757 research outputs found
Classes of random walks on temporal networks with competing timescales
Random walks find applications in many areas of science and are the heart of
essential network analytic tools. When defined on temporal networks, even basic
random walk models may exhibit a rich spectrum of behaviours, due to the
co-existence of different timescales in the system. Here, we introduce random
walks on general stochastic temporal networks allowing for lasting
interactions, with up to three competing timescales. We then compare the mean
resting time and stationary state of different models. We also discuss the
accuracy of the mathematical analysis depending on the random walk model and
the structure of the underlying network, and pay particular attention to the
emergence of non-Markovian behaviour, even when all dynamical entities are
governed by memoryless distributions.Comment: 16 pages, 5 figure
First principles calculation of the phonons modes in the hexagonal ferroelectric and paraelectric phases
The lattice dynamics of the magneto-electric compound has been
investigated using density functional calculations, both in the ferroelectric
and the paraelectric phases. The coherence between the computed and
experimental data is very good in the low temperature phase. Using group
theory, modes continuity and our calculations we were able to show that the
phonons modes observed by Raman scattering at 1200K are only compatible with
the ferroelectric space group, thus supporting the idea of a
ferroelectric to paraelectric phase transition at higher temperature. Finally
we proposed a candidate for the phonon part of the observed electro-magnon.
This mode, inactive both in Raman scattering and in Infra-Red, was shown to
strongly couple to the Mn-Mn magnetic interactions
The Road to Understanding the Confrontation Clause: Ohio v. Clark Makes a U-Turn
The article discusses the Confrontation Clause and summarizes the state of the law before the U.S. Supreme Court\u27s decision in the case Ohio v. Clark. Topics discussed include problems that the decision caused and how these problems affect the admissibility of statements into evidence; and ways in which use of Confrontation Clause teat can eliminate confusion related to issue
Delay induced Turing-like waves for one species reaction-diffusion model on a network
A one species time-delay reaction-diffusion system defined on a complex
networks is studied. Travelling waves are predicted to occur as follows a
symmetry breaking instability of an homogenous stationary stable solution,
subject to an external non homogenous perturbation. These are generalized
Turing-like waves that materialize in a single species populations dynamics
model, as the unexpected byproduct of the imposed delay in the diffusion part.
Sufficient conditions for the onset of the instability are mathematically
provided by performing a linear stability analysis adapted to time delayed
differential equation. The method here developed exploits the properties of the
Lambert W-function. The prediction of the theory are confirmed by direct
numerical simulation carried out for a modified version of the classical Fisher
model, defined on a Watts-Strogatz networks and with the inclusion of the
delay
Random walk on temporal networks with lasting edges
We consider random walks on dynamical networks where edges appear and
disappear during finite time intervals. The process is grounded on three
independent stochastic processes determining the walker's waiting-time, the
up-time and down-time of edges activation. We first propose a comprehensive
analytical and numerical treatment on directed acyclic graphs. Once cycles are
allowed in the network, non-Markovian trajectories may emerge, remarkably even
if the walker and the evolution of the network edges are governed by memoryless
Poisson processes. We then introduce a general analytical framework to
characterize such non-Markovian walks and validate our findings with numerical
simulations.Comment: 18 pages, 18 figure
Eddies and interface deformations induced by optical streaming
We study flows and interface deformations produced by the scattering of a
laser beam propagating through non-absorbing turbid fluids. Light scattering
produces a force density resulting from the transfer of linear momentum from
the laser to the scatterers. The flow induced in the direction of the beam
propagation, called 'optical streaming', is also able to deform the interface
separating the two liquid phases and to produce wide humps. The viscous flow
taking place in these two liquid layers is solved analytically, in one of the
two liquid layers with a stream function formulation, as well as numerically in
both fluids using a boundary integral element method. Quantitative comparisons
are shown between the numerical and analytical flow patterns. Moreover, we
present predictive simulations regarding the effects of the geometry, of the
scattering strength and of the viscosities, on both the flow pattern and the
deformation of the interface. Finally, theoretical arguments are put forth to
explain the robustness of the emergence of secondary flows in a two-layer fluid
system
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