Stability and flow fields structure for interfacial dynamics with interfacial mass flux

We analyze from a far field the evolution of an interface that separates ideal incompressible fluids of different densities and has an interfacial mass flux. We develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations, and analyze the interplay of interface stability with flow fields structure, by directly linking rigorous mathematical attributes to physical observables. New mechanisms are identified of the interface stabilization and destabilization. We find that interfacial dynamics is stable when it conserves the fluxes of mass, momentum and energy. The stabilization is due to inertial effects causing small oscillations of the interface velocity. In the classic Landau dynamics, the postulate of perfect constancy of the interface velocity leads to the development of the Landau-Darrieus instability. This destabilization is also associated with the imbalance of the perturbed energy at the interface, in full consistency with the classic results. We identify extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including formal properties of fundamental solutions and qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology

Local virial relation for self-gravitating system

We demonstrate that the quasi-equilibrium state in self-gravitating $N$-body system after cold collapse are uniquely characterized by the local virial relation using numerical simulations. Conversely assuming the constant local virial ratio and Jeans equation for spherically steady state system, we investigate the full solution space of the problem under the constant anisotropy parameter and obtain some relevant solutions. Especially, the local virial relation always provides a solution which has a power law density profile in both the asymptotic regions $r\to 0$ and $\infty$. This type of solutions observed commonly in many numerical simulations. Only the anisotropic velocity dispersion controls this asymptotic behavior of density profile.Comment: 9 pages, 15 eps figures, RevTex, submitted to PR

Stability and flow fields structure for interfacial dynamics with interfacial mass flux

We analyze from a far field the evolution of an interface that separates ideal incompressible fluids of different densities and has an interfacial mass flux. We develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations, and analyze the interplay of interface stability with flow fields structure, by directly linking rigorous mathematical attributes to physical observables. New mechanisms are identified of the interface stabilization and destabilization. We find that interfacial dynamics is stable when it conserves the fluxes of mass, momentum and energy. The stabilization is due to inertial effects causing small oscillations of the interface velocity. In the classic Landau dynamics, the postulate of perfect constancy of the interface velocity leads to the development of the Landau-Darrieus instability. This destabilization is also associated with the imbalance of the perturbed energy at the interface, in full consistency with the classic results. We identify extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including formal properties of fundamental solutions and qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.Comment: More comments for the quantitative estimation of chaos are added, and some inappropriate terms are changed. This will appear on Class. Quant. Gra

Synthesis of macrocyclic receptors with intrinsic fluorescence featuring quinizarin moieties

An unprecedented class of macrocycles with intrinsic fluorescence consisting of phenolic trimers and quinizarin is developed. Though they are lacking strong hydrogen bonds as observed in calixarenes, the two examples introduced here each adopt a vase-like conformation with all four aromatic units pointing in one direction (syn orientation). This “cone” conformation has been confirmed by NMR spectroscopy, molecular modeling, and X-ray crystallography. The laminar, electron-rich fluorophore as part of the macrocycle allows additional contacts to enclosed guest molecules

Perinatal Asphyxia Reduces Dentate Granule Cells and Exacerbates Methamphetamine-Induced Hyperlocomotion in Adulthood

Background: Obstetric complications have been regarded as a risk factor for schizophrenia later in life. One of the mechanisms underlying the association is postulated to be a hypoxic process in the brain in the offspring around the time of birth. Hippocampus is one of the brain regions implicated in the late-onset dopaminergic dysfunction associated with hypoxic obstetric complications. Methodology/Principal Findings: We used an animal model of perinatal asphyxia, in which rat pups were exposed to 15 min of intrauterine anoxia during Cesarean section birth. At 6 and 12 weeks after birth, the behavior of the pups was assessed using a methamphetamine-induced locomotion test. In addition, the histopathology of the hippocampus was examined by means of stereology. At 6 weeks, there was no change in the methamphetamine-induced locomotion. However, at 12 weeks of age, we found an elevation in methamphetamine-induced locomotor activity, which was associated with an increase of dopamine release in the nucleus accumbens. At the same age, we also found a reduction of the dentate granule cells of the hippocampus. Conclusions/Significance: These results suggest that the dopaminergic dysregulation after perinatal asphyxia is associated with a reduction in hippocampal dentate granule cells, and this may partly contribute to the pathogenesis of schizophrenia.浜松医科大学学位論文　医博第548号(平成２１年３月１８日

Association of Transcription Factor Gene LMX1B with Autism

Multiple lines of evidence suggest a serotoninergic dysfunction in autism. The role of LMX1B in the development and maintenance of serotoninergic neurons is well known. In order to examine the role, if any, of LMX1B with autism pathophysiology, a trio-based SNP association study using 252 family samples from the AGRE was performed. Using pair-wise tagging method, 24 SNPs were selected from the HapMap data, based on their location and minor allele frequency. Two SNPs (rs10732392 and rs12336217) showed moderate association with autism with p values 0.018 and 0.022 respectively in transmission disequilibrium test. The haplotype AGCGTG also showed significant association (p = 0.008). Further, LMX1B mRNA expressions were studied in the postmortem brain tissues of autism subjects and healthy controls samples. LMX1B transcripts was found to be significantly lower in the anterior cingulate gyrus region of autism patients compared with controls (p = 0.049). Our study suggests a possible role of LMX1B in the pathophysiology of autism. Based on previous reports, it is likely to be mediated through a seretoninergic mechanism. This is the first report on the association of LMX1B with autism, though it should be viewed with some caution considering the modest associations we report

Generation and Characterization of Conditional Heparin-Binding EGF-Like Growth Factor Knockout Mice

Recently, neurotrophic factors and cytokines have been shown to be associated in psychiatric disorders, such as schizophrenia, bipolar disorder, and depression. Heparin-binding epidermal growth factor-like growth factor (HB-EGF) is a member of the EGF family, serves as a neurotrophic molecular and plays a significant role in the brain. We generated mice in which HB-EGF activity is disrupted specifically in the ventral forebrain. These knockout mice showed (a) behavioral abnormalities similar to those described in psychiatric disorders, which were ameliorated by typical or atypical antipsychotics, (b) altered dopamine and serotonin levels in the brain, (c) decreases in spine density in neurons of the prefrontal cortex, (d) reductions in the protein levels of the NR1 subunit of the N-methyl-D-aspartate (NMDA) receptor and post-synaptic protein-95 (PSD-95), (e) decreases in the EGF receptor, and in the calcium/calmodulin-dependent protein kinase II (CaMK II) signal cascade. These results suggest the alterations affecting HB-EGF signaling could comprise a contributing factor in psychiatric disorder