Institute Fisica Of Cantabria Uc And Csic

Santander, Spain

Institute Fisica Of Cantabria Uc And Csic

Santander, Spain

Time filter

Source Type

Revelli J.A.,Institute Fisica Of Cantabria Uc And Csic | Rodriguez M.A.,Institute Fisica Of Cantabria Uc And Csic | Wio H.S.,Institute Fisica Of Cantabria Uc And Csic
Advances in Atmospheric Sciences | Year: 2010

Rank Histograms are suitable tools to assess the quality of ensembles within an ensemble prediction system or framework. By counting the rank of a given variable in the ensemble, we are basically making a sample analysis, which does not allow us to distinguish if the origin of its variability is external noise or comes from chaotic sources. The recently introduced Mean to Variance Logarithmic (MVL) Diagram accounts for the spatial variability, being very sensitive to the spatial localization produced by infinitesimal perturbations of spatiotemporal chaotic systems. By using as a benchmark a simple model subject to noise, we show the distinct information given by Rank Histograms and MVL Diagrams. Hence, the main effects of the external noise can be visualized in a graphic. From the MVL diagram we clearly observe a reduction of the amplitude growth rate and of the spatial localization (chaos suppression), while from the Rank Histogram we observe changes in the reliability of the ensemble. We conclude that in a complex framework including spatiotemporal chaos and noise, both provide a more complete forecasting picture. © 2010 Chinese National Committee for International Association of Meteorology and Atmospheric Sciences, Institute of Atmospheric Physics, Science Press and Springer-Verlag Berlin Heidelberg.


Wio H.S.,Institute Fisica Of Cantabria Uc And Csic | Revelli J.A.,Institute Fisica Of Cantabria Uc And Csic | Deza R.R.,CONICET | Escudero C.,ICMAT CSIC UAM UC3M UCM | De La Lama M.S.,Max Planck Institute for Dynamics and Self-Organization
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

In order to perform numerical simulations of the Kardar-Parisi-Zhang (KPZ) equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf-Cole transformation applied to a diffusion equation (with multiplicative noise) is shown here to strongly restrict the arbitrariness in the choice of spatial discretization schemes. On one hand, the discretization prescriptions for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen. On the other hand, since the discretization is an operation performed on space and the Hopf-Cole transformation is local both in space and time, the former should be the same regardless of the field to which it is applied. It is shown that whereas some discretization schemes pass both consistency tests, known examples in the literature do not. The requirement of consistency for the discretization of Lyapunov functionals is argued to be a natural and safe starting point in choosing spatial discretization schemes. We also analyze the relation between real-space and pseudospectral discrete representations. In addition we discuss the relevance of the Galilean-invariance violation in these consistent discretization schemes and the alleged conflict of standard discretization with the fluctuation-dissipation theorem, peculiar of one dimension. © 2010 The American Physical Society.


Wio H.S.,Institute Fisica Of Cantabria Uc And Csic | Revelli J.A.,Institute Fisica Of Cantabria Uc And Csic | Deza R.R.,CONICET | Escudero C.,ICMAT CSIC UAM UC3M UCM | De La Lama M.S.,Institute Fisica Of Cantabria Uc And Csic
EPL | Year: 2010

Strong constraints are drawn for the choice of real-space discretization schemes, using the known fact that the KPZ equation results from a diffusion equation (with multiplicative noise) through a Hopf-Cole transformation. Whereas the nearest-neighbor discretization passes the consistency tests, known examples in the literature do not. We emphasize the importance of the Lyapunov functional as natural starting point for real-space discretization and, in the light of these findings, challenge the mainstream opinion on the relevance of Galilean invariance. © 2010 EPLA.


Wio H.S.,Institute Fisica Of Cantabria Uc And Csic | Revelli J.A.,National University of Cordoba | Escudero C.,University Aut Of Madrid | Deza R.R.,CONICET | De La Lama M.S.,Max Planck Institute
AIP Conference Proceedings | Year: 2011

Starting from a variational formulation of the Kardar-Parisi-Zhang (KPZ) equation, we point out some strong constraints and consistency tests, to be fulfilled by real-space discretization schemes. In the light of these findings, the mainstream opinion on the relevance of Galilean invariance and the fluctuation - dissipation theorem (peculiar of 1D) is challenged. © 2011 American Institute of Physics.


Wio H.S.,Institute Fisica Of Cantabria Uc And Csic | Deza R.R.,CONICET | Revelli J.A.,CONICET | Escudero C.,Autonomous University of Madrid
Acta Physica Polonica B | Year: 2013

We discuss a tentative path-integral approach to numerically follow the scaling properties of the mean rugosity (and other typical averages) of an interface whose growth is described by the Kardar-Parisi-Zhang equation. It resorts to functional minimization and a cellular automata-like algorithm, and can be regarded as a kind of importance-sampling approach. This method is intended to predict the crossover time as a function of the coefficient of the nonlinear term, through the comparison of the weight of the different terms in the "stochastic action".


