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.

Study Of Fluid-Flow And Residence-Time Distribution In A Continuous Slab Casting Mold

The fluid-flow pattern and residence-time distribution (r.t.d.) of the fluid in a continuous casting mould have been studied using a water model. The two recirculating zones below the discharge ports have been found to be asymmetric. The effect of casting speed, discharge port diameter, shroud well depth and the immersion depth on r.t.d. have been investigated. The r.t.d. curve has been well represented by a model of two backmix cells of equal volume in series. The exist of the fluid has been found to be non-uniform across the cross-section of the mould. The fluid-flow pattern has been observed to change with time in a random fashion. Dead volume of upto 31.8% has been found with smaller discharge ports.

Hydrologic drought prediction under climate change: Uncertainty modeling with Dempster-Shafer and Bayesian approaches

Representation and quantification of uncertainty in climate change impact studies are a difficult task. Several sources of uncertainty arise in studies of hydrologic impacts of climate change, such as those due to choice of general circulation models (GCMs), scenarios and downscaling methods. Recently, much work has focused on uncertainty quantification and modeling in regional climate change impacts. In this paper, an uncertainty modeling framework is evaluated, which uses a generalized uncertainty measure to combine GCM, scenario and downscaling uncertainties. The Dempster-Shafer (D-S) evidence theory is used for representing and combining uncertainty from various sources. A significant advantage of the D-S framework over the traditional probabilistic approach is that it allows for the allocation of a probability mass to sets or intervals, and can hence handle both aleatory or stochastic uncertainty, and epistemic or subjective uncertainty. This paper shows how the D-S theory can be used to represent beliefs in some hypotheses such as hydrologic drought or wet conditions, describe uncertainty and ignorance in the system, and give a quantitative measurement of belief and plausibility in results. The D-S approach has been used in this work for information synthesis using various evidence combination rules having different conflict modeling approaches. A case study is presented for hydrologic drought prediction using downscaled streamflow in the Mahanadi River at Hirakud in Orissa, India. Projections of n most likely monsoon streamflow sequences are obtained from a conditional random field (CRF) downscaling model, using an ensemble of three GCMs for three scenarios, which are converted to monsoon standardized streamflow index (SSFI-4) series. This range is used to specify the basic probability assignment (bpa) for a Dempster-Shafer structure, which represents uncertainty associated with each of the SSFI-4 classifications. These uncertainties are then combined across GCMs and scenarios using various evidence combination rules given by the D-S theory. A Bayesian approach is also presented for this case study, which models the uncertainty in projected frequencies of SSFI-4 classifications by deriving a posterior distribution for the frequency of each classification, using an ensemble of GCMs and scenarios. Results from the D-S and Bayesian approaches are compared, and relative merits of each approach are discussed. Both approaches show an increasing probability of extreme, severe and moderate droughts and decreasing probability of normal and wet conditions in Orissa as a result of climate change. (C) 2010 Elsevier Ltd. All rights reserved.

Wigner distribution for angle coordinates in quantum mechanics

The method of Wigner distribution functions, and the Weyl correspondence between quantum and classical variables, are extended from the usual kind of canonically conjugate position and momentum operators to the case of an angle and angular momentum operator pair. The sense in which one has a description of quantum mechanics using classical phase‐space language is much clarified by this extension.

Existence Theorems for Generalized Hammerstein Equations

In this paper we obtain existence theorems for generalized Hammerstein-type equations K(u)Nu + u = 0, where for each u in the dual X* of a real reflexive Banach space X, K(u): X -- X* is a bounded linear map and N: X* - X is any map (possibly nonlinear). The method we adopt is totally different from the methods adopted so far in solving these equations. Our results in the reflexive spacegeneralize corresponding results of Petry and Schillings.

A note on "effects of couple stresses on the blood flow through an artery with mild stenosis"

Some errors have been observed in the analytical expression for the resistance to flow (lambda R), and in the computation of shear stress distribution (tau R) in the analysis of Prawal Sinha and Chandan Singh (1). These errors have been rectified in the present analysis. Also, better values have been suggested for the couple stress parameter alpha for getting better results for lambda R and tau R.

