2,193 research outputs found
Kardar-Parisi-Zhang asymptotics for the two-dimensional noisy Kuramoto-Sivashinsky equation
We study numerically the Kuramoto-Sivashinsky (KS) equation forced by
external white noise in two space dimensions, that is a generic model for e.g.
surface kinetic roughening in the presence of morphological instabilities.
Large scale simulations using a pseudospectral numerical scheme allow us to
retrieve Kardar-Parisi-Zhang (KPZ) scaling as the asymptotic state of the
system, as in the 1D case. However, this is only the case for sufficiently
large values of the coupling and/or system size, so that previous conclusions
on non-KPZ asymptotics are demonstrated as finite size effects. Crossover
effects are comparatively stronger for the 2D case than for the 1D system.Comment: 5 pages, 3 figures; supplemental material available at journal web
page and/or on reques
Application of Constrained Optimization Techniques in Optimal Shape Design of a Freezer to Dosing Line Splitter for Ice Cream Production
Design of multiple branches splitting of equal mass flow rate in complex rheological flows like ice cream near melting point temperature can be a challenging task. Pulsations in flow rate due to air pumping process and small fluctuations in temperature affecting flow rheology can determine a consistent difference in internal pipe velocity distribution, resulting in a significant difference in the distribution of ice cream dosage. Computational sciences and engineering techniques have allowed a major change in the way products and equipment can be engineered, as a computational model simulating physical processes can be more easily obtained, rather than making prototypes and performing multiple experiments. Among such techniques, optimal shape design (OSD) represents an interesting approach. In OSD, the essential element with respect to classical numerical simulations in fixed geometrical configurations relays on the introduction a certain amount of geometrical degrees of freedom as a part of the unknowns. This implies that the geometry is not completely defined, but part of it is allowed to move dynamically in order to minimize or maximize an objective function. From a mathematical point of view, OSD is a branch of differentiable optimization and more precisely the application of optimal control for distributed systems. OSD is still today numerically difficult to implement, because it relies on a computer intensive activity and moreover because the concept of “optimal” is a compromise between shapes that are good with respect to several criteria. In this work, the applications of a multivariate constrained optimization algorithm is proposed in the case of a mechanical ice cream 1 to 5 splitting system, required to distribute in an evenly way from one freezer into five dosing valves. Results allowed to design a retro-fitting system on an existing production plant reducing the dosing error down to 3% on the average
Paroxysmal eye–head movements in Glut1 deficiency syndrome
Objective:To describe a characteristic paroxysmal eye–head movement disorder that occurs in infants with Glut1 deficiency syndrome (Glut1 DS).Methods:We retrospectively reviewed the medical charts of 101 patients with Glut1 DS to obtain clinical data about episodic abnormal eye movements and analyzed video recordings of 18 eye movement episodes from 10 patients.Results:A documented history of paroxysmal abnormal eye movements was found in 32/101 patients (32%), and a detailed description was available in 18 patients, presented here. Episodes started before age 6 months in 15/18 patients (83%), and preceded the onset of seizures in 10/16 patients (63%) who experienced both types of episodes. Eye movement episodes resolved, with or without treatment, by 6 years of age in 7/8 patients with documented long-term course. Episodes were brief (usually <5 minutes). Video analysis revealed that the eye movements were rapid, multidirectional, and often accompanied by a head movement in the same direction. Eye movements were separated by clear intervals of fixation, usually ranging from 200 to 800 ms. The movements were consistent with eye–head gaze saccades. These movements can be distinguished from opsoclonus by the presence of a clear intermovement fixation interval and the association of a same-direction head movement.Conclusions:Paroxysmal eye–head movements, for which we suggest the term aberrant gaze saccades, are an early symptom of Glut1 DS in infancy. Recognition of the episodes will facilitate prompt diagnosis of this treatable neurodevelopmental disorder.</jats:sec
Spectra of Empirical Auto-Covariance Matrices
We compute spectra of sample auto-covariance matrices of second order
stationary stochastic processes. We look at a limit in which both the matrix
dimension and the sample size used to define empirical averages
diverge, with their ratio kept fixed. We find a remarkable scaling
relation which expresses the spectral density of sample
auto-covariance matrices for processes with dynamical correlations as a
continuous superposition of appropriately rescaled copies of the spectral
density for a sequence of uncorrelated random
variables. The rescaling factors are given by the Fourier transform
of the auto-covariance function of the stochastic process. We also obtain a
closed-form approximation for the scaling function
