Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Impact of energy quantisation in single electron transistor island on hybrid complementary metal oxide semiconductor-single electron transistor integrated circuits

For the first time, the impact of energy quantisation in single electron transistor (SET) island on the performance of hybrid complementary metal oxide semiconductor (CMOS)-SET transistor circuits has been studied. It has been shown through simple analytical models that energy quantisation primarily increases the Coulomb Blockade area and Coulomb Blockade oscillation periodicity of the SET device and thus influences the performance of hybrid CMOS-SET circuits. A novel computer aided design (CAD) framework has been developed for hybrid CMOS-SET co-simulation, which uses Monte Carlo (MC) simulator for SET devices along with conventional SPICE for metal oxide semiconductor devices. Using this co-simulation framework, the effects of energy quantisation have been studied for some hybrid circuits, namely, SETMOS, multiband voltage filter and multiple valued logic circuits. Although energy quantisation immensely deteriorates the performance of the hybrid circuits, it has been shown that the performance degradation because of energy quantisation can be compensated by properly tuning the bias current of the current-biased SET devices within the hybrid CMOS-SET circuits. Although this study is primarily done by exhaustive MC simulation, effort has also been put to develop first-order compact model for SET that includes energy quantisation effects. Finally, it has been demonstrated that one can predict the SET behaviour under energy quantisation with reasonable accuracy by slightly modifying the existing SET compact models that are valid for metallic devices having continuous energy states.

Curved composite beams—optimum lay-up for buckling by ranking

Instability of laminated curved composite beams made of repeated sublaminate construction is studied using finite element method. In repeated sublaminate construction, a full laminate is obtained by repeating a basic sublaminate which has a smaller number of plies. This paper deals with the determination of optimum lay-up for buckling by ranking of such composite curved beams (which may be solid or sandwich). For this purpose, use is made of a two-noded, 16 degress of freedom curved composite beam finite element. The displacements u, v, w of the element reference axis are expressed in terms of one-dimensional first-order Hermite interpolation polynomials, and line member assumptions are invoked in formulation of the elastic stiffness matrix and geometric stiffness matrix. The nonlinear expressions for the strains, occurring in beams subjected to axial, flexural and torsional loads, are incorporated in a general instability analysis. The computer program developed has been used, after extensive checking for correctness, to obtain optimum orientation scheme of the plies in the sublaminate so as to achieve maximum buckling load for typical curved solid/sandwich composite beams.

Infinite dimensional slow modulations in a well known delayed model for cutting tool vibrations

We apply the method of multiple scales (MMS) to a well-known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the timescale of typical cutting tool oscillations. The MMS up to second order, recently developed for such systems, is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than the first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy in that plotted solutions of moderate amplitudes are visually near-indistinguishable. The advantages of the present analysis are that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space; lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS; the strong sensitivity of the slow modulation dynamics to small changes in parameter values, peculiar to such systems with large delays, is seen clearly; and though certain parameters are treated as small (or, reciprocally, large), the analysis is not restricted to infinitesimal distances from the Hopf bifurcation.

Metal-Insulator Transition in the Hubbard Model on a Triangular Lattice

We discuss the results of an extensive mean-field investigation of the half-filled Hubbard model on a triangular lattice at zero temperature. At intermediate U we find a first-order metal-insulator transition from an incommensurate spiral magnetic metal to a semiconducting state with a commensurate linear spin density wave ordering stabilized by the competition between the kinetic energy and the frustrated nature of the magnetic interaction. At large U the ground state is that of a classical triangular antiferromagnet within our approximation. In the incommensurate spiral metallic phase the Fermi surface has parts in which the wave function renormalization Z is extremely small. The evolution of the Fermi surface and the broadening of the quasi-particle band along with the variation of the plasma frequency and a charge stiffness constant with U/t are discussed.

A real transformation for modal analysis of flexible damped spacecraft

Modal approach is widely used for the analysis of dynamics of flexible structures. However, space analysts yet lack an intimate modal analysis of current spacecraft which are rich with flexibility and possess both structural and discrete damping. Mathematical modeling of such spacecraft incapacitates the existing real transformation procedure, for it cannot include discrete damping, demands uncomputable inversion of a modal matrix inaccessible due to its overwhelming size and does not permit truncation. On the other hand, complex transformation techniques entail more computational time and cannot handle structural damping. This paper presents a real transformation strategy which averts inversion of the associated real transformation matrix, allows truncation and accommodates both forms of damping simultaneously. This is accomplished by establishing a key relation between the real transformation matrix and its adjoint. The relation permits truncation of the matrices and leads to uncoupled pairs of coupled first order equations which contain a number of adjoint eigenvectors. Finally these pairs are solved to obtain a literal modal response of forced gyroscopic damped flexibile systems at arbitrary initial conditions.

