252 research outputs found
Asymptotic description of transients and synchronized states of globally coupled oscillators
A two-time scale asymptotic method has been introduced to analyze the
multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in
the high-frequency limit. The method allows to uncouple the probability density
in different components corresponding to the different peaks of the oscillator
frequency distribution. Each component evolves toward a stationary state in a
comoving frame and the overall order parameter can be reconstructed by
combining them. Synchronized phases are a combination of traveling waves and
incoherent solutions depending on parameter values. Our results agree very well
with direct numerical simulations of the nonlinear Fokker-Planck equation for
the probability density. Numerical results have been obtained by finite
differences and a spectral method in the particular case of bimodal (symmetric
and asymmetric) frequency distribution with or without external field. We also
recover in a very easy and intuitive way the only other known analytical
results: those corresponding to reflection-symmetric bimodal frequency
distributions near bifurcation points.Comment: Revtex,12 pag.,9 fig.;submitted to Physica
Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold
We consider the asymptotic behaviour of positive solutions of the
fast diffusion equation
posed for x\in\RR^d, , with a precise value for the exponent
. The space dimension is so that , and even
for . This case had been left open in the general study \cite{BBDGV} since
it requires quite different functional analytic methods, due in particular to
the absence of a spectral gap for the operator generating the linearized
evolution.
The linearization of this flow is interpreted here as the heat flow of the
Laplace-Beltrami operator of a suitable Riemannian Manifold (\RR^d,{\bf g}),
with a metric which is conformal to the standard \RR^d metric.
Studying the pointwise heat kernel behaviour allows to prove {suitable
Gagliardo-Nirenberg} inequalities associated to the generator. Such
inequalities in turn allow to study the nonlinear evolution as well, and to
determine its asymptotics, which is identical to the one satisfied by the
linearization. In terms of the rescaled representation, which is a nonlinear
Fokker--Planck equation, the convergence rate turns out to be polynomial in
time. This result is in contrast with the known exponential decay of such
representation for all other values of .Comment: 37 page
Dynamical aspects of mean field plane rotators and the Kuramoto model
The Kuramoto model has been introduced in order to describe synchronization
phenomena observed in groups of cells, individuals, circuits, etc... We look at
the Kuramoto model with white noise forces: in mathematical terms it is a set
of N oscillators, each driven by an independent Brownian motion with a constant
drift, that is each oscillator has its own frequency, which, in general,
changes from one oscillator to another (these frequencies are usually taken to
be random and they may be viewed as a quenched disorder). The interactions
between oscillators are of long range type (mean field). We review some results
on the Kuramoto model from a statistical mechanics standpoint: we give in
particular necessary and sufficient conditions for reversibility and we point
out a formal analogy, in the N to infinity limit, with local mean field models
with conservative dynamics (an analogy that is exploited to identify in
particular a Lyapunov functional in the reversible set-up). We then focus on
the reversible Kuramoto model with sinusoidal interactions in the N to infinity
limit and analyze the stability of the non-trivial stationary profiles arising
when the interaction parameter K is larger than its critical value K_c. We
provide an analysis of the linear operator describing the time evolution in a
neighborhood of the synchronized profile: we exhibit a Hilbert space in which
this operator has a self-adjoint extension and we establish, as our main
result, a spectral gap inequality for every K>K_c.Comment: 18 pages, 1 figur
Multiple Front Propagation Into Unstable States
The dynamics of transient patterns formed by front propagation in extended
nonequilibrium systems is considered. Under certain circumstances, the state
left behind a front propagating into an unstable homogeneous state can be an
unstable periodic pattern. It is found by a numerical solution of a model of
the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of
decay of such periodic unstable states is the propagation of a second front
which replaces the unstable pattern by a another unstable periodic state with
larger wavelength. The speed of this second front and the periodicity of the
new state are analytically calculated with a generalization of the marginal
stability formalism suited to the study of front propagation into periodic
unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+rComment: 12 page
Electronic Structure of Calcium Hexaboride within the Weighted Density Approximation
We report calculations of the electronic structure of CaB using the
weighted density approximation (WDA) to density functional theory. We find a
semiconducting band structure with a sizable gap, in contrast to local density
approximation (LDA) results, but in accord with recent experimental data. In
particular, we find an -point band gap of 0.8 eV. The WDA correction of the
LDA error in describing the electronic structure of CaB is discussed in
terms of the orbital character of the bands and the better cancelation of
self-interactions within the WDA.Comment: 1 figur
Further analysis of the quantum critical point of CeLaRuSi
New data on the spin dynamics and the magnetic order of
CeLaRuSi are presented. The importance of the Kondo
effect at the quantum critical point of this system is emphasized from the
behaviour of the relaxation rate at high temperature and from the variation of
the ordered moment with respect to the one of the N\'eel temperature for
