Consistent thermodynamic derivative estimates for tabular equations of state

Numerical simulations of compressible fluid flows require an equation of state (EOS) to relate the thermodynamic variables of density, internal energy, temperature, and pressure. A valid EOS must satisfy the thermodynamic conditions of consistency (derivation from a free energy) and stability (positive sound speed squared). When phase transitions are significant, the EOS is complicated and can only be specified in a table. For tabular EOS's such as SESAME from Los Alamos National Laboratory, the consistency and stability conditions take the form of a differential equation relating the derivatives of pressure and energy as functions of temperature and density, along with positivity constraints. Typical software interfaces to such tables based on polynomial or rational interpolants compute derivatives of pressure and energy and may enforce the stability conditions, but do not enforce the consistency condition and its derivatives. We describe a new type of table interface based on a constrained local least squares regression technique. It is applied to several SESAME EOS's showing how the consistency condition can be satisfied to round-off while computing first and second derivatives with demonstrated second-order convergence. An improvement of 14 orders of magnitude over conventional derivatives is demonstrated, although the new method is apparently two orders of magnitude slower, due to the fact that every evaluation requires solving an 11-dimensional nonlinear system.Comment: 29 pages, 9 figures, 16 references, submitted to Phys Rev

The long cross-over dynamics of capillary imbibition

Spontaneous capillary imbibition is a classical problem in interfacial fluid dynamics with a broad range of applications, from microfluidics to agriculture. Here we study the duration of the cross-over between an initial linear growth of the imbibition front to the diffusive-like growth limit of Washburn's law. We show that local-resistance sources, such as the inertial resistance and the friction caused by the advancing meniscus, always limit the motion of an imbibing front. Both effects give rise to a cross-over of the growth exponent between the linear and the diffusive-like regimes. We show how this cross-over is much longer than previously thought - even longer than the time it takes the liquid to fill the porous medium. Such slowly slowing-down dynamics is likely to cause similar long cross-over phenomena in processes governed by wetting

Kelvin-Helmholtz instabilities with Godunov SPH

Numerical simulations for the non-linear development of Kelvin-Helmholtz instability in two different density layers have been performed with the particle-based method (Godunov SPH) developed by Inutsuka (2002). The Godunov SPH can describe the Kelvin-Helmholtz instability even with a high density contrast, while the standard SPH shows the absence of the instability across a density gradient (Agertz et al. 2007). The interaction of a dense blob with a hot ambient medium has been performed also. The Godunov SPH describes the formation and evolution of the fingers due to the combinations of Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instabilities. The blob test result coincides well with the results of the grid-based codes. An inaccurate handling of a density gradient in the standard SPH has been pointed out as the direct reason of the absence of the instabilities. An unphysical force happens at the density gradient even in a pressure equilibrium, and repulses particles from the initial density discontinuity. Therefore, the initial perturbation damps, and a gap forms at the discontinuity. The unphysical force has been studied in terms of the consistency of a numerical scheme. Contrary to the standard SPH, the momentum equation of the Godunov SPH doesnt use the particle approximation, and has been derived from the kernel convolution or a new Lagrangian function. The new Lagrangian function used in the Godunov SPH is more analogous to the real Lagrangian function for continuum. The momentum equation of the Godunov SPH has much better linear consistency, so the unphysical force is greatly reduced compared to the standard SPH in a high density contrast.Comment: 11 pages, 7 figures, Accepted for publication in MNRA

Identification of the chicken toll-like receptor 4 (TLR4) gene and its role in the susceptibility to Salmonella infection

Lipopolysaccharide (LPS) from Gram-negative bacteria triggers a protective inflammatory response in a normal host. In classical laboratory inbred strains of mice, the Lps locus controls the rate of exponential Salmonella growth in spleen and liver during the early phase of infection through its effect on innate immunity. The gene encoding the Lps mutation was recently identified as the Toll-like receptor 4 (Tlr4 ). Toll-like receptors are a group of evolutionarily conserved pattern recognition receptors involved in the activation of the immune system in response to pathogen. The discovery of mouse Tlr4 as being the gene encoding the Lps mutation provided the possibility of studying the role of this gene in chicken susceptibility to infection with Salmonella typhimurium. To achieve this goal we have cloned the chicken orthologue of mouse Tlr4, determined its sequence, mapped it in the chicken genome and showed its linkage to susceptibility to infection with Salmonella typhimurium in the chicken

Allelic Variation in TLR4 Is Linked to Susceptibility to Salmonella enterica Serovar Typhimurium Infection in Chickens

Toll-like receptor 4 (TLR4) is part of a group of evolutionarily conserved pattern recognition receptors involved in the activation of the immune system in response to various pathogens and in the innate defense against infection. We describe here the cloning and characterization of the avian orthologue of mammalian TLR4. Chicken TLR4 encodes a 843-amino-acid protein that contains a leucine-rich repeat extracellular domain, a short transmembrane domain typical of type I transmembrane proteins, and a Toll-interleukin-1R signaling domain characteristic of all TLR proteins. The chicken TLR4 protein shows 46% identity (64% similarity) to human TLR4 and 41% similarity to other TLR family members. Northern blot analysis reveals that TLR4 is expressed at approximately the same level in all tissues tested, including brain, thymus, kidney, intestine, muscle, liver, lung, bursa of Fabricius, heart, and spleen. The probe detected only one transcript of ca. 4.4 kb in length for all tissues except muscle where the size of TLR4 mRNA was ca. 9.6 kb. We have mapped TLR4 to microchromosome E41W17 in a region harboring the gene for tenascin C and known to be well conserved between the chicken and mammalian genomes. This region of the chicken genome was shown previously to harbor a Salmonella susceptibility locus. By using linkage analysis, TLR4 was shown to be linked to resistance to infection with Salmonella enterica serovar Typhimurium in chickens (likelihood ratio test of 10.2, P = 0.00138), suggesting a role of TLR4 in the host response of chickens to Salmonella infection

Effects of Passage Number and Differentiation Protocol on the Generation of Dopaminergic Neurons from Rat Bone Marrow-Derived Mesenchymal Stem Cells

Multiple studies have demonstrated the ability of mesenchymal stem cells (MSCs) to differentiate into dopamine-producing cells, in vitro and in vivo, indicating their potential to be used in the treatment of Parkinson’s disease (PD). However, there are discrepancies among studies regarding the optimal time (i.e., passage number) and method for dopaminergic induction, in vitro. In the current study, we compared the ability of early (P4) and later (P40) passaged bone marrow-derived MSCs to differentiate into dopaminergic neurons using two growth-factor-based approaches. A direct dopaminergic induction (DDI) was used to directly convert MSCs into dopaminergic neurons, and an indirect dopaminergic induction (IDI) was used to direct MSCs toward a neuronal lineage prior to terminal dopaminergic differentiation. Results indicate that both early and later passaged MSCs exhibited positive expression of neuronal and dopaminergic markers following either the DDI or IDI protocols. Additionally, both early and later passaged MSCs released dopamine and exhibited spontaneous neuronal activity following either the DDI or IDI. Still, P4 MSCs exhibited significantly higher spiking and bursting frequencies as compared to P40 MSCs. Findings from this study provide evidence that early passaged MSCs, which have undergone the DDI, are more efficient at generating dopaminergic-like cells in vitro, as compared to later passaged MSCs or MSCs that have undergone the IDI