8,131 research outputs found

    Tumbling of a rigid rod in a shear flow

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    The tumbling of a rigid rod in a shear flow is analyzed in the high viscosity limit. Following Burgers, the Master Equation is derived for the probability distribution of the orientation of the rod. The equation contains one dimensionless number, the Weissenberg number, which is the ratio of the shear rate and the orientational diffusion constant. The equation is solved for the stationary state distribution for arbitrary Weissenberg numbers, in particular for the limit of high Weissenberg numbers. The stationary state gives an interesting flow pattern for the orientation of the rod, showing the interplay between flow due to the driving shear force and diffusion due to the random thermal forces of the fluid. The average tumbling time and tumbling frequency are calculated as a function of the Weissenberg number. A simple cross-over function is proposed which covers the whole regime from small to large Weissenberg numbers.Comment: 22 pages, 9 figure

    Strongly coupled modes in a weakly driven micromechanical resonator

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    We demonstrate strong coupling between the flexural vibration modes of a clamped-clamped micromechanical resonator vibrating at low amplitudes. This coupling enables the direct measurement of the frequency response via amplitude- and phase modulation schemes using the fundamental mode as a mechanical detector. In the linear regime, a frequency shift of 0.8Hz\mathrm{0.8\,Hz} is observed for a mode with a line width of 5.8Hz\mathrm{5.8\,Hz} in vacuum. The measured response is well-described by the analytical model based on the Euler-Bernoulli beam including tension. Calculations predict an upper limit for the room-temperature Q-factor of 4.5×105\mathrm{4.5\times10^5} for our top-down fabricated micromechanical beam resonators.Comment: 9 pages, 2 figure

    Conserving Approximations in Time-Dependent Density Functional Theory

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    In the present work we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid nineties. Due to this feature the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio

    Combining Hebbian and reinforcement learning in a minibrain model

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    A toy model of a neural network in which both Hebbian learning and reinforcement learning occur is studied. The problem of `path interference', which makes that the neural net quickly forgets previously learned input-output relations is tackled by adding a Hebbian term (proportional to the learning rate η\eta) to the reinforcement term (proportional to ρ\rho) in the learning rule. It is shown that the number of learning steps is reduced considerably if 1/4<η/ρ<1/21/4 < \eta/\rho < 1/2, i.e., if the Hebbian term is neither too small nor too large compared to the reinforcement term

    Multi-dimensional population modelling using frbpoppy: magnetars can produce the observed Fast Radio Burst sky

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    Fast Radio Bursts (FRBs) are energetic, short, bright transients that occur frequently over the entire radio sky. The observational challenges following from their fleeting, generally one-off nature have prevented identification of the underlying sources producing the bursts. As the population of detected FRBs grows, the observed distributions of brightness, pulse width and dispersion measure now begin to take shape. Meaningful direct interpretation of these distributions is, however, made impossible by the selection effects that telescope and search pipelines invariably imprint on each FRB survey. Here we show that multi-dimensional FRB population synthesis can find a single, self-consistent population of FRB sources that can reproduce the real-life results of the major ongoing FRB surveys. This means that individual observed distributions can now be combined to derive the properties of the intrinsic FRB source population. The characteristics of our best-fit model for one-off FRBs agree with a population of magnetars. We extrapolate this model and predict the number of FRBs future surveys will find. For surveys that have commenced, the method we present here can already determine the composition of the FRB source class, and potentially even its subpopulations.Comment: 12 pages, 4 figures, accepted by Astronomy & Astrophysic

    Numerical simulations on the motion of atoms travelling through a standing-wave light field

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    The motion of metastable helium atoms travelling through a standing light wave is investigated with a semi-classical numerical model. The results of a calculation including the velocity dependence of the dipole force are compared with those of the commonly used approach, which assumes a conservative dipole force. The comparison is made for two atom guiding regimes that can be used for the production of nanostructure arrays; a low power regime, where the atoms are focused in a standing wave by the dipole force, and a higher power regime, in which the atoms channel along the potential minima of the light field. In the low power regime the differences between the two models are negligible and both models show that, for lithography purposes, pattern widths of 150 nm can be achieved. In the high power channelling regime the conservative force model, predicting 100 nm features, is shown to break down. The model that incorporates velocity dependence, resulting in a structure size of 40 nm, remains valid, as demonstrated by a comparison with quantum Monte-Carlo wavefunction calculations.Comment: 9 pages, 4 figure

    Waiting and Residence Times of Brownian Interface Fluctuations

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    We report on the residence times of capillary waves above a given height hh and on the typical waiting time in between such fluctuations. The measurements were made on phase separated colloid-polymer systems by laser scanning confocal microscopy. Due to the Brownian character of the process, the stochastics vary with the chosen measurement interval Δt\Delta t. In experiments, the discrete scanning times are a practical cutoff and we are able to measure the waiting time as a function of this cutoff. The measurement interval dependence of the observed waiting and residence times turns out to be solely determined by the time dependent height-height correlation function g(t)g(t). We find excellent agreement with the theory presented here along with the experiments.Comment: 5 figure
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