Cauchy problem for the Boltzmann-BGK model near a global Maxwellian

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the initial perturbation is sufficiently small in a high order energy norm. We also establish an asymptotic decay estimate and uniform $L^2$-stability for nonlinear perturbations.Comment: 26 page

Hopanoids Play a Role in Membrane Integrity and pH Homeostasis in Rhodopseudomonas palustris TIE-1

Sedimentary hopanes are pentacyclic triterpenoids that serve as biomarker proxies for bacteria and certain bacterial metabolisms, such as oxygenic photosynthesis and aerobic methanotrophy. Their parent molecules, the bacteriohopanepolyols (BHPs), have been hypothesized to be the bacterial equivalent of sterols. However, the actual function of BHPs in bacterial cells is poorly understood. Here, we report the physiological study of a mutant in Rhodopseudomonas palustris TIE-1 that is unable to produce any hopanoids. The deletion of the gene encoding the squalene-hopene cyclase protein (Shc), which cyclizes squalene to the basic hopene structure, resulted in a strain that no longer produced any polycyclic triterpenoids. This strain was able to grow chemoheterotrophically, photoheterotrophically, and photoautotrophically, demonstrating that hopanoids are not required for growth under normal conditions. A severe growth defect, as well as significant morphological damage, was observed when cells were grown under acidic and alkaline conditions. Although minimal changes in shc transcript expression were observed under certain conditions of pH shock, the total amount of hopanoid production was unaffected; however, the abundance of methylated hopanoids significantly increased. This suggests that hopanoids may play an indirect role in pH homeostasis, with certain hopanoid derivatives being of particular importance

Uniform shear flow in dissipative gases. Computer simulations of inelastic hard spheres and (frictional) elastic hard spheres

In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor $(1+\alpha)/2$ (where $\alpha$ is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range $0.5\leq \alpha\leq 0.95$ and two values of the imposed shear rate $a$. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. The EHS results are in general hardly distinguishable from the IHS ones if $\alpha\gtrsim 0.7$, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipationsComment: 23 pages; 18 figures; Figs. 2 and 9 include new simulations; two new figures added; few minor changes; accepted for publication in PR

System of elastic hard spheres which mimics the transport properties of a granular gas

The prototype model of a fluidized granular system is a gas of inelastic hard spheres (IHS) with a constant coefficient of normal restitution $\alpha$. Using a kinetic theory description we investigate the two basic ingredients that a model of elastic hard spheres (EHS) must have in order to mimic the most relevant transport properties of the underlying IHS gas. First, the EHS gas is assumed to be subject to the action of an effective drag force with a friction constant equal to half the cooling rate of the IHS gas, the latter being evaluated in the local equilibrium approximation for simplicity. Second, the collision rate of the EHS gas is reduced by a factor $(1+\alpha)/2$, relative to that of the IHS gas. Comparison between the respective Navier-Stokes transport coefficients shows that the EHS model reproduces almost perfectly the self-diffusion coefficient and reasonably well the two transport coefficients defining the heat flux, the shear viscosity being reproduced within a deviation less than 14% (for $\alpha\geq 0.5$). Moreover, the EHS model is seen to agree with the fundamental collision integrals of inelastic mixtures and dense gases. The approximate equivalence between IHS and EHS is used to propose kinetic models for inelastic collisions as simple extensions of known kinetic models for elastic collisionsComment: 20 pages; 6 figures; change of title; few minor changes; accepted for publication in PR

Migraine and gastrointestinal disorders in middle and old age: A UK Biobank study

Introduction: Migraine is a prevalent condition causing a substantial level of disability worldwide. Despite this, the pathophysiological mechanisms are not fully understood. Migraine often co-occurs with gastrointestinal disorders, but the direction of a potential causal link is unclear. The aim of this project was to investigate the associations between migraine and several gastrointestinal disorders in the same cohort in order to determine the relative strengths of these associations. Methods: This cross-sectional study examined whether migraine is associated with irritable bowel syndrome (IBS), peptic ulcers, Helicobacter pylori (HP) infections, celiac disease, Crohn's disease and ulcerative colitis. Baseline data covering 489,753 UK Biobank participants (migraine group: n = 14,180) were analyzed using Pearson's chi-square tests and adjusted binary logistic regression models. Results: Migraine was significantly associated with IBS (odds ratio [OR] 2.24, 95% confidence interval [CI] 2.08–2.40, p <.001) and peptic ulcers (OR 1.55, 95% CI 1.35–1.77, p <.001). Migraine was not associated with HP infection (OR 1.34, 95% CI 1.04–1.73, p =.024), celiac disease (OR 1.29, 95% CI 1.04–1.60, p =.023), Crohn's disease (OR 1.08, 95% CI 0.80–1.45, p =.617) or ulcerative colitis (OR 1.00, 95% CI 0.79–1.27, p =.979) after adjusting for multiple testing. Conclusions: Migraine was associated with IBS and peptic ulcers in this large population-based cohort. The associations with HP infection, celiac disease, Crohn's disease, and ulcerative colitis did not reach significance, suggesting a weaker link between migraine and autoimmune gastrointestinal conditions or HP infection

