Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

A DFT study of the chain growth probability in Fischer-Tropsch synthesis

The chain growth probability (alpha value) is one of the most significant parameters in Fischer-Tropsch (FT) synthesis. To gain insight into the chain growth probability, we systematically studied the hydrogenation and C-C coupling reactions with different chain lengths on the stepped Co(0001) surface using density functional theory calculations. Our findings elucidate the relationship between the barriers of these elementary reactions and the chain length. Moreover, we derived a general expression of the chain growth probability and investigated the behavior of the alpha value observed experimentally. The high methane yield results from the lower chain growth rate for C-1 + C-1 coupling compared with the other coupling reactions. After C-1, the deviation of product distribution in FT synthesis from the Anderson-Schulz-Flory distribution is due to the chain length-dependent paraffin/olefin ratio. (C) 2008 Elsevier Inc. All rights reserved.

Experimenting with the Coxian Phase-Type Distribution to Uncover Suitable Fits

In the past few decades, Coxian phase-type distributions have become increasingly more popular as a means of representing survival times. In healthcare, they are considered suitable for modelling the length of stay of patients in hospital and more recently for modelling the patient waiting times in Accident and Emergency Departments. The Coxian phase-type distribution has not only been shown to provide a good representation of real survival data, but its interpretation seems reasonably initiative to the medical experts. The drawback, however, is fitting the distribution to the data. There have been many attempts at accurately estimating the Coxian phase-type parameters. This paper wishes to examine the most promising of the approaches reported in the literature to determine the most accurate. Three performance measures are introduced to assess the fitting process of the algorithms along with the likelihood values and AIC to examine the goodness of fit and complexity of the model. Previous research suggests that the fitting process is strongly influenced by the initial parameter estimates and the data itself being quite variable. To overcome this, one experiment in this research paper will use the same initial parameter values for each estimation and perform the fits on the data simulated from a Coxian phase-type distribution with known parameters.

On the Distribution of Signal Phase in Body Area Networks

In this letter, we investigate the distribution of the phase component of the complex received signal observed in practical experiments using body area networks. Two phase distributions, the recently proposed kappa-mu and eta-mu probability densities, which together encompass the most widely used fading models, namely Semi-Gaussian, Rayleigh, Hoyt, Rice, and Nakagami-m, have been compared with measurement data. The kappa-mu distribution has been found to provide the best fit over a range of on-body links, while the user was mobile. The experiments were carried out in two dissimilar indoor environments at opposite ends of the multipath spectrum. It has also been found that the uniform phase distribution has not arisen in anyone of the experiments.

Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Structure observed in measured electron energy distribution functions in capacitively coupled radio frequency hydrogen plasmas

Electron energy probability functions measured with a passively compensated Langmuir probe in asymmetric capacitively coupled hydrogen and deuterium plasmas exhibit structure. The otherwise relatively continuous distribution appears to have an abrupt peak in electron density near 5 eV. This structure occurs at a higher energy in deuterium than hydrogen and there is a correlation between floating potential and the voltage at which the structure is observed in the second derivative of the I(V) characteristic. While the cause of the structure has yet to be clarified, spectroscopic observations and computer-based hydrogen models indicate that the high energy tail of the distribution is strongly modulated during the radio frequency cycle. The effect of this modulation on plasma properties and probe measurements has yet to be explored. (C) 1999 American Institute of Physics. [S0003-6951(99)00819-0].

Predicting the impacts of climate change on the distribution of threatened forest-restricted birds in Madagascar

The greatest common threat to birds in Madagascar has historically been from anthropogenic deforestation. During recent decades, global climate change is now also regarded as a significant threat to biodiversity. This study uses Maximum Entropy species distribution modeling to explore how potential climate change could affect the distribution of 17 threatened forest endemic bird species, using a range of climate variables from the Hadley Center's HadCM3 climate change model, for IPCC scenario B2a, for 2050. We explore the importance of forest cover as a modeling variable and we test the use of pseudo-presences drawn from extent of occurrence distributions. Inclusion of the forest cover variable improves the models and models derived from real-presence data with forest layer are better predictors than those from pseudo-presence data. Using real-presence data, we analyzed the impacts of climate change on the distribution of nine species. We could not predict the impact of climate change on eight species because of low numbers of occurrences. All nine species were predicted to experience reductions in their total range areas, and their maximum modeled probabilities of occurrence. In general, species range and altitudinal contractions follow the reductive trend of the Maximum presence probability. Only two species (Tyto soumagnei and Newtonia fanovanae) are expected to expand their altitude range. These results indicate that future availability of suitable habitat at different elevations is likely to be critical for species persistence through climate change. Five species (Eutriorchis astur, Neodrepanis hypoxantha, Mesitornis unicolor, Euryceros prevostii, and Oriola bernieri) are probably the most vulnerable to climate change. Four of them (E. astur, M. unicolor, E. prevostii, and O. bernieri) were found vulnerable to the forest fragmentation during previous research. Combination of these two threats in the future could negatively affect these species in a drastic way. Climate change is expected to act differently on each species and it is important to incorporate complex ecological variables into species distribution models.

