The Hall Algebras of Annuli

We refine and prove the central conjecture of our first paper for annuli with at least two marked intervals on each boundary component by computing the derived Hall algebras of their Fukaya categories.Comment: 33 pgs, 5 fi

Binary Information from Open Clusters Using SEDS (BINOCS) Project: The Dynamical Evolution of the Binary Populations in Cluster Environments

Studying the internal dynamics of stellar clusters is conducted primarily through N-Body simulations. One of the major inputs into N-Body simulations is the binary star frequency and mass distribution, which is currently constrained by relations derived from field binary stars. However to truly understand how clustered environments evolve, binary data from within star clusters is needed including masses. Detailed information on binaries masses, primary and secondary, in star clusters has been limited to date. The primary technique currently available has been radial velocity surveys that are limited in depth. Using previous two-band photometry-based studies that may cover different mass ranges produce potentially discrepant interpretations of the observed binary population. We introduce a new binary detection method, Binary INformation from Open Clusters Using SEDs (BINOCS) that covers the wide mass range needed to improve cluster N-body simulation inputs and comparisons. Using newly-observed multi-wavelength photometric catalogs (0.3 - 8 microns) of the key open clusters with a range of ages, we can show that the BINOCS method determines accurate binary component masses for unresolved cluster binaries through comparison to available RV-based studies. Using this method, we present results on the dynamical evolution of binaries from 0.4 - 2.5 solar masses within five prototypical clusters, spaning 30 Myr to 3.5 Gyr, and how the binary populations evolve as a function of mass.Comment: 2 pages, 1 figure, IAU symposium 316 "Formation, evolution, and survival of massive star clusters

Scaling behavior of topologically constrained polymer rings in a melt

Large scale molecular dynamics simulations on graphic processing units (GPUs) are employed to study the scaling behavior of ring polymers with various topological constraints in melts. Typical sizes of rings containing $3_1$, $5_1$ knots and catenanes made up of two unknotted rings scale like $N^{1/3}$ in the limit of large ring sizes $N$. This is consistent with the crumpled globule model and similar findings for unknotted rings. For small ring lengths knots occupy a significant fraction of the ring. The scaling of typical ring sizes for small $N$ thus depends on the particular knot type and the exponent is generally larger than 0.4.Comment: 5 pages, 5 figure

Spincaloric properties of epitaxial Co2_2MnSi/MgO/Co2_2MnSi magnetic tunnel junctions

The electronic transport and spincaloric properties of epitaxial magnetic tunnel junctions with half-metallic Co$_2$MnSi Heusler electrodes, MgO tunneling barriers, and different interface terminations are investigated by using first-principles calculations. A new approach to spincaloric properties is presented that circumvents the linear response approximation inherent in the Seebeck coefficient and compared to the method of Sivan and Imry. This approach supports two different temperatures in the two electrodes and provides the exact current and/or voltage response of the system. Moreover, it accounts for temperature-dependent chemical potentials in the electrodes and finite-bias effects. We find that especially the former are important for obtaining qualitatively correct results, even if the variations of the chemical potentials are small. It is shown how the spincaloric properties can be tailored by the choice of the growth conditions. We find a large effective and spin-dependent Seebeck coefficient of $-65$ $\mu$V/K at room temperature for the purely Co-terminated interface. We suggest to use such interfaces in thermally operated magnetoresistive random access memory modules, which exploit the magneto-Seebeck effect, to maximize the thermally induced readout voltage.Comment: 12 pages, 13 figure

Asymptotic Phase for Stochastic Oscillators

Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence of noise, the asymptotic phase is no longer well defined. We introduce a new definition of asymptotic phase in terms of the slowest decaying modes of the Kolmogorov backward operator. Our stochastic asymptotic phase is well defined for noisy oscillators, even when the oscillations are noise dependent. It reduces to the classical asymptotic phase in the limit of vanishing noise. The phase can be obtained either by solving an eigenvalue problem, or by empirical observation of an oscillating density's approach to its steady state.Comment: 5 pages, 3 figure

Stochastic scalar conservation laws driven by rough paths

We prove the existence and uniqueness of solutions to a class of stochastic scalar conservation laws with joint space-time transport noise and affine-linear noise driven by a geometric p-rough path. In particular, stability of the solutions with respect to the driving rough path is obtained, leading to a robust approach to stochastic scalar conservation laws. As immediate corollaries we obtain support theorems, large deviation results and the generation of a random dynamical system.Comment: 29 page

