Miguel Angel Rodríguez
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
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Miguel Angel Rodríguez has a total of 105 co-authors. Here are the top co-authors by number of shared publications:
- Juan M. Lopez
Instituto de Física de Cantabria (IFCA)
36 shared publications L. Pesquera
Instituto de Física de Cantabria (Consejo Superior de Investigaciones Científicas–Universidad de Cantabria), Facultad de Ciencias, Avenida de los Castros, E-39005 Santander, Spain
21 shared publications- Diego Pazó
Instituto de Física de Cantabria (IFCA), Universidad de Cantabria—CSIC 2 , 39005 Santander
14 shared publications - Maxi San Miguel
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB) Campus Universitat Illes Balears E-07122 Palma de Mallorca Spain
12 shared publications - Aurora Hernandez-Machado
Department of Condensed Matter Physics, University of Barcelona (UB), Barcelona, Spain
10 shared publications - José Manuel Gutiérrez
Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
10 shared publications
Latest Publications
- Open Access
The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
Interfaces of rather different natures—as, e.g., bacterial colony or forest fire boundaries, or semiconductor layers grown by different methods (MBE, sputtering, etc.)—are self-affine fractals, and feature scaling with universal exponents (depending on the substrate’s dimensionality d and global topology, as well as on the driving randomness’ spatial and temporal correlations but not on the underlying mechanisms). Adding lateral growth as an essential (non-equilibrium) ingredient to the known equilibrium ones (randomness and interface relaxation), the Kardar–Parisi–Zhang (KPZ) equation succeeded in finding (via the dynamic renormalization group) the correct exponents for flat substrates and (spatially and temporally) uncorrelated randomness. It is this interplay which gives rise to the unique, non-Gaussian scaling properties characteristic of the specific, universal type of non-equilibrium roughening. Later on, the asymptotic statistics of process fluctuations in the scaling regime was also analytically found for substrates. For substrates, however, one has to rely on numerical simulations. Here we review a variational approach that allows for analytical progress regardless of substrate dimensionality. After reviewing our previous numerical results in , 2, and 3 on the time evolution of one of the functionals—which we call the non-equilibrium potential (NEP)—as well as its scaling behavior with the nonlinearity parameter , we discuss the stochastic thermodynamics of the roughening process and the memory of process in KPZ and in the related Golubović–Bruinsma (GB) model, providing numerical evidence for the significant dependence on initial conditions of the NEP’s asymptotic behavior in both models. Finally, we highlight some open questions.Open AccessThe KPZ Equation of Kinetic Interface Roughening: A Variational Perspective
Interfaces of rather different natures—as, e.g., bacterial colony or forest fire boundaries, or semiconductor layers grown by different methods (MBE, sputtering, etc.)—are self-affine fractals, and feature scaling with universal exponents (depending on the substrate’s dimensionality d and global topology, as well as on the driving randomness’ spatial and temporal correlations but not on the underlying mechanisms). Adding lateral growth as an essential (non-equilibrium) ingredient to the known equilibrium ones (randomness and interface relaxation), the Kardar–Parisi–Zhang (KPZ) equation succeeded in finding (via the dynamic renormalization group) the correct exponents for flat substrates and (spatially and temporally) uncorrelated randomness. It is this interplay which gives rise to the unique, non-Gaussian scaling properties characteristic of the specific, universal type of non-equilibrium roughening. Later on, the asymptotic statistics of process fluctuations in the scaling regime was also analytically found for substrates. For substrates, however, one has to rely on numerical simulations. Here we review a variational approach that allows for analytical progress regardless of substrate dimensionality. After reviewing our previous numerical results in , 2, and 3 on the time evolution of one of the functionals—which we call the non-equilibrium potential (NEP)—as well as its scaling behavior with the nonlinearity parameter , we discuss the stochastic thermodynamics of the roughening process and the memory of process in KPZ and in the related Golubović–Bruinsma (GB) model, providing numerical evidence for the significant dependence on initial conditions of the NEP’s asymptotic behavior in both models. Finally, we highlight some open questions. - 1 July 2020
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 30 (7) , 073107
Variational approach to KPZ: Fluctuation theorems and large deviation function for entropy production
Motivated by the time behavior of the functional arising in the variational approach to the Kardar-Parisi-Zhang (KPZ) equation, and in order to study fluctuation theorems in such a system, we have adapted a path-integral scheme that adequately fits to this kind of study dealing with unstable systems. As the KPZ system has no stationary probability distribution, we show how to proceed for obtaining detailed as well as integral fluctuation theorems. This path-integral methodology, together with the variational approach, in addition to allowing analyze fluctuation theorems, can be exploited to determine a large deviation function for entropy production.
