PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite

This is the author accepted manuscript. The final version is available frpm Springer Verlag via the DOI in this record5th International Congress on Mathematical Software (ICMS 2016), 11-14 July 2016, Berlin, GermanySCIP is a solver for a wide variety of mathematical optimization problems. It is written in C and extendable due to its plug-in based design. However, dealing with all C specifics when extending SCIP can be detrimental to development and testing of new ideas. This paper attempts to provide a remedy by introducing PySCIPOpt, a Python interface to SCIP that enables users to write new SCIP code entirely in Python. We demonstrate how to intuitively model mixed-integer linear and quadratic optimization problems and moreover provide examples on how new Python plug-ins can be added to SCIP.German Federal Ministry of Education and Researc

Persistence and Quiescence of Seismicity on Fault Systems

We study the statistics of simulated earthquakes in a quasistatic model of two parallel heterogeneous faults within a slowly driven elastic tectonic plate. The probability that one fault remains dormant while the other is active for a time Dt following the previous activity shift is proportional to the inverse of Dt to the power 1+x, a result that is robust in the presence of annealed noise and strength weakening. A mean field theory accounts for the observed dependence of the persistence exponent x as a function of heterogeneity and distance between faults. These results continue to hold if the number of competing faults is increased. This is related to the persistence phenomenon discovered in a large variety of systems, which specifies how long a relaxing dynamical system remains in a neighborhood of its initial configuration. Our persistence exponent is found to vary as a function of heterogeneity and distance between faults, thus defining a novel universality class.Comment: 4 pages, 3 figures, Revte

Statistics of Earthquakes in Simple Models of Heterogeneous Faults

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distribution of small events combined with characteristic system size events. The studies employ various analytic methods as well as simulations.Comment: 4 pages, RevTex, 3 figures (eps-files), uses eps

Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ``overshoot'') effects (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed.Comment: 21 pages, RevTex, 6 figures (ps, eps

Segmentation of Fault Networks Determined from Spatial Clustering of Earthquakes

We present a new method of data clustering applied to earthquake catalogs, with the goal of reconstructing the seismically active part of fault networks. We first use an original method to separate clustered events from uncorrelated seismicity using the distribution of volumes of tetrahedra defined by closest neighbor events in the original and randomized seismic catalogs. The spatial disorder of the complex geometry of fault networks is then taken into account by defining faults as probabilistic anisotropic kernels, whose structures are motivated by properties of discontinuous tectonic deformation and previous empirical observations of the geometry of faults and of earthquake clusters at many spatial and temporal scales. Combining this a priori knowledge with information theoretical arguments, we propose the Gaussian mixture approach implemented in an Expectation-Maximization (EM) procedure. A cross-validation scheme is then used and allows the determination of the number of kernels that should be used to provide an optimal data clustering of the catalog. This three-steps approach is applied to a high quality relocated catalog of the seismicity following the 1986 Mount Lewis ($M_l=5.7$) event in California and reveals that events cluster along planar patches of about 2 km$^2$, i.e. comparable to the size of the main event. The finite thickness of those clusters (about 290 m) suggests that events do not occur on well-defined euclidean fault core surfaces, but rather that the damage zone surrounding faults may be seismically active at depth. Finally, we propose a connection between our methodology and multi-scale spatial analysis, based on the derivation of spatial fractal dimension of about 1.8 for the set of hypocenters in the Mnt Lewis area, consistent with recent observations on relocated catalogs

Static and Dynamic Properties of Inhomogeneous Elastic Media on Disordered Substrate

The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of a $D$-dimensional random manifold embedded in $(D+D)$-dimensions. The analogy is found to be very robust, applicable to a wide range of elastic media, including those which are amorphous or nearly-periodic, with local or nonlocal elasticity. Also demonstrated explicitly is the equivalence between the dynamic depinning transition obtained at a constant driving force, and the self-organized, near-critical behavior obtained by a (small) constant velocity drive.Comment: 20 pages, RevTeX. Related (p)reprints also available at http://matisse.ucsd.edu/~hwa/pub.htm

The Causes of Foehn Warming in the Lee of Mountains

The foehn effect is well known as the warming, drying, and cloud clearance experienced on the lee side of mountain ranges during “flow over” conditions. Foehn flows were first described more than a century ago when two mechanisms for this warming effect were postulated: an isentropic drawdown mechanism, where potentially warmer air from aloft is brought down adiabatically, and a latent heating and precipitation mechanism, where air cools less on ascent—owing to condensation and latent heat release—than on its dry descent on the lee side. Here, for the first time, the direct quantitative contribution of these and other foehn warming mechanisms is shown. The results suggest a new paradigm is required after it is demonstrated that a third mechanism, mechanical mixing of the foehn flow by turbulence, is significant. In fact, depending on the flow dynamics, any of the three warming mechanisms can dominate. A novel Lagrangian heat budget model, back trajectories, high-resolution numerical model output, and aircraft observations are all employed. The study focuses on a unique natural laboratory—one that allows unambiguous quantification of the leeside warming—namely, the Antarctic Peninsula and Larsen C Ice Shelf. The demonstration that three foehn warming mechanisms are important has ramifications for weather forecasting in mountainous areas and associated hazards such as ice shelf melt and wildfires

Compulsive buying and branding phenomena

The purpose of this paper was to explore the impact of brand variables such as brand awareness, brand loyalty, brand attachment, and perceived brand quality on compulsive buying behavior. A self-administered questionnaire, containing demographic items and items related to compulsive buying, brand awareness, brand loyalty, brand attachment and perceived quality, was used to collect data. Participants were 269 US university students at a large mid-western university (138 men, 131 women; mean age = 21.96). Data were analyzed using descriptive statistics, t-test and MANOVA/ANOVA. Reliability of all scales was acceptable. In the current study, 18% of the participants were classified as compulsive buyers. Women showed higher compulsive buying tendency than men. Participants with greater compulsive buying tendency scored higher on brand attachment and brand loyalty and lower on brand awareness; there was no difference in scores on perceived brand quality. Results support that brand variables such as brand awareness, brand loyalty, and brand attachment are related to compulsive buying behavior. New perceptions and implications for both academicians and practitioners are provided

Secondary Ice Production : Current State of the Science and Recommendations for the Future

Measured ice crystal concentrations in natural clouds at modest supercooling (temperature ~>-10°C) are often orders of magnitude greater than the number concentration of primary ice nucleating particles. Therefore, it has long been proposed that a secondary ice production process must exist that is able to rapidly enhance the number concentration of the ice population following initial primary ice nucleation events. Secondary ice production is important for the prediction of ice crystal concentration and the subsequent evolution of some types of clouds, but the physical basis of the process is not understood and the production rates are not well constrained. In November 2015 an international workshop was held to discuss the current state of the science and future work to constrain and improve our understanding of secondary ice production processes. Examples and recommendations for in situ observations, remote sensing, laboratory investigations, and modeling approaches are presented.Peer reviewe