Identification and characterization of Rhodopseudomonas palustris TIE-1 hopanoid biosynthesis mutants

Hopanes preserved in both modern and ancient sediments are recognized as the molecular fossils of bacteriohopanepolyols, pentacyclic hopanoid lipids. Based on the phylogenetic distribution of hopanoid production by extant bacteria, hopanes have been used as indicators of specific bacterial groups and/or their metabolisms. However, our ability to interpret them ultimately depends on understanding the physiological roles of hopanoids in modern bacteria. Toward this end, we set out to identify genes required for hopanoid biosynthesis in the anoxygenic phototroph Rhodopseudomonas palustris TIE-1 to enable selective control of hopanoid production. We attempted to delete 17 genes within a putative hopanoid biosynthetic gene cluster to determine their role, if any, in hopanoid biosynthesis. Two genes, hpnH and hpnG, are required to produce both bacteriohopanetetrol and aminobacteriohopanetriol, whereas a third gene, hpnO, is required only for aminobacteriohopanetriol production. None of the genes in this cluster are required to exclusively synthesize bacteriohopanetetrol, indicating that at least one other hopanoid biosynthesis gene is located elsewhere on the chromosome. Physiological studies with the different deletion mutants demonstrated that unmethylated and C_30 hopanoids are sufficient to maintain cytoplasmic but not outer membrane integrity. These results imply that hopanoid modifications, including methylation of the A-ring and the addition of a polar head group, may have biologic functions beyond playing a role in membrane permeability

Causal Relativistic Fluid Dynamics

We derive causal relativistic fluid dynamical equations from the relaxation model of kinetic theory as in a procedure previously applied in the case of non-relativistic rarefied gases. By treating space and time on an equal footing and avoiding the iterative steps of the conventional Chapman-Enskog --- CE---method, we are able to derive causal equations in the first order of the expansion in terms of the mean flight time of the particles. This is in contrast to what is found using the CE approach. We illustrate the general results with the example of a gas of identical ultrarelativistic particles such as photons under the assumptions of homogeneity and isotropy. When we couple the fluid dynamical equations to Einstein's equation we find, in addition to the geometry-driven expanding solution of the FRW model, a second, matter-driven nonequilibrium solution to the equations. In only the second solution, entropy is produced at a significant rate.Comment: 23 pages (CQG, in press

A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory

We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae at each order by using results from previous orders. In this way, we are able to derive a new set of fluid dynamical equations from kinetic theory, as we illustrate here for the relaxation model for monatomic gases. We obtain a stress tensor that contains a dynamical pressure term (or bulk viscosity) that is process-dependent and our heat current depends on the gradients of both temperature and density. On account of these features, the equations apply to a greater range of Knudsen number (the ratio of mean free path to macroscopic scale) than do the Navier-Stokes equations, as we see in the accompanying paper. In the limit of vanishing Knudsen number, our equations reduce to the usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page

Планування ЗЕД на підприємствах малого та середнього бізнесу

Pheochromocytomas (PCC) and abdominal paragangliomas (PGL) display a highly diverse genetic background and recent gene expression profiling studies have shown that PCC and PGL (together PPGL) alter either kinase signaling pathways or the pseudo-hypoxia response pathway dependent of the genetic composition. Recurrent mutations in the Harvey rat sarcoma viral oncogene homolog (HRAS) have recently been verified in sporadic PPGLs. In order to further establish the HRAS mutation frequency and to characterize the associated expression profiles of HRAS mutated tumors, 156 PPGLs for exon 2 and 3 hotspot mutations in the HRAS gene was screened, and compared with microarray-based gene expression profiles for 93 of the cases. The activating HRAS mutations G13R, Q61R, and Q61K were found in 10/142 PCC (7.0%) and a Q61L mutation was revealed in 1/14 PGL (7.1%). All HRAS mutated cases included in the mRNA expression profiling grouped in Cluster 2, and 21 transcripts were identified as altered when comparing the mutated tumors with 91 HRAS wild-type PPGL. Somatic HRAS mutations were not revealed in cases with known PPGL susceptibility gene mutations and all HRAS mutated cases were benign. The HRAS mutation prevalence of all PPGL published up to date is 5.2% (49/950), and 8.8% (48/548) among cases without a known PPGL susceptibility gene mutation. The findings support a role of HRAS mutations as a somatic driver event in benign PPGL without other known susceptibility gene mutations. HRAS mutated PPGL cluster together with NF1- and RET-mutated tumors associated with activation of kinase-signaling pathways.Funding Agencies|Swedish Cancer Foundation; StratCan; Swedish Research Council; Cancer Research Foundations of Radiumhemmet; Karolinska Institutet; Stockholm County Council</p

Knudsen Effect in a Nonequilibrium Gas

From the molecular dynamics simulation of a system of hard-core disks in which an equilibrium cell is connected with a nonequilibrium cell, it is confirmed that the pressure difference between two cells depends on the direction of the heat flux. From the boundary layer analysis, the velocity distribution function in the boundary layer is obtained. The agreement between the theoretical result and the numerical result is fairly good.Comment: 4pages, 4figure