Postglacial dispersal, rather than in situ glacial survival, best explains the disjunct distribution of the Lusitanian plant species Daboecia cantabrica (Ericaceae)

Aim:

The distribution of the Lusitanian flora and fauna, species which are found only in southern and western Ireland and in northern Spain and Portugal but which are absent from intervening countries, represents one of the classic conundrums of biogeography. The aim of the present study was to determine whether the distribution of the Lusitanian plant species Daboecia cantabrica was due to persistence in separate Irish and Iberian refugia, or has resulted from post-glacial recolonization followed by subsequent extinction of intervening populations.

Location:

Northern Spain and Co. Galway, western Ireland.

Methods:

Palaeodistribution modelling using Maxent was employed to identify putative refugial areas for D. cantabrica at the Last Glacial Maximum (LGM). Phylogeographical analysis of samples from 64 locations in Ireland and Spain were carried out using a chloroplast marker (atpB–rbcL), the nuclear ITS region, and an anonymous nuclear single-copy locus.

Results:

The palaeodistribution model indicated areas with a high probability of survival for D. cantabrica at the LGM off the western coast of Galicia in Spain, and in the Bay of Biscay. Spanish populations exhibited substantially higher genetic diversity than Irish populations at all three loci, as well as geographical structuring of haplotypes within Spain consistent with divergence in separate refugia. Spanish populations also exhibited far more endemic haplotypes. Divergence time between Irish and Spanish populations associated with the putative Biscay refugium was estimated as 3.333–32 ka.

Main conclusions:

Our data indicate persistence by D. cantabrica throughout the LGM in two separate southern refugia: one in western Galicia and one in the area off the coast of western France which now lies in the Bay of Biscay. Spain was recolonized from both refugia, whilst Ireland was most likely recolonized from the Biscay refugium. On the balance of evidence across the three marker types and the palaeodistribution modelling, our findings do not support the idea of in situ survival of D. cantabrica in Ireland, contrary to earlier suggestions. The fact that we cannot conclusively rule out the existence of a small, more northerly refugium, however, highlights the need for further analysis of Lusitanian plant species.

On the brightness distribution of type ia supernovae from violent white dwarf mergers

We investigate the brightness distribution expected for thermonuclear explosions that might result from the ignition of a detonation during the violent merger of white dwarf (WD) binaries. Violent WD mergers are a subclass of the canonical double degenerate scenario where two carbon-oxygen (CO) WDs merge when the larger WD fills its Roche lobe. Determining their brightness distribution is critical for evaluating whether such an explosion model could be responsible for a significant fraction of the observed population of Type Ia supernovae (SNe Ia). We argue that the brightness of an explosion realized via the violent merger model is mainly determined by the mass of Ni produced in the detonation of the primary COWD. To quantify this link, we use a set of sub-Chandrasekhar mass WD detonation models to derive a relationship between primary WD mass (m) and expected peak bolometric brightness (M). We use this m-M relationship to convert the masses of merging primary WDs from binary population models to a predicted distribution of explosion brightness. We also investigate the sensitivity of our results to assumptions about the conditions required to realize a detonation during violent mergers ofWDs. We find a striking similarity between the shape of our theoretical peak-magnitude distribution and that observed for SNe Ia: our model produces a M distribution that roughly covers the range and matches the shape of the one observed for SNe Ia. However, this agreement hinges on a particular phase of mass accretion during binary evolution: the primary WD gains ~0.15-0.35M? from a slightly evolved helium star companion. In our standard binary evolution model, such an accretion phase is predicted to occur for about 43 per cent of all binary systems that ultimately give rise to binary CO WD mergers. We also find that with high probability, violent WD mergers involving the most massive primaries (?1.3M?, which should produce bright SNe) have delay times ?500 Myr. © 2012 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.

