionless processes. Filamentation (beam-Weibel) instabilities give rise to the growth of strong electromagnetic fields. These fields thermalize the interpenetrating plasmas. 

Aims. Hitherto, the effects imposed by a spatial non-uniformity on filamentation instabilities have remained unexplored. We examine the interaction between spatially uniform background electrons and a minuscule cloud of electrons and positrons. The cloud size is comparable to that created in recent laboratory experiments and such clouds may exist close to internal and external shocks of leptonic jets. The purpose of our study is to determine the prevalent instabilities, their ability to generate electromagnetic fields and the mechanism, by which the lepton micro-cloud transfers energy to the background plasma. 

Methods. A square micro-cloud of equally dense electrons and positrons impinges in our particle-in-cell (PIC) simulation on a spatially uniform plasma at rest. The latter consists of electrons with a temperature of 1 keV and immobile ions. The initially charge- and current neutral micro-cloud has a temperature of 100 keV and a side length of 2.5 plasma skin depths of the micro-cloud. The side length is given in the reference frame of the background plasma. The mean speed of the micro-cloud corresponds to a relativistic factor of 15, which is relevant for laboratory experiments and for relativistic astrophysical outflows. The spatial distributions of the leptons and of the electromagnetic fields are examined at several times. 

Results. A filamentation instability develops between the magnetic field carried by the micro-cloud and the background electrons. The electromagnetic fields, which grow from noise levels, redistribute the electrons and positrons within the cloud, which boosts the peak magnetic field amplitude. The current density and the moduli of the electromagnetic fields grow aperiodically in time and steadily along the direction that is anti-parallel to the cloud's velocity vector. The micro-cloud remains conjoined during the simulation. The instability induces an electrostatic wakefield in the background plasma. 

Conclusions. Relativistic clouds of leptons can generate and amplify magnetic fields even if they have a microscopic size, which implies that the underlying processes can be studied in the laboratory. The interaction of the localized magnetic field and high-energy leptons will give rise to synchrotron jitter radiation. The wakefield in the background plasma dissipates the kinetic energy of the lepton cloud. Even the fastest lepton micro-clouds can be slowed down by this collisionless mechanism. Moderately fast charge- and current neutralized lepton micro-clouds will deposit their energy close to relativistic shocks and hence they do not constitute an energy loss mechanism for the shock.

Predicting low velocity impact damage and Compression-After-Impact (CAI) behaviour of composite laminates

Low-velocity impact damage can drastically reduce the residual strength of a composite structure even when the damage is barely visible. The ability to computationally predict the extent of damage and compression-after-impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant time and cost penalties. A high-fidelity three-dimensional composite damage model, to predict both low-velocity impact damage and CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The intralaminar damage model component accounts for physically-based tensile and compressive failure mechanisms, of the fibres and matrix, when subjected to a three-dimensional stress state. Cohesive behaviour was employed to model the interlaminar failure between plies with a bi-linear traction–separation law for capturing damage onset and subsequent damage evolution. The virtual tests, set up in ABAQUS/Explicit, were executed in three steps, one to capture the impact damage, the second to stabilize the specimen by imposing new boundary conditions required for compression testing, and the third to predict the CAI strength. The observed intralaminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing without the need of model calibration which is often required with other damage models.

Numerical prediction of the low-velocity impact damage and compression after impact strength of composite laminates

Low-velocity impact damage can drastically reduce the residual mechanical properties of the composite structure even when there is barely visible impact damage. The ability to computationally predict the extent of damage and compression after impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant development time and cost penalties. A three-dimensional damage model, to predict both low-velocity impact damage and compression after impact CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The virtual tests were executed in two steps, one to capture the impact damage and the other to predict the CAI strength. The observed intra-laminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing.