An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

Asymtotic solution of the Frieman and Book equation for the pair-correlation function

Using Thomé's procedure, the asymptotic solutions of the Frieman and Book equation for the two-particle correlation in a plasma have been obtained in a complete form. The solution is interpreted in terms of the Lorentz distance. The exact expressions for the internal energy and pressure are evaluated and they are found to be a generalization of the result obtained earlier by others.

An online-implementable differential evolution tuned all-aspect guidance law

This paper proposes a differential evolution based method of improving the performance of conventional guidance laws at high heading errors, without resorting to techniques from optimal control theory, which are complicated and suffer from several limitations. The basic guidance law is augmented with a term that is a polynomial function of the heading error. The values of the coefficients of the polynomial are found by applying the differential evolution algorithm. The results are compared with the basic guidance law, and the all-aspect proportional navigation laws in the literature. A scheme for online implementation of the proposed law for application in practice is also given. (c) 2010 Elsevier Ltd. All rights reserved.

In vivo and in vitro studies on the differential role of luteinizing hormone and follicle-stimulating hormone in regulating follicular function in the bonnet monkey (Macaca radiata) using specific gonadotropin antibodies

Although a distinct need for FSH in the regulation of follicular maturation in the primate is well recognized, it is not clear how FSH controls the functionality of different cellular compartments of the follicle. It is also not evident whether there is a requirement for LH in follicular maturation in the primate. In the first part of the present study, female bonnet monkeys were administered a well-characterized ovine (o) LH antiserum to neutralize endogenous monkey LH for different periods during the follicular phase, and the effect on the overall follicular maturation process was assessed by analyzing serum estrogen (E) and progesterone (P) profiles. Neither continuous LH deprivation from Day 8 of the cycle nor deprivation of LH on any one day between Days 6 and 10 had a significant effect on serum E and P profiles and the follicular maturation process. The period for which the antiserum was effective was dependent upon the dose injected; 1 ml of the antiserum given on Day 8 blocked ovulation but not follicular maturation. To assess the effect of deprivation of LH/FSH at the cellular level, animals were deprived in vivo of LH (on Days 8 and 9 of the cycle) or of FSH (on Day 6 of the cycle) by injection of highly characterized hCG and ovine (o) FSH antisera, respectively; the in vitro responsiveness of granulosa and thecal cells isolated on Day 10 from these animals was then determined.(ABSTRACT TRUNCATED AT 250 WORDS)

Conjectures about phase turbulence in the complex Ginzburg-Landau equation

In the complex Ginzburg-Landau equation, we consider possible ''phase turbulent'' regimes, where asymptotic correlations are controlled by phase fluctuations rather than by topological defects. Conjecturing that the decay of such correlations is governed by the Kardar-Parisi-Zhang (KPZ) model of growing interfaces, we derive the following results: (1) A scaling ansatz implies that equal-time spatial correlations in 1d, 2d, and 3d decay like e(-Ax2 zeta), where A is a nonuniversal constant, and zeta=1/2 in 1d. (2) Temporal correlations decay as exp(-t(2 beta)h(t/L(z))), with the scaling law <(beta)over bar> = <(zeta)over bar>/z, where z = 3/2, 1.58..., and 1.66..., for d = 1,2, and 3 respectively. The scaling function h(y) approaches a constant as y --> 0, and behaves like y(2(beta-<(beta)over bar>)), for large y. If in 3d the associated KPZ model turns out to be in its weak-coupling (''smooth'') phase, then, instead of the above behavior, the CGLE exhibits rotating long-range order whose connected correlations decay like 1/x in space or 1/t(1/2) in time. (3) For system sizes, L, and times t respectively less than a crossover length, L(c), and time, t(c), correlations are governed by the free-field or Edwards-Wilkinson (EW) equation, rather than the KPZ model. In 1d, we find that L(c) is large: L(c) similar to 35,000; for L < L(c) we show numerical evidence for stretched exponential decay of temporal correlations with an exponent consistent with the EW value beta(EW)= 1/4.

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.

