Bayesian Analysis of a Superimposed Renewal Process

Stochastic behavior of an aero-engine failure/repair process has been analyzed from a Bayesian perspective. Number of failures/repairs in the component-sockets of this multi-component system are assumed to follow independent renewal processes with Weibull inter-arrival times. Based on the field failure/repair data of a large number of such engines and independent Gamma priors on the scale parameters and log-concave priors on the shape parameters, an exact method of sampling from the resulting posterior distributions of the parameters has been proposed. These generated parameter values are next utilised in obtaining the posteriors of the expected number of system repairs, system failure rate, and the conditional intensity function, which are computed using a recursive formula.

Theory of laminar flame propagation with non-normal diffusion.

A study has been made of the problem of steady, one-dimensional, laminar flame propagation in premixed gases, with the Lewis number differing from (and equal to) unity. Analytical solutions, using the method of matched asymptotic expansions, have been obtained for large activation energies. Numerical solutions have been obtained for a wide range of the reduced activation temperature parameter (n {geometrically equal to} E/RTb), and the Lewis number δ. The studies reveal that the flame speed eigenvalue is linear in Lewis number for first order and quadratic in Lewis number for second order reactions. For a quick determination of flame speeds, with reasonable accuracy, a simple rule, expressing the flame speed eigenvalue as a function of the Lewis number and the centroid of the reaction rate function, is proposed. Comparisons have been made with some of the earlier works, for both first and second order reactions.

Guessing Revisited: A Large Deviations Approach

The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation property with a certain rate function, then the limiting guessing exponent exists and is a scalar multiple of the Legendre-Fenchel dual of the rate function. Other sufficient conditions related to certain continuity properties of the information spectrum are briefly discussed. This approach highlights the importance of the information spectrum in determining the limiting guessing exponent. All known prior results are then re-derived as example applications of our unifying approach.

Tradeoff of average service cost and average delay for the state dependent M/M/1 queue

The optimal tradeoff between average service cost rate and average delay, is addressed for a M/M/1 queueing model with queue-length dependent service rates, chosen from a finite set. We provide an asymptotic characterization of the minimum average delay, when the average service cost rate is a small positive quantity V more than the minimum average service cost rate required for stability. We show that depending on the value of the arrival rate, the assumed service cost rate function, and the possible values of the service rates, the minimum average delay either a) increases only to a finite value, b) increases without bound as log(1/V), or c) increases without bound as 1/V, when V down arrow 0. We apply the analysis to a flow-level resource allocation model for a wireless downlink. We also investigate the asymptotic tradeoff for a sequence of policies which are obtained from an approximate fluid model for the M/M/1 queue.

Wireless scheduling with partial channel state information: large deviations and optimality

We consider a server serving a time-slotted queued system of multiple packet-based flows, where not more than one flow can be serviced in a single time slot. The flows have exogenous packet arrivals and time-varying service rates. At each time, the server can observe instantaneous service rates for only a subset of flows ( selected from a fixed collection of observable subsets) before scheduling a flow in the subset for service. We are interested in queue length aware scheduling to keep the queues short. The limited availability of instantaneous service rate information requires the scheduler to make a careful choice of which subset of service rates to sample. We develop scheduling algorithms that use only partial service rate information from subsets of channels, and that minimize the likelihood of queue overflow in the system. Specifically, we present a new joint subset-sampling and scheduling algorithm called Max-Exp that uses only the current queue lengths to pick a subset of flows, and subsequently schedules a flow using the Exponential rule. When the collection of observable subsets is disjoint, we show that Max-Exp achieves the best exponential decay rate, among all scheduling algorithms that base their decision on the current ( or any finite past history of) system state, of the tail of the longest queue. To accomplish this, we employ novel analytical techniques for studying the performance of scheduling algorithms using partial state, which may be of independent interest. These include new sample-path large deviations results for processes obtained by non-random, predictable sampling of sequences of independent and identically distributed random variables. A consequence of these results is that scheduling with partial state information yields a rate function significantly different from scheduling with full channel information. In the special case when the observable subsets are singleton flows, i.e., when there is effectively no a priori channel state information, Max-Exp reduces to simply serving the flow with the longest queue; thus, our results show that to always serve the longest queue in the absence of any channel state information is large deviations optimal.

Optimal maintenance policy of a machine subject to failure

Optimal maintenance policies for a machine with degradation in performance with age and subject to failure are derived using optimal control theory. The optimal policies are shown to be, normally, of bang-coast nature, except in the case when probability of machine failure is a function of maintenance. It is also shown, in the deterministic case that a higher depreciation rate tends to reverse this policy to coast-bang. When the probability of failure is a function of maintenance, considerable computational effort is needed to obtain an optimal policy and the resulting policy is not easily implementable. For this case also, an optimal policy in the class of bang-coast policies is derived, using a semi-Markov decision model. A simple procedure for modifying the probability of machine failure with maintenance is employed. The results obtained extend and unify the recent results for this problem along both theoretical and practical lines. Numerical examples are presented to illustrate the results obtained.

Regression Rate Studies in Hypergolic System

Regression ra tes of a hypergolic combination of fuel and oxidiser have been experimentally measured as a function of chamber pressure, mass flux and the percentage component of the hypergolic compound in natural rubber. The hypergolic compound used is difurfurylidene cyclohexanone (DFCH) which is hypergolic with the oxidiser red fuming nitric acid (RFNA) with ignition dela y of 60-70 ms. The data of weight loss versus time is obtained for burn times varying between 5 and 20 seconds. Two methods of correlating the data using mass flux of oxidiser and the total flux of hot gases have shown that index n of the regression law r=aGoxn or r=aGnxn-1 (x the axial distance) is about 0.5 or a little lower and not 0.8 even though the flow through the port is turbulent. It is argued that the reduction of index n is due to heterogeneous reaction between the liquid oxidiser and the hypergolic fuel component on the surface.

