Spreading Sequences for Asynchronous Spectrally Phase Encoded Optical CDMA

In phase encoding optical CDMA (OCDMA) the spreading is achieved by encoding the phase of signal spectrum. In this paper we first derive a mathematical model for the output of phase encoding OCDMA systems. Based on this model we introduce a metric to design spreading sequences for asynchronous transmission. Then we connect the phase encoding sequence design problem to OFDM PMEPR (peak to mean envelope power ratio) problem. Using this connection we conclude that designing sequences with good properties for samples of timing delay guarantees that the same sequence to be good for all timing delays. Finally using generalized bent function we manage to construct a family of sequences which are good for asynchronous phase encoding OCDMA systems and using these sequences we introduce an M-ary modulation scheme for phase encoding OCDMA

Determination of surge-diverter voltage/current characteristic

A mathematical model has been proposed to determine the voltage/current characteristic of the surge diverter for a wide range of currents of short duration of 8/20 and 4/10ÿs waveshapes. Experimental data agree well with the proposed model.

Determination of the follow current in surge diverters

Using a suitable mathematical model, computations of power/follow current in surge diverters (lightning arresters) have been made from the known short-circuit capacity of the power-frequency source and the nonlinear resistor characteristics. Also the effect of the initiation angle is studied. Typical verifications with the available data have been carried out. The influence of arc drop in the surge-diverter spark gap is neglected.

Error, Confidence, and Cost in Engineering Computations

The questions that one should answer in engineering computations - deterministic, probabilistic/randomized, as well as heuristic - are (i) how good the computed results/outputs are and (ii) how much the cost in terms of amount of computation and the amount of storage utilized in getting the outputs is. The absolutely errorfree quantities as well as the completely errorless computations done in a natural process can never be captured by any means that we have at our disposal. While the computations including the input real quantities in nature/natural processes are exact, all the computations that we do using a digital computer or are carried out in an embedded form are never exact. The input data for such computations are also never exact because any measuring instrument has inherent error of a fixed order associated with it and this error, as a matter of hypothesis and not as a matter of assumption, is not less than 0.005 per cent. Here by error we imply relative error bounds. The fact that exact error is never known under any circumstances and any context implies that the term error is nothing but error-bounds. Further, in engineering computations, it is the relative error or, equivalently, the relative error-bounds (and not the absolute error) which is supremely important in providing us the information regarding the quality of the results/outputs. Another important fact is that inconsistency and/or near-consistency in nature, i.e., in problems created from nature is completely nonexistent while in our modelling of the natural problems we may introduce inconsistency or near-inconsistency due to human error or due to inherent non-removable error associated with any measuring device or due to assumptions introduced to make the problem solvable or more easily solvable in practice. Thus if we discover any inconsistency or possibly any near-inconsistency in a mathematical model, it is certainly due to any or all of the three foregoing factors. We do, however, go ahead to solve such inconsistent/near-consistent problems and do get results that could be useful in real-world situations. The talk considers several deterministic, probabilistic, and heuristic algorithms in numerical optimisation, other numerical and statistical computations, and in PAC (probably approximately correct) learning models. It highlights the quality of the results/outputs through specifying relative error-bounds along with the associated confidence level, and the cost, viz., amount of computations and that of storage through complexity. It points out the limitation in error-free computations (wherever possible, i.e., where the number of arithmetic operations is finite and is known a priori) as well as in the usage of interval arithmetic. Further, the interdependence among the error, the confidence, and the cost is discussed.

Scientific rationale toward cupola design

Numerous improvements in cupola design and operation have been made in the past to increase productivity, spout temperature and fuel efficiency. However, these improvements have been based on practice and experience. The present work establishes a scientific rationale for cupola design and operation using a mathematical model. The improved performance of a divided-blast cupola over the conventional one has been successfully explained by the model. Performance of a cupola, as influenced by the important design parameter--the distance of separation between the two rows of tuyeres and operational parameters, such as size of coke and metallic charge, blast rate and charge level--was analyzed. For a divided-blast cupola, an optimum distance of 800-900 mm separation between the two rows of tuyeres was found to be ideal, irrespective of the size of cupola.

