Avalanches in the athermal 2d Random-Field Ising model: front propagation versus nucleation and growth dynamics

Màster Oficial en Física Avançada, , Facultat de Física, Universitat de Barcelona, Curs: 2015, Tutor: Eduard Vives i Santa-EulaliaThe two-dimensional zero-temperature Random Field Ising Model with local adiabatic relaxation dynamics is studied. When externally driven, this model allows to analyse the properties of an advancing front for different amounts of disorder. By imposing special forced boundary conditions and allowing for systems with rectangular geometry, we favour the existence of a unique interface which is the boundary of a 1d spanning avalanche. We show that the description of an advancing front in terms of a univalued function x(y) lacks of a relevant contribution in the thermodynamic limit: the existence of overhangs and islands which are characteristic of the nucleation and growth dynamic

The Barkhausen Effect

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2014, Tutor: Eduard Vives i Santa-EulàliaThis work presents an introduction to the Barkhausen e ect. First, experimental measurements of Barkhausen noise detected in a soft iron sample will be exposed and analysed. Two di erent kinds of simulations of the 2-d Out of Equilibrium Random Field Ising Model (RFIM) at T=0 will be performed in order to explain this e ect: one with periodic boundary conditions (PBC) and the other with xed boundary conditions (FBC). The rst model represents a spin nucleation dynamics whereas the second one represents the dynamics of a single domain wall. Results from these two di erent models will be contrasted and discussed in order to understand the nature of this e ect

Increasing power-law range in avalanche amplitude and energy distributions

Power-law type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constrains that limit the power-law range for the distributions of different avalanche observables like amplitude, energy, duration or size. By considering catalogs of events that cover different observation windows, maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under- compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the later case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.Comment: 23 pages, 7 figure

No Signifcant Efect of Coulomb Stress on the Gutenberg-Richter Law after the Landers Earthquake

Coulomb-stress theory has been used for years in seismology to understand how earthquakes trigger each other. Whenever an earthquake occurs, the stress feld changes, and places with positive increases are brought closer to failure. Earthquake models that relate earthquake rates and Coulomb stress after a main event, such as the rate-and-state model, assume that the magnitude distribution of earthquakes is not afected by the change in the Coulomb stress. By using diferent slip models, we calculate the change in Coulomb stress in the fault plane for every aftershock after the Landers event (California, USA, 1992, moment magnitude 7.3). Applying several statistical analyses to test whether the distribution of magnitudes is sensitive to the sign of the Coulomb-stress increase, we are not able to fnd any signifcant efect. Further, whereas the events with a positive increase of the stress are characterized by a much larger proportion of strike-slip events in comparison with the seismicity previous to the mainshock, the events happening despite a decrease in Coulomb stress show no relevant diferences in focal-mechanism distribution with respect to previous seismicity.Spanish Ministry of Economy and Competitiveness (MINECO, Spain), through the "Maria de Maeztu" Program for Units of Excellence in R D MDM-2014-0445MINECO FIS2015-71851-P FIS-PGC2018-099629-B-I00 MAT2015-69777-REDTMICIU FIS2015-71851-P FIS-PGC2018-099629-B-I00 MAT2015-69777-RED

Com es comporta un terratrèmol? : Avaluació del model físic de predicció

La magnitud d'un terratrèmol és la dada més important per a poder avaluar la seva capacitat destructiva. Els models sismològics, encara en estat molt embrionari, intenten definir un model adequat per al seu estudi. En aquest treball, dut a terme per investigadors del Centre de Recerca Matemàtica (CRM) i del Departament de Matemàtiques en col·laboració amb el Departament de Computació i Intel·ligència Artificial de Granada, s'ha comprovat que la predicció dels models físics pot millorar aquella dels models estadístics. Els resultats representen una aportació de gran valor en aportar dades fiables i robustes que permeten afermar el coneixement sobre com es comporta aquest tipus de fenòmens i poder establir pronòstics ferms enfront d'emergències.La magnitud de un terremoto es el dato más importante para poder evaluar su capacidad destructiva. Los modelos sismológicos, aún en estado muy embrionario, intentan definir un modelo adecuado para su estudio. En este trabajo, llevado a cabo por investigadores del Centre de Recerca Matemàtica (CRM) y del Departamento de Matemáticas en colaboración con el Departamento de Computación e Inteligencia Artificial de Granada, se ha comprobado que la predicción de los modelos físicos puede mejorar aquella de los modelos estadísticos. Los resultados representan una aportación de gran valor al aportar datos fiables y robustos que permiten afianzar el conocimiento sobre cómo se comporta este tipo de fenómenos y poder establecer pronósticos firmes frente a emergencias

Increasing power-law range in avalanche amplitude and energy distributions

Power-law-type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constraints that limit the range of truncated power-law distributions. By considering catalogs of events that cover different observation windows, the maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under-compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the latter case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior

Crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model

We present extensive numerical studies of the crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model with metastable dynamics. Bivariate finite-size scaling hypotheses are presented for systems with sizes L °ø L °ø l which explain the size-driven critical crossover from two dimensions (l = const, L→∞) to three dimensions (l ∝ L→∞). A model of effective critical disorder Reffc (l,L) with a unique fitting parameter and no free parameters in the Reffc (l,L→∞) limit is proposed, together with expressions for the scaling of avalanche distributions bringing important implications for related experimental data analysis, especially in the case of thin three-dimensional systems

Universality of power-law exponents by means of maximum-likelihood estimation

Power-law-type distributions are extensively found when studying the behavior of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult to establish power-law behavior unambiguously. In this work we present a statistical procedure to merge different datasets, with two different aims. First, we obtain a broader fitting range for the statistics of different experiments or observations of the same system. Second, we establish whether two or more different systems may belong to the same universality class. By means of maximum likelihood estimation, this methodology provides rigorous statistical information to discern whether power-law exponents characterizing different datasets can be considered equal among them or not. This procedure is applied to the Gutenberg-Richter law for earthquakes and for synthetic earthquakes (acoustic emission events) generated in the laboratory: labquakes. Different earthquake catalogs have been merged finding a Gutenberg-Richter law holding for more than eight orders of magnitude in seismic moment. The value of the exponent of the energy distribution of labquakes depends on the material used in the compression experiments. By means of the procedure proposed in this manuscript, we find that the Gutenberg-Richter law for earthquakes and charcoal labquakes can be characterized by the same power-law exponent, whereas Vycor labquakes exhibit a significantly different exponent