various .Comment: Contribution for the Festschrift on the occasion of Hilbert von
Loehneysen 60 th birthday. To be published as a special issue in the Journal
of Low Temperature Physic
Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators
We discuss the general theoretical arguments advanced earlier for the T=0
global phase diagram of antiferromagnetic Kondo lattice systems, distinguishing
between the established and the conjectured. In addition to the well-known
phase of a paramagnetic metal with a "large" Fermi surface (P_L), there is also
an antiferromagnetic phase with a "small" Fermi surface (AF_S). We provide the
details of the derivation of a quantum non-linear sigma-model (QNLsM)
representation of the Kondo lattice Hamiltonian, which leads to an effective
field theory containing both low-energy fermions in the vicinity of a Fermi
surface and low-energy bosons near zero momentum. An asymptotically exact
analysis of this effective field theory is made possible through the
development of a renormalization group procedure for mixed fermion-boson
systems. Considerations on how to connect the AF_S and P_L phases lead to a
global phase diagram, which not only puts into perspective the theory of local
quantum criticality for antiferromagnetic heavy fermion metals, but also
provides the basis to understand the surprising recent experiments in
chemically-doped as well as pressurized YbRh2Si2. We point out that the AF_S
phase still occurs for the case of an equal number of spin-1/2 local moments
and conduction electrons. This observation raises the prospect for a global
phase diagram of heavy fermion systems in the Kondo-insulator regime. Finally,
we discuss the connection between the Kondo breakdown physics discussed here
for the Kondo lattice systems and the non-Fermi liquid behavior recently
studied from a holographic perspective.Comment: (v3) leftover typos corrected. (v2) Published version. 32 pages, 4
figures. Section 7, on the connection between the Kondo lattice systems and
the holographic models of non-Fermi liquid, is expanded. (v1) special issue
of JLTP on quantum criticalit
Local fluctuations in quantum critical metals
We show that spatially local, yet low-energy, fluctuations can play an
essential role in the physics of strongly correlated electron systems tuned to
a quantum critical point. A detailed microscopic analysis of the Kondo lattice
model is carried out within an extended dynamical mean-field approach. The
correlation functions for the lattice model are calculated through a
self-consistent Bose-Fermi Kondo problem, in which a local moment is coupled
both to a fermionic bath and to a bosonic bath (a fluctuating magnetic field).
A renormalization-group treatment of this impurity problem--perturbative in
, where is an exponent characterizing the spectrum
of the bosonic bath--shows that competition between the two couplings can drive
the local-moment fluctuations critical. As a result, two distinct types of
quantum critical point emerge in the Kondo lattice, one being of the usual
spin-density-wave type, the other ``locally critical.'' Near the locally
critical point, the dynamical spin susceptibility exhibits scaling
with a fractional exponent. While the spin-density-wave critical point is
Gaussian, the locally critical point is an interacting fixed point at which
long-wavelength and spatially local critical modes coexist. A Ginzburg-Landau
description for the locally critical point is discussed. It is argued that
these results are robust, that local criticality provides a natural description
of the quantum critical behavior seen in a number of heavy-fermion metals, and
that this picture may also be relevant to other strongly correlated metals.Comment: 20 pages, 12 figures; typos in figure 3 and in the main text
corrected, version as publishe
Effect of initial conditions on the speed of reaction-diffusion fronts
The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed
Self-persuasion as marketing technique: the role of consumers’ involvement
Purpose
This paper aims to demonstrate that self-persuasion can be used as a marketing technique to increase consumers’ generosity and that the efficacy of this approach is dependent on consumers’ involvement with target behavior.
Design/methodology/approach
An experimental field-study was conducted to investigate the effects of self-persuasion versus direct persuasion attempts versus no persuasion attempts on consumers’ tipping behavior in a lunchroom. Additionally, in a lab experiment, the moderating role of involvement on self-persuasion versus direct persuasion was tested.
Findings
The results reveal that self-persuasion is more effective than direct persuasion attempts or no persuasive messages in increasing consumers’ generosity. This is moderated by consumers’ involvement with the target behavior. For consumers with high involvement, self-persuasion is more effective than direct persuasion, while no differences were found for consumers with moderate or low involvement.
Practical implications
The scope of self-persuasion is not limited to the inhibition of undesired behavior, but it also extends to the facilitation of desired behavior, which considerably broadens the scope of this technique. Self-persuasion might be used as a marketing technique to influence consumers’ purchase behavior. This might be particularly viable in situations in which consumers feel high involvement with products or behavior.
Originality/value
Recently, research in health psychology demonstrated that self-persuasion is a very effective way of inhibiting undesired, addictive behavior and being more successful than direct persuasion. Yet, insufficient knowledge is available about the efficacy of self-persuasion with regard to promoting other target behaviors. In particular, its potential as a marketing technique to influence consumers’ behavior and its boundary conditions are still understudied
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