A Novel Operator-Splitting Technique for One-Dimensional Laminar Premixed Flames

This paper is concerned the calculation of flame structure of one-dimensional laminar premixed flames using the technique of operator-splitting. The technique utilizes an explicit method of solution with one step Euler for chemistry and a novel probabilistic scheme for diffusion. The relationship between diffusion phenomenon and Gauss-Markoff process is exploited to obtain an unconditionally stable explicit difference scheme for diffusion. The method has been applied to (a) a model problem, (b) hydrazine decomposition, (c) a hydrogen-oxygen system with 28 reactions with constant Dρ 2 approximation, and (d) a hydrogen-oxygen system (28 reactions) with trace diffusion approximation. Certain interesting aspects of behaviour of the solution with non-unity Lewis number are brought out in the case of hydrazine flame. The results of computation in the most complex case are shown to compare very favourably with those of Warnatz, both in terms of accuracy of results as well as computational time, thus showing that explicit methods can be effective in flame computations. Also computations using the Gear-Hindmarsh for chemistry and the present approach for diffusion have been carried out and comparison of the two methods is presented.

On the determination of energy eigenvalues and coupling strengths using duality

The Shifman-Vainshtein-Zakharov method of determining the eigenvalues and coupling strengths, from the operator product expansion, for the current correlation functions is studied in the nonrelativistic context, using the semiclassical expansion. The relationship between the low-lying eigenvalues, and the leading corrections to the imaginary-time Green function is elucidated by comparing systems which have almost identical spectra. In the case of an anharmonic oscillator it is found that with the procedure stated in the paper, that inclusion of more terms to the asymptotic expansion does not show any simple trend towards convergence to the exact values. Generalization to higher partial waves is given. In particular for the P-level of the oscillator, the procedure gives poorer results than for the S-level, although the ratio of the two comes out much better.

Note on the locally product and almost locally product structures

This paper is concerned with a study of some of the properties of locally product and almost locally product structures on a differentiable manifold X n of class C k . Every locally product space has certain almost locally product structures which transform the local tangent space to X n at an arbitrary point P in a set fashion: this is studied in Theorem (2.2). Theorem (2.3) considers the nature of transformations that exist between two co-ordinate systems at a point whenever an almost locally product structure has the same local representation in each of these co-ordinate systems. A necessary and sufficient condition for X n to be a locally product manifold is obtained in terms of the pseudo-group of co-ordinate transformations on X n and the subpseudo-groups [cf., Theoren (2.1)]. Section 3 is entirely devoted to the study of integrable almost locally product structures.

A Wavelet based Teager Energy Operator for Spike Detection in Microelectrode Array Recordings

Spike detection in neural recordings is the initial step in the creation of brain machine interfaces. The Teager energy operator (TEO) treats a spike as an increase in the `local' energy and detects this increase. The performance of TEO in detecting action potential spikes suffers due to its sensitivity to the frequency of spikes in the presence of noise which is present in microelectrode array (MEA) recordings. The multiresolution TEO (mTEO) method overcomes this shortcoming of the TEO by tuning the parameter k to an optimal value m so as to match to frequency of the spike. In this paper, we present an algorithm for the mTEO using the multiresolution structure of wavelets along with inbuilt lowpass filtering of the subband signals. The algorithm is efficient and can be implemented for real-time processing of neural signals for spike detection. The performance of the algorithm is tested on a simulated neural signal with 10 spike templates obtained from [14]. The background noise is modeled as a colored Gaussian random process. Using the noise standard deviation and autocorrelation functions obtained from recorded data, background noise was simulated by an autoregressive (AR(5)) filter. The simulations show a spike detection accuracy of 90%and above with less than 5% false positives at an SNR of 2.35 dB as compared to 80% accuracy and 10% false positives reported [6] on simulated neural signals.

Time Dependent Operator-split and Unsplit Schemes for One Dimensional Premixed Flames

This paper is concerned with a study of an operator split scheme and unsplit scheme for the computation of adiabatic freely propagating one-dimensional premixed flames. The study uses unsteady method for both split and unsplit schemes employing implicit chemistry and explicit diffusion, a combination which is stable and convergent. Solution scheme is not sensitive to the initial starting estimate and provides steady state even with straight line profiles (far from steady state) in small number of time steps. Two systems H2-Air and H2-NO (involving complex nitrogen chemistry) are considered in presentinvestigation. Careful comparison shows that the operator split approach is slightly superior than the unsplit when chemistry becomes complex. Comparison of computational times with those of existing steady and unsteady methods seems to suggest that the method employing implicit-explicit algorithm is very efficient and robust.

Squeezed states, metaplectic group, and operator möbius transformations

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically

Squeezed vacuum as an eigenstate of two-photon annihilation operator

We introduce the inverse annihilation and creation operators a-1 and a(dagger-1) by their actions on the number states. We show that the squeezed vacuum exp(1/2xia(dagger2)]\0] and squeezed first number state exp[1.2xia(dagger2)]\n = 1] are respectively the eigenstates of the operators (a(dagger-1)a) and (aa(dagger-1)) with the eigenvalue xi.

