Exponentially growing solutions in homogeneous Rayleigh-Benard convection

It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full non-linear system of equations. These solutions are clearly manifest in numerical simulations above a computable critical value of the Rayleigh number. In our numerical simulations they are subject to secondary numerical noise and resolution dependent instabilities that limit their growth to produce statistically steady turbulent transport.Comment: 4 pages, 3 figures, to be published in Phys. Rev. E - rapid communication

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation

RNA interference screening reveals host CaMK4 as a regulator of cryptococcal uptake and pathogenesis

ABSTRACT Cryptococcus neoformans , the causative agent of cryptococcosis, is an opportunistic fungal pathogen that kills over 200,000 individuals annually. This yeast may grow freely in body fluids, but it also flourishes within host cells. Despite extensive research on cryptococcal pathogenesis, host genes involved in the initial engulfment of fungi and subsequent stages of infection are woefully understudied. To address this issue, we combined short interfering RNA silencing and a high-throughput imaging assay to identify host regulators that specifically influence cryptococcal uptake. Of 868 phosphatase and kinase genes assayed, we discovered 79 whose silencing significantly affected cryptococcal engulfment. For 25 of these, the effects were fungus specific, as opposed to general alterations in phagocytosis. Four members of this group significantly and specifically altered cryptococcal uptake; one of them encoded CaMK4, a calcium/calmodulin-dependent protein kinase. Pharmacological inhibition of CaMK4 recapitulated the observed defects in phagocytosis. Furthermore, mice deficient in CaMK4 showed increased survival compared to wild-type mice upon infection with C. neoformans . This increase in survival correlated with decreased expression of pattern recognition receptors on host phagocytes known to recognize C. neoformans . Altogether, we have identified a kinase that is involved in C. neoformans internalization by host cells and in host resistance to this deadly infection. </jats:p

Coherent State path-integral simulation of many particle systems

The coherent state path integral formulation of certain many particle systems allows for their non perturbative study by the techniques of lattice field theory. In this paper we exploit this strategy by simulating the explicit example of the diffusion controlled reaction $A+A\to 0$. Our results are consistent with some renormalization group-based predictions thus clarifying the continuum limit of the action of the problem.Comment: 20 pages, 4 figures. Minor corrections. Acknowledgement and reference correcte

Destabilizing Taylor-Couette flow with suction

We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linearly unstable steady spiralling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in the earth's polar vortex.Comment: 34 pages, 9 figure

Laminar and turbulent dissipation in shear flow with suction

The rate of viscous energy dissipation in a shear layer of incompressible Newtonian fluid with injection and suction is studied by means of exact solutions, nonlinear and linearized stability theory, and rigorous upper bounds. For large enough values of the injection angle a steady laminar flow is nonlinearly stable for all Reynolds numbers, while for small but nonzero angles the laminar flow is linearly unstable at high Reynolds numbers. The upper bound on the energy dissipation rate—valid even for turbulent solutions of the Navier-Stokes equations—scales precisely the same as that in the steady laminar solution with regard to the viscosity in the vanishing viscosity limit. Both the laminar dissipation and the upper bound on turbulent dissipation display scaling in which the energy dissipation rate becomes independent of the viscosity for high Reynolds numbers. Hence the laminar energy dissipation rate and the largest possible turbulent energy dissipation rate for flows in this geometry differ by just a prefactor that depends only on injection angle. This result establishes the sharpness of the upper bound’s scaling in the vanishing viscosity limit for these boundary conditions, and this system provides an analytic illustration of the delicacy of corrections to scaling (e.g., logarithmic terms as appearing in the “law of the wall”) to perturbations in the boundary conditions. © 2000 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87605/2/497_1.pd

Energy dissipation in a shear layer with suction

The rate of viscous energy dissipation in a shear layer of incompressible Newtonian fluid with injection and suction is studied by means of exact solutions, nonlinear and linearized stability theory, and rigorous upper bounds. The injection and suction rates are maintained constant and equal and this leads to solutions with constant throughput. For strong enough suction, expressed in terms of the entry angle between the injection velocity and the boundaries, a steady laminar flow is nonlinearly stable for all Reynolds numbers. For a narrow range of small but nonzero angles, the laminar flow is linearly unstable at high Reynolds numbers. The upper bound on the energy dissipation rate—valid even for turbulent solutions of the Navier–Stokes equations—scales with viscosity in the same way as the laminar dissipation in the vanishing viscosity limit. For both the laminar and turbulent flows, the energy dissipation rate becomes independent of the viscosity for high Reynolds numbers. Hence the laminar energy dissipation rate and the largest possible turbulent energy dissipation rate for flows in this geometry differ by only a prefactor that depends only on the angle of entry. © 2000 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69712/2/PHFLE6-12-8-1955-1.pd

On the universality of a class of annihilation-coagulation models

A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are established. For the one-dimensional case, it is shown how correlations in the initial state can lead to non-universal amplitudes for time-dependent particles density.Comment: 18 pages with no figures. Latex file using REVTE