4,310 research outputs found
Contest based on a directed polymer in a random medium
We introduce a simple one-parameter game derived from a model describing the
properties of a directed polymer in a random medium. At his turn, each of the
two players picks a move among two alternatives in order to maximize his final
score, and minimize opponent's return. For a game of length , we find that
the probability distribution of the final score develops a traveling wave
form, , with the wave profile unusually
decaying as a double exponential for large positive and negative . In
addition, as the only parameter in the game is varied, we find a transition
where one player is able to get his maximum theoretical score. By extending
this model, we suggest that the front velocity is selected by the nonlinear
marginal stability mechanism arising in some traveling wave problems for which
the profile decays exponentially, and for which standard traveling wave theory
applies
Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
We study the problem of initiation of excitation waves in the FitzHugh-Nagumo
model. Our approach follows earlier works and is based on the idea of
approximating the boundary between basins of attraction of propagating waves
and of the resting state as the stable manifold of a critical solution. Here,
we obtain analytical expressions for the essential ingredients of the theory by
singular perturbation using two small parameters, the separation of time scales
of the activator and inhibitor, and the threshold in the activator's kinetics.
This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2
Erosion waves: transverse instabilities and fingering
Two laboratory scale experiments of dry and under-water avalanches of
non-cohesive granular materials are investigated. We trigger solitary waves and
study the conditions under which the front is transversally stable. We show the
existence of a linear instability followed by a coarsening dynamics and finally
the onset of a fingering pattern. Due to the different operating conditions,
both experiments strongly differ by the spatial and time scales involved.
Nevertheless, the quantitative agreement between the stability diagram, the
wavelengths selected and the avalanche morphology reveals a common scenario for
an erosion/deposition process.Comment: 4 pages, 6 figures, submitted to PR
Shift in the velocity of a front due to a cut-off
We consider the effect of a small cut-off epsilon on the velocity of a
traveling wave in one dimension. Simulations done over more than ten orders of
magnitude as well as a simple theoretical argument indicate that the effect of
the cut-off epsilon is to select a single velocity which converges when epsilon
tends to 0 to the one predicted by the marginal stability argument. For small
epsilon, the shift in velocity has the form K(log epsilon)^(-2) and our
prediction for the constant K agrees very well with the results of our
simulations. A very similar logarithmic shift appears in more complicated
situations, in particular in finite size effects of some microscopic stochastic
systems. Our theoretical approach can also be extended to give a simple way of
deriving the shift in position due to initial conditions in the
Fisher-Kolmogorov or similar equations.Comment: 12 pages, 3 figure
Non-Fermi-liquid behavior in Ce(RuFe)Ge: cause and effect
We present inelastic neutron scattering measurements on the intermetallic
compounds Ce(RuFe)Ge (=0.65, 0.76 and 0.87). These
compounds represent samples in a magnetically ordered phase, at a quantum
critical point and in the heavy-fermion phase, respectively. We show that at
high temperatures the three compositions have the identical response of a local
moment system. However, at low temperatures the spin fluctuations in the
critical composition are given by non-Fermi-liquid dynamics, while the spin
fluctuations in the heavy fermion system show a simple exponential decay in
time. In both compositions, the lifetime of the fluctuations is determined
solely by the distance to the quantum critical point. We discuss the
implications of these observations regarding the possible origins of
non-Fermi-liquid behavior in this system.Comment: 4 figures, submitted to PR
Perturbative Linearization of Reaction-Diffusion Equations
We develop perturbative expansions to obtain solutions for the initial-value
problems of two important reaction-diffusion systems, viz., the Fisher equation
and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of
our expansion is the corresponding singular-perturbation solution. This
approach transforms the solution of nonlinear reaction-diffusion equations into
the solution of a hierarchy of linear equations. Our numerical results
demonstrate that this hierarchy rapidly converges to the exact solution.Comment: 13 pages, 4 figures, latex2
On the Convergence of the Born Series in Optical Tomography with Diffuse Light
We provide a simple sufficient condition for convergence of Born series in
the forward problem of optical diffusion tomography. The condition does not
depend on the shape or spatial extent of the inhomogeneity but only on its
amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem
Interplay of gravitation and linear superposition of different mass eigenstates
The interplay of gravitation and the quantum-mechanical principle of linear
superposition induces a new set of neutrino oscillation phases. These ensure
that the flavor-oscillation clocks, inherent in the phenomenon of neutrino
oscillations, redshift precisely as required by Einstein's theory of
gravitation. The physical observability of these phases in the context of the
solar neutrino anomaly, type-II supernovae, and certain atomic systems is
briefly discussed
Integration of professional judgement and decision-making in high-level adventure sports coaching practice
This study examined the integration of professional judgement and decision-making processes in adventure sports coaching. The study utilised a thematic analysis approach to investigate the decision-making practices of a sample of high-level adventure sports coaches over a series of sessions. Results revealed that, in order to make judgements and decisions in practice, expert coaches employ a range of practical and pedagogic management strategies to create and opportunistically use time for decision-making. These approaches include span of control and time management strategies to facilitate the decision-making process regarding risk management, venue selection, aims, objectives, session content, and differentiation of the coaching process. The implication for coaches, coach education, and accreditation is the recognition and training of the approaches thatâcreate timeâ for the judgements in practice, namelyâcreating space to thinkâ. The paper concludes by offering a template for a more expertise-focused progression in adventure sports coachin
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