- 1 July 2020
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 30 (7) , 073107
Variational approach to KPZ: Fluctuation theorems and large deviation function for entropy production
Motivated by the time behavior of the functional arising in the variational approach to the Kardar-Parisi-Zhang (KPZ) equation, and in order to study fluctuation theorems in such a system, we have adapted a path-integral scheme that adequately fits to this kind of study dealing with unstable systems. As the KPZ system has no stationary probability distribution, we show how to proceed for obtaining detailed as well as integral fluctuation theorems. This path-integral methodology, together with the variational approach, in addition to allowing analyze fluctuation theorems, can be exploited to determine a large deviation function for entropy production.
- 6 September 2019
- Published by American Physical Society (APS) in Physical Review E
- Vol. 100 (3) , 032111
Stochastic entropies and fluctuation theorems for a discrete one-dimensional Kardar-Parisi-Zhang system
The statistical properties of stochastic entropies in a discrete stationary one-dimensional Kardar-Parisi-Zhang system are numerically studied. As the usual time-independent solution of the associated Fokker-Planck equation is not strictly stationary, it is necessary to transform the current variables to other variables with zero spatial mean. We resorted to discrete representations in order to prove the statistical properties of entropies, and we performed a direct test of the fluctuation theorem. We discuss the connection between fluctuation theorems and the deviation from Gaussian distribution for the entropy.
- 6 September 2019
- Published by American Physical Society (APS) in Physical Review E
- Vol. 100 (3) , 032111
Stochastic entropies and fluctuation theorems for a discrete one-dimensional Kardar-Parisi-Zhang system
The statistical properties of stochastic entropies in a discrete stationary one-dimensional Kardar-Parisi-Zhang system are numerically studied. As the usual time-independent solution of the associated Fokker-Planck equation is not strictly stationary, it is necessary to transform the current variables to other variables with zero spatial mean. We resorted to discrete representations in order to prove the statistical properties of entropies, and we performed a direct test of the fluctuation theorem. We discuss the connection between fluctuation theorems and the deviation from Gaussian distribution for the entropy.
- Open Access
- 30 June 2017
- Published by American Physical Society (APS) in Physical Review E
- Vol. 95 (6) , 062309
Relating the large-scale structure of time series and visibility networks
The structure of time series is usually characterized by means of correlations. A new proposal based on visibility networks has been considered recently. Visibility networks are complex networks mapped from surfaces or time series using visibility properties. The structures of time series and visibility networks are closely related, as shown by means of fractional time series in recent works. In these works, a simple relationship between the Hurst exponent of fractional time series and the exponent of the distribution of edges of the corresponding visibility network, which exhibits a power law, is shown. To check and generalize these results, in this paper we delve into this idea of connected structures by defining both structures more properly. In addition to the exponents used before, and , which take into account local properties, we consider two more exponents that, as we will show, characterize global properties. These are the exponent for time series, which gives the scaling of the variance with the size as , and the exponent of their corresponding network, which gives the scaling of the averaged maximum of the number of edges, . With this representation, a more precise connection between the structures of general time series and their associated visibility network is achieved. Similarities and differences are more clearly established, and new scaling forms of complex networks appear in agreement with their respective classes of time series.- 30 June 2017
- Published by American Physical Society (APS) in Physical Review E
- Vol. 95 (6) , 062309
Open AccessRelating the large-scale structure of time series and visibility networks
