6,635 research outputs found

    Stochastics theory of log-periodic patterns

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    We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge

    Quantum theory of successive projective measurements

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    We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The complex modification term is a measure of measurement disturbance. A selective phase rotation is needed to obtain the imaginary part. This leads to a complex quasiprobability, the Kirkwood distribution. We show that the Kirkwood distribution contains full information about the state if the two observables are maximal and complementary. The Kirkwood distribution gives a new picture of state reduction. In a nonselective measurement, the modification term vanishes. A selective measurement leads to a quantum state as a nonnegative conditional probability. We demonstrate the special significance of the Schwinger basis.Comment: 6 page

    The fate of planetesimals formed at planetary gap edges

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    The presence of rings and gaps in protoplanetary discs are often ascribed to planet-disc interactions, where dust and pebbles are trapped at the edges of planetary induced gas gaps. Recent work has shown that these are likely sites for planetesimal formation via the streaming instability. Given the large amount of planetesimals that potentially form at gap edges, we address the question of their fate and ability to radially transport solids in protoplanetary discs. We perform a series of N-body simulations of planetesimal orbits, taking into account the effect of gas drag and mass loss via ablation. We consider two planetary systems: one akin to the young Solar System, and another one inspired by HL Tau. In both systems, the close proximity to the gap-opening planets results in large orbital excitations, causing the planetesimals to leave their birth locations and spread out across the disc soon after formation. Planetesimals that end up on eccentric orbits interior of 10au experience efficient ablation, and lose all mass before they reach the innermost disc region. In our nominal Solar System simulation with M˙0=107Myr1\dot{M}_0=10^{-7}\, M_{\odot}\, \textrm{yr}^{-1} and α=102\alpha=10^{-2}, we find that 70% of the initial planetesimal mass has been ablated after 500kyr. The ablation rate in HL Tau is lower, and only 11% of the initial planetesimal mass has been ablated after 1Myr. The ablated material consist of a mixture of solid grains and vaporized ices, where a large fraction of the vaporized ices re-condense to form solid ice. Assuming that the solids grow to pebbles in the disc midplane, this results in a pebble flux of 10100MMyr1\sim 10-100\,M_{\oplus}\textrm{Myr}^{-1} through the inner disc. Our results demonstrate that scattered planetesimals can carry a significant flux of solids past planetary-induced gaps in young and massive protoplanetary discs.Comment: Accepted for publication in A&

    Buckling instability in type-II superconductors with strong pinning

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    We predict a novel buckling instability in the critical state of thin type-II superconductors with strong pinning. This elastic instability appears in high perpendicular magnetic fields and may cause an almost periodic series of flux jumps visible in the magnetization curve. As an illustration we apply the obtained criteria to a long rectangular strip.Comment: Submitted to Phys. Rev. Let

    Conservation Status Assessment of the Egg-mimic Darter (Percidae: \u3ci\u3eEtheostoma pseudovulatum\u3c/i\u3e) Using a Multi-faceted Approach

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    The imperiled Egg-mimic Darter (Etheostoma pseudovulatum) is a headwater-adapted fish restricted to an area less than 1000 km2 in Tennessee. It is found in only six tributaries of the Duck River and the large, mainstem of this system may act as a barrier to dispersal, restricting population connectivity. The only status assessment of this species was over two decades ago; genetic diversity and the degree of population connectivity have never been evaluated. We conducted a conservation status assessment using a multi-faceted approach to better inform conservation management plans, including examining its current distribution, assessing habitat quality, estimating abundance, population size and haplotype diversity, and evaluating historical population connectivity. Surveys were conducted in spring and fall (2014) and population size was estimated using the Petersen mark-recapture method at a subset of localities, which were then regressed to obtain population estimates at all localities. Haplotype diversity and population connectivity were examined using the mitochondrial ND2 gene. The Egg-mimic Darter was present at all localities and was relatively abundant, comparable to historical observations. Habitat quality did not appear to be substantially degraded. Overall haplotype and nucleotide diversity were low compared to widespread darters and comparable to other imperiled darters; however, demographic analyses indicated the species has remained stable over contemporary and historical timeframes. The Egg-mimic Darter has likely maintained gene flow historically at five of the six tributary systems, suggesting the mainstem Duck has not been a long-standing barrier to dispersal. One haplotype was shared across all tributary systems except Beaverdam Creek, which had a largely unique assemblage of haplotypes. Overall, the conservation status of the Egg-mimic Darter appears to be stable. However, we recommend regular monitoring with special consideration given to smaller tributary systems and the genetically distinct Beaverdam Creek population. Even though there was evidence of historical population connectivity, the risk of local extirpation remains, considering the small population sizes in several tributary systems. We also recommend assessments of contemporary genetic structure and population connectivity

    Topological field theory and physics

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    Topological Yang-Mills theory with the Belavin-Polyakov-Schwarz-Tyupkin SU(2)SU(2) instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind of matter (hyperinstantons). The physical relevance of topological field theory and its invariants is discovered. By embedding topological Yang-Mills theory into pure Yang-Mills theory, it is shown that the topological version TQFT of a quantum field theory QFT allows us to formulate consistently the perturbative expansion of QFT in the topologically nontrivial sectors. In particular, TQFT classifies the set of good measures over the instanton moduli space and solves the inconsistency problems of the previous approaches. The qualitatively new physical implications are pointed out. Link numbers in QCD are related to a non abelian analogoue of the Aharonov-Bohm effect.Comment: 23 pages, 1 figure. Revision: additional explanation
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