. This depends on the shape parameter , but
is otherwise universal: it is independent of the details of the underlying
random variables, provided only they have finite variance. Our results are
corroborated by numerical simulations using auto-regressive processes.Comment: 4 pages, 2 figure
DEVELOPMENT POLICIES IN SOUTHERN ITALY BETWEEN GOVERNMENT AND GOVERNANCE
The paper has analysed outputs generated by the development policies implemented in last decades in the South of Italy, starting from the Extraordinary Intervention (since 1950, until 1992) to the European cohesion policy (since 1996). The first one was a high-centralized development policy. Differently, the European cohesion policy is based on multilevel governance, and follows a bottom-up approach oriented to stimulate local stakeholders’ participation. The analysis, exposed in previous paragraphs, has described these two different policy experiences, the related effects on local development and on convergence between North and South of Italy and among European regions. The paper has tried to answer to a fundamental question: what factors have negatively affected the implementation of these policies, generating unexpected effects
Cavity and replica methods for the spectral density of sparse symmetric random matrices
We review the problem of how to compute the spectral density of sparse
symmetric random matrices, i.e. weighted adjacency matrices of undirected
graphs. Starting from the Edwards-Jones formula, we illustrate the milestones
of this line of research, including the pioneering work of Bray and Rodgers
using replicas. We focus first on the cavity method, showing that it quickly
provides the correct recursion equations both for single instances and at the
ensemble level. We also describe an alternative replica solution that proves to
be equivalent to the cavity method. Both the cavity and the replica derivations
allow us to obtain the spectral density via the solution of an integral
equation for an auxiliary probability density function. We show that this
equation can be solved using a stochastic population dynamics algorithm, and we
provide its implementation. In this formalism, the spectral density is
naturally written in terms of a superposition of local contributions from nodes
of given degree, whose role is thoroughly elucidated. This paper does not
contain original material, but rather gives a pedagogical overview of the
topic. It is indeed addressed to students and researchers who consider entering
the field. Both the theoretical tools and the numerical algorithms are
discussed in detail, highlighting conceptual subtleties and practical aspects.Comment: 52 pag., 5 fig. Typos fixed. Submission to SciPos
Number statistics for -ensembles of random matrices: applications to trapped fermions at zero temperature
Let be the probability that a
-ensemble of random matrices with confining potential
has eigenvalues inside an interval of the real
line. We introduce a general formalism, based on the Coulomb gas technique and
the resolvent method, to compute analytically for large . We show that this probability scales for large
as , where is the Dyson index of the
ensemble. The rate function , independent of ,
is computed in terms of single integrals that can be easily evaluated
numerically. The general formalism is then applied to the classical
-Gaussian (), -Wishart () and
-Cauchy () ensembles. Expanding the rate function
around its minimum, we find that generically the number variance exhibits a non-monotonic behavior as a function of the size
of the interval, with a maximum that can be precisely characterized. These
analytical results, corroborated by numerical simulations, provide the full
counting statistics of many systems where random matrix models apply. In
particular, we present results for the full counting statistics of zero
temperature one-dimensional spinless fermions in a harmonic trap.Comment: 34 pages, 19 figure
Jacobi Crossover Ensembles of Random Matrices and Statistics of Transmission Eigenvalues
We study the transition in conductance properties of chaotic mesoscopic
cavities as time-reversal symmetry is broken. We consider the Brownian motion
model for transmission eigenvalues for both types of transitions, viz.,
orthogonal-unitary and symplectic-unitary crossovers depending on the presence
or absence of spin-rotation symmetry of the electron. In both cases the
crossover is governed by a Brownian motion parameter {\tau}, which measures the
extent of time-reversal symmetry breaking. It is shown that the results
obtained correspond to the Jacobi crossover ensembles of random matrices. We
derive the level density and the correlation functions of higher orders for the
transmission eigenvalues. We also obtain the exact expressions for the average
conductance, average shot-noise power and variance of conductance, as functions
of {\tau}, for arbitrary number of modes (channels) in the two leads connected
to the cavity. Moreover, we give the asymptotic result for the variance of
shot-noise power for both the crossovers, the exact results being too long. In
the {\tau} \rightarrow 0 and {\tau} \rightarrow \infty limits the known results
for the orthogonal (or symplectic) and unitary ensembles are reproduced. In the
weak time-reversal symmetry breaking regime our results are shown to be in
agreement with the semiclassical predictions.Comment: 24 pages, 5 figure
- …