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

The extended Enskog operator for simple fluids with continuous potentials: single particle and collective properties

We generalized the Enskog theory originally developed for the hard-sphere fluid to fluids with continuous potentials, such as the Lennard–Jones. We derived the expression for the k and ω dependent transport coefficient matrix which enables us to calculate the transport coefficients for arbitrary length and time scales. Our results reduce to the conventional Chapman–Enskog expression in the low density limit and to the conventional k dependent Enskog theory in the hard-sphere limit. As examples, the self-diffusion of a single atom, the vibrational energy relaxation, and the activated barrier crossing dynamics problem are discussed.

Almost quarter-pinched Kähler metrics and Chern numbers

Given n is an element of Z(+) and epsilon > 0, we prove that there exists delta = delta(epsilon, n) > 0 such that the following holds: If (M(n),g) is a compact Kahler n-manifold whose sectional curvatures K satisfy -1 -delta <= K <= -1/4 and c(I)(M), c(J)(M) are any two Chern numbers of M, then |c(I)(M)/c(J)(M) - c(I)(0)/c(J)(0)| < epsilon, where c(I)(0), c(J)(0) are the corresponding characteristic numbers of a complex hyperbolic space form. It follows that the Mostow-Siu surfaces and the threefolds of Deraux do not admit Kahler metrics with pinching close to 1/4.

A Convex Optimization Framework for Almost Budget Balanced Allocation of a Divisible Good

We address the problem of allocating a single divisible good to a number of agents. The agents have concave valuation functions parameterized by a scalar type. The agents report only the type. The goal is to find allocatively efficient, strategy proof, nearly budget balanced mechanisms within the Groves class. Near budget balance is attained by returning as much of the received payments as rebates to agents. Two performance criteria are of interest: the maximum ratio of budget surplus to efficient surplus, and the expected budget surplus, within the class of linear rebate functions. The goal is to minimize them. Assuming that the valuation functions are known, we show that both problems reduce to convex optimization problems, where the convex constraint sets are characterized by a continuum of half-plane constraints parameterized by the vector of reported types. We then propose a randomized relaxation of these problems by sampling constraints. The relaxed problem is a linear programming problem (LP). We then identify the number of samples needed for ``near-feasibility'' of the relaxed constraint set. Under some conditions on the valuation function, we show that value of the approximate LP is close to the optimal value. Simulation results show significant improvements of our proposed method over the Vickrey-Clarke-Groves (VCG) mechanism without rebates. In the special case of indivisible goods, the mechanisms in this paper fall back to those proposed by Moulin, by Guo and Conitzer, and by Gujar and Narahari, without any need for randomization. Extension of the proposed mechanisms to situations when the valuation functions are not known to the central planner are also discussed. Note to Practitioners-Our results will be useful in all resource allocation problems that involve gathering of information privately held by strategic users, where the utilities are any concave function of the allocations, and where the resource planner is not interested in maximizing revenue, but in efficient sharing of the resource. Such situations arise quite often in fair sharing of internet resources, fair sharing of funds across departments within the same parent organization, auctioning of public goods, etc. We study methods to achieve near budget balance by first collecting payments according to the celebrated VCG mechanism, and then returning as much of the collected money as rebates. Our focus on linear rebate functions allows for easy implementation. The resulting convex optimization problem is solved via relaxation to a randomized linear programming problem, for which several efficient solvers exist. This relaxation is enabled by constraint sampling. Keeping practitioners in mind, we identify the number of samples that assures a desired level of ``near-feasibility'' with the desired confidence level. Our methodology will occasionally require subsidy from outside the system. We however demonstrate via simulation that, if the mechanism is repeated several times over independent instances, then past surplus can support the subsidy requirements. We also extend our results to situations where the strategic users' utility functions are not known to the allocating entity, a common situation in the context of internet users and other problems.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Dilations of Gamma-contractions by solving operator equations

For a contraction P and a bounded commutant S of P. we seek a solution X of the operator equation S - S*P = (1 - P* P)(1/2) X (1 - P* P)(1/2) where X is a bounded operator on (Ran) over bar (1 - P* P)(1/2) with numerical radius of X being not greater than 1. A pair of bounded operators (S, P) which has the domain Gamma = {(z(1) + z(2), z(2)): vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar <= 1} subset of C-2 as a spectral set, is called a P-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a Gamma-contraction (S, P). This allows us to construct an explicit Gamma-isometric dilation of a Gamma-contraction (S, P). We prove the other way too, i.e., for a commuting pair (S, P) with parallel to P parallel to <= 1 and the spectral radius of S being not greater than 2, the existence of a solution to the above equation implies that (S, P) is a Gamma-contraction. We show that for a pure F-contraction (S, P), there is a bounded operator C with numerical radius not greater than 1, such that S = C + C* P. Any Gamma-isometry can be written in this form where P now is an isometry commuting with C and C. Any Gamma-unitary is of this form as well with P and C being commuting unitaries. Examples of Gamma-contractions on reproducing kernel Hilbert spaces and their Gamma-isometric dilations are discussed. (C) 2012 Elsevier Inc. All rights reserved.