Models for spin-state transitions in solids

The model for spin-state transitions described by Bari and Sivardiere (1972) is static and can be solved exactly even when the dynamics of the lattice are included; the dynamic model does not, however, show any phase transition. A coupling between the octahedra, on the other hand, leads to a phase transition in the dynamical two-sublattice displacement model. A coupling of the spin states to the cube of the sublattice displacement leads to a first-order phase transition. The most reasonable model appears to be a two-phonon model in which an ion-cage mode mixes the spin states, while a breathing mode couples to the spin states without mixing. This model explains the non-zero population of high-spin states at low temperatures, temperature-dependent variations in the inverse susceptibility and the spin-state population ratio, as well as the structural phase transitions accompanying spin-state transitions found in some systems.

Kinetic studies on the interaction of gold(III) with nucleic acids. I. Native DNA-Au(III) system-spectrophotometric studies

Kinetics of the interaction of Au(III) with native calf thymus DNA has been studied spectrophotometrically to determine the kinetic parameters and to examine their dependency on the concentrations of DNA and Au(III), temperature, ionic strength and pH. The reaction is of the first order with respect to both the nucleotide unit of DNA and Au(III) in the stoichiometry of 2∶1 respectively. The rate constants vary with the initial ratio of DNA to Au(III) and is attributed to the effect of free chloride ions and the existence of a number of reaction sites with slight difference in the rate constants. The activation energies of this interaction have been found to be 14–16 kcal/mol. From the effect of ionic strength the reaction is found to occur between a positive and a negative ion in the rate-limiting step. The logarithm of rate constants are the linear function of pH and the slopes are dependent on ther-values. A plausible mechanism has been proposed which involves a primary dissociation of the major existing species (AuCl2(OH)2)−, to give (AuCl2)+ which then reacts with a site in the nucleotide unit of DNA in the rate-liminting step followed by a rapid binding to another site on the complementary strand of the DNA double helix. There exist a number of binding sites with slight difference in reactivity.

Development of a structured program for conversion to prenex normal form

The method of structured programming or program development using a top-down, stepwise refinement technique provides a systematic approach for the development of programs of considerable complexity. The aim of this paper is to present the philosophy of structured programming through a case study of a nonnumeric programming task. The problem of converting a well-formed formula in first-order logic into prenex normal form is considered. The program has been coded in the programming language PASCAL and implemented on a DEC-10 system. The program has about 500 lines of code and comprises 11 procedures.

Structure, dielectric, and magnetic properties of Sr2TiMnO6 ceramics

Sr2TiMnO6, a double perovskite associated with high degree of B-site cation disorder was investigated in detail for its structural, magnetic, and dielectric properties. Though x-ray powder diffraction analysis confirms its cubic structure, first order Raman scattering and infrared reflectivity spectra indicate a breaking of the local cubic symmetry. The magnetization study reveals an anomaly at 14 K owing to a ferrimagnetic/canted antiferromagneticlike ordering arising from local Mn-O-Mn clusters. Saturated M-H hysteresis loops obtained at 5 K also reflect the weak ferromagnetic exchange interactions present in the system and an approximate estimation of Mn3+/Mn4+ was done using the magnetization data for the samples sintered at different temperatures. The conductivity and dielectric behavior of this system has been investigated in a broad temperature range of 10 to 300 K. Intrinsic permittivity was obtained only below 100 K whereas giant permittivity due to conductivity and Maxwell-Wagner polarization was observed at higher temperatures. X-ray photoemission studies further confirmed the presence of mixed oxidation states of Mn and the valence band spectra analysis was carried out in detail. (C) 2010 American Institute of Physics. doi: 10.1063/1.3500369]

Development of a New Finite Element for the Analysis of Sandwich Beams with Soft Core

A new super convergent sandwich beam finite element formulation is presented in this article. This element is a two-nodded, six degrees of freedom (dof) per node (3 dof u(0), w, phi for top and bottom face sheets each), which assumes that all the axial and flexural loads are taken by face sheets, while the core takes only the shear loads. The beam element is formulated based on first-order shear deformation theory for the face sheets and the core displacements are assumed to vary linearly across the thickness. A number of numerical experiments involving static, free vibration, and wave propagation analysis examples are solved with an aim to show the super convergent property of the formulated element. The examples presented in this article consider both metallic and composite face sheets. The formulated element is verified in most cases with the results available in the published literature.

