Dynamics of crystal size distributions with size-dependent rates

The growth and dissolution dynamics of nonequilibrium crystal size distributions (CSDs) can be determined by solving the governing population balance equations (PBEs) representing reversible addition or dissociation. New PBEs are considered that intrinsically incorporate growth dispersion and yield complete CSDs. We present two approaches to solving the PBEs, a moment method and a numerical scheme. The results of the numerical scheme agree with the moment technique, which can be solved exactly when powers on mass-dependent growth and dissolution rate coefficients are either zero or one. The numerical scheme is more general and can be applied when the powers of the rate coefficients are non-integers or greater than unity. The influence of the size dependent rates on the time variation of the CSDs indicates that as equilibrium is approached, the CSDs become narrow when the exponent on the growth rate is less than the exponent on the dissolution rate. If the exponent on the growth rate is greater than the exponent on the dissolution rate, then the polydispersity continues to broaden. The computation method applies for crystals large enough that interfacial stability issues, such as ripening, can be neglected. (C) 2002 Elsevier Science B.V. All rights reserved.

Very large array detection of radio recombination lines from the radio nucleus of NGC 253: Ionization by a weak active galactic nucleus, an obscured super star cluster, or a compact supernova remnant?

We have imaged the H92alpha and H75alpha radio recombination line (RRL) emissions from the starburst galaxy NGC 253 with a resolution of similar to4 pc. The peak of the RRL emission at both frequencies coincides with the unresolved radio nucleus. Both lines observed toward the nucleus are extremely wide, with FWHMs of similar to200 km s(-1). Modeling the RRL and radio continuum data for the radio nucleus shows that the lines arise in gas whose density is similar to10(4) cm(-3) and mass is a few thousand M., which requires an ionizing flux of (6-20) x 10(51) photons s(-1). We consider a supernova remnant (SNR) expanding in a dense medium, a star cluster, and also an active galactic nucleus (AGN) as potential ionizing sources. Based on dynamical arguments, we rule out an SNR as a viable ionizing source. A star cluster model is considered, and the dynamics of the ionized gas in a stellar-wind driven structure are investigated. Such a model is only consistent with the properties of the ionized gas for a cluster younger than similar to10(5) yr. The existence of such a young cluster at the nucleus seems improbable. The third model assumes the ionizing source to be an AGN at the nucleus. In this model, it is shown that the observed X-ray flux is too weak to account for the required ionizing photon flux. However, the ionization requirement can be explained if the accretion disk is assumed to have a big blue bump in its spectrum. Hence, we favor an AGN at the nucleus as the source responsible for ionizing the observed RRLs. A hybrid model consisting of an inner advection-dominated accretion flow disk and an outer thin disk is suggested, which could explain the radio, UV, and X-ray luminosities of the nucleus.

Performance Analysis of TCP Uploads in WLANs with Multiple Rates

Throughput analysis of bulk TCP downloads in cases where all WLAN stations are associated at the same rate with the AP is available in the literature. In this paper,we extend the analysis to TCP uploads for the case of multirate associations. The approach is based on a two-dimensional semi- Markov model for the number of backlogged stations. Analytical results are in excellent agreement with simulations performed using QUALNET 4.5.

Electrochemical phase formation. Time-dependent nucleation and growth rates

The theory of phase formation is generalised for any arbitrary time dependence of nucleation and growth rates. Some sources of this time dependence are time-dependent potential inputs, ohmic drop and the ingestion effect. Particular cases, such as potentiostatic and, especially, linear potential sweep, are worked out for the two limiting cases of nucleation, namely instantaneous and progressive. The ohmic drop is discussed and a procedure for this correction is indicated. Recent results of Angerstein-Kozlowska, Conway and Klinger are critically investigated. Several earlier results are deduced as special cases. Evans' overlap formula is generalised for the time-dependent case and the equivalence between Avrami's and Evans' equations established.

Maximum Margin Classifiers with Specified False Positive and False Negative Error Rates

This paper addresses the problem of maximum margin classification given the moments of class conditional densities and the false positive and false negative error rates. Using Chebyshev inequalities, the problem can be posed as a second order cone programming problem. The dual of the formulation leads to a geometric optimization problem, that of computing the distance between two ellipsoids, which is solved by an iterative algorithm. The formulation is extended to non-linear classifiers using kernel methods. The resultant classifiers are applied to the case of classification of unbalanced datasets with asymmetric costs for misclassification. Experimental results on benchmark datasets show the efficacy of the proposed method.