Insights into differential modulation of receptor function by hinge region using novel agonistic lutropin receptor and inverse agonistic thyrotropin receptor antibodies

We report two antibodies, scFv 13B1 and MAb PD1.37, against the hinge regions of LHR and TSHR, respectively, which have similar epitopes but different effects on receptor function. While neither of them affected hormone binding, with marginal effects on hormone response, scFv 13B1 stimulated LHR in a dose-dependent manner, whereas MAb PD1.37 acted as an inverse agonist of TSHR. Moreover, PD1.37 could decrease the basal activity of hinge region CAMs, but had varied effects on those present in ECLs, whereas 13B1 was refractory to any CAMs in LHR. Using truncation mutants and peptide phage display, we compared the differential roles of the hinge region cysteine box-2/3 as well as the exoloops in the activation of these two homologus receptors. (C) 2012 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Differential evolution based 3-D guidance law for a realistic interceptor model

This paper presents a novel, soft computing based solution to a complex optimal control or dynamic optimization problem that requires the solution to be available in real-time. The complexities in this problem of optimal guidance of interceptors launched with high initial heading errors include the more involved physics of a three dimensional missile-target engagement, and those posed by the assumption of a realistic dynamic model such as time-varying missile speed, thrust, drag and mass, besides gravity, and upper bound on the lateral acceleration. The classic, pure proportional navigation law is augmented with a polynomial function of the heading error, and the values of the coefficients of the polynomial are determined using differential evolution (DE). The performance of the proposed DE enhanced guidance law is compared against the existing conventional laws in the literature, on the criteria of time and energy optimality, peak lateral acceleration demanded, terminal speed and robustness to unanticipated target maneuvers, to illustrate the superiority of the proposed law. (C) 2013 Elsevier B. V. All rights reserved.

Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time-dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier-Stokes equations and the energy equation governing the flow and the heat transfer admit a self-similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses dong the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Genome-Wide Gene Expression Analysis Reveals a Dynamic Interplay between Luteotropic and Luteolytic Factors in the Regulation of Corpus Luteum Function in the Bonnet Monkey (Macaca radiata)

Although LH is essential for survival and function of the corpus luteum (CL) in higher primates, luteolysis occurs during nonfertile cycles without a discernible decrease in circulating LH levels. Using genome-wide expression analysis, several experiments were performed to examine the processes of luteolysis and rescue of luteal function in monkeys. Induced luteolysis with GnRH receptor antagonist (Cetrorelix) resulted in differential regulation of 3949 genes, whereas replacement with exogenous LH (Cetrorelix plus LH) led to regulation of 4434 genes (1563 down-regulation and 2871 up-regulation). A model system for prostaglandin (PG) F-2 alpha-induced luteolysis in the monkey was standardized and demonstrated that PGF(2 alpha) regulated expression of 2290 genes in the CL. Analysis of the LH-regulated luteal transcriptome revealed that 120 genes were regulated in an antagonistic fashion by PGF(2 alpha). Based on the microarray data, 25 genes were selected for validation by real-time RT-PCR analysis, and expression of these genes was also examined in the CL throughout the luteal phase and from monkeys treated with human chorionic gonadotropin (hCG) to mimic early pregnancy. The results indicated changes in expression of genes favorable to PGF(2 alpha) action during the late to very late luteal phase, and expressions of many of these genes were regulated in an opposite manner by exogenous hCG treatment. Collectively, the findings suggest that curtailment of expression of downstream LH-target genes possibly through PGF(2 alpha) action on the CL is among the mechanisms underlying cross talk between the luteotropic and luteolytic signaling pathways that result in the cessation of luteal function, but hCG is likely to abrogate the PGF(2 alpha)-responsive gene expression changes resulting in luteal rescue crucial for the maintenance of early pregnancy. (Endocrinology 150: 1473-1484, 2009)

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Low-intensity differential photocapacitance of MOS structures

Some new observations on the phenomenon of photocapacitane on n-type silicon MOS structures under low intensities of illumination are reported. The difference between the illuminated and dark C---characteristics is automatically followed as a function of the applied bias thereby obtaining the differential photocapacitance and the resulting characteristics has been termed as the Low Intensity Differential Photocapacitance (LIDP). For an MOS capacitor, the LIDP characteristics is seen to go through a well defined maximum. The phenomenon has been investigated under different ambient conditions like light intensity, temperature, dependance of the frequency of the light etc. and it has been found that the phenomenon is due to a band excband excitation. In this connection, a novel sensitive technique for the measurement of the capacitance based upon following the frequency changes of a tank circuit is also described in some detail. It is also shown that the phenomenon can be understood by a simple theoretical model.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.