Temperature dependent free energy surface of polymer folding from equilibrium and quench studies

Langevin dynamics simulation studies have been employed to calculate the temperature dependent free energy surface and folding characteristics of a 500 monomer long linear alkane (polyethylene) chain with a realistic interaction potential. Both equilibrium and temperature quench simulation studies have been carried out. Using the shape anisotropy parameter (S) of the folded molecule as the order parameter, we find a weakly first order phase transition between the high-temperature molten globule and low-temperature rodlike crystalline states separated by a small barrier of the order of k(B)T. Near the melting temperature (580 K), we observe an intriguing intermittent fluctuation with pronounced ``1/f noise characteristics'' between these two states with large difference in shape and structure. We have also studied the possibilities of different pathways of folding to states much below the melting point. At 300 K starting from the all-trans linear configuration, the chain folds stepwise into a very regular fourfold crystallite with very high shape anisotropy. Whereas, when quenched from a high temperature (900 K) random coil regime, we identify a two step transition from the random coiled state to a molten globulelike state and, further, to a anisotropic rodlike state. The trajectory reveals an interesting coupling between the two order parameters, namely, radius of gyration (R-g) and the shape anisotropy parameter (S). The rodlike final state of the quench trajectory is characterized by lower shape anisotropy parameter and significantly larger number of gauche defects as compared to the final state obtained through equilibrium simulation starting from all-trans linear chain. The quench study shows indication of a nucleationlike pathway from the molten globule to the rodlike state involving an underlying rugged energy landscape. (C) 2010 American Institute of Physics. doi:10.1063/1.3509398]

A new approach to the kinetics of size reduction in ball milling

The rate of breakage of feed in ball milling is usually represented in the form of a first-order rate equation. The equation was developed by treating a simple batch test mill as a well mixed reactor. Several case of deviation from the rule have been reported in the literature. This is attributed to the fact that accumulated fines interfere with the feed material and breaking events are masked by these fines. In the present paper, a new rate equation is proposed which takes into account the retarding effect of fines during milling. For this purpose the analogy of diffusion of ions through permeable membranes is adopted, with suitable modifications. The validity of the model is cross checked with the data obtained in batch grinding of ?850/+600 ?m size quartz. The proposed equation enables calculation of the rate of breakage of the feed at any instant of time.

Effect of uncertainty on helicopter performance predictions

The effect of uncertainties on performance predictions of a helicopter is studied in this article. The aeroelastic parameters such as the air density, blade profile drag coefficient, main rotor angular velocity, main rotor radius, and blade chord are considered as uncertain variables. The propagation of these uncertainties in the performance parameters such as thrust coefficient, figure of merit, induced velocity, and power required are studied using Monte Carlo simulation and the first-order reliability method. The Rankine-Froude momentum theory is used for performance prediction in hover, axial climb, and forward flight. The propagation of uncertainty causes large deviations from the baseline deterministic predictions, which undoubtedly affect both the achievable performance and the safety of the helicopter. The numerical results in this article provide useful bounds on helicopter power requirements.

Dye sensitized visible light degradation of phenolic compounds

The present research work reports the eosin Y (EY) and fluorescein (FL) sensitized visible light degradation of phenol, 4-chlorophenol (CP), 2,4-dichlorophenol (DCP) and 2,4,6-trichlorophenol (TCP) using combustion synthesized nano-TiO2 (CS TiO2). The rate of degradation of the phenolic compounds was higher in the presence of EY/CS TiO2 compared to FL/CS TiO2 system. A detailed mechanism of sensitized degradation was proposed and a mechanistic model for the rate of degradation of the phenolic compound was derived using the pyramidal network reduction technique. It was found that at low initial dye concentrations, the rate of degradation of the phenolic compound is first order in the concentration of the dye, while at high initial dye concentrations, the rate is first order in the concentration of the phenolic compound. The order of degradation of the different phenolic compounds follows: CP > TCP > DCP > phenol. The different phenolic and dye intermediates that were formed during the degradation were identified by liquid chromatography-mass spectrometry (LC-MS) and the most probable pathway of degradation is proposed. (C) 2010 Elsevier B.V. All rights reserved.