Pricing a Shared Access Link for Fair and Efficient Operation with Variable User Data Rates

The literature on pricing implicitly assumes an "infinite data" model, in which sources can sustain any data rate indefinitely. We assume a more realistic "finite data" model, in which sources occasionally run out of data; this leads to variable user data rates. Further, we assume that users have contracts with the service provider, specifying the rates at which they can inject traffic into the network. Our objective is to study how prices can be set such that a single link can be shared efficiently and fairly among users in a dynamically changing scenario where a subset of users occasionally has little data to send. User preferences are modelled by concave increasing utility functions. Further, we introduce two additional elements: a convex increasing disutility function and a convex increasing multiplicative congestion-penally function. The disutility function takes the shortfall (contracted rate minus present rate) as its argument, and essentially encourages users to send traffic at their contracted rates, while the congestion-penalty function discourages heavy users from sending excess data when the link is congested. We obtain simple necessary and sufficient conditions on prices for fair and efficient link sharing; moreover, we show that a single price for all users achieves this. We illustrate the ideas using a simple experiment.

Growth and consumption rates of the phase layers during interdiffusion in a diffusion couple with finite end member

The relations for the growth and consumption rates of a layer with finite thickness as an end member and the product phases in the interdiffusion zone are developed. We have used two different methodologies, the diffusion based and the physico-chemical approach to develop the same relations. We have shown that the diffusion based approach is rather straightforward; however, the physico-chemical approach is much more versatile than the other method. It was found that the position of the marker plane becomes vague in the second stage of the interdiffusion process in pure A thin layer/B couple, where two phases grow simultaneously.

Effect of gas injection on drag and surface heat transfer rates for a 30 degrees semi-apex angle blunt body flying at Mach 5.75

Effect of coolant gas injection in the stagnation region on the surface heat transfer rates and aerodynamic drag for a large angle blunt body flying at hypersonic Mach number is reported for two stagnation enthalpies. A 60° apex-angle blunt cone model is employed for this purpose with air injection at the nose through a hole of 2mm diameter. The convective surface heating rates and aerodynamic drag are measured simultaneously using surface mounted platinum thin film sensors and internally mounted accelerometer balance system, respectively. About 35–40% reduction in surface heating rates is observed in the vicinity of stagnation region whereas 15–25% reduction in surface heating rates is felt beyond the stagnation region at stagnation enthalpy of 1.6MJ/kg. The aerodynamic drag expressed in terms of drag coefficient is found to increase by 20% due to the air injection.

Aggregate download throughput for TCP-controlled long file transfers in a WLAN with multiple STA-AP association rates

We consider several WLAN stations associated at rates r(1), r(2), ... r(k) with an Access Point. Each station (STA) is downloading a long file from a local server, located on the LAN to which the Access Point (AP) is attached, using TCP. We assume that a TCP ACK will be produced after the reception of d packets at an STA. We model these simultaneous TCP-controlled transfers using a semi-Markov process. Our analytical approach leads to a procedure to compute aggregate download, as well as per-STA throughputs, numerically, and the results match simulations very well. (C) 2012 Elsevier B.V. All rights reserved.

Optimal Control of Markov Processes with Age-Dependent Transition Rates

We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite horizon average cost problems. Our approach is via the construction of an equivalent semi-Markov decision process. We characterise the value function and optimal controls for both discounted and average cost cases.

Analysis of Strain Rates and Microstructural Evaluation during Metal Forming: Role of Surface Texture and Friction

The surface texture of a die plays an important role in friction during metal forming. In the present study, unidirectional and random surface finishes were produced on hardened steel plate surfaces. To understand the influence of surface texture on friction, experiments were conducted using Al-Mg alloy pins that slid against steel plates of different surface textures. In the sliding experiments, a high coefficient of friction was observed when the pins slid perpendicular to the unidirectional grinding marks and low friction occurred when the pins slid on the random surfaces. Finite element simulations were performed using the measured friction values to understand the stress and strain evolutions in the deforming material using dies with various friction. The numerical results showed that the states of stress and strain rates are strongly influenced by the friction at the interface and hence would influence the final material microstructure. To substantiate the numerical results, laboratory compression tests were conducted. Different surface textures were obtained in order to experience different friction values at different locations. A large variation in the microstructure at these locations was observed during experiments, verifying that surface texture and die friction significantly influence fundamental material formation behavior.

