Earthquake recurrence as a record breaking process

Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record breaking events with edges between nodes in a graph generates a complex dynamical network isolated from any length, time or magnitude scales set by the observer. For Southern California, the network of recurrences reveals new statistical features of seismicity with robust scaling laws. The rupture length and its scaling with magnitude emerges as a generic measure for distance between recurrent events. Further, the relative separations for subsequent records in space (or time) form a hierarchy with unexpected scaling properties

Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs

Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first order behaviors in two different classes of models: The first are generalized epidemic processes (GEP) that describe in their spatially embedded version - either on or off a regular lattice - compact or fractal cluster growth in random media at zero temperature. A random graph version of GEP is mapped onto a model previously proposed for complex social contagion. We compute detailed phase diagrams and compare our numerical results at the tricritical point in d = 3 with field theory predictions of Janssen et al. [Phys. Rev. E 70, 026114 (2004)]. The second class consists of exponential ("Hamiltonian", or formally equilibrium) random graph models and includes the Strauss and the 2-star model, where 'chemical potentials' control the densities of links, triangles or 2-stars. When the chemical potentials in either graph model are O(logN), the percolation transition can coincide with a first order phase transition in the density of links, making the former also discontinuous. Hysteresis loops can then be of mixed order, with second order behavior for decreasing link fugacity, and a jump (first order) when it increases

On the Origin of Metallicity and Stability of the Metastable Phase in Chemically Exfoliated MoS2_2

Chemical exfoliation of MoS$_2$ via Li-intercalation route has led to many desirable properties and spectacular applications due to the presence of a metastable state in addition to the stable H phase. However, the nature of the specific metastable phase formed, and its basic charge conduction properties have remained controversial. Using spatially resolved Raman spectroscopy (~1 micrometer resolution) and photoelectron spectroscopy (~120 nm resolution), we probe such chemically exfoliated MoS$_2$ samples in comparison to a mechanically exfoliated H phase sample and confirm that the dominant metastable state formed by this approach is a distorted T' state with a small semiconducting gap. Investigating two such samples with different extents of Li residues present, we establish that Li+ ions, not only help to exfoliate MoS$_2$ into few layer samples, but also contribute to enhancing the relative stability of the metastable state as well as dope the system with electrons, giving rise to a lightly doped small bandgap system with the T' structure, responsible for its spectacular properties.Comment: 34 pages, Main manuscript + Supplementary Materia

Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares

Introducing thresholds to analyze time series of emission from the Sun enables a new and simple definition of solar flare events, and their interoccurrence times. Rescaling time by the rate of events, the waiting and quiet time distributions both conform to scaling functions that are independent of the intensity threshold over a wide range. The scaling functions are well described by a two parameter function, with parameters that depend on the phase of the solar cycle. For flares identified according to the current, standard definition, similar behavior is found.Comment: 5 pages, 4 figures, revtex

Energy bounds for codes and designs in Hamming spaces

We obtain universal bounds on the energy of codes and for designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow unified treatment, and can be viewed as a generalization of the Levenshtein bounds for maximal codes.Comment: 25 page