Filtered density function for large eddy simulation of turbulent reacting flows

A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Itô-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). These comparative assessments are conducted by implementations of all three schemes (FDF, DNS and LES-FD) in a temporally developing mixing layer and a spatially developing planar jet under both non-reacting and reacting conditions. In non-reacting flows, the Monte Carlo solution of the FDF yields results similar to those via LES-FD. The advantage of the FDF is demonstrated by its use in reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. The FDF results show a much closer agreement with filtered DNS results. © 1998 American Institute of Physics.

Classical integrability in the BTZ black hole

Using the fact the BTZ black hole is a quotient of AdS(3) we show that classical string propagation in the BTZ background is integrable. We construct the flat connection and its monodromy matrix which generates the non-local charges. From examining the general behaviour of the eigen values of the monodromy matrix we determine the set of integral equations which constrain them. These equations imply that each classical solution is characterized by a density function in the complex plane. For classical solutions which correspond to geodesics and winding strings we solve for the eigen values of the monodromy matrix explicitly and show that geodesics correspond to zero density in the complex plane. We solve the integral equations for BMN and magnon like solutions and obtain their dispersion relation. We show that the set of integral equations which constrain the eigen values of the monodromy matrix can be identified with the continuum limit of the Bethe equations of a twisted SL(2, R) spin chain at one loop. The Landau-Lifshitz equations from the spin chain can also be identified with the sigma model equations of motion.

Fault-Diagnostic System using Support Vector Machines for Power Transmission Systems

This paper presents an approach for identifying the faulted line section and fault location on transmission systems using support vector machines (SVMs) for diagnosis/post-fault analysis purpose. Power system disturbances are often caused by faults on transmission lines. When fault occurs on a transmission system, the protective relay detects the fault and initiates the tripping operation, which isolates the affected part from the rest of the power system. Based on the fault section identified, rapid and corrective restoration procedures can thus be taken to minimize the power interruption and limit the impact of outage on the system. The approach is particularly important for post-fault diagnosis of any mal-operation of relays following a disturbance in the neighboring line connected to the same substation. This may help in improving the fault monitoring/diagnosis process, thus assuring secure operation of the power systems. In this paper we compare SVMs with radial basis function neural networks (RBFNN) in data sets corresponding to different faults on a transmission system. Classification and regression accuracy is reported for both strategies. Studies on a practical 24-Bus equivalent EHV transmission system of the Indian Southern region is presented for indicating the improved generalization with the large margin classifiers in enhancing the efficacy of the chosen model.

Fuel Cell Efficiency Redefined; Carnot Limit Reassessed

There are deficiencies in current definition of thermodynamic efficiency of fuel cells (ηcth = ΔG/ΔH); efficiency greater than unity is obtained when AS for the cell reaction is positive, and negative efficiency is obtained for endothermic reactions. The origin of the flow is identified. A new definition of thennodynamic efficiency is proposed that overcomes these limitations. Consequences of the new definition are examined. Against the conventional view that fuel cells are not Carnot limited, several recent articles have argued that the second law of thermodynamics restricts fuel cell energy conversion in the same way as heat engines. This controversy is critically examined. A resolution is achieved in part from an understanding of the contextual assumptions in the different approaches and in part from identifying some conceptual limitations.

Chimeras of Escherichia coli and Mycobacterium tuberculosis Single-Stranded DNA Binding Proteins: Characterization and Function in Escherichia coli

Single stranded DNA binding proteins (SSBs) are vital for the survival of organisms. Studies on SSBs from the prototype, Escherichia coli (EcoSSB) and, an important human pathogen, Mycobacterium tuberculosis (MtuSSB) had shown that despite significant variations in their quaternary structures, the DNA binding and oligomerization properties of the two are similar. Here, we used the X-ray crystal structure data of the two SSBs to design a series of chimeric proteins (m beta 1, m beta 1'beta 2, m beta 1-beta 5, m beta 1-beta 6 and m beta 4-beta 5) by transplanting beta 1, beta 1'beta 2, beta 1-beta 5, beta 1-beta 6 and beta 4-beta 5 regions, respectively of the N-terminal (DNA binding) domain of MtuSSB for the corresponding sequences in EcoSSB. In addition, m beta 1'beta 2(ESWR) SSB was generated by mutating the MtuSSB specific `PRIY' sequence in the beta 2 strand of m beta 1'beta 2 SSB to EcoSSB specific `ESWR' sequence. Biochemical characterization revealed that except for m beta 1 SSB, all chimeras and a control construct lacking the C-terminal domain (Delta C SSB) bound DNA in modes corresponding to limited and unlimited modes of binding. However, the DNA on MtuSSB may follow a different path than the EcoSSB. Structural probing by protease digestion revealed that unlike other SSBs used, m beta 1 SSB was also hypersensitive to chymotrypsin treatment. Further, to check for their biological activities, we developed a sensitive assay, and observed that m beta 1-beta 6, MtuSSB, m beta 1'beta 2 and m beta 1-beta 5 SSBs complemented E. coli Delta ssb in a dose dependent manner. Complementation by the m beta 1-beta 5 SSB was poor. In contrast, m beta 1'beta 2(ESWR) SSB complemented E. coli as well as EcoSSB. The inefficiently functioning SSBs resulted in an elongated cell/filamentation phenotype of E. coli. Taken together, our observations suggest that specific interactions within the DNA binding domain of the homotetrameric SSBs are crucial for their biological function.