Wio H.S.,Institute Fisica Of Cantabria Uc And Csic | Escudero C.,ICMAT CSIC UAM UC3M UCM | Revelli J.A.,Institute Fisica Of Cantabria Uc And Csic | Deza R.R.,CONICET | De La Lama M.S.,Max Planck Institute for Dynamics and Self-Organization
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences | Year: 2011

The stochastic nonlinear partial differential equation known as the Kardar-Parisi-Zhang (KPZ) equation is a highly successful phenomenological mesoscopic model of surface and interface growth processes. Its suitability for analytical work, its explicit symmetries and its prediction of an exact dynamic scaling relation for a one-dimensional substratum led people to adopt it as a 'standard' model in the field during the last quarter of a century. At the same time, several conjectures deserving closer scrutiny were established as dogmas throughout the community. Among these, we find the beliefs that 'genuine' non-equilibrium processes are non-variational in essence, and that the exactness of the dynamic scaling relation owes its existence to a Galilean symmetry. Additionally, the equivalence among planar and radial interface profiles has been generally assumed in the literature throughout the years. Here-among other topics-we introduce a variational formulation of the KPZ equation, remark on the importance of consistency in discretization and challenge the mainstream view on the necessity for scaling of both Galilean symmetry and the one-dimensional fluctuation-dissipation theorem. We also derive the KPZ equation on a growing domain as a first approximation to radial growth, and outline the differences with respect to the classical case that arises in this new situation. This journal is © 2011 The Royal Society.


Dell'Erba M.G.,CONICET | Izus G.G.,CONICET | Deza R.R.,CONICET | Wio H.S.,Institute Fisica Of Cantabria Uc And Csic
European Physical Journal D | Year: 2011

The nonequilibrium Ising-Bloch front bifurcation of the FitzHugh-Nagumo model with nondiffusing inhibitor provides a beautiful instance of an extended bistable system made up of propagating (Bloch) fronts. Moreover, these fronts are chiral and parity-related, and the barrier between them is nonetheless but a stationary Ising front. By means of numerical simulation in the neighborhood of this bifurcation, we demonstrate the existence of stochastic resonance in the transition between Bloch fronts of opposite chiralities, when an additive noise is included. The signal-to-noise ratio is numerically observed to scale with the distance to the critical point. This scaling law is theoretically characterized in terms of an effective nonequilibrium potential. © 2010 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.


Wio H.S.,Institute Fisica Of Cantabria Uc And Csic
Journal of Physics: Conference Series | Year: 2010

We analyze the stochastic resonance response in an extended system, considering different transport/coupling mechanisms: diffusion, KPZ, and also include the possibility of a non-local interaction. Our aim, since these mechanisms correspond to different forms of coupling of resonant units leading to an extended system, is to obtain information about the way to optimize the system's response to weak signals. To reach such a goal, we exploit the knowledge of the so called "non-equilibrium potential" for the above indicated situations. © 2010 IOP Publishing Ltd.


PubMed | Institute Fisica Of Cantabria Uc And Csic
Type: Journal Article | Journal: Physical review. E, Statistical, nonlinear, and soft matter physics | Year: 2010

In order to perform numerical simulations of the Kardar-Parisi-Zhang (KPZ) equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf-Cole transformation applied to a diffusion equation (with multiplicative noise) is shown here to strongly restrict the arbitrariness in the choice of spatial discretization schemes. On one hand, the discretization prescriptions for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen. On the other hand, since the discretization is an operation performed on space and the Hopf-Cole transformation is local both in space and time, the former should be the same regardless of the field to which it is applied. It is shown that whereas some discretization schemes pass both consistency tests, known examples in the literature do not. The requirement of consistency for the discretization of Lyapunov functionals is argued to be a natural and safe starting point in choosing spatial discretization schemes. We also analyze the relation between real-space and pseudospectral discrete representations. In addition we discuss the relevance of the Galilean-invariance violation in these consistent discretization schemes and the alleged conflict of standard discretization with the fluctuation-dissipation theorem, peculiar of one dimension.


PubMed | Institute Fisica Of Cantabria Uc And Csic
Type: Journal Article | Journal: Philosophical transactions. Series A, Mathematical, physical, and engineering sciences | Year: 2010

The stochastic nonlinear partial differential equation known as the Kardar-Parisi-Zhang (KPZ) equation is a highly successful phenomenological mesoscopic model of surface and interface growth processes. Its suitability for analytical work, its explicit symmetries and its prediction of an exact dynamic scaling relation for a one-dimensional substratum led people to adopt it as a standard model in the field during the last quarter of a century. At the same time, several conjectures deserving closer scrutiny were established as dogmas throughout the community. Among these, we find the beliefs that genuine non-equilibrium processes are non-variational in essence, and that the exactness of the dynamic scaling relation owes its existence to a Galilean symmetry. Additionally, the equivalence among planar and radial interface profiles has been generally assumed in the literature throughout the years. Here--among other topics--we introduce a variational formulation of the KPZ equation, remark on the importance of consistency in discretization and challenge the mainstream view on the necessity for scaling of both Galilean symmetry and the one-dimensional fluctuation-dissipation theorem. We also derive the KPZ equation on a growing domain as a first approximation to radial growth, and outline the differences with respect to the classical case that arises in this new situation.

Loading Institute Fisica Of Cantabria Uc And Csic collaborators
Loading Institute Fisica Of Cantabria Uc And Csic collaborators