A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Laminar Free Convection from a Vertically-Oriented Concentrated Photovoltaic Cell with Uniform Surface Heat Flux

This research project uses field measurements to investigate the cooling of a triple-junction, photovoltaic cell under natural convection when subjected to various amounts of insolation. The team built an experimental apparatus consisting of a mirror and Fresnel lens to concentrate light onto a triple-junction photovoltaic cell, mounted vertically on a copper heat sink. Measurements were taken year-round to provide a wide range of ambient conditions. A surface was then generated, in MATLAB, using Sparrow’s model for natural convection on a vertical plate under constant heat flux. This surface can be used to find the expected operating temperature of a cell at any location, given the ambient temperature and insolation. This research is an important contribution to the industry because it utilizes field data that represents how a cell would react under normal operation. It also extends the use of a well-known model from a one-sun environment to a multi-sun one.

Strong ergodicity of monotone transition functions

By revealing close links among strong ergodicity, monotone, and the Feller–Reuter–Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.

Ergodicity and stability of generalised Markov branching processes with resurrection

This paper concentrates on investigating ergodicity and stability for generalised Markov branching processes with resurrection. Easy checking criteria including several clear-cut corollaries are established for ordinary and strong ergodicity of such processes. The equilibrium distribution is given in an elegant closed form for the ergodic case. The probabilistic interpretation of the results is clear and thus explained.

Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan.

A uniform, quality controlled Surface Ocean CO2 Atlas (SOCAT)

A well documented, publicly available, global data set of surface ocean carbon dioxide (CO2) parameters has been called for by international groups for nearly two decades. The Surface Ocean CO2 Atlas (SOCAT) project was initiated by the international marine carbon science community in 2007 with the aim of providing a comprehensive, publicly available, regularly updated, global data set of marine surface CO2, which had been subject to quality control (QC). Many additional CO2 data, not yet made public via the Carbon Dioxide Information Analysis Center (CDIAC), were retrieved from data originators, public websites and other data centres. All data were put in a uniform format following a strict protocol. Quality control was carried out according to clearly defined criteria. Regional specialists performed the quality control, using state-of-the-art web-based tools, specially developed for accomplishing this global team effort. SOCAT version 1.5 was made public in September 2011 and holds 6.3 million quality controlled surface CO2 data points from the global oceans and coastal seas, spanning four decades (1968–2007). Three types of data products are available: individual cruise files, a merged complete data set and gridded products. With the rapid expansion of marine CO2 data collection and the importance of quantifying net global oceanic CO2 uptake and its changes, sustained data synthesis and data access are priorities.

A uniform, quality controlled Surface Ocean CO2 Atlas (SOCAT)

A well-documented, publicly available, global data set of surface ocean carbon dioxide (CO2) parameters has been called for by international groups for nearly two decades. The Surface Ocean CO2 Atlas (SOCAT) project was initiated by the international marine carbon science community in 2007 with the aim of providing a comprehensive, publicly available, regularly updated, global data set of marine surface CO2, which had been subject to quality control (QC). Many additional CO2 data, not yet made public via the Carbon Dioxide Information Analysis Center (CDIAC), were retrieved from data originators, public websites and other data centres. All data were put in a uniform format following a strict protocol. Quality control was carried out according to clearly defined criteria. Regional specialists performed the quality control, using state-of-the-art web-based tools, specially developed for accomplishing this global team effort. SOCAT version 1.5 was made public in September 2011 and holds 6.3 million quality controlled surface CO2 data points from the global oceans and coastal seas, spanning four decades (1968–2007). Three types of data products are available: individual cruise files, a merged complete data set and gridded products. With the rapid expansion of marine CO2 data collection and the importance of quantifying net global oceanic CO2 uptake and its changes, sustained data synthesis and data access are priorities.

Simple control of the polarisation in uniform hybrid waveguide-planar leaky-wave antennas

A simple and original mechanism to control the polarisation of uniform hybrid waveguide-planar leaky-wave antennas is proposed. The operation is based on introducing simple modifications of the planar dimensions of the structure cross-section, which is shown to control the horizontal and vertical components of the radiated fields. The proposed antenna dispenses with the need for periodic elements, commonly used in flexible polarised leaky-wave antennas, and therefore significantly reduces the design complexity. Parametric curves have been obtained to assist in the simple and efficient design of the proposed antenna. The novel mechanism is illustrated by means of several antenna prototypes operating at 5.7 GHz, producing linear, elliptical and circular polarisations. Commercial three-dimensional Finite Element Method has been used for the simulations, and the results are validated with experimental testing.[br].

On the Capacity of Non-Uniform Phase MIMO Nakagami-m Fading Channels

This letter investigates the ergodic capacity of MIMO Nakagami-m fading channels with both uniformly and non-uniformly distributed phases. We first obtain a tight capacity upper bound for the channel and then derive exact expressions for the low signal-to-noise ratio (SNR) capacity metrics, based on which we examine the impact of fading parameter m on the capacity.

EVALUATION OF A FOAM BUFFER TARGET DESIGN FOR SPATIALLY UNIFORM ABLATION OF LASER-IRRADIATED PLASMAS

Experimental observations are presented demonstrating that the use of a gold-coated foam layer on the surface of a laser-driven target substantially reduces its hydrodynamic breakup during the acceleration phase. The data suggest that this results from enhanced thermal smoothing during the early-time imprint stage of the interaction. The target's kinetic energy and the level of parametric instability growth are shown to remain essentially unchanged from that of a conventionally driven target.