297 research outputs found
Dynamics of the vortex line density in superfluid counterflow turbulence
Describing superfluid turbulence at intermediate scales between the
inter-vortex distance and the macroscale requires an acceptable equation of
motion for the density of quantized vortex lines . The closure of such
an equation for superfluid inhomogeneous flows requires additional inputs
besides and the normal and superfluid velocity fields. In this paper
we offer a minimal closure using one additional anisotropy parameter .
Using the example of counterflow superfluid turbulence we derive two coupled
closure equations for the vortex line density and the anisotropy parameter
with an input of the normal and superfluid velocity fields. The
various closure assumptions and the predictions of the resulting theory are
tested against numerical simulations.Comment: 7 pages, 5 figure
Athermal Nonlinear Elastic Constants of Amorphous Solids
We derive expressions for the lowest nonlinear elastic constants of amorphous
solids in athermal conditions (up to third order), in terms of the interaction
potential between the constituent particles. The effect of these constants
cannot be disregarded when amorphous solids undergo instabilities like plastic
flow or fracture in the athermal limit; in such situations the elastic response
increases enormously, bringing the system much beyond the linear regime. We
demonstrate that the existing theory of thermal nonlinear elastic constants
converges to our expressions in the limit of zero temperature. We motivate the
calculation by discussing two examples in which these nonlinear elastic
constants play a crucial role in the context of elasto-plasticity of amorphous
solids. The first example is the plasticity-induced memory that is typical to
amorphous solids (giving rise to the Bauschinger effect). The second example is
how to predict the next plastic event from knowledge of the nonlinear elastic
constants. Using the results of this paper we derive a simple differential
equation for the lowest eigenvalue of the Hessian matrix in the external strain
near mechanical instabilities; this equation predicts how the eigenvalue
vanishes at the mechanical instability and the value of the strain where the
mechanical instability takes place.Comment: 17 pages, 2 figures
Mix and match: a strategyproof mechanism for multi-hospital kidney exchange
As kidney exchange programs are growing, manipulation by hospitals becomes more of an issue. Assuming that hospitals wish to maximize the number of their own patients who receive a kidney, they may have an incentive to withhold some of their incompatible donor–patient pairs and match them internally, thus harming social welfare. We study mechanisms for two-way exchanges that are strategyproof, i.e., make it a dominant strategy for hospitals to report all their incompatible pairs. We establish lower bounds on the welfare loss of strategyproof mechanisms, both deterministic and randomized, and propose a randomized mechanism that guarantees at least half of the maximum social welfare in the worst case. Simulations using realistic distributions for blood types and other parameters suggest that in practice our mechanism performs much closer to optimal
Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation I: Basic Principles
We develop an athermal version of the shear-transformation-zone (STZ) theory
of amorphous plasticity in materials where thermal activation of irreversible
molecular rearrangements is negligible or nonexistent. In many respects, this
theory has broader applicability and yet is simpler than its thermal
predecessors. For example, it needs no special effort to assure consistency
with the laws of thermodynamics, and the interpretation of yielding as an
exchange of dynamic stability between jammed and flowing states is clearer than
before. The athermal theory presented here incorporates an explicit
distribution of STZ transition thresholds. Although this theory contains no
conventional thermal fluctuations, the concept of an effective temperature is
essential for understanding how the STZ density is related to the state of
disorder of the system.Comment: 7 pages, 2 figures; first of a two-part serie
Fractal dimension crossovers in turbulent passive scalar signals
The fractal dimension of turbulent passive scalar signals is
calculated from the fluid dynamical equation. depends on the
scale. For small Prandtl (or Schmidt) number one gets two ranges,
for small scale r and =5/3 for large r, both
as expected. But for large one gets a third, intermediate range in
which the signal is extremely wrinkled and has . In that
range the passive scalar structure function has a plateau. We
calculate the -dependence of the crossovers. Comparison with a numerical
reduced wave vector set calculation gives good agreement with our predictions.Comment: 7 pages, Revtex, 3 figures (postscript file on request
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