Role of Predalors, Habitat Attributes, and Spatial Autocorrelation on the Distribution of Eggs in the Northern Spectacled Salamander (Salamandrina perspicillata)

We predicted that the probability of egg occurrence of salamander Salamandrina perspicillata depended on stream features and predation by native crayfish Austropotamobius fulcisianus and the introduced trout Salmo trutta. We assessed the presence of S. perspicillata at 54 sites within a natural reserve of southern Tuscany, Italy. Generalized linear models with binomial errors were constructed using egg presence/absence and altitude, stream mean size and slope, electrical conductivity, water pH and temperature, and a predation factor, defined according to the presence/absence of crayfish and trout. Some competing models also included an autocovariate term, which estimated how much the response variable at any one sampling point reflected response values at surrounding points. The resulting models were compared using Akaike's information criterion. Model selection led to a subset of 14 models with Delta AIC(c) <7 (i.e., models ranging from substantial support to considerably less support), and all but one of these included an effect of predation. Models with the autocovariate term had considerably more support than those without the term. According to multimodel inference, the presence of trout and crayfish reduced the probability of egg occurrence from a mean level of 0.90 (SE limits: 0.98-0.55) to 0.12 (SE limits: 0.34-0.04). The presence of crayfish alone had no detectable effects (SE limits: 0.86-0.39). The results suggest that introduced trout have a detrimental effect on the reproductive output of S. perspicillata and confirm the fundamental importance of distinguishing the roles of endogenous and exogenous forces that act on population distribution.

Modelling local-scale determinants and the probability of microarthropod species occurrence in Antarctic soils

Soil fauna in the extreme conditions of Antarctica consists of a few microinvertebrate species patchily distributed at different spatial scales. Populations of the prostigmatic mite Stereotydeus belli and the collembolan Gressittacantha terranova from northern Victoria Land (Antarctica) were used as models to study the effect of soil properties on microarthropod distributions. In agreement with the general assumption that the development and distribution of life in these ecosystems is mainly controlled by abiotic factors, we found that the probability of occurrence of S. belli depends on soil moisture and texture and on the sampling period (which affects the general availability of water); surprisingly, none of the analysed variables were significantly related to the G. terranova distribution. Based on our results and literature data, we propose a theoretical model that introduces biotic interactions among the major factors driving the local distribution of collembolans in Antarctic terrestrial ecosystems. (c) 2007 Elsevier Ltd. All rights reserved.

Effective grain size distribution analysis for interpretation of tidal-deltaic facies: West Bengal Sundarbans

Research over the past two decades on the Holocene sediments from the tide dominated west side of the lower Ganges delta has focussed on constraining the sedimentary environment through grain size distributions (GSD). GSD has traditionally been assessed through the use of probability density function (PDF) methods (e.g. log-normal, log skew-Laplace functions), but these approaches do not acknowledge the compositional nature of the data, which may compromise outcomes in lithofacies interpretations. The use of PDF approaches in GSD analysis poses a series of challenges for the development of lithofacies models, such as equifinal distribution coefficients and obscuring the empirical data variability. In this study a methodological framework for characterising GSD is presented through compositional data analysis (CODA) plus a multivariate statistical framework. This provides a statistically robust analysis of the fine tidal estuary sediments from the West Bengal Sundarbans, relative to alternative PDF approaches.

On the Multivariate Gamma-Gamma (ΓΓ) Distribution with Arbitrary Correlation and Applications in Wireless Communications

The statistical properties of the multivariate GammaGamma (ΓΓ) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate ΓΓ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the su m of ΓΓ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.

The VLT-FLAMES tarantula survey:X. Evidence for a bimodal distribution of rotational velocities for the single early B-type stars

Aims. Projected rotational velocities (ve sin i) have been estimated for 334 targets in the VLT-FLAMES Tarantula Survey that do not manifest significant radial velocity variations and are not supergiants. They have spectral types from approximately O9.5 to B3. The estimates have been analysed to infer the underlying rotational velocity distribution, which is critical for understanding the evolution of massive stars. Methods. Projected rotational velocities were deduced from the Fourier transforms of spectral lines, with upper limits also being obtained from profile fitting. For the narrower lined stars, metal and non-diffuse helium lines were adopted, and for the broader lined stars, both non-diffuse and diffuse helium lines; the estimates obtained using the different sets of lines are in good agreement. The uncertainty in the mean estimates is typically 4% for most targets. The iterative deconvolution procedure of Lucy has been used to deduce the probability density distribution of the rotational velocities. Results. Projected rotational velocities range up to approximately 450 kms-1 and show a bi-modal structure. This is also present in the inferred rotational velocity distribution with 25% of the sample having 0 <ve <100 km s^-1 and the high velocity component having v_e ∼ 250 km s^-1. There is no evidence from the spatial and radial velocity distributions of the two components that they represent either field and cluster populations or different episodes of star formation. Be-type stars have also been identified. Conclusions. The bi-modal rotational velocity distribution in our sample resembles that found for late-B and early-A type stars.While magnetic braking appears to be a possible mechanism for producing the low-velocity component, we can not rule out alternative explanations. © ESO 2013.