Rate of steady-state reconnection in an incompressible plasma

The reconnection rate is obtained for the simplest case of 2D symmetric reconnection in an incompressible plasma. In the short note (Erkaev et al., Phys. Rev. Lett.,84, 1455 (2000)), the reconnection rate is found by matching the outer Petschek solution and the inner diffusion region solution. Here the details of the numerical simulation of the diffusion region are presented and the asymptotic procedure which is used for deriving the reconnection rate is described. The reconnection rate is obtained as a decreasing function of the diffusion region length. For a sufficiently large diffusion region scale, the reconnection rate becomes close to that obtained in the Sweet-Parker solution with the inverse square root dependence on the magnetic Reynolds number, determined for the global size of the current sheet. On the other hand, for a small diffusion region length scale, the reconnection rate turns out to be very similar to that obtained in the Petschek model with a logarithmic dependence on the magnetic Reynolds number. This means that the Petschek regime seems to be possible only in the case of a strongly localized conductivity corresponding to a small scale of the diffusion region.Comment: 11 pages, 3 figure

The m−m-dissimilarity map and representation theory of SLmSL_m

We give another proof that $m$-dissimilarity vectors of weighted trees are points on the tropical Grassmanian, as conjectured by Cools, and proved by Giraldo in response to a question of Sturmfels and Pachter. We accomplish this by relating $m$-dissimilarity vectors to the representation theory of $SL_m.$Comment: 11 pages, 8 figure

Recovering rearranged cancer chromosomes from karyotype graphs

BACKGROUND: Many cancer genomes are extensively rearranged with highly aberrant chromosomal karyotypes. Structural and copy number variations in cancer genomes can be determined via abnormal mapping of sequenced reads to the reference genome. Recently it became possible to reconcile both of these types of large-scale variations into a karyotype graph representation of the rearranged cancer genomes. Such a representation, however, does not directly describe the linear and/or circular structure of the underlying rearranged cancer chromosomes, thus limiting possible analysis of cancer genomes somatic evolutionary process as well as functional genomic changes brought by the large-scale genome rearrangements. RESULTS: Here we address the aforementioned limitation by introducing a novel methodological framework for recovering rearranged cancer chromosomes from karyotype graphs. For a cancer karyotype graph we formulate an Eulerian Decomposition Problem (EDP) of finding a collection of linear and/or circular rearranged cancer chromosomes that are determined by the graph. We derive and prove computational complexities for several variations of the EDP. We then demonstrate that Eulerian decomposition of the cancer karyotype graphs is not always unique and present the Consistent Contig Covering Problem (CCCP) of recovering unambiguous cancer contigs from the cancer karyotype graph, and describe a novel algorithm CCR capable of solving CCCP in polynomial time. We apply CCR on a prostate cancer dataset and demonstrate that it is capable of consistently recovering large cancer contigs even when underlying cancer genomes are highly rearranged. CONCLUSIONS: CCR can recover rearranged cancer contigs from karyotype graphs thereby addressing existing limitation in inferring chromosomal structures of rearranged cancer genomes and advancing our understanding of both patient/cancer-specific as well as the overall genetic instability in cancer

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

There are some hydrodynamic equations that, while their parent kinetic equation satisfies fundamental mechanical properties, appear themselves to violate mechanical or thermodynamic properties. This article aims to shed some light on the source of this problem. Starting with diffusive volume hydrodynamic models, the microscopic temporal and spatial scales are first separated at the kinetic level from the macroscopic scales at the hydrodynamic level. Then we consider Klimontovich’s spatial stochastic version of the Boltzmann kinetic equation, and show that, for small local Knudsen numbers, the stochastic term vanishes and the kinetic equation becomes the Boltzmann equation. The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a sub-domain of the continuum range which the conventional Knudsen number classification does not account for appropriately. In this sub-domain, it is possible to obtain a fully mechanically-consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics

Vertical structure of recent arctic warming from observed data and reanalysis products

The final publication is available at Springer via http://dx.doi.org/10.1007/s10584-011-0192-8Spatiotemporal patterns of recent (1979–2008) air temperature trends are evaluated using three reanalysis datasets and radiosonde data. Our analysis demonstrates large discrepancies between the reanalysis datasets, possibly due to differences in the data assimilation procedures as well as sparseness and inhomogeneity of high-latitude observations. We test the robustness of Arctic tropospheric warming based on the ERA-40 dataset. ERA-40 Arctic atmosphere temperatures tend to be closer to the observed ones in terms of root mean square error compare to other reanalysis products used in the article. However, changes in the ERA-40 data assimilation procedure produce unphysical jumps in atmospheric temperatures, which may be the likely reason for the elevated tropospheric warming trend in 1979-2002. NCEP/NCAR Reanalysis show that the near-surface upward temperature trend over the same period is greater than the tropospheric trend, which is consistent with direct radiosonde observations and inconsistent with ERA-40 results. A change of sign in the winter temperature trend from negative to positive in the late 1980s is documented in the upper troposphere/lower stratosphere with a maximum over the Canadian Arctic, based on radiosonde data. This change from cooling to warming tendency is associated with weakening of the stratospheric polar vortex and shift of its center toward the Siberian coast and possibly can be explained by the changes in the dynamics of the Arctic Oscillation. This temporal pattern is consistent with multi-decadal variations of key Arctic climate parameters like, for example, surface air temperature and oceanic freshwater content. Elucidating the mechanisms behind these changes will be critical to understanding the complex nature of high-latitude variability and its impact on global climate change.acceptedVersio

Magnetopause mapping to the ionosphere for northward IMF

International audienceWe study the topological structure of the magnetosphere for northward IMF. Using a magnetospheric magnetic field model we study the high-latitude response to prolonged periods of northward IMF. For forced solar wind conditions we investigate the location of the polar cap region, the polar cap potential drop, and the field-aligned acceleration potentials, depending on the solar wind pressure and IMF By and Bx changes. The open field line bundles, which connect the Earth's polar ionosphere with interplanetary space, are calculated. The locations of the magnetospheric plasma domains relative to the polar ionosphere are studied. The specific features of the open field line regions arising when IMF is northward are demonstrated. The coefficients of attenuation of the solar wind magnetic and electric fields which penetrate into the magnetosphere are determined

Three ways to lattice Boltzmann: A unified time-marching picture

It is shown that the lattice Boltzmann equation LBE corresponds to an explicit Verlet time-marching scheme for a continuum generalized Boltzmann equation with a memory delay equal to a half time step. This proves second-order accuracy of LBE with respect to this generalized equation, with no need of resorting to any implicit time-marching procedure Crank-Nicholson and associated nonlinear variable transformations. It is also shown, and numerically demonstrated, that this equivalence is not only formal, but it also translates into a complete equivalence of the corresponding computational schemes with respect to the hydrodynamic equa- tions. Second-order accuracy with respect to the continuum kinetic equation is also numerically demonstrated for the case of the Taylor-Green vortex. It is pointed out that the equivalence is however broken for the case in which mass and/or momentum are not conserved, such as for chemically reactive flows and mixtures. For such flows, the time-centered implicit formulation may indeed offer a better numerical accuracy