Directed Percolation and Generalized Friendly Walkers

We show that the problem of directed percolation on an arbitrary lattice is equivalent to the problem of m directed random walkers with rather general attractive interactions, when suitably continued to m=0. In 1+1 dimensions, this is dual to a model of interacting steps on a vicinal surface. A similar correspondence with interacting self-avoiding walks is constructed for isotropic percolation.Comment: 4 pages, 3 figures, to be published in Phys. Rev. Let

Cosmo-dynamics and dark energy with a quadratic EoS: anisotropic models, large-scale perturbations and cosmological singularities

In general relativity, for fluids with a linear equation of state (EoS) or scalar fields, the high isotropy of the universe requires special initial conditions, and singularities are anisotropic in general. In the brane world scenario anisotropy at the singularity is suppressed by an effective quadratic equation of state. There is no reason why the effective EoS of matter should be linear at the highest energies, and a non-linear EoS may describe dark energy or unified dark matter (Paper I, astro-ph/0512224). In view of this, here we study the effects of a quadratic EoS in homogenous and inhomogeneous cosmological models in general relativity, in order to understand if in this context the quadratic EoS can isotropize the universe at early times. With respect to Paper I, here we use the simplified EoS P=alpha rho + rho^2/rho_c, which still allows for an effective cosmological constant and phantom behavior, and is general enough to analyze the dynamics at high energies. We first study anisotropic Bianchi I and V models, focusing on singularities. Using dynamical systems methods, we find the fixed points of the system and study their stability. We find that models with standard non-phantom behavior are in general asymptotic in the past to an isotropic fixed point IS, i.e. in these models even an arbitrarily large anisotropy is suppressed in the past: the singularity is matter dominated. Using covariant and gauge invariant variables, we then study linear perturbations about the homogenous and isotropic spatially flat models with a quadratic EoS. We find that, in the large scale limit, all perturbations decay asymptotically in the past, indicating that the isotropic fixed point IS is the general asymptotic past attractor for non phantom inhomogeneous models with a quadratic EoS. (Abridged)Comment: 16 pages, 6 figure

Low-density series expansions for directed percolation IV. Temporal disorder

We introduce a model for temporally disordered directed percolation in which the probability of spreading from a vertex $(t,x)$, where $t$ is the time and $x$ is the spatial coordinate, is independent of $x$ but depends on $t$. Using a very efficient algorithm we calculate low-density series for bond percolation on the directed square lattice. Analysis of the series yields estimates for the critical point $p_c$ and various critical exponents which are consistent with a continuous change of the critical parameters as the strength of the disorder is increased.Comment: 11 pages, 3 figure

The AGeS2 (Awards for Geochronology Student research 2) Program: Supporting Community Geochronology Needs and Interdisciplinary Science

Geochronology is essential in the geosciences. It is used to resolve the durations and rates of earth processes, as well as test causative relationships among events. Such data are increasingly required to conduct cutting-edge, transformative, earth-science research. The growing need for geochronology is accompanied by strong demand to enhance the ability of labs to meet this pressure and to increase community awareness of how these data are produced and interpreted. For example, a 2015 National Science Foundation (NSF) report on opportunities and challenges for U.S. geochronology research noted: While there has never been a time when users have had greater access to geo-chronologic data, they remain, by and large, dissatisfied with the available style/ quantity/cost/efficiency (Harrison et al., 2015, p. 1). And the 2012 National Research Council NROES (New Research Opportunities in the Earth Sciences) report (Lay et al., 2012, p. 82) recommended: [NSF] EAR should explore new mechanisms for geochronology laboratories that will service the geochronology requirements of the broad suite of research opportunities while sustaining technical advances in methodologies. The AGeS (Awards for Geochronology Student research) program is one way that these calls are being answered

Toxin release by conditional remodelling of ParDE1 from Mycobacterium tuberculosis leads to gyrase inhibition