Scheduling identical parallel machines with machine eligibility restrictions to minimize total weighted flowtime in automobile gear manufacturing

In this paper, we address a scheduling problem for minimizing total weighted flowtime, observed in automobile gear manufacturing. Specifically, the bottleneck operation of the pre-heat treatment stage of gear manufacturing process has been dealt with in scheduling. Many real-life scenarios like unequal release times, sequence dependent setup times, and machine eligibility restrictions have been considered. A mathematical model taking into account dynamic starting conditions has been proposed. The problem is derived to be NP-hard. To approach the problem, a few heuristic algorithms have been proposed. Based on planned computational experiments, the performance of the proposed heuristic algorithms is evaluated: (a) in comparison with optimal solution for small-size problem instances and (b) in comparison with the estimated optimal solution for large-size problem instances. Extensive computational analyses reveal that the proposed heuristic algorithms are capable of consistently yielding near-statistically estimated optimal solutions in a reasonable computational time.

Viral Kinetics Suggests a Reconciliation of the Disparate Observations of the Modulation of Claudin-1 Expression on Cells Exposed to Hepatitis C Virus

The tight junction protein claudin-1 (CLDN1) is necessary for hepatitis C virus (HCV) entry into target cells. Recent studies have made disparate observations of the modulation of the expression of CLDN1 on cells following infection by HCV. In one study, the mean CLDN1 expression on cells exposed to HCV declined, whereas in another study HCV infected cells showed increased CLDN1 expression compared to uninfected cells. Consequently, the role of HCV in modulating CLDN1 expression, and hence the frequency of cellular superinfection, remains unclear. Here, we present a possible reconciliation of these disparate observations. We hypothesized that viral kinetics and not necessarily HCV-induced receptor modulation underlies these disparate observations. To test this hypothesis, we constructed a mathematical model of viral kinetics in vitro that mimicked the above experiments. Model predictions provided good fits to the observed evolution of the distribution of CLDN1 expression on cells following exposure to HCV. Cells with higher CLDN1 expression were preferentially infected and outgrown by cells with lower CLDN1 expression, resulting in a decline of the mean CLDN1 expression with time. At the same time, because the susceptibility of cells to infection increased with CLDN1 expression, infected cells tended to have higher CLDN1 expression on average than uninfected cells. Our study thus presents an explanation of the disparate observations of CLDN1 expression following HCV infection and points to the importance of considering viral kinetics in future studies of receptor expression on cells exposed to HCV.

Influence of Bottom Bubbling Rate on Formation of Metal Emulsion in Al-Cu Alloy and Molten Salt System

In steel refining process, an increase of interfacial area between the metal and slag through the metal droplets emulsified into the slag, so-called ``metal emulsion'', is one prevailing view for improving the reaction rate. The formation of metal emulsion was experimentally evaluated using Al-Cu alloy as metal phase and chloride salt as slag phase under the bottom bubbling condition. Samples were collected from the center of the salt phase in the container. Large number of metal droplets were separated from the salt by dissolving it into water. The number, surface area, and weight of the droplets increased with the gas flow rate and have local maximum values. The formation and sedimentation rates of metal droplets were estimated using a mathematical model. The formation rate increased with the gas flow rate and has a local maximum value as a function of gas flow rate, while the sedimentation rate is independent of the gas flow rate under the bottom bubbling condition. Three types of formation mode of metal emulsion, which occurred by the rupture of metal film around the bubble, were observed using high speed camera. During the process, an elongated column covered with metal film was observed with the increasing gas flow rate. This elongated column sometimes reached to the top surface of the salt phase. In this case, it is considered that fine droplets were not formed and in consequence, the weight of metal emulsion decreased at higher gas flow rate.

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part I: zero and extrapolated boundary conditions

The mathematical model for diffuse fluorescence spectroscopy/imaging is represented by coupled partial differential equations (PDEs), which describe the excitation and emission light propagation in soft biological tissues. The generic closed-form solutions for these coupled PDEs are derived in this work for the case of regular geometries using the Green's function approach using both zero and extrapolated boundary conditions. The specific solutions along with the typical data types, such as integrated intensity and the mean time of flight, for various regular geometries were also derived for both time-and frequency-domain cases. (C) 2013 Optical Society of America

Optimization of thermoacoustic refrigerator using response surface methodology

Thermoacoustic refrigerator (TAR) converts acoustic waves into heat without any moving parts. The study presented here aims to optimize the parameters like frequency, stack position, stack length, and plate spacing involving in designing TAR using the Response Surface Methodology (RSM). A mathematical model is developed using the RSM based on the results obtained from DeltaEC software. For desired temperature difference of 40 K, optimized parameters suggested by the RSM are the frequency 254 Hz, stack position 0.108 m, stack length 0.08 m, and plate spacing 0.0005 m. The experiments were conducted with optimized parameters and simulations were performed using the Design Environment for Low-amplitude ThermoAcoustic Energy Conversion (DeltaEC) which showed similar results.

