Diffusion of particles moving with constant speed

The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the constraint of constant speed of the photon in the medium. A Fokker-Planck equation is derived for the probability distribution in the phase space assuming the transverse fluctuating force to be a white noise. Analytic expressions for the moments of the displacement $$ along with an approximate expression for the marginal probability distribution function $P(x,t)$ are obtained. Exact numerical solutions for the phase space probability distribution for various geometries are presented. The results show that the velocity distribution randomizes in a time of about eight times the mean free time ($8t^*$) only after which the diffusion approximation becomes valid. This factor of eight is a well known experimental fact. A persistence exponent of $0.435 \pm 0.005$ is calculated for this process in two dimensions by studying the survival probability of the particle in a semi-infinite medium. The case of a stochastic amplifying medium is also discussed.Comment: 9 pages, 9 figures(Submitted to Phys. Rev. E

A tale of two capitalisms: preliminary spatial and historical comparisons of homicide rates in Western Europe and the USA

This article examines comparative homicide rates in the United States and Western Europe in an era of increasingly globalized neoliberal economics. The main finding of this preliminary analysis is that historical and spatial correlations between distinct forms of political economy and homicide rates are consistent enough to suggest that social democratic regimes are more successful at fostering the socio-cultural conditions necessary for reduced homicide rates. Thus Western Europe and all continents and nations should approach the importation of American neo-liberal economic policies with extreme caution. The article concludes by suggesting that the indirect but crucial causal connection between political economy and homicide rates, prematurely pushed into the background of criminological thought during the ‘cultural turn’, should be returned to the foreground

Multiple Interactions and the Structure of Beam Remnants

Recent experimental data have established some of the basic features of multiple interactions in hadron-hadron collisions. The emphasis is therefore now shifting, to one of exploring more detailed aspects. Starting from a brief review of the current situation, a next-generation model is developed, wherein a detailed account is given of correlated flavour, colour, longitudinal and transverse momentum distributions, encompassing both the partons initiating perturbative interactions and the partons left in the beam remnants. Some of the main features are illustrated for the Tevatron and the LHC.Comment: 69pp, 33 figure

Interactions between arbuscular mycorrhizal fungi and intraspecific competition affect size and size inequality of Plantago lanceolata L.

Intraspecific competition causes decreases in plant size and increases in size inequality. Arbuscular mycorrhizas usually increase the size and inequality of non-competing plants, but mycorrhizal effects often disappear when plants begin competing. We hypothesized that mycorrhizal effects on size inequality would be determined by the experimental conditions, and conducted simultaneous field and glasshouse experiments to investigate how AM fungi and intraspecific competition determine size inequality in Plantago lanceolata. 2 As predicted, plant size was reduced when plants were competing, in both field and controlled conditions. However, size inequality was unexpectedly reduced by competition. Plants may have competed in a symmetric fashion, probably for nutrients, rather than the more common situation, in which plant competition is strongly asymmetric. 3 Mycorrhizas had no effect on plant size or size inequality in competing plants in either field or controlled conditions, possibly because competition for nutrients was intense and negated any benefit the fungi could provide. 4 The effects of mycorrhizas on non-competing plants were also unexpected. In field-grown plants, AM fungi increased plant size, but decreased size inequality: mycorrhizal plants were more even in size, with few very small individuals. In glasshouse conditions, mycorrhizal colonization was extremely high, and was generally antagonistic, causing a reduction in plant size. Here, however, mycorrhizas caused an increase in size inequality, supporting our original hypothesis. This was because most plants were heavily colonized and small, but a few had low levels of colonization and grew relatively large. 5 This study has important implications for understanding the forces that structure plant communities. AM fungi can have a variety of effects on size inequality and thus potentially important influences on long-term plant population dynamics, by affecting the genetic contribution of individuals to the next generation. However, these effects differ, depending on whether plants are competing or not, the degree of mycorrhizal colonization and the responsiveness of the plant to different colonization densities

Genome-wide meta-analyses reveal novel loci for verbal short-term memory and learning

Understanding the genomic basis of memory processes may help in combating neurodegenerative disorders. Hence, we examined the associations of common genetic variants with verbal short-term memory and verbal learning in adults without dementia or stroke (N = 53,637). We identified novel loci in the intronic region of CDH18, and at 13q21 and 3p21.1, as well as an expected signal in the APOE/APOC1/TOMM40 region. These results replicated in an independent sample. Functional and bioinformatic analyses supported many of these loci and further implicated POC1. We showed that polygenic score for verbal learning associated with brain activation in right parieto-occipital region during working memory task. Finally, we showed genetic correlations of these memory traits with several neurocognitive and health outcomes. Our findings suggest a role of several genomic loci in verbal memory processes

DISC1 genetics, biology and psychiatric illness

Psychiatric disorders are highly heritable, and in many individuals likely arise from the combined effects of genes and the environment. A substantial body of evidence points towards DISC1 being one of the genes that influence risk of schizophrenia, bipolar disorder and depression, and functional studies of DISC1 consequently have the potential to reveal much about the pathways that lead to major mental illness. Here, we review the evidence that DISC1 influences disease risk through effects upon multiple critical pathways in the developing and adult brain