Timescales for dynamical relaxation to the Born rule

We illustrate through explicit numerical calculations how the Born-rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie-Bohm pilot-wave theory. The time evolution of a particle distribution initially not equal to the absolute square of the wave function is calculated for a particle in a two-dimensional infinite potential square well. Under the de Broglie-Bohm ontology, the box contains an objectively-existing 'pilot wave' which guides the electron trajectory, and this is represented mathematically by a Schroedinger wave function composed of a finite out-of-phase superposition of M energy eigenstates (with M ranging from 4 to 64). The electron density distributions are found to evolve naturally into the Born-rule ones and stay there; in analogy with the classical case this represents a decay to 'quantum equilibrium'. The proximity to equilibrium is characterized by the coarse-grained subquantum H-function which is found to decrease roughly exponentially towards zero over the course of time. The timescale tau for this relaxation is calculated for various values of M and the coarse-graining length epsilon. Its dependence on M is found to disagree with an earlier theoretical prediction. A power law - tau inversely proportional to M - is found to be fairly robust for all coarse-graining lengths and, although a weak dependence of tau on epsilon is observed, it does not appear to follow any straightforward scaling. A theoretical analysis is presented to explain these results. This improvement in our understanding of timescales for relaxation to quantum equilibrium is likely to be of use in the development of models of relaxation in the early universe, with a view to constraining possible violations of the Born rule in inflationary cosmology.Comment: 27 pages, 8 figures; Replacement with small number of changes reflecting referees' comment

A moving mesh method for one-dimensional hyperbolic conservation laws

We develop an adaptive method for solving one-dimensional systems of hyperbolic conservation laws that employs a high resolution Godunov-type scheme for the physical equations, in conjunction with a moving mesh PDE governing the motion of the spatial grid points. Many other moving mesh methods developed to solve hyperbolic problems use a fully implicit discretization for the coupled solution-mesh equations, and so suffer from a significant degree of numerical stiffness. We employ a semi-implicit approach that couples the moving mesh equation to an efficient, explicit solver for the physical PDE, with the resulting scheme behaving in practice as a two-step predictor-corrector method. In comparison with computations on a fixed, uniform mesh, our method exhibits more accurate resolution of discontinuities for a similar level of computational work

Effects of low energy proton, electron, and simultaneously combined proton and electron environments in silicon and GaAs solar cells

Degradation of silicon and GaAs solar cells due to exposures to low energy proton and electron environments and annealing data for these cells are discussed. Degradation of silicon cells in simultaneously combined electron and low energy proton environments and previous experimental work is summarized and evaluated. The deficiencies in current solar array damage prediction techniques indicated by these data and the relevance of these deficiencies to specific missions such as intermediate altitude orbits and orbital transfer vehicles using solar electric propulsion systems are considered

Terlipressin or norepinephrine in septic shock: do we have the answer?

Comment on Terlipressin versus norepinephrine as infusion in patients with septic shock: a multicentre, randomised, double-blinded trial. [Intensive Care Med. 2018

Recovering a lost baseline: missing kelp forests from a metropolitan coast

© 2008 AuthorThere is concern about historical and continuing loss of canopy-forming algae across the world’s temperate coastline. In South Australia, the sparse cover of canopy-forming algae on the Adelaide metropolitan coast has been of public concern with continuous years of anecdotal evidence culminating in 2 competing views. One view considers that current patterns existed before the onset of urbanisation, whereas the alternate view is that they developed after urbanisation. We tested hypotheses to distinguish between these 2 models, each centred on the reconstruction of historical covers of canopies on the metropolitan coast. Historically, the metropolitan sites were indistinguishable from contemporary populations of reference sites across 70 km (i.e. Gulf St. Vincent), and could also represent a random subset of exposed coastal sites across 2100 km of the greater biogeographic province. Thus there was nothing ‘special’ about the metropolitan sites historically, but today they stand out because they have sparser covers of canopies compared to equivalent locations and times in the gulf and the greater province. This is evidence of wholesale loss of canopy-forming algae (up to 70%) on parts of the Adelaide metropolitan coast since major urbanisation. These findings not only set a research agenda based on the magnitude of loss, but they also bring into question the logic that smaller metropolitan populations of humans create impacts that are trivial relative to that of larger metropolitan centres. Instead, we highlight a need to recognise the ecological context that makes some coastal systems more vulnerable or resistant to increasing human-domination of the world’s coastlines. We discuss challenges to this kind of research that receive little ecological discussion, particularly better leadership and administration, recognising that the systems we study out-live the life spans of individual research groups and operate on spatial scales that exceed the capacity of single research providers.Sean D. Connell, Bayden D. Russell, David J. Turner, Scoresby A. Shepherd, Timothy Kildea, David Miller, Laura Airoldi, Anthony Cheshir

Decoherence in Quantum Walks on the Hypercube

We study a natural notion of decoherence on quantum random walks over the hypercube. We prove that in this model there is a decoherence threshold beneath which the essential properties of the hypercubic quantum walk, such as linear mixing times, are preserved. Beyond the threshold, we prove that the walks behave like their classical counterparts.Comment: 7 pages, 3 figures; v2:corrected typos in references; v3:clarified section 2.1; v4:added references, expanded introduction; v5: final journal versio

Nickel hydrogen bipolar battery electrode design

The preferred approach of the NASA development effort in nickel hydrogen battery design utilizes a bipolar plate stacking arrangement to obtain the required voltage-capacity configuration. In a bipolar stack, component designs must take into account not only the typical design considerations such as voltage, capacity and gas management, but also conductivity to the bipolar (i.e., intercell) plate. The nickel and hydrogen electrode development specifically relevant to bipolar cell operation is discussed. Nickel oxide electrodes, having variable type grids and in thicknesses up to .085 inch are being fabricated and characterized to provide a data base. A selection will be made based upon a system level tradeoff. Negative (hydrpogen) electrodes are being screened to select a high performance electrode which can function as a bipolar electrode. Present nickel hydrogen negative electrodes are not capable of conducting current through their cross-section. An electrode was tested which exhibits low charge and discharge polarization voltages and at the same time is conductive. Test data is presented

Bayesian Spatial Binary Regression for Label Fusion in Structural Neuroimaging

Many analyses of neuroimaging data involve studying one or more regions of interest (ROIs) in a brain image. In order to do so, each ROI must first be identified. Since every brain is unique, the location, size, and shape of each ROI varies across subjects. Thus, each ROI in a brain image must either be manually identified or (semi-) automatically delineated, a task referred to as segmentation. Automatic segmentation often involves mapping a previously manually segmented image to a new brain image and propagating the labels to obtain an estimate of where each ROI is located in the new image. A more recent approach to this problem is to propagate labels from multiple manually segmented atlases and combine the results using a process known as label fusion. To date, most label fusion algorithms either employ voting procedures or impose prior structure and subsequently find the maximum a posteriori estimator (i.e., the posterior mode) through optimization. We propose using a fully Bayesian spatial regression model for label fusion that facilitates direct incorporation of covariate information while making accessible the entire posterior distribution. We discuss the implementation of our model via Markov chain Monte Carlo and illustrate the procedure through both simulation and application to segmentation of the hippocampus, an anatomical structure known to be associated with Alzheimer's disease.Comment: 24 pages, 10 figure