A Minimalist Model of Characteristic Earthquakes

In a spirit akin to the sandpile model of self-organized criticality, we present a simple statistical model of the cellular-automaton type which produces an avalanche spectrum similar to the characteristic-earthquake behavior of some seismic faults. This model, that has no parameter, is amenable to an algebraic description as a Markov Chain. This possibility illuminates some important results, obtained by Monte Carlo simulations, such as the earthquake size-frequency relation and the recurrence time of the characteristic earthquake.Comment: 9 pages, 4 figure

Venus Atmosphere Profile from a Maximum Entropy Principle

The variational method with constraints recently developed by Verkley and Gerkema to describe maximum-entropy atmospheric profiles is generalized to ideal gases but with temperature-dependent specific heats. In so doing, an extended and non standard potential temperature is introduced that is well suited for tackling the problem under consideration. This new formalism is successfully applied to the atmosphere of Venus. Three well defined regions emerge in this atmosphere up to a height of $100 km$ from the surface: the lowest one up to about $35 km$ is adiabatic, a transition layer located at the height of the cloud deck and finally a third region which is practically isothermal.Comment: 6 pages, 3 figure

Dynamics of Rumor Spreading in Complex Networks

We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present analytical and Monte Carlo calculations for homogeneous networks and compare the results with those obtained by the numerical method. Then, we study the spreading process in detail for random scale-free networks. The time profiles for several quantities are numerically computed, which allow us to distinguish among different variants of rumor spreading algorithms. Our conclusions are directed to possible applications in replicated database maintenance, peer to peer communication networks and social spreading phenomena.Comment: Final version to appear in PR

Using synchronization to improve earthquake forecasting in a cellular automaton model

A new forecasting strategy for stochastic systems is introduced. It is inspired by the concept of anticipated synchronization between pairs of chaotic oscillators, recently developed in the area of Dynamical Systems, and by the earthquake forecasting algorithms in which different pattern recognition functions are used for identifying seismic premonitory phenomena. In the new strategy, copies (clones) of the original system (the master) are defined, and they are driven using rules that tend to synchronize them with the master dynamics. The observation of definite patterns in the state of the clones is the signal for connecting an alarm in the original system that efficiently marks the impending occurrence of a catastrophic event. The power of this method is quantitatively illustrated by forecasting the occurrence of characteristic earthquakes in the so-called Minimalist Model.Comment: 4 pages, 3 figure

Predictability of the large relaxations in a cellular automaton model

A simple one-dimensional cellular automaton model with threshold dynamics is introduced. The cumulative distribution of the size of the relaxations is analytically computed and behaves as a power law with an exponent equal to -1. This coincides with the phenomenological Gutenberg-Richter behavior observed in Seismology for the cumulative statistics of earthquakes at the regional or global scale. The key point of the model is the zero-load state of the system after the occurrence of any relaxation, no matter what its size. This leads to an equipartition of probability between all possible load configurations in the system during the successive loading cycles. Each cycle ends with the occurrence of the greatest -or characteristic- relaxation in the system. The duration of the cycles in the model is statistically distributed with a coefficient of variation ranging from 0.5 to 1. The predictability of the characteristic relaxations is evaluated by means of error diagrams. This model illustrates the value of taking into account the refractory periods to obtain a considerable gain in the quality of the predictions.Comment: A note has been added in which it is discussed the possible application of the model to describe some properties of the dynamics of microtubules, growth and catastrophe. It has been also added the Acknowledgments that were forgotten in the first versio

Fabrication, Detection, and Operation of a Three-Dimensional Nanomagnetic Conduit.

Three-dimensional (3D) nanomagnetic devices are attracting significant interest due to their potential for computing, sensing, and biological applications. However, their implementation faces great challenges regarding fabrication and characterization of 3D nanostructures. Here, we show a 3D nanomagnetic system created by 3D nanoprinting and physical vapor deposition, which acts as a conduit for domain walls. Domains formed at the substrate level are injected into a 3D nanowire, where they are controllably trapped using vectorial magnetic fields. A dark-field magneto-optical method for parallel, independent measurement of different regions in individual 3D nanostructures is also demonstrated. This work will facilitate the advanced study and exploitation of 3D nanomagnetic systems

Fabrication of Scaffold-Based 3D Magnetic Nanowires for Domain Wall Applications.

Three-dimensional magnetic nanostructures hold great potential to revolutionize information technologies and to enable the study of novel physical phenomena. In this work, we describe a hybrid nanofabrication process combining bottom-up 3D nano-printing and top-down thin film deposition, which leads to the fabrication of complex magnetic nanostructures suitable for the study of new 3D magnetic effects. First, a non-magnetic 3D scaffold is nano-printed using Focused Electron Beam Induced Deposition; then a thin film magnetic material is thermally evaporated onto the scaffold, leading to a functional 3D magnetic nanostructure. Scaffold geometries are extended beyond recently developed single-segment geometries by introducing a dual-pitch patterning strategy. Additionally, by tilting the substrate during growth, low-angle segments can be patterned, circumventing a major limitation of this nano-printing process; this is demonstrated by the fabrication of ‘staircase’ nanostructures with segments parallel to the substrate. The suitability of nano-printed scaffolds to support thermally evaporated thin films is discussed, outlining the importance of including supporting pillars to prevent deformation during the evaporation process. Employing this set of methods, a set of nanostructures tailored to precisely match a dark-field magneto-optical magnetometer have been fabricated and characterized. This work demonstrates the versatility of this hybrid technique and the interesting magnetic properties of the nanostructures produced, opening a promising route for the development of new 3D devices for applications and fundamental studies