The structure of time series is usually characterized by means of correlations. A new proposal based on visibility networks has been considered recently. Visibility networks are complex networks mapped from surfaces or time series using visibility properties. The structures of time series and visibility networks are closely related, as shown by means of fractional time series in recent works. In these works, a simple relationship between the Hurst exponent of fractional time series and the exponent of the distribution of edges of the corresponding visibility network, which exhibits a power law, is shown. To check and generalize these results, in this paper we delve into this idea of connected structures by defining both structures more properly. In addition to the exponents used before, and , which take into account local properties, we consider two more exponents that, as we will show, characterize global properties. These are the exponent for time series, which gives the scaling of the variance with the size as , and the exponent of their corresponding network, which gives the scaling of the averaged maximum of the number of edges, . With this representation, a more precise connection between the structures of general time series and their associated visibility network is achieved. Similarities and differences are more clearly established, and new scaling forms of complex networks appear in agreement with their respective classes of time series. - Open Access
- 18 January 2017
- Published by Frontiers Media SA in Frontiers in Physics
- Vol. 4
d-Dimensional KPZ Equation as a Stochastic Gradient Flow in an Evolving Landscape: Interpretation and Time Evolution of Its Generating Functional
The deterministic KPZ equation has been recently formulated as a gradient flow. Its nonequilibrium analog of a free energy---the "nonequilibrium potential'' Φ[h], providing at each time the landscape where the stochastic dynamics of h(x ⃗,t) takes place---is however unbounded, and its exact evaluation involves all the detailed histories leading from some initial configuration h(x ⃗,0) to a final one h(x ⃗,t). After pinpointing some implications of these facts, we study the time behavior of 〈Φ[h] 〉 (the average of Φ[h] over noise realizations at time t) and show the interesting consequences of its structure when an external driving force F is included (i.e. the KPZ behavior as an activation-like process). The asymptotic form of the time derivative Φ ̇[h] is shown to be valid for any substrate dimensionality d, thus providing a valuable tool for studies in d>1.
- 18 January 2017
- Published by Frontiers Media SA in Frontiers in Physics
- Vol. 4
Open Accessd-Dimensional KPZ Equation as a Stochastic Gradient Flow in an Evolving Landscape: Interpretation and Time Evolution of Its Generating Functional
The deterministic KPZ equation has been recently formulated as a gradient flow. Its nonequilibrium analog of a free energy---the "nonequilibrium potential'' Φ[h], providing at each time the landscape where the stochastic dynamics of h(x ⃗,t) takes place---is however unbounded, and its exact evaluation involves all the detailed histories leading from some initial configuration h(x ⃗,0) to a final one h(x ⃗,t). After pinpointing some implications of these facts, we study the time behavior of 〈Φ[h] 〉 (the average of Φ[h] over noise realizations at time t) and show the interesting consequences of its structure when an external driving force F is included (i.e. the KPZ behavior as an activation-like process). The asymptotic form of the time derivative Φ ̇[h] is shown to be valid for any substrate dimensionality d, thus providing a valuable tool for studies in d>1.
- Open Access
- 26 July 2016
- Published by American Physical Society (APS) in Physical Review E
- Vol. 94 (1) , 012314
Graphicality conditions for general scale-free complex networks and their application to visibility graphs
We obtain graphicality conditions for general types of scale-free networks. The same conditions obtained for uncorrelated networks are obtained in the general case. Then an upper bound relating , the exponent of the degree distribution, with the cutoff exponent , as is established. This bound is valid for all networks with a well-defined power-law degree distribution in the range . Some recent numerical research on visibility networks arising from persistent fractional Brownian motion (fBm) processes are reviewed since they do not fulfill these conditions. As a consequence, a new relationship between the exponent of the degree distribution and the Hurst exponent of the fBm process, , is postulated.- 26 July 2016
- Published by American Physical Society (APS) in Physical Review E
- Vol. 94 (1) , 012314
