710,904 research outputs found
On dissipation in crackling noise systems
We consider the amount of energy dissipated during individual avalanches at
the depinning transition of disordered and athermal elastic systems. Analytical
progress is possible in the case of the Alessandro-Beatrice-Bertotti-Montorsi
(ABBM) model for Barkhausen noise, due to an exact mapping between the energy
released in an avalanche and the area below a Brownian path until its first
zero-crossing. Scaling arguments and examination of an extended mean-field
model with internal structure show that dissipation relates to a critical
exponent recently found in a study of the rounding of the depinning transition
in presence of activated dynamics. A new numerical method to compute the
dynamic exponent at depinning in terms of blocked and marginally stable
configurations is proposed, and a kind of `dissipative anomaly'- with
potentially important consequences for nonequilibrium statistical mechanics- is
discussed. We conclude that for depinning systems the size of an avalanche does
not constitute by itself a univocal measure of the energy dissipated.Comment: 7 pages, 3 figures, final accepted versio
Rapid internationalization and long-term performance: The knowledge link
Drawing on the knowledge-based view and organizational learning theory, we develop and test a set of hypotheses to provide a first attempt at analyzing the effect of speed of internationalization on long-term performance. Using a panel-data sample of Spanish listed firms (1986-2010), we find that there is an inverted U-shaped relationship between speed of internationalization and long-term performance. We also find that whereas technological knowledge steepens this relationship, the diversity of prior international experience flattens it. Our results contribute to the existing IB literature on the performance of FDI, cross-country knowledge transferability, and nonsequential entry
Matrix models for classical groups and ToeplitzHankel minors with applications to Chern-Simons theory and fermionic models
We study matrix integration over the classical Lie groups
and , using symmetric function theory and the equivalent formulation
in terms of determinants and minors of ToeplitzHankel matrices. We
establish a number of factorizations and expansions for such integrals, also
with insertions of irreducible characters. As a specific example, we compute
both at finite and large the partition functions, Wilson loops and Hopf
links of Chern-Simons theory on with the aforementioned symmetry
groups. The identities found for the general models translate in this context
to relations between observables of the theory. Finally, we use character
expansions to evaluate averages in random matrix ensembles of Chern-Simons
type, describing the spectra of solvable fermionic models with matrix degrees
of freedom.Comment: 32 pages, v2: Several improvements, including a Conclusions and
Outlook section, added. 36 page
Symmetry for the duration of entropy-consuming intervals
We introduce the violation fraction as the cumulative fraction of
time that a mesoscopic system spends consuming entropy at a single trajectory
in phase space. We show that the fluctuations of this quantity are described in
terms of a symmetry relation reminiscent of fluctuation theorems, which involve
a function, , which can be interpreted as an entropy associated to the
fluctuations of the violation fraction.
The function , when evaluated for arbitrary stochastic realizations of
the violation fraction, is odd upon the symmetry transformations which are
relevant for the associated stochastic entropy production. This fact leads to a
detailed fluctuation theorem for the probability density function of .
We study the steady-state limit of this symmetry in the paradigmatic case of
a colloidal particle dragged by optical tweezers through an aqueous solution.
Finally, we briefly discuss on possible applications of our results for the
estimation of free-energy differences from single molecule experiments.Comment: 11 pages, 4 figures. Last revised. Version accepted for publication
in Phys. Rev.
Duration of local violations of the second law of thermodynamics along single trajectories in phase space
We define the {\it violation fraction} as the cumulative fraction of
time that the entropy change is negative during single realizations of
processes in phase space. This quantity depends both on the number of degrees
of freedom and the duration of the time interval . In the
large- and large- limit we show that, for ergodic and microreversible
systems, the mean value of scales as
. The
exponent is positive and generally depends on the protocol for the
external driving forces, being for a constant drive. As an example,
we study a nontrivial model where the fluctuations of the entropy production
are non-Gaussian: an elastic line driven at a constant rate by an anharmonic
trap. In this case we show that the scaling of with
and agrees with our result. Finally, we discuss how this scaling law may
break down in the vicinity of a continuous phase transition.Comment: 8 pages, 2 figures, Final version, as accepted for publication in
Phys. Rev.
Toeplitz minors and specializations of skew Schur polynomials
We express minors of Toeplitz matrices of finite and large dimension in terms
of symmetric functions. Comparing the resulting expressions with the inverses
of some Toeplitz matrices, we obtain explicit formulas for a Selberg-Morris
integral and for specializations of certain skew Schur polynomials.Comment: v2: Added new results on specializations of skew Schur polynomials,
abstract and title modified accordingly and references added; v3: final,
published version; 18 page
Video Prioritization for Unequal Error Protection
We analyze the effect of packet losses in video sequences and propose a lightweight Unequal Error Protection strategy which, by choosing which packet is discarded, reduces strongly the Mean Square Error of the received sequenc
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