Mycobacterium tuberculosis, the causative agent of tuberculosis, is a growing threat to global health, with recent efforts towards its eradication being reversed in the wake of the COVID-19 pandemic. Increasing resistance to gyrase-targeting second-line fluoroquinolone antibiotics indicates the necessity to develop both novel therapeutics and our understanding of M. tuberculosis growth during infection. ParDE toxin-antitoxin systems also target gyrase and are regulated in response to both host-associated and drug-induced stress during infection. Here, we present microbiological, biochemical, structural, and biophysical analyses exploring the ParDE1 and ParDE2 systems of M. tuberculosis H37Rv. The structures reveal conserved modes of toxin-antitoxin recognition, with complex-specific interactions. ParDE1 forms a novel heterohexameric ParDE complex, supported by antitoxin chains taking on two distinct folds. Curiously, ParDE1 exists in solution as a dynamic equilibrium between heterotetrameric and heterohexameric complexes. Conditional remodelling into higher order complexes can be thermally driven in vitro. Remodelling induces toxin release, tracked through concomitant inhibition and poisoning of gyrase activity. Our work aids our understanding of gyrase inhibition, allowing wider exploration of toxin-antitoxin systems as inspiration for potential therapeutic agents. [Abstract copyright: © The Author(s) 2023. Published by Oxford University Press on behalf of Nucleic Acids Research.

Non-autonomous 2-periodic Gumovski-Mira difference equations

We consider two types of non-autonomous 2-periodic Gumovski-Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the 2-periodic ones differ dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence.Comment: 20 pages, 11 figure

Devil's Staircase in Magnetoresistance of a Periodic Array of Scatterers

The nonlinear response to an external electric field is studied for classical non-interacting charged particles under the influence of a uniform magnetic field, a periodic potential, and an effective friction force. We find numerical and analytical evidence that the ratio of transversal to longitudinal resistance forms a Devil's staircase. The staircase is attributed to the dynamical phenomenon of mode-locking.Comment: two-column 4 pages, 5 figure

Paleoseismology of the Xorxol Segment of the Central Altyn Tagh Fault, Xinjiang, China

Although the Altyn Tagh Fault (ATF) is thought to play a key role in accommodating India-Eurasian convergence, little is known about its earthquake history. Studies of this strike-slip fault are important for interpretation of the role of faulting versus distributed deformation in the accommodation of the India- Eurasia collision. In addition, the > 1200 km long fault represents one of the most important and exemplary intracontinental strike-slip faults in the world. We mapped fault trace geometry and interpreted paleoseismic trench exposures to characterize the seismogenic behavior of the ATF. We identified 2 geometric segment boundaries in a 270 km long reach of the central ATF. These boundaries define the westernmost Wuzhunxiao, the Central Pingding, and the easternmost Xorxol (also written as Suekuli or Suo erkuli) segments. In this paper, we present the results from the Camel paleoseismic site along the Xorxol Segment at 91.759°E, 38.919°N. There evidence for the last two earthquakes is clear and 14C dates from layers exposed in the excavation bracket their ages. The most recent earthquake occurred between 1456 and 1775 cal A.D. and the penultimate event was between 60 and 980 cal A.D. Combining the Camel interpretations with our published results for the central ATF, we conclude that multiple earthquakes with shorter rupture lengths (?? 50 km) rather than complete rupture of the Xorxol Segment better explain the paleoseismic data. We found 2-3 earthquakes in the last 2-3 kyr. When coupled with typical amounts of slip per event (5-10 m), the recurrence times are tentatively consistent with 1-2 cm/yr slip rates. This result favors models that consider the broader distribution of collisional deformation, rather than those with northward motion of India into Asia absorbed along a few faults bounding rigid blocks

Phase transitions in packet traffic on regular networks: a comparison of source types and topologies

Abstract We extend the packet traffic network models developed in recent years for rectangular grids to other regular networks, and to fragmented networks. The packet transfer mechanism is open-loop as before. The nodes of the network are either hosts or routers. Both can receive and transmit packets towards their destination; hosts can also create and receive packets. Long range dependent traffic with varying Hurst parameter is introduced at the host nodes of these networks, and comparative studies of the onset of congestion are carried out. Results show statistical robustness when the rectangular grid is adapted to form other regular networks. Qualitative behavior is the same, and simple mean field models accurately predict critical points as in the rectangular case. R/S-statistics show the presence of long range dependence even when sources are short range dependent. Results indicate that this long range dependence is closely linked to the queueing mechanism