5,379 research outputs found
Stochastic Shell Models driven by a multiplicative fractional Brownian--motion
We prove existence and uniqueness of the solution of a stochastic
shell--model. The equation is driven by an infinite dimensional fractional
Brownian--motion with Hurst--parameter , and contains a
non--trivial coefficient in front of the noise which satisfies special
regularity conditions. The appearing stochastic integrals are defined in a
fractional sense. First, we prove the existence and uniqueness of variational
solutions to approximating equations driven by piecewise linear continuous
noise, for which we are able to derive important uniform estimates in some
functional spaces. Then, thanks to a compactness argument and these estimates,
we prove that these variational solutions converge to a limit solution, which
turns out to be the unique pathwise mild solution associated to the
shell--model with fractional noise as driving process.Comment: 23 page
Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node
Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced
quantum phase transition between a semimetallic phase at weak disorder and a
diffusive-metallic phase at strong disorder. Despite considerable effort, both
numerically and analytically, the critical exponents and of this
phase transition are not known precisely. Here we report a numerical
calculation of the critical exponent using a minimal
single-Weyl node model and a finite-size scaling analysis of conductance. Our
high-precision numerical value for is incompatible with previous
numerical studies on tight-binding models and with one- and two-loop
calculations in an -expansion scheme. We further obtain
from the scaling of the conductivity with chemical potential
Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients
In this paper we study the longtime dynamics of mild solutions to retarded
stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a
preparation for this purpose we have to show the existence and uniqueness of a
cocycle solution of such an equation. We do not assume that the noise is given
in additive form or that it is a very simple multiplicative noise. However, we
need some smoothing property for the coefficient in front of the noise. The
main idea of this paper consists of expressing the stochastic integral in terms
of non-stochastic integrals and the noisy path by using an integration by
parts. This latter term causes that in a first moment only a local mild
solution can be obtained, since in order to apply the Banach fixed point
theorem it is crucial to have the H\"older norm of the noisy path to be
sufficiently small. Later, by using appropriate stopping times, we shall derive
the existence and uniqueness of a global mild solution. Furthermore, the
asymptotic behavior is investigated by using the {\it Random Dynamical Systems
theory}. In particular, we shall show that the global mild solution generates a
random dynamical system that, under an appropriate smallness condition for the
time lag, have associated a random attractor
Cross-Correlation in the Auditory Coincidence Detectors of Owls
Interaural time difference (ITD) plays a central role in many auditory functions, most importantly in sound localization. The classic model for how ITD is computed was put forth by Jeffress (1948). One of the predictions of the Jeffress model is that the neurons that compute ITD should behave as cross-correlators. Whereas cross-correlation-like properties of the ITD-computing neurons have been reported, attempts to show that the shape of the ITD response function is determined by the spectral tuning of the neuron, a core prediction of cross-correlation, have been unsuccessful. Using reverse correlation analysis, we demonstrate in the barn owl that the relationship between the spectral tuning and the ITD response of the ITD-computing neurons is that predicted by cross-correlation. Moreover, we show that a model of coincidence detector responses derived from responses to binaurally uncorrelated noise is consistent with binaural interaction based on cross-correlation. These results are thus consistent with one of the key tenets of the Jeffress model. Our work sets forth both the methodology to answer whether cross-correlation describes coincidence detector responses and a demonstration that in the barn owl, the result is that expected by theory
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