920 research outputs found
Travelling Randomly on the Poincar\'e Half-Plane with a Pythagorean Compass
A random motion on the Poincar\'e half-plane is studied. A particle runs on
the geodesic lines changing direction at Poisson-paced times. The hyperbolic
distance is analyzed, also in the case where returns to the starting point are
admitted. The main results concern the mean hyperbolic distance (and also the
conditional mean distance) in all versions of the motion envisaged. Also an
analogous motion on orthogonal circles of the sphere is examined and the
evolution of the mean distance from the starting point is investigated
From white elephant to Nobel Prize: Dennis Gabor’s wavefront reconstruction
Dennis Gabor devised a new concept for optical imaging in 1947 that went by a variety of names over the following decade: holoscopy, wavefront reconstruction, interference microscopy, diffraction microscopy and Gaboroscopy. A well-connected and creative research engineer, Gabor worked actively to publicize and exploit his concept, but the scheme failed to capture the interest of many researchers. Gabor’s theory was repeatedly deemed unintuitive and baffling; the technique was appraised by his contemporaries to be of dubious practicality and, at best, constrained to a narrow branch of science. By the late 1950s, Gabor’s subject had been assessed by its handful of practitioners to be a white elephant. Nevertheless, the concept was later rehabilitated by the research of Emmett Leith and Juris Upatnieks at the University of Michigan, and Yury Denisyuk at the Vavilov Institute in Leningrad. What had been judged a failure was recast as a success: evaluations of Gabor’s work were transformed during the 1960s, when it was represented as the foundation on which to construct the new and distinctly different subject of holography, a re-evaluation that gained the Nobel Prize for Physics for Gabor alone in 1971. This paper focuses on the difficulties experienced in constructing a meaningful subject, a practical application and a viable technical community from Gabor’s ideas during the decade 1947-1957
Ionization degree of the electron-hole plasma in semiconductor quantum wells
The degree of ionization of a nondegenerate two-dimensional electron-hole
plasma is calculated using the modified law of mass action, which takes into
account all bound and unbound states in a screened Coulomb potential.
Application of the variable phase method to this potential allows us to treat
scattering and bound states on the same footing. Inclusion of the scattering
states leads to a strong deviation from the standard law of mass action. A
qualitative difference between mid- and wide-gap semiconductors is
demonstrated. For wide-gap semiconductors at room temperature, when the bare
exciton binding energy is of the order of T, the equilibrium consists of an
almost equal mixture of correlated electron-hole pairs and uncorrelated free
carriers.Comment: 22 pages, 6 figure
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Operating experience with the 50 MeV 10kA ATA power conditioning system
The Advanced Test Accelerator (ATA) has been operational for over one year and has achieved full parameters in the power conditioning system. The pulsed power system has been previously described, however, during the past year of operation a considerable amount of statistical data has been accumulated on the 211 gas blown spark gaps that perform the main switching function in the ATA. These spark gaps were designed for 250kV, 40 kA and 70ns pulse. The parameter that made this spark gap somewhat unique was the requirement that it be able to provide a burst of ten pulses at one kilohertz with an average repetition rate of 5Hz. 2 references, 7 figures
Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces
A branching process of particles moving at finite velocity over the geodesic
lines of the hyperbolic space (Poincar\'e half-plane and Poincar\'e disk) is
examined. Each particle can split into two particles only once at Poisson paced
times and deviates orthogonally when splitted. At time , after
Poisson events, there are particles moving along different geodesic
lines. We are able to obtain the exact expression of the mean hyperbolic
distance of the center of mass of the cloud of particles. We derive such mean
hyperbolic distance from two different and independent ways and we study the
behavior of the relevant expression as increases and for different values
of the parameters (hyperbolic velocity of motion) and (rate of
reproduction). The mean hyperbolic distance of each moving particle is also
examined and a useful representation, as the distance of a randomly stopped
particle moving over the main geodesic line, is presented
1/f Noise in Electron Glasses
We show that 1/f noise is produced in a 3D electron glass by charge
fluctuations due to electrons hopping between isolated sites and a percolating
network at low temperatures. The low frequency noise spectrum goes as
\omega^{-\alpha} with \alpha slightly larger than 1. This result together with
the temperature dependence of \alpha and the noise amplitude are in good
agreement with the recent experiments. These results hold true both with a
flat, noninteracting density of states and with a density of states that
includes Coulomb interactions. In the latter case, the density of states has a
Coulomb gap that fills in with increasing temperature. For a large Coulomb gap
width, this density of states gives a dc conductivity with a hopping exponent
of approximately 0.75 which has been observed in recent experiments. For a
small Coulomb gap width, the hopping exponent approximately 0.5.Comment: 8 pages, Latex, 6 encapsulated postscript figures, to be published in
Phys. Rev.
Stochastic resonance-free multiple time-step algorithm for molecular dynamics with very large time steps
Molecular dynamics is one of the most commonly used approaches for studying
the dynamics and statistical distributions of many physical, chemical, and
biological systems using atomistic or coarse-grained models. It is often the
case, however, that the interparticle forces drive motion on many time scales,
and the efficiency of a calculation is limited by the choice of time step,
which must be sufficiently small that the fastest force components are
accurately integrated. Multiple time-stepping algorithms partially alleviate
this inefficiency by assigning to each time scale an appropriately chosen
step-size. However, such approaches are limited by resonance phenomena, wherein
motion on the fastest time scales limits the step sizes associated with slower
time scales. In atomistic models of biomolecular systems, for example,
resonances limit the largest time step to around 5-6 fs. In this paper, we
introduce a set of stochastic isokinetic equations of motion that are shown to
be rigorously ergodic and that can be integrated using a multiple time-stepping
algorithm that can be easily implemented in existing molecular dynamics codes.
The technique is applied to a simple, illustrative problem and then to a more
realistic system, namely, a flexible water model. Using this approach outer
time steps as large as 100 fs are shown to be possible
Wetting films on chemically heterogeneous substrates
Based on a microscopic density functional theory we investigate the
morphology of thin liquidlike wetting films adsorbed on substrates endowed with
well-defined chemical heterogeneities. As paradigmatic cases we focus on a
single chemical step and on a single stripe. In view of applications in
microfluidics the accuracy of guiding liquids by chemical microchannels is
discussed. Finally we give a general prescription of how to investigate
theoretically the wetting properties of substrates with arbitrary chemical
structures.Comment: 56 pages, RevTeX, 20 Figure
Poles and Zeros – Examples of the Behavioral Approach Applied to Discrete Linear Repetitive Processes
Shrinking a large dataset to identify variables associated with increased risk of Plasmodium falciparum infection in Western Kenya
Large datasets are often not amenable to analysis using traditional single-step approaches. Here, our general objective was to apply imputation techniques, principal component analysis (PCA), elastic net and generalized linear models to a large dataset in a systematic approach to extract the most meaningful predictors for a health outcome. We extracted predictors for Plasmodium falciparum infection, from a large covariate dataset while facing limited numbers of observations, using data from the People, Animals, and their Zoonoses (PAZ) project to demonstrate these techniques: data collected from 415 homesteads in western Kenya, contained over 1500 variables that describe the health, environment, and social factors of the humans, livestock, and the homesteads in which they reside. The wide, sparse dataset was simplified to 42 predictors of P. falciparum malaria infection and wealth rankings were produced for all homesteads. The 42 predictors make biological sense and are supported by previous studies. This systematic data-mining approach we used would make many large datasets more manageable and informative for decision-making processes and health policy prioritization
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