Open AccessGraphicality conditions for general scale-free complex networks and their application to visibility graphs
We obtain graphicality conditions for general types of scale-free networks. The same conditions obtained for uncorrelated networks are obtained in the general case. Then an upper bound relating , the exponent of the degree distribution, with the cutoff exponent , as is established. This bound is valid for all networks with a well-defined power-law degree distribution in the range . Some recent numerical research on visibility networks arising from persistent fractional Brownian motion (fBm) processes are reviewed since they do not fulfill these conditions. As a consequence, a new relationship between the exponent of the degree distribution and the Hurst exponent of the fBm process, , is postulated. - 18 July 2016
- Published by SPIE-Intl Soc Optical Eng
- Vol. 9905, 99050S
Toward large μ-calorimeters x-ray matrices based on metal-insulator sensors and HEMTs/SiGe cryo-electronics
The launch of ASTRO-H/ITOMI ,the X-ray Japanese/US mission, in February 2016 with μ-calorimeters based on Metal-Insulator-Sensors (M.I.S) experiment with a 4.5eV spectral resolution, would certainly generate renewed interest on the high impedance M.I.S based on Si P:B. Since 2009 we are involved in a large program to build a camera consisting of a 2x2 mosaic of 32x32 pixel matrices using this sensor type. Since we rely on very similar approach of ASTRO-H/ITOMI design, we have concentred our efforts on the use of collective all-silicon technologies only. We have already presented the building block such as thermometers, sensors and cryo-electronics. Now, thanks to our new 32x32 CAD, we are today in the process of building 4 32x32 matrices per wafer. ASTRO-H/SXS uses degenerated Si as output wiring of the pixel and an HgTe semi-conductor absorber. Thanks to the use of superconducting wiring and composite superconducting Tantalum absorber, we hope to enhance the spectral resolution of this matrix onto that of SXS. Moreover, our development benefits of an ultra low power consumption Cryo-Electronics chain. This chain is based on High Electron Mobility Transistors (HEMTs, with an AsGa/AlAsGa hetero-junction) and SiGe ASICs, and handles 34:1 multiplexing. It has been successfully tested under cryogenic conditions. The composite Tantalum absorber have been tested with 6keV X-rays, and our M.I.S. exhibit good and homogeneous sensitivity. To be compatible with the 1μW at 50mK thermal budget allowed in present day spatial cryo-coolers, we have also developed new thermal insulation techniques that will allow us to easily handle more than 4000 independent pixels within this tiny power budget.
- 18 July 2016
- Published by SPIE-Intl Soc Optical Eng
- Vol. 9905, 99050S
Toward large μ-calorimeters x-ray matrices based on metal-insulator sensors and HEMTs/SiGe cryo-electronics
The launch of ASTRO-H/ITOMI ,the X-ray Japanese/US mission, in February 2016 with μ-calorimeters based on Metal-Insulator-Sensors (M.I.S) experiment with a 4.5eV spectral resolution, would certainly generate renewed interest on the high impedance M.I.S based on Si P:B. Since 2009 we are involved in a large program to build a camera consisting of a 2x2 mosaic of 32x32 pixel matrices using this sensor type. Since we rely on very similar approach of ASTRO-H/ITOMI design, we have concentred our efforts on the use of collective all-silicon technologies only. We have already presented the building block such as thermometers, sensors and cryo-electronics. Now, thanks to our new 32x32 CAD, we are today in the process of building 4 32x32 matrices per wafer. ASTRO-H/SXS uses degenerated Si as output wiring of the pixel and an HgTe semi-conductor absorber. Thanks to the use of superconducting wiring and composite superconducting Tantalum absorber, we hope to enhance the spectral resolution of this matrix onto that of SXS. Moreover, our development benefits of an ultra low power consumption Cryo-Electronics chain. This chain is based on High Electron Mobility Transistors (HEMTs, with an AsGa/AlAsGa hetero-junction) and SiGe ASICs, and handles 34:1 multiplexing. It has been successfully tested under cryogenic conditions. The composite Tantalum absorber have been tested with 6keV X-rays, and our M.I.S. exhibit good and homogeneous sensitivity. To be compatible with the 1μW at 50mK thermal budget allowed in present day spatial cryo-coolers, we have also developed new thermal insulation techniques that will allow us to easily handle more than 4000 independent pixels within this tiny power budget.
