70 research outputs found
On selection criteria for problems with moving inhomogeneities
We study mechanical problems with multiple solutions and introduce a
thermodynamic framework to formulate two different selection criteria in terms
of macroscopic energy productions and fluxes. Studying simple examples for
lattice motion we then compare the implications for both resting and moving
inhomogeneities.Comment: revised version contains new introduction, numerical simulations of
Riemann problems, and a more detailed discussion of the causality principle;
18 pages, several figure
Action minimizing fronts in general FPU-type chains
We study atomic chains with nonlinear nearest neighbour interactions and
prove the existence of fronts (heteroclinic travelling waves with constant
asymptotic states). Generalizing recent results of Herrmann and Rademacher we
allow for non-convex interaction potentials and find fronts with non-monotone
profile. These fronts minimize an action integral and can only exists if the
asymptotic states fulfil the macroscopic constraints and if the interaction
potential satisfies a geometric graph condition. Finally, we illustrate our
findings by numerical simulations.Comment: 19 pages, several figure
Evolution equations of curvature tensors along the hyperbolic geometric flow
We consider the hyperbolic geometric flow introduced by Kong and Liu [KL]. When the Riemannian
metric evolve, then so does its curvature. Using the techniques and ideas of
S.Brendle [Br,BS], we derive evolution equations for the Levi-Civita connection
and the curvature tensors along the hyperbolic geometric flow. The method and
results are computed and written in global tensor form, different from the
local normal coordinate method in [DKL1]. In addition, we further show that any
solution to the hyperbolic geometric flow that develops a singularity in finite
time has unbounded Ricci curvature.Comment: 15 page
Controlled variations in stimulus similarity during learning determine visual discrimination capacity in freely moving mice
The mouse is receiving growing interest as a model organism for studying visual perception. However, little is known about how discrimination and learning interact to produce visual conditioned responses. Here, we adapted a two-alternative forced-choice visual discrimination task for mice and examined how training with equiprobable stimuli of varying similarity influenced conditioned response and discrimination performance as a function of learning. Our results indicate that the slope of the gradients in similarity during training determined the learning rate, the maximum performance and the threshold for successful discrimination. Moreover, the learning process obeyed an inverse relationship between discrimination performance and discriminative resolution, implying that sensitivity within a similarity range cannot be improved without sacrificing performance in another. Our study demonstrates how the interplay between discrimination and learning controls visual discrimination capacity and introduces a new training protocol with quantitative measures to study perceptual learning and visually-guided behavior in freely moving mice
GAUSS-newton-like methods for nonlinear least squares with equality constraints-local convergence and applications
The pedicled corticocancellous iliac bone graft perfused by the deep branch of the superior gluteal artery—A new concept for revascularisation surgery in femoral head necrosis of adults
- …