Brownian particles in stationary and moving traps: The mean and variance of the heat distribution function

A recent theoretical model developed by Imparato et al. Phys of the experimentally measured heat and work effects produced by the thermal fluctuations of single micron-sized polystyrene beads in stationary and moving optical traps has proved to be quite successful in rationalizing the observed experimental data. The model, based on the overdamped Brownian dynamics of a particle in a harmonic potential that moves at a constant speed under a time-dependent force, is used to obtain an approximate expression for the distribution of the heat dissipated by the particle at long times. In this paper, we generalize the above model to consider particle dynamics in the presence of colored noise, without passing to the overdamped limit, as a way of modeling experimental situations in which the fluctuations of the medium exhibit long-lived temporal correlations, of the kind characteristic of polymeric solutions, for instance, or of similar viscoelastic fluids. Although we have not been able to find an expression for the heat distribution itself, we do obtain exact expressions for its mean and variance, both for the static and for the moving trap cases. These moments are valid for arbitrary times and they also hold in the inertial regime, but they reduce exactly to the results of Imparato et al. in appropriate limits. DOI: 10.1103/PhysRevE.80.011118 PACS.

Satellite Telemetry and Long-Range Bat Movements.

Background: Understanding the long-distance movement of bats has direct relevance to studies of population dynamics, ecology, disease emergence, and conservation. Methodology/Principal Findings: We developed and trialed several collar and platform terminal transmitter (PTT) combinations on both free-living and captive fruit bats (Family Pteropodidae: Genus Pteropus). We examined transmitter weight, size, profile and comfort as key determinants of maximized transmitter activity. We then tested the importance of bat-related variables (species size/weight, roosting habitat and behavior) and environmental variables (day-length, rainfall pattern) in determining optimal collar/PTT configuration. We compared battery- and solar-powered PTT performance in various field situations, and found the latter more successful in maintaining voltage on species that roosted higher in the tree canopy, and at lower density, than those that roost more densely and lower in trees. Finally, we trialed transmitter accuracy, and found that actual distance errors and Argos location class error estimates were in broad agreement. Conclusions/Significance: We conclude that no single collar or transmitter design is optimal for all bat species, and that species size/weight, species ecology and study objectives are key design considerations. Our study provides a strategy for collar and platform choice that will be applicable to a larger number of bat species as transmitter size and weight continue to decrease in the future.

The short-term effects of a routine poisoning campaign on the movements and detectability of a social top-predator

Top-predators can be important components of resilient ecosystems, but they are still controlled in many places to mitigate a variety of economic, environmental and/or social impacts. Lethal control is often achieved through the broad-scale application of poisoned baits. Understanding the direct and indirect effects of such lethal control on subsequent movements and behaviour of survivors is an important pre-requisite for interpreting the efficacy and ecological outcomes of top-predator control. In this study, we use GPS tracking collars to investigate the fine-scale and short-term movements of dingoes (Canis lupus dingo and other wild dogs) in response to a routine poison-baiting program as an example of how a common, social top-predator can respond (behaviourally) to moderate levels of population reduction. We found no consistent control-induced differences in home range size or location, daily distance travelled, speed of travel, temporal activity patterns or road/trail usage for the seven surviving dingoes we monitored immediately before and after a typical lethal control event. These data suggest that the spatial behaviour of surviving dingoes was not altered in ways likely to affect their detectability, and if control-induced changes in dingoes' ecological function did occur, these may not be related to altered spatial behaviour or movement patterns.

Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Orbital diamagnetism of a charged Brownian particle undergoing a birth-death process

Considers the magnetic response of a charged Brownian particle undergoing a stochastic birth-death process. The latter simulates the electron-hole pair production and recombination in semiconductors. The authors obtain non-zero, orbital diamagnetism which can be large without violating the Van Leeuwen theorem (1921).

Eye movements and road hazard detection: Effects of blur and distractors

Purpose To examine the effects of optical blur, auditory distractors and age on eye movement patterns while performing a driving hazard perception test (HPT). Methods Twenty young (mean age 27.1 ± 4.6 years) and 20 older (73.3 ± 5.7 years) drivers with normal vision completed a HPT in a repeated-measures counterbalanced design while their eye movements were recorded. Testing was performed under two visual (best-corrected vision and with +2.00DS blur) and two distractor (with and without auditory distraction) conditions. Participants were required to respond to road hazards appearing in the HPT videos of real-world driving scenes and their hazard response times were recorded. Results Blur and distractors each significantly delayed hazard response time, by 0.42 and 0.76s respectively (p<0.05). A significant interaction between age and distractors indicated that older drivers were more affected by distractors than young drivers (response with distractors delayed by 0.96 and 0.60s respectively). There were no other two- or three-way interaction effect on response time. With blur, both groups fixated significantly longer on hazards before responding compared to best-corrected vision. In the presence of distractors, both groups exhibited delayed first fixation on the hazards and spent less time fixating on the hazards. There were also significant differences in eye movement characteristics between groups, where older drivers exhibited smaller saccades, delayed first fixation on hazards, and shorter fixation duration on hazards compared to the young drivers. Conclusions Collectively, the findings of delayed hazard response times and alterations in eye movement patterns with blur and distractors provide further evidence that visual impairment and distractors are independently detrimental to driving safety given that delayed hazard response times are linked to increased crash risk.

