Exact renormalization-group analysis of first order phase transitions in clock models

We analyze the exact behavior of the renormalization group flow in one-dimensional clock-models which undergo first order phase transitions by the presence of complex interactions. The flow, defined by decimation, is shown to be single-valued and continuous throughout its domain of definition, which contains the transition points. This fact is in disagreement with a recently proposed scenario for first order phase transitions claiming the existence of discontinuities of the renormalization group. The results are in partial agreement with the standard scenario. However in the vicinity of some fixed points of the critical surface the renormalized measure does not correspond to a renormalized Hamiltonian for some choices of renormalization blocks. These pathologies although similar to Griffiths-Pearce pathologies have a different physical origin: the complex character of the interactions. We elucidate the dynamical reason for such a pathological behavior: entire regions of coupling constants blow up under the renormalization group transformation. The flows provide non-perturbative patterns for the renormalization group behavior of electric conductivities in the quantum Hall effect.Comment: 13 pages + 3 ps figures not included, TeX, DFTUZ 91.3

Estimation of Kalman filter model parameters from an ensemble of tests

A methodology for estimating initial mean and covariance parameters in a Kalman filter model from an ensemble of nonidentical tests is presented. In addition, the problem of estimating time constants and process noise levels is addressed. Practical problems such as developing and validating inertial instrument error models from laboratory test data or developing error models of individual phases of a test are generally considered

Filamin cross-linked semiflexible networks: Fragility under strain

The semiflexible F-actin network of the cytoskeleton is cross-linked by a variety of proteins including filamin, which contain Ig-domains that unfold under applied tension. We examine a simple semiflexible network model cross-linked by such unfolding linkers that captures the main mechanical features of F-actin networks cross-linked by filamin proteins and show that under sufficiently high strain the network spontaneously self-organizes so that an appreciable fraction of the filamin cross-linkers are at the threshold of domain unfolding. We propose an explanation of this organization based on a mean-field model and suggest a qualitative experimental signature of this type of network reorganization under applied strain that may be observable in intracellular microrheology experiments of Crocker et al.Comment: 4 Pages, 3 figures, Revtex4, submitted to PR

An exactly solvable dissipative transport model

We introduce a class of one-dimensional lattice models in which a quantity, that may be thought of as an energy, is either transported from one site to a neighbouring one, or locally dissipated. Transport is controlled by a continuous bias parameter q, which allows us to study symmetric as well as asymmetric cases. We derive sufficient conditions for the factorization of the N-body stationary distribution and give an explicit solution for the latter, before briefly discussing physically relevant situations.Comment: 7 pages, 1 figure, submitted to J. Phys.

The approach to criticality in sandpiles

A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model should be equal to the threshold density of the corresponding fixed-energy sandpile. This "density conjecture" has been proved for the underlying graph Z. We show (by simulation or by proof) that the density conjecture is false when the underlying graph is any of Z^2, the complete graph K_n, the Cayley tree, the ladder graph, the bracelet graph, or the flower graph. Driven dissipative sandpiles continue to evolve even after a constant fraction of the sand has been lost at the sink. These results cast doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the abelian sandpile model at stationarity.Comment: 30 pages, 8 figures, long version of arXiv:0912.320

Dynamic instabilities of fracture under biaxial strain using a phase field model

We present a phase field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under bi-axial load. Our model again reproduces well observed supercritical Hopf bifurcation, and is therefore the first simulation which does so

Geologic application of thermal inertia imaging using HCMM data

Three test sites in the western US were selected to discriminate among surface geologic materials on the basis of their thermal properties as determined from HCMM data. Attempts to determine quantitatively accurate thermal inertia values from HCMM digital data met with only partial success due to the effects of sensor miscalibrations, radiative transfer in the atmosphere, and varying meteorology and elevation across a scene. In most instances, apparent thermal inertia was found to be an excellent qualitative representation of true thermal inertia. Computer processing of digital day and night HCMM data allowed construction of geologically useful images. At some test sites, more information was provided by data than LANDSAT data. Soil moisture effects and differences in spectrally dark materials were more effectively displayed using the thermal data

Critical phase in non-conserving zero-range processes and equilibrium networks

Zero-range processes, in which particles hop between sites on a lattice, are closely related to equilibrium networks, in which rewiring of links take place. Both systems exhibit a condensation transition for appropriate choices of the dynamical rules. The transition results in a macroscopically occupied site for zero-range processes and a macroscopically connected node for networks. Criticality, characterized by a scale-free distribution, is obtained only at the transition point. This is in contrast with the widespread scale-free real-life networks. Here we propose a generalization of these models whereby criticality is obtained throughout an entire phase, and the scale-free distribution does not depend on any fine-tuned parameter.Comment: 4 pages, 4 figure

Triple-Star Candidates Among the Kepler Binaries

We present the results of a search through the photometric database of eclipsing Kepler binaries (Prsa et al. 2011; Slawson et al. 2011) looking for evidence of hierarchical triple star systems. The presence of a third star orbiting the binary can be inferred from eclipse timing variations. We apply a simple algorithm in an automated determination of the eclipse times for all 2157 binaries. The "calculated" eclipse times, based on a constant period model, are subtracted from those observed. The resulting O-C (observed minus calculated times) curves are then visually inspected for periodicities in order to find triple-star candidates. After eliminating false positives due to the beat frequency between the ~1/2-hour Kepler cadence and the binary period, 39 candidate triple systems were identified. The periodic O-C curves for these candidates were then fit for contributions from both the classical Roemer delay and so-called "physical" delay, in an attempt to extract a number of the system parameters of the triple. We discuss the limitations of the information that can be inferred from these O-C curves without further supplemental input, e.g., ground-based spectroscopy. Based on the limited range of orbital periods for the triple star systems to which this search is sensitive, we can extrapolate to estimate that at least 20% of all close binaries have tertiary companions.Comment: 19 pages, 13 figures, 3 tables; ApJ, 2013, 768, 33; corrected Fig. 7, updated references, minor fixes to tex

Cold collisions of OH and Rb. I: the free collision

We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the Rb($^1 S$) + OH($^2 \Pi_{3/2}$) system, including fine-structure and hyperfine effects. We have developed a new set of five potential energy surfaces for Rb-OH($^2 \Pi$) from high-level {\em ab initio} electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of $10^{-13}$ cm$^2$ are predicted for temperatures typical of Stark decelerators. We also conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.Comment: 20 pages, 16 figure