Magnetic phase separation in ordered alloys

We present a lattice model to study the equilibrium phase diagram of ordered alloys with one magnetic component that exhibits a low temperature phase separation between paramagnetic and ferromagnetic phases. The model is constructed from the experimental facts observed in Cu$_{3-x}$AlMn$_{x}$ and it includes coupling between configurational and magnetic degrees of freedom which are appropriated for reproducing the low temperature miscibility gap. The essential ingredient for the occurrence of such a coexistence region is the development of ferromagnetic order induced by the long-range atomic order of the magnetic component. A comparative study of both mean-field and Monte Carlo solutions is presented. Moreover, the model may enable the study of the structure of the ferromagnetic domains embedded in the non-magnetic matrix. This is relevant in relation to phenomena such as magnetoresistance and paramagnetism.Comment: 12 pages, 11 figures, accepted in Phys. Rev.

First and second order optimality conditions for optimal control problems of state constrained integral equations

This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions

New Insights into White-Light Flare Emission from Radiative-Hydrodynamic Modeling of a Chromospheric Condensation

(abridged) The heating mechanism at high densities during M dwarf flares is poorly understood. Spectra of M dwarf flares in the optical and near-ultraviolet wavelength regimes have revealed three continuum components during the impulsive phase: 1) an energetically dominant blackbody component with a color temperature of T $\sim$ 10,000 K in the blue-optical, 2) a smaller amount of Balmer continuum emission in the near-ultraviolet at lambda $<$ 3646 Angstroms and 3) an apparent pseudo-continuum of blended high-order Balmer lines. These properties are not reproduced by models that employ a typical "solar-type" flare heating level in nonthermal electrons, and therefore our understanding of these spectra is limited to a phenomenological interpretation. We present a new 1D radiative-hydrodynamic model of an M dwarf flare from precipitating nonthermal electrons with a large energy flux of $10^{13}$ erg cm$^{-2}$ s$^{-1}$. The simulation produces bright continuum emission from a dense, hot chromospheric condensation. For the first time, the observed color temperature and Balmer jump ratio are produced self-consistently in a radiative-hydrodynamic flare model. We find that a T $\sim$ 10,000 K blackbody-like continuum component and a small Balmer jump ratio result from optically thick Balmer and Paschen recombination radiation, and thus the properties of the flux spectrum are caused by blue light escaping over a larger physical depth range compared to red and near-ultraviolet light. To model the near-ultraviolet pseudo-continuum previously attributed to overlapping Balmer lines, we include the extra Balmer continuum opacity from Landau-Zener transitions that result from merged, high order energy levels of hydrogen in a dense, partially ionized atmosphere. This reveals a new diagnostic of ambient charge density in the densest regions of the atmosphere that are heated during dMe and solar flares.Comment: 50 pages, 2 tables, 13 figures. Accepted for publication in the Solar Physics Topical Issue, "Solar and Stellar Flares". Version 2 (June 22, 2015): updated to include comments by Guest Editor. The final publication is available at Springer via http://dx.doi.org/10.1007/s11207-015-0708-

Dissipation and noise in adiabatic quantum pumps

We investigate the distribution function, the heat flow and the noise properties of an adiabatic quantum pump for an arbitrary relation of pump frequency $\omega$ and temperature. To achieve this we start with the scattering matrix approach for ac-transport. This approach leads to expressions for the quantities of interest in terms of the side bands of particles exiting the pump. The side bands correspond to particles which have gained or lost a modulation quantum $\hbar \omega$. We find that our results for the pump current, the heat flow and the noise can all be expressed in terms of a parametric emissivity matrix. In particular we find that the current cross-correlations of a multiterminal pump are directly related a to a non-diagonal element of the parametric emissivity matrix. The approach allows a description of the quantum statistical correlation properties (noise) of an adiabatic quantum pump

A Conformally Invariant Holographic Two-Point Function on the Berger Sphere

We apply our previous work on Green's functions for the four-dimensional quaternionic Taub-NUT manifold to obtain a scalar two-point function on the homogeneously squashed three-sphere (otherwise known as the Berger sphere), which lies at its conformal infinity. Using basic notions from conformal geometry and the theory of boundary value problems, in particular the Dirichlet-to-Robin operator, we establish that our two-point correlation function is conformally invariant and corresponds to a boundary operator of conformal dimension one. It is plausible that the methods we use could have more general applications in an AdS/CFT context.Comment: 1+49 pages, no figures. v2: Several typos correcte

Discrete integrable systems and Poisson algebras from cluster maps

We consider nonlinear recurrences generated from cluster mutations applied to quivers that have the property of being cluster mutation-periodic with period 1. Such quivers were completely classified by Fordy and Marsh, who characterised them in terms of the skew-symmetric matrix that defines the quiver. The associated nonlinear recurrences are equivalent to birational maps, and we explain how these maps can be endowed with an invariant Poisson bracket and/or presymplectic structure. Upon applying the algebraic entropy test, we are led to a series of conjectures which imply that the entropy of the cluster maps can be determined from their tropical analogues, which leads to a sharp classification result. Only four special families of these maps should have zero entropy. These families are examined in detail, with many explicit examples given, and we show how they lead to discrete dynamics that is integrable in the Liouville-Arnold sense.Comment: 49 pages, 3 figures. Reduced to satisfy journal page restrictions. Sections 2.4, 4.5, 6.3, 7 and 8 removed. All other results remain, with minor editin

Reducing sequence risk using trend following and the CAPE ratio

The risk of experiencing bad investment outcomes at the wrong time, or sequence risk, is a poorly understood, but crucial aspect of the risk faced by investors, in particular those in the decumulation phase of their savings journey, typically over the period of retirement financed by a defined contributions pension scheme. Using US equity return data from 1872-2014 we show how this risk can be significantly reduced by applying trend-following investment strategies. We also demonstrate that knowledge of a valuation ratio such as the CAPE ratio at the beginning of a decumulation period is useful for enhancing sustainable investment income

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types