Turbulence model reduction by deep learning

A central problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence produces anomalous fluxes via cross-correlations between fluctuations. In this work, we introduce a new, data-driven method for parameterizing these fluxes. The method uses deep supervised learning to infer a reduced mean-field model from a set of numerical simulations. We apply the method to a simple drift-wave turbulence system and find a significant new effect which couples the particle flux to the local \emph{gradient} of vorticity. Notably, here, this effect is much stronger than the oft-invoked shear suppression effect. We also recover the result via a simple calculation. The vorticity gradient effect tends to modulate the density profile. In addition, our method recovers a model for spontaneous zonal flow generation by negative viscosity, stabilized by nonlinear and hyperviscous terms. We highlight the important role of symmetry to implementation of the new method.Comment: To be published in Phys. Rev. E Rap. Comm. 6 pages, 7 figure

How sharp are PV measures?

Properties of sharp observables (normalized PV measures) in relation to smearing by a Markov kernel are studied. It is shown that for a sharp observable $P$ defined on a standard Borel space, and an arbitrary observable $M$, the following properties are equivalent: (a) the range of $P$ is contained in the range of $M$; (b) $P$ is a function of $M$; (c) $P$ is a smearing of $M$.Comment: 9 page

On Wireless Scheduling Using the Mean Power Assignment

In this paper the problem of scheduling with power control in wireless networks is studied: given a set of communication requests, one needs to assign the powers of the network nodes, and schedule the transmissions so that they can be done in a minimum time, taking into account the signal interference of concurrently transmitting nodes. The signal interference is modeled by SINR constraints. Approximation algorithms are given for this problem, which use the mean power assignment. The problem of schduling with fixed mean power assignment is also considered, and approximation guarantees are proven

Odd Decays from Even Anomalies: Gauge Mediation Signatures Without SUSY

We analyze the theory and phenomenology of anomalous global chiral symmetries in the presence of an extra dimension. We propose a simple extension of the Standard Model in 5D whose signatures closely resemble those of supersymmetry with gauge mediation, and we suggest a novel scalar dark matter candidate.Comment: 26 pages, 1 figure; v2: references added; discussion of direct collider constraints added; v3: corrected dark matter calculation in chapter 4.2 and replaced figure 1

Termodynaamiset rajat massiivi-tyypin anortosiittien ja niiden kantamagmojen synnylle

Development of computational modeling tools has revolutionized studies of magmatic processes over the last four decades. Their refinement from binary mixing equations to thermodynamically controlled geochemical assimilation models has provided more comprehensive and detailed modeling constraints of an array of magmatic systems. One of the questions that has not yet been vigorously studied using thermodynamic constraints is the origin of massif-type anorthosites. The parental melts to these intrusions are hypothesized to be either mantle-derived high-Al basaltic melts that undergo crustal contamination or monzodioritic melts derived directly from lower crust. On the other hand, many studies suggest that the monzodioritic rocks do not represent parental melts but instead represent crystal remnants of residual liquids left after crystal fractionation of parental melts. Regardless of the source or composition, magmas that produce massif-type anorthosites have been suggested to have undergone polybaric (~1000–100 MPa) fractional crystallization while ascending through the lithosphere. We conducted lower crustal melting, assimilation-fractional crystallization, and isobaric and polybaric fractional crystallization major element modeling using two thermodynamically constrained modeling tools, the Magma Chamber Simulator (MCS) and rhyolite-MELTS, to test the suitability of these tools and to study the petrogenesis of massif-type anorthosites. Comparison of our models with a large suite of whole-rock data suggests that the massif-type anorthosite parental melts were high-Al basalts that were produced when hot mantle-derived partial melts assimilated lower crustal material at Moho levels. These contaminated basaltic parental magmas then experienced polybaric fractional crystallization at different crustal levels (~40 to 5 km) producing residual melts that crystallized as monzodioritic rocks. Model outcomes also support the suggestion that the cumulates produced during polybaric fractional crystallization likely underwent density separation, thus producing the plagioclase-rich anorthositic rocks. The modeled processes are linked to a four-stage model that describes the key petrogenetic processes that generate massif-type anorthosites. The presented framework enables further detailed thermodynamic and geochemical modeling of individual anorthosite intrusions using MCS and involving trace element and isotope constrains.Peer reviewe

Reverse Khas'minskii condition

The aim of this paper is to present and discuss some equivalent characterizations of p-parabolicity in terms of existence of special exhaustion functions. In particular, Khas'minskii in [K] proved that if there exists a 2-superharmonic function k defined outside a compact set such that $\lim_{x\to \infty} k(x)=\infty$, then R is 2-parabolic, and Sario and Nakai in [SN] were able to improve this result by showing that R is 2-parabolic if and only if there exists an Evans potential, i.e. a 2-harmonic function $E:R\setminus K \to \R^+$ with \lim_{x\to \infty} \E(x)=\infty. In this paper, we will prove a reverse Khas'minskii condition valid for any p>1 and discuss the existence of Evans potentials in the nonlinear case.Comment: final version of the article available at http://www.springer.co