The rheology of dense, polydisperse granular fluids under shear

The solution of the Enskog equation for the one-body velocity distribution of a moderately dense, arbitrary mixture of inelastic hard spheres undergoing planar shear flow is described. A generalization of the Grad moment method, implemented by means of a novel generating function technique, is used so as to avoid any assumptions concerning the size of the shear rate. The result is illustrated by using it to calculate the pressure, normal stresses and shear viscosity of a model polydisperse granular fluid in which grain size, mass and coefficient of restitution varies amoungst the grains. The results are compared to a numerical solution of the Enskog equation as well as molecular dynamics simulations. Most bulk properties are well described by the Enskog theory and it is shown that the generalized moment method is more accurate than the simple (Grad) moment method. However, the description of the distribution of temperatures in the mixture predicted by Enskog theory does not compare well to simulation, even at relatively modest densities.Comment: 8 postscript figures Replaced with new version correcting an error in the SME calculations and misc. small corrections. Second replacement with final correction of SME calculation

MicroRNA-Mediated mRNA Translation Activation in Quiescent Cells and Oocytes Involves Recruitment of a Nuclear microRNP

MicroRNAs can promote translation of specific mRNAs in quiescent (G0) mammalian cells and immature Xenopus laevis oocytes. We report that microRNA-mediated upregulation of target mRNAs in oocytes is dependent on nuclear entry of the microRNA; cytoplasmically-injected microRNA repress target mRNAs. Components of the activation microRNP, AGO, FXR1 (FXR1-iso-a) and miR16 are present in the nucleus and cytoplasm. Importantly, microRNA target mRNAs for upregulation, Myt1, TNFα and a reporter bearing the TNFα AU-rich, microRNA target sequence, are associated with AGO in immature oocyte nuclei and AGO2 in G0 human nuclei, respectively. mRNAs that are repressed or lack target sites are not associated with nuclear AGO. Crosslinking-coupled immunopurification revealed greater association of AGO2 with FXR1 in the nucleus compared to cytoplasm. Consistently, overexpression of FXR1-iso-a rescues activation of cytoplasmically-injected RNAs and in low density, proliferating cells. These data indicate the importance of a compartmentalized AGO2-FXR1-iso-a complex for selective recruitment for microRNA-mediated upregulation

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy

On the High-Temperature Behaviour of the Closed Superstring

The high-temperature expansion for closed superstring one-loop free energy is studied. The Laurent series representation is obtained and its sum is analytically continued in order to investigate the nature of the critical (Hagedorn) temperature. It is found that beyond this critical temperature the statistical sum contribution of the free energy is finite but has an imaginary part, signalling a possible metastability of the system.Comment: 7 pages, UTF32

Power-law velocity distributions in granular gases

We report a general class of steady and transient states of granular gases. We find that the kinetic theory of inelastic gases admits stationary solutions with a power-law velocity distribution, f(v) ~ v^(-sigma). The exponent sigma is found analytically and depends on the spatial dimension, the degree of inelasticity, and the homogeneity degree of the collision rate. Driven steady-states, with the same power-law tail and a cut-off can be maintained by injecting energy at a large velocity scale, which then cascades to smaller velocities where it is dissipated. Associated with these steady-states are freely cooling time-dependent states for which the cut-off decreases and the velocity distribution is self-similar.Comment: 11 pages, 9 figure

Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Due to the bilinearity of the energy functional,I have obtained its exact partition function.By investigation of the system,I conjectured that an expectation value at a critical point of this system obeys the Painlev\'e equation of the first kind and its related equations extended by the KdV hierarchy.Furthermore I also commented onthe relation between the MKdV hierarchy and BRS transformationin this system.Comment: AMS-Tex Us

On general measures of deformation

Each particle of a continuum is assigned a second order tensor which is taken as a measure of the deformation of some neighborhood of the particle, and which is determined by a functional depending on the configurations of that neighborhood. Two invariance restrictions are imposed on the functional whose values are spatial strain tensors, that is, associated with the deformed configuration. The first requirement is that a time shift and rigid transformation of the deformed configuration leave the spatial deformation tensor unaltered relative to it. The second requires that if particles of distinct continua undergo the same deformation, the corresponding deformation tensors should be the same. For the special case in which the functional depends on the deformation in the smallest neighborhood of a particle, the restrictions imply that the deformation tensors associated with the deformed and reference configurations are isotropic functions of the left and right Cauchy-Green tensors, respectively. Jedem Teilchen eines Kontinuums wird ein Tensor zweiter Stufe als Maß für die Deformation einer gewissen Nachbarschaft dieses Teilchen zugeordnet, der durch ein Funktional bestimmt wird, das von der Konfiguration dieser Nachbarschaft abhängt. Zwei Invarianzbedingungen werden diesem Funktional, dessen Werte räumliche Verzerrungstensoren darstellen, auferlegt, und zwar im Hindblick auf die deformierte Konfiguration. Die erste Forderung besagt, daß eine Zeitverschiebung und eine starre Transformation der deformierten Konfiguration den räumlichen Verzerrungstensor im Hinblick auf diese ungeändert lassen. Die zweite Einschränkung besagt, daß entsprechende Deformationstensoren von Partikeln verschiedener Kontinua, die dieselbe Verformung erlitten haben, gleich sein sollen. Im Spezialfall, daß die Funktionale nur von der Deformation in der nächsten Umgebung des Partikels abhängen, beinhalten die Einschränkungen die Aussage, daß die mit dem deformierten und dem undeformierten Zustand verknüpften Deformationstensoren nur isotrope Funktionen des linken und des rechten Cauchy-Green Tensors sein können.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41717/1/707_2005_Article_BF01172146.pd