Wheeler-Feynman absorber revisited: a useful technique to calculate decay rates and lifetimes in small scale optical systems

The Wheeler-Feynman (WF) absorber theory of radiation though no more of interest in explaining self interaction of an electron, can be very useful in today's research in small scale optical systems. The significance of the WF absorber is the use of time-symmetrical solution of Maxwell's equations as opposed to only the retarded solution. The radiative coupling of emitters to nano wires in the near field and change in their lifetimes due to small mode volume enclosures have been elucidated with the retarded solutions before. These solutions have also been shown to agree with quantum electrodynamics, thus allowing for classical electromagnetic approaches in such problems. It is here assumed that the radiative coupling of the emitter with a body is in proportion to its contribution to the classical force of radiative reaction as derived in the WF absorber theory. Representing such nano structures as a partial WF absorber acting on the emitter makes the computations considerably easier than conventional electromagnetic solutions for full boundary conditions.

Modeling harvest rates and numbers from age and sex ratios: A demonstration for elephant populations

Illegal harvest rates of wildlife populations are often unknown or difficult to estimate from field data due to under-reporting or incomplete detection of carcasses. This is especially true for elephants that are killed for ivory or in conflicts with people. We describe a method to infer harvest rates from coarse field data of three population parameters, namely, adult female to male ratio, male old-adult to young-adult ratio, and proportion of adult males in the population using Jensen's (2000) 2-sex, density-dependent Leslie matrix model. The specific combination of male and female harvest rates and numbers can be determined from the history of harvest and estimate of population size. We applied this technique to two populations of elephants for which data on age structure and records of mortality were available-a forest-dwelling population of the Asian elephant (at Nagarahole, India) and an African savannah elephant population (at Samburu, Kenya) that had experienced male-biased harvest regimes over 2-3 decades. For the Nagarahole population, the recorded numbers of male and female elephants killed illegally during 1981-2000 were 64% and 88% of the values predicted by the model, respectively, implying some non-detection or incomplete reporting while for the Samburu population the recorded and modeled numbers of harvest during 1990-1999 closely matched. This technique, applicable to any animal population following logistic growth model, can be especially useful for inferring illegal harvest numbers of forest elephants in Africa and Asia.

Functional analysis of ultra high information rates conveyed by rat vibrissal primary afferents

Sensory receptors determine the type and the quantity of information available for perception. Here, we quantified and characterized the information transferred by primary afferents in the rat whisker system using neural system identification. Quantification of ``how much'' information is conveyed by primary afferents, using the direct method (DM), a classical information theoretic tool, revealed that primary afferents transfer huge amounts of information (up to 529 bits/s). Information theoretic analysis of instantaneous spike-triggered kinematic stimulus features was used to gain functional insight on ``what'' is coded by primary afferents. Amongst the kinematic variables tested-position, velocity, and acceleration-primary afferent spikes encoded velocity best. The other two variables contributed to information transfer, but only if combined with velocity. We further revealed three additional characteristics that play a role in information transfer by primary afferents. Firstly, primary afferent spikes show preference for well separated multiple stimuli (i.e., well separated sets of combinations of the three instantaneous kinematic variables). Secondly, neurons are sensitive to short strips of the stimulus trajectory (up to 10 ms pre-spike time), and thirdly, they show spike patterns (precise doublet and triplet spiking). In order to deal with these complexities, we used a flexible probabilistic neuron model fitting mixtures of Gaussians to the spike triggered stimulus distributions, which quantitatively captured the contribution of the mentioned features and allowed us to achieve a full functional analysis of the total information rate indicated by the DM. We found that instantaneous position, velocity, and acceleration explained about 50% of the total information rate. Adding a 10 ms pre-spike interval of stimulus trajectory achieved 80-90%. The final 10-20% were found to be due to non-linear coding by spike bursts.

Two-point correlation function of an exclusion process with hole-dependent rates

We consider an exclusion process on a ring in which a particle hops to an empty neighboring site with a rate that depends on the number of vacancies n in front of it. In the steady state, using the well-known mapping of this model to the zero-range process, we write down an exact formula for the partition function and the particle-particle correlation function in the canonical ensemble. In the thermodynamic limit, we find a simple analytical expression for the generating function of the correlation function. This result is applied to the hop rate u(n) = 1 + (b/n) for which a phase transition between high-density laminar phase and low-density jammed phase occurs for b > 2. For these rates, we find that at the critical density, the correlation function decays algebraically with a continuously varying exponent b - 2. We also calculate the two-point correlation function above the critical density and find that the correlation length diverges with a critical exponent nu = 1/(b - 2) for b < 3 and 1 for b > 3. These results are compared with those obtained using an exact series expansion for finite systems.