Preferential Attachment and Vertex Arrival Times

We study preferential attachment mechanisms in random graphs that are parameterized by (i) a constant bias affecting the degree-biased distribution on the vertex set and (ii) the distribution of times at which new vertices are created by the model. The class of random graphs so defined admits a representation theorem reminiscent of residual allocation, or "stick-breaking" schemes. We characterize how the vertex arrival times affect the asymptotic degree distribution, and relate the latter to neutral-to-the-left processes. Our random graphs generate edges "one end at a time", which sets up a one-to-one correspondence between random graphs and random partitions of natural numbers; via this map, our representation induces a result on (not necessarily exchangeable) random partitions that generalizes a theorem of Griffiths and Span\'o. A number of examples clarify how the class intersects with several known random graph models.Comment: 34 pages, 1 figur

Comment on "Asymptotic Phase for Stochastic Oscillators"

In his Comment [arXiv:1501.02126 (2015)] on our recent paper [Phys. Rev. Lett., v. 113, 254101 (2014)], Pikovsky compares two methods for defining the "phase" of a stochastic oscillator. We reply to his Comment by showing that neither method can unambiguously identify a unique system of isochrons, when multiple oscillations coexist in the same system.Comment: 1.5 pages, 1 figure. Reply to arXiv:1501.02126v

Phase descriptions of a multidimensional Ornstein-Uhlenbeck process

Stochastic oscillators play a prominent role in different fields of science. Their simplified description in terms of a phase has been advocated by different authors using distinct phase definitions in the stochastic case. One notion of phase that we put forward previously, the \emph{asymptotic phase of a stochastic oscillator}, is based on the eigenfunction expansion of its probability density. More specifically, it is given by the complex argument of the eigenfunction of the backward operator corresponding to the least negative eigenvalue. Formally, besides the `backward' phase, one can also define the `forward' phase as the complex argument of the eigenfunction of the forward Kolomogorov operator corresponding to the least negative eigenvalue. Until now, the intuition about these phase descriptions has been limited. Here we study these definitions for a process that is analytically tractable, the two-dimensional Ornstein-Uhlenbeck process with complex eigenvalues. For this process, (i) we give explicit expressions for the two phases; (ii) we demonstrate that the isochrons are always the spokes of a wheel, but that (iii) the spacing of these isochrons (their angular density) is different for backward and forward phases; (iv) we show that the isochrons of the backward phase are completely determined by the deterministic part of the vector field, whereas the forward phase also depends on the noise matrix; and (v) we demonstrate that the mean progression of the backward phase in time is always uniform, whereas this is not true for the forward phase except in the rotationally symmetric case. We illustrate our analytical results for a number of qualitatively different cases

A graviton statistics approach to dark energy, inflation and black holes

We derive two new equations of quantum gravity and combine them with reinterpretations of previously proposed concepts of dark energy, inflation and black holes into a theory which may be a first step toward a comprehensive description of all three phenomena. The resulting theory also predicts new tests which can be experimentally checked within just a few years. The two new equations are : A) a creation equation to give stimulated emission for any surface filled with gravitons, pulling energy from a background, and B) the association of an outgoing soliton wave of gravitons, a "shell front" with a large Lorentz factor derived from the uncertainties in both space and time. These new equations are combined with the common notions of an all-pervasive background of gravitons at the Planck limit, the "Planck sea"; the identification of the thermodynamic limit with the emission of gravitons in a "shell front", i.e. what is usually called the entropy of black holes is identified with the outgoing gravitons; the concept of black holes as a membrane full of gravitons at a large Lorentz factor, the "Planck shell"; the emission of gravitons created in a "horizon shell" during inflation. These equations result in stimulated emission of gravitons by the interaction with the background, the "Planck sea", to describe dark energy, black holes, the inflationary period of the universe, and the arrow of time. These proposals lead to gravitational waves constituting dark energy. These waves should be detectable within a few years with pulsar timing arrays. These gravitational waves can be characterized as uncorrelated solitons, and should also be detectable with ultra-high precision lunar laser ranging, as well as with correspondingly precise clocks. The extremely high, but finite Lorentz factor for signal propagation may be expected to have further consequences in particle interactions.Comment: 75 pages, 7 figures, additional text to clarify key points, typographical errors corrected, additional references, the model and its predictions are unchange