- Open Access
KPZ dynamics from a variational perspective: potential landscape, time behavior, and other issues
The deterministic KPZ equation has been recently formulated as a gradient flow, in a nonequilibrium potential (NEP) \[\Phi[h(\mathbf{x},t)]=\int\mathrm{d}\mathbf{x}\left[\frac{\nu}{2}(\nabla h)^2-\frac{\lambda}{2}\int_{h_0(\mathbf{x},0)}^{h(\mathbf{x},t)}\mathrm{d}\psi(\nabla\psi)^2\right].\] This NEP---which provides at time $t$ the landscape where the stochastic dynamics of $h(\mathbf{x},t)$ takes place---is however unbounded, and its exact evaluation involves all the detailed histories leading to $h(\mathbf{x},t)$ from some initial configuration $h_0(\mathbf{x},0)$. After pinpointing some consequences of these facts, we study the time behavior of the NEP's first few moments and analyze its signatures when an external driving force $F$ is included. We finally show that the asymptotic form of the NEP's time derivative $\dot\Phi[h]$ turns out to be valid for any substrate dimensionality $d$, thus providing a valuable tool for studies in $d>1$.Open AccessKPZ dynamics from a variational perspective: potential landscape, time behavior, and other issues
The deterministic KPZ equation has been recently formulated as a gradient flow, in a nonequilibrium potential (NEP) \[\Phi[h(\mathbf{x},t)]=\int\mathrm{d}\mathbf{x}\left[\frac{\nu}{2}(\nabla h)^2-\frac{\lambda}{2}\int_{h_0(\mathbf{x},0)}^{h(\mathbf{x},t)}\mathrm{d}\psi(\nabla\psi)^2\right].\] This NEP---which provides at time $t$ the landscape where the stochastic dynamics of $h(\mathbf{x},t)$ takes place---is however unbounded, and its exact evaluation involves all the detailed histories leading to $h(\mathbf{x},t)$ from some initial configuration $h_0(\mathbf{x},0)$. After pinpointing some consequences of these facts, we study the time behavior of the NEP's first few moments and analyze its signatures when an external driving force $F$ is included. We finally show that the asymptotic form of the NEP's time derivative $\dot\Phi[h]$ turns out to be valid for any substrate dimensionality $d$, thus providing a valuable tool for studies in $d>1$. - Open Access
- 8 July 2015
- Published by American Physical Society (APS) in Physical Review E
- Vol. 92 (1) , 012112
Class of perfectnoise and the low-frequency cutoff paradoxThe low-frequency cutoff paradox occurring in processes has been revisited in a recent Letter [M. Niemann, H. Kantz, and E. Barkai, Phys. Rev. Lett. 110, 140603 (2013)]. A model of independent pulses exhibiting an integrable power spectrum with explains this paradox. In this paper we explore a complementary possibility based on the use of multiplicative models to generate integrable processes. Three distinct types of models are considered. One of the most used methods of generating processes based on correlated pulses is among these models. Consequently we find that, contrary to what is generally thought, the low-frequency cutoff is not necessary to avoid the postulated divergence in a wide variety of processes.- 8 July 2015
- Published by American Physical Society (APS) in Physical Review E
- Vol. 92 (1) , 012112
Open AccessClass of perfectnoise and the low-frequency cutoff paradoxThe low-frequency cutoff paradox occurring in processes has been revisited in a recent Letter [M. Niemann, H. Kantz, and E. Barkai, Phys. Rev. Lett. 110, 140603 (2013)]. A model of independent pulses exhibiting an integrable power spectrum with explains this paradox. In this paper we explore a complementary possibility based on the use of multiplicative models to generate integrable processes. Three distinct types of models are considered. One of the most used methods of generating processes based on correlated pulses is among these models. Consequently we find that, contrary to what is generally thought, the low-frequency cutoff is not necessary to avoid the postulated divergence in a wide variety of processes. - 20 October 2014
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 24 (4) , 043115
Synchronizing spatio-temporal chaos with imperfect models: A stochastic surface growth picture
We study the synchronization of two spatially extended dynamical systems where the models have imperfections. We show that the synchronization error across space can be visualized as a rough surface governed by the Kardar-Parisi-Zhang equation with both upper and lower bounding walls corresponding to nonlinearities and model discrepancies, respectively. Two types of model imperfections are considered: parameter mismatch and unresolved fast scales, finding in both cases the same qualitative results. The consistency between different setups and systems indicates that the results are generic for a wide family of spatially extended systems.
- 20 October 2014
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 24 (4) , 043115
Synchronizing spatio-temporal chaos with imperfect models: A stochastic surface growth picture
We study the synchronization of two spatially extended dynamical systems where the models have imperfections. We show that the synchronization error across space can be visualized as a rough surface governed by the Kardar-Parisi-Zhang equation with both upper and lower bounding walls corresponding to nonlinearities and model discrepancies, respectively. Two types of model imperfections are considered: parameter mismatch and unresolved fast scales, finding in both cases the same qualitative results. The consistency between different setups and systems indicates that the results are generic for a wide family of spatially extended systems.