An Empirical Study of the Mixture of Time and Movements in Prices

This paper investigates the persistent pattern in the Helsinki Exchanges. The persistent pattern is analyzed using a time and a price approach. It is hypothesized that arrival times are related to movements in prices. Thus, the arrival times are defined as durations and formulated as an Autoregressive Conditional Duration (ACD) model as in Engle and Russell (1998). The prices are defined as price changes and formulated as a GARCH process including duration measures. The research question follows from market microstructure predictions about price intensities defined as time between price changes. The microstructure theory states that long transaction durations might be associated with both no news and bad news. Accordingly, short durations would be related to high volatility and long durations to low volatility. As a result, the spread will tend to be larger under intensive moments. The main findings of this study are 1) arrival times are positively autocorrelated and 2) long durations are associated with low volatility in the market.

Change in spectrum of Brownian fluctuations of optically trapped red blood cells due to malarial infection

We study the properties of single red blood cells (RBCs) held in an optical-tweezers trap. We observe a change in the spectrum of Brownian fluctuations between RBCs from normal and malaria-infected samples. The change, caused by infection-induced structural changes in the cell, appears as a statistical increase in the mean (by 25%) and standard deviation (by 200%) of the corner frequency measured over similar to 100 cells. The increase is observed even though the ensemble of cells being measured consists mostly of cells that do not actually host the parasite, but are from an infected pool. This bystander effect appears to vindicate other observations that infected cells can affect the biomechanical properties of uninfected cells. The change is also observed to be independent of the stage of infection and its duration, highlighting its potential for disease detection. (C) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3427142].

Brownian motion of spins; generalized spin Langevin equation

We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concommitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature.

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Path integral description of polymers using fractional Brownian walks

The statistical properties of fractional Brownian walks are used to construct a path integral representation of the conformations of polymers with different degrees of bond correlation. We specifically derive an expression for the distribution function of the chains’ end‐to‐end distance, and evaluate it by several independent methods, including direct evaluation of the discrete limit of the path integral, decomposition into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coordinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of the monomer along the chain backbone, now depend on an index h, the degree of correlation of the fractional Brownian walk. The special case of h=1/2 corresponds to the random walk. In constructing the normal mode picture of the chain, we conjecture the existence of a theorem regarding the zeros of the Bessel function.

Solvation dynamics in a Brownian dipolar lattice. Comparison between computer simulation and various molecular theories of solvation dynamics

Several recent theoretical and computer simulation studies have considered solvation dynamics in a Brownian dipolar lattice which provides a simple model solvent for which detailed calculations can be carried out. In this article a fully microscopic calculation of the solvation dynamics of an ion in a Brownian dipolar lattice is presented. The calculation is based on the non‐Markovian molecular hydrodynamic theory developed recently. The main assumption of the present calculation is that the two‐particle orientational correlation functions of the solid can be replaced by those of the liquid state. It is shown that such a calculation provides an excellent agreement with the computer simulation results. More importantly, the present calculations clearly demonstrate that the frequency‐dependent dielectric friction plays an important role in the long time decay of the solvation time correlation function. We also find that the present calculation provides somewhat better agreement than either the dynamic mean spherical approximation (DMSA) or the Fried–Mukamel theory which use the simulated frequency‐dependent dielectric function. It is found that the dissipative kernels used in the molecular hydrodynamic approach and in the Fried–Mukamel theory are vastly different, especially at short times. However, in spite of this disagreement, the two theories still lead to comparable results in good agreement with computer simulation, which suggests that even a semiquantitatively accurate dissipative kernel may be sufficient to obtain a reliable solvation time correlation function. A new wave vector and frequency‐dependent dissipative kernel (or memory function) is proposed which correctly goes over to the appropriate expressions in both the single particle and the collective limits. This form is expected to lead to better results than all the existing descriptions.

Dynamic scheduling in manufacturing systems using brownian approximations

Recently, Brownian networks have emerged as an effective stochastic model to approximate multiclass queueing networks with dynamic scheduling capability, under conditions of balanced heavy loading. This paper is a tutorial introduction to dynamic scheduling in manufacturing systems using Brownian networks. The article starts with motivational examples. It then provides a review of relevant weak convergence concepts, followed by a description of the limiting behaviour of queueing systems under heavy traffic. The Brownian approximation procedure is discussed in detail and generic case studies are provided to illustrate the procedure and demonstrate its effectiveness. This paper places emphasis only on the results and aspires to provide the reader with an up-to-date understanding of dynamic scheduling based on Brownian approximations.