Stability analysis of aperiodic messages scheduled in the dynamic segment of flex ray protocol

In a cyber physical system like vehicles number of signals to be communicated in a network system has an increasing trend. More and more mechanical and hydraulic parts are replaced by electronic control units and infotainment and multimedia applications has increased in vehicles. Safety critical hard real time messages and aperiodic messages communicated between electronic control units have been increased in recent times. Flexray is a high bandwidth protocol consisting of static segment for supporting hard real time messages and a dynamic segment for transmitting soft and non real time messages. In this paper, a method to obtain the stability region for the random arrival of messages in each electronic control units which is scheduled in the dynamic segment of Flexray protocol is presented. Number of mini slots available in the dynamic segment of Flexray restricts the arrival rate of tasks to the micro controllers or the number of micro controllers connected to the Flexray bus. Stability region of mathematical model of the system is compared with the Flexray protocol simulation results.

EFFECT OF CORE-SHELL STRUCTURE OF HYDROGEL BEADS ON THE THRESHOLD CONCENTRATION OF WATER FOR SWELLING AND ITS PH SENSITIVITY

In this paper we investigate the effect of core-shell structure of Sodium Alginate based hydrogel beads and their size on certain activation threshold concentration of water for applications in swelling and pH sensing. This type of hydrogel experiences diffusive pressure due to transport of certain free charges across its interface with a solvent or electrolyte. This process is essentially a dynamic equilibrium of the electric force field, stress in the polymeric network with cage like structure and molecular diffusion including phase transformation due to pressure imbalance between the hydrogel and its surroundings. The effect of pH of the solvant on the swelling rate of these beads has been studied experimentally. A mathematical model of the swelling process has been developed by considering Nernst-Planck equation representing the migration of mobile ions and Er ions, Poisson equation representing the equilibrium of the electric field and mechanical field equation representing swelling of the gel. An attempt has been made to predict the experimentally observed phenomena using these numerical simulations. It is observed experimentally that certain minimum concentration called activation threshold concentration of the water molecules must be present in the hydrogel in order to activate the swelling process. For the required activation threshold concentration of water in the beads, the pH induced change in the rate of swelling is also investigated. This effect is analyzed for various different core-shell structures of the beads.

Modelling of metal-slag emulsion

Many industrial processes involve reaction between the two immiscible liquid systems. It is very important to increase the efficiency and productivity of such reactions. One of the important processes that involve such reactions is the metal-slag system. To increase the reaction rate or efficiency, one must increase the contact surface area of one of the phases. This is either done by emulsifying the slag into the metal phase or the metal into the slag phase. The latter is preferred from the stability viewpoint. Recently, we have proposed a simple and elegant mathematical model to describe metal emulsification in the presence of bottom gas bubbling. The same model is being extended here. The effect of slag and metal phase viscosity, density and metal droplet size on the metal droplet velocity in the slag phase is discussed for the above mentioned metal emulsification process. The models results have been compared with experimental data.

Dynamic state estimation for identifying earthquake support motions in instrumented structures

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

Minimizing total weighted tardiness on heterogeneous batch processors with incompatible job families

In this paper, we address a scheduling problem for minimizing total weighted tardiness. The background for the paper is derived from the automobile gear manufacturing process. We consider the bottleneck operation of heat treatment stage of gear manufacturing. Real-life scenarios like unequal release times, incompatible job families, nonidentical job sizes, heterogeneous batch processors, and allowance for job splitting have been considered. We have developed a mathematical model which takes into account dynamic starting conditions. The problem considered in this study is NP-hard in nature, and hence heuristic algorithms have been proposed to address it. For real-life large-size problems, the performance of the proposed heuristic algorithms is evaluated using the method of estimated optimal solution available in literature. Extensive computational analyses reveal that the proposed heuristic algorithms are capable of consistently obtaining near-optimal statistically estimated solutions in very reasonable computational time.