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example

Influence of Cooling Rate on the Enthalpy Relaxation and Fragility of a Metallic Glass

Structural relaxation behavior of a rapidly quenched (RQ) and a slowly cooled Pd40Cu30Ni10P20 metallic glass was investigated and compared. Differential scanning calorimetry was employed to monitor the relaxation enthalpies at the glass transition temperature, T-g , and the Kolrausch-Williams-Watts (KWW) stretched exponential function was used to describe its variation with annealing time. It was found that the rate of enthalpy recovery is higher in the ribbon, implying that the bulk is more resistant to relaxation at low temperatures of annealing. This was attributed to the possibility of cooling rate affecting the locations where the glasses get trapped within the potential energy landscape. The RQ process traps a larger amount of free volume, resulting in higher fragility, and in turn relaxes at the slightest thermal excitation (annealing). The slowly cooled bulk metallic glass (BMG), on the other hand, entraps lower free volume and has more short-range ordering, hence requiring a large amount of perturbation to access lower energy basins.

Structure determination and biochemical studies on Bacillus stearothermophilus E53Q serine hydroxymethyltransferase and its complexes provide insights on function and enzyme memory

Serine hydroxymethyltransferase (SHMT) belongs to the alpha-family of pyridoxal 5'-phosphate-dependent enzymes and catalyzes the reversible conversion of L-Ser and etrahydrofolate to Gly and 5,10-methylene tetrahydrofolate. 5,10-Methylene tetrahydrofolate serves as a source of one-carbon fragment in many biological processes. SHMT also catalyzes the tetrahydrofolate-independent conversion of L-allo-Thr to Gly and acetaldehyde. The crystal structure of Bacillus stearothermophilus SHMT (bsSHMT) suggested that E53 interacts with the substrate, L-Ser and etrahydrofolate. To elucidate the role of E53, it was mutated to Q and structural and biochemical studies were carried out with the mutant enzyme. The internal aldimine structure of E53QbsSHMT was similar to that of the except for significant changes at Q53, Y60 and Y61. The wild-type enzyme, carboxyl of Gly and side chain of L-Ser were in two conformations in the respective external aldimine structures. The mutant enzyme was completely inactive for tetrahydrofolate-depen dent cleavage of L-Ser, whereas there was a 1.5-fold increase in the rate of tetrahydrofolate-independent reaction with L-allo-Thr. The results obtained from these studies suggest that E53 plays an essential role in tetrahydrofolate/5-formyl tetrahydrofolate binding and in the proper positioning of C beta of L-Ser for direct attack by N5 of tetrahydrofolate. Most interestingly, the structure of the complex obtained by cocrystallization of E53QbsSHMT with Gly and 5-formyl tetrahydrofolate revealed the gem-diamine form of pyridoxal 5'-phosphate bound to Gly and active site Lys. However, density for 5-formyl tetrahydrofolate was not observed. Gly carboxylate was in a single conformation, whereas pyridoxal 5'-phosphate had two distinct conformations. The differences between the structures of this complex and Gly external aldimine suggest that the changes induced by initial binding of 5-formyl tetrahydrofolate are retained even though 5-formyl tetrahydrofolate is absent in the final structure. Spectral studies carried out with this mutant enzyme also suggest that 5-formyl tetrahydrofolate binds to the E53QbsSHMT-Gly complex forming a quinonoid intermediate and falls off within 4 h of dialysis, leaving behind the mutant enzyme in the gemdiamine form. This is the first report to provide direct evidence for enzyme memory based on the crystal structure of enzyme complexes.

Extraordinary high strain rate superplasticity in electrodeposited nano-nickel and alloys

Superplastic materials exhibit very large elongations to failure,typically >500%, and this enables commercial forming of complex shaped components at slow strain rates of similar to 10(-4) s(-1). We report extraordinary record superplastic elongations to failure of up to 5300% at both high strain rates and low temperature in electrodeposited nanocrystalline Ni and some Ni alloys. Superplasticity is not related to the presence of sulfur or a low melting phase at grain boundaries. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

An evaluation of rate-controlling obstacles for low-temperature deformation of zirconium

The low-temperature plastic flow of alpha-zirconium was studied by employing constantrate tensile tests and differential-stress creep experiments. The activation parameters, enthalpy and area, have been obtained as a function of stress for pure, as well as commercial zirconium. The activation area is independent of grain size and purity and falls to about 9b2 at high stresses. The deformation mechanism below about 700° K is found to be controlled by a single thermally activated process, and not a two-stage activation mechanism. Several dislocation mechanisms are examined and it is concluded that overcoming the Peierls energy humps by the formation of kink pairs in a length of dislocation is the rate-controlling mechanism. The total energy needed to nucleate a double kink is about 0.8 eV in pure zirconium and 1 eV in commercial zirconium

High-Rate,2-Group ML-Decodable STBCs for 2(m) Transmit Antennas

A Space-Time Block Code (STBC) in K-variables is said to be g-Group ML-Decodable (GMLD) if its Maximum-Likelihood (ML) decoding metric can be written as a sum of g independent terms, with each term being a function of a subset of the K variables. In this paper, a construction method to obtain high-rate, 2-GMLD STBCs for 2(m) transmit antennas, m > 1, is presented. The rate of the STBC obtained for 2(m) transmit antennas is 2(m-2) + 1/2(m), complex symbols per channel use. The design method is illustrated for the case of 4 and 8 transmit antennas. The code obtained for 4 transmit antennas is equivalent to the rate-5/4 Quasi-Orthogonal design (QOD) proposed by Yuen, Guan and Tjung.