arXiv subjects
Publications and source records attributed to C. R. Doering.
The claim by He et al. [Physical Review Letters 108, 024502 (2012)] that their experiment reached the 'ultimate' regime of turbulent Rayleigh-Bénard convection is not justified by their data.
In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.
A procedure is suggested for testing the resolution and comparing the relative accuracy of numerical schemes for integration of the incompressible Euler equations.
The relation between the shape of the force driving a turbulent flow and the upper bound on the dimensionless dissipation factor $β$ is presented. We are interested in non-trivial (more than two wave numbers) forcing functions in a three dimensional domain periodic in all directions. A comparative analysis between results given by the optimization problem and the results of Direct Numerical Simulations is performed. We report that the bound on the dissipation factor in the case of infinite Reynolds numbers have the same qualitative behavior as for the dissipation factor at finite Reynolds number. As predicted by the analysis, the dissipation factor depends strongly on the force shape. However, the optimization problem does not predict accurately the quantitative behavior. We complete our study by analyzing the mean flow profile in relation to the Stokes flow profile and the optimal multiplier profile shape for different force-shapes. We observe that in our 3D-periodic domain, the mean velocity profile and the Stokes flow profile reproduce all the characteristic features of the force-shape. The optimal multiplier proves to be linked to the intensity of the wave numbers of the forcing function.
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.
Energy theory for incompressible Newtonian fluids is, in many cases, capable of producing strong absolute stability criteria for steady flows. In those fluids the kinetic energy naturally defines a norm in which perturbations decay monotonically in time at sufficiently low (but non-zero) Reynolds numbers. There are, however, at least two obstructions to the generalization of such methods to Oldroyd-B fluids. One previously recognized problem is the fact that the natural energy does not correspond to a proper functional norm on perturbations. Another problem, original to this work, is the fact that fluctuations in Oldroyd-B fluids may be subject to non-normal amplification at arbitrarily low Reynolds numbers (albeit at sufficiently large Weissenberg numbers). Such transient growth, occuring even when the base flow is linearly stable, precludes the uniform monotonic decay of any reasonable measure of the disturbance's amplitude.
We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation describes the crossover from the mean-field rate-equation behavior at short times to the universal, fluctuation-dominated behavior at large times. The approximation becomes quantitatively accurate when the system is initially close to the continuum behavior, i.e., for small initial density and fast reaction. For large initial density and slow reaction, lattice effects are nonnegligible for an extended initial time interval. In such cases our approximation provides the correct description of the initial mean-field as well as the asymptotic large-time, fluctuation-dominated behavior. However, the intermediate-time crossover between the two regimes is described only semiquantitatively.