Distributed Function Computation over Fields and Rings via Linear Compression of Sources

The setting considered in this paper is one of distributed function computation. More specifically, there is a collection of N sources possessing correlated information and a destination that would like to acquire a specific linear combination of the N sources. We address both the case when the common alphabet of the sources is a finite field and the case when it is a finite, commutative principal ideal ring with identity. The goal is to minimize the total amount of information needed to be transmitted by the N sources while enabling reliable recovery at the destination of the linear combination sought. One means of achieving this goal is for each of the sources to compress all the information it possesses and transmit this to the receiver. The Slepian-Wolf theorem of information theory governs the minimum rate at which each source must transmit while enabling all data to be reliably recovered at the receiver. However, recovering all the data at the destination is often wasteful of resources since the destination is only interested in computing a specific linear combination. An alternative explored here is one in which each source is compressed using a common linear mapping and then transmitted to the destination which then proceeds to use linearity to directly recover the needed linear combination. The article is part review and presents in part, new results. The portion of the paper that deals with finite fields is previously known material, while that dealing with rings is mostly new.Attempting to find the best linear map that will enable function computation forces us to consider the linear compression of source. While in the finite field case, it is known that a source can be linearly compressed down to its entropy, it turns out that the same does not hold in the case of rings. An explanation for this curious interplay between algebra and information theory is also provided in this paper.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation eta and eta + d eta, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice.We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation η and η + dη, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary

Abstract Characteristic Function

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S)(z, w) = ( 1 - z(w)over bar)- 1 for |z|, |w| < 1, by means of (1/k(S))( T, T *) = 0, we consider an arbitrary open connected domain Omega in C(n), a kernel k on Omega so that 1/k is a polynomial and a tuple T = (T(1), T(2), ... , T(n)) of commuting bounded operators on a complex separable Hilbert spaceHsuch that (1/k)( T, T *) >= 0. Under some standard assumptions on k, it turns out that whether a characteristic function can be associated with T or not depends not only on T, but also on the kernel k. We give a necessary and sufficient condition. When this condition is satisfied, a functional model can be constructed. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples T.

Structure-function relationship in serine hydroxymethyltransferase

Serine hydroxymethyltransferase (SHMT), a pyridoxal-5V-phosphate (PLP)-dependent enzyme catalyzes thetetrahydrofolate (H4-folate)- dependent retro-aldol cleavage of serine to form 5,10-methylene H4-folate and glycine. The structure–function relationship of SHMT wasstudied in our laboratory initially by mutation of residues that are conserved in all SHMTs and later by structure-based mutagenesis of residues located in the active site. The analysis of mutants showed that K71, Y72, R80, D89, W110, S202, C203, H304, H306 and H356 residues are involved in maintenance of the oligomeric structure. The mutation of D227, a residue involved in charge relay system, led to the formation of inactive dimers, indicating that this residue has a role in maintaining the tetrameric structure and catalysis. E74, a residue appropriately positioned in the structure of the enzyme to carry out proton abstraction, was shown by characterization of E74Q and E74K mutants to be involved in conversion of the enzyme from an ‘open’ to ‘closed’ conformation rather than proton abstraction from the hydroxylgroup of serine. K256, the residue involved in the formation of Schiffs base with PLP, also plays a crucial role in the maintenance of the tetrameric structure. Mutation of R262 residue established the importance of distal interactions in facilitating catalysis and Y82 is not involved in the formaldehyde transfer via the postulated hemiacetal intermediate but plays a role in stabilizing the quinonoid intermediate.The mutational analysis of scSHMT along with the structure of recombinant Bacillus stearothermophilus SHMT and its substrate(s)complexes was used to provide evidence for a direct transfer mechanism rather than retro-aldol cleavage for the reaction catalyzed by SHMT.

From anomalies in neat liquid to structure, dynamics and function in the biological world

Water brings its remarkable thermodynamic and dynamic anomalies in the pure liquid state to biological world where water molecules face a multitude of additional interactions that frustrate its hydrogen bond network. Yet the water molecules participate and control enormous number of biological processes in manners which are yet to be understood at a molecular level. We discuss thermodynamics, structure, dynamics and properties of water around proteins and DNA, along with those in reverse micelles. We discuss the roles of water in enzyme kinetics, in drug-DNA intercalation and in kinetic-proof reading ( the theory of lack of errors in biosynthesis). We also discuss how water may play an important role in the natural selection of biomolecules. (C) 2011 Elsevier B. V. All rights reserved.