Control of Agent Swarms using Generalized Centroidal Cyclic Pursuit Laws

One of the major tasks in swarm intelligence is to design decentralized but homogenoeus strategies to enable controlling the behaviour of swarms of agents. It has been shown in the literature that the point of convergence and motion of a swarm of autonomous mobile agents can be controlled by using cyclic pursuit laws. In cyclic pursuit, there exists a predefined cyclic connection between agents and each agent pursues the next agent in the cycle. In this paper we generalize this idea to a case where an agent pursues a point which is the weighted average of the positions of the remaining agents. This point correspond to a particular pursuit sequence. Using this concept of centroidal cyclic pursuit, the behavior of the agents is analyzed such that, by suitably selecting the agents' gain, the rendezvous point of the agents can be controlled, directed linear motion of the agents can be achieved, and the trajectories of the agents can be changed by switching between the pursuit sequences keeping some of the behaviors of the agents invariant. Simulation experiments are given to support the analytical proofs.

Turbulent flow computations on a hybrid cartesian point distribution using meshless solver LSFD-U

This paper may be considered as a sequel to one of our earlier works pertaining to the development of an upwind algorithm for meshless solvers. While the earlier work dealt with the development of an inviscid solution procedure, the present work focuses on its extension to viscous flows. A robust viscous discretization strategy is chosen based on positivity of a discrete Laplacian. This work projects meshless solver as a viable cartesian grid methodology. The point distribution required for the meshless solver is obtained from a hybrid cartesian gridding strategy. Particularly considering the importance of an hybrid cartesian mesh for RANS computations, the difficulties encountered in a conventional least squares based discretization strategy are highlighted. In this context, importance of discretization strategies which exploit the local structure in the grid is presented, along with a suitable point sorting strategy. Of particular interest is the proposed discretization strategies (both inviscid and viscous) within the structured grid block; a rotated update for the inviscid part and a Green-Gauss procedure based positive update for the viscous part. Both these procedures conveniently avoid the ill-conditioning associated with a conventional least squares procedure in the critical region of structured grid block. The robustness and accuracy of such a strategy is demonstrated on a number of standard test cases including a case of a multi-element airfoil. The computational efficiency of the proposed meshless solver is also demonstrated. (C) 2010 Elsevier Ltd. All rights reserved.

Impact of physical processes on the chlorophyll distribution in the Bay of Bengal

Satellite-derived chlorophyll a concentration (chl a) maps show three regions with high chl a in the Bay of Bengal. First among these is close to the coast, particularly off river mouths, with high values coinciding with the season of peak discharge; second is in the southwestern bay during the northeast monsoon, which is forced by local Ekman pumping; and the third is to the east of Sri Lanka in response to the summer monsoon winds. Chlorophyll-rich water from the mouths of rivers flows either along the coast or in an offshore direction, up to several hundred kilometers, depending on the prevailing ocean current pattern. The Irrawady River plume flows toward offshore and then turns northwestward during October–December, but it flows along the coast into the Andaman Sea for the rest of the year. From the Ganga-Brahmaputra river mouth, chl a–rich water flows directly southward into the open bay during spring but along the Indian coast during summer and winter. Along the Indian coast, the flow of chl a–rich water is determined by the East India Coastal Current (EICC). Whenever the EICC meanders off the Indian coast, it leads to an offshore outbreak of chl a–rich water from the coastal region into open ocean. The EICC as well as open ocean circulation in the bay is made up of several eddies, and these eddies show relatively higher chl a. Eddies near the coast, however, can often have higher chl a because of advection from the coastal region rather than generation within the eddy itself. The bay experiences several cyclones in a year, most of them occurring during October–November. These cyclones cause a drop in the sea surface temperature, a dip in the sea level, and a local increase in chl a. The impact of a cyclone is weaker in the northern part of the bay because of stronger stratification compared to the southern parts.

Surface acoustic wave distribution and acousto-optic interaction in proton exchanged LiNbO3 waveguides

The efficiency of acoustooptic (AO) interaction in YZ-cut proton exchanged (PE) LiNbO3 waveguides is theoretically analysed by determining the overlap between the optical and acoustic field distributions. The present analysis takes into account the perturbed SAW field distribution due to the presence of the PE layer on the LiNbO3 substrate determined by the rigorous layered medium approach. The overlap is found to be significant upto very high acoustic frequencies of the order of 5 GHz, whereas in the earlier analysis by vonHelmolt and Schaffer [6] for diffused waveguides, it was shown that the overlap integral rolls down to nearly zero at this high frequency range.