Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Thickness-dependent fcc-hcp phase transformation in polycrystalline titanium thin films

Polycrystalline Ti thin films are shown to gradually transform from face-centered cubic (fcc) to hexagonal close-packed structure (hcp) with increasing film thickness. Diffraction stress analysis revealed that the fcc phase is formed in a highly compressive hcp matrix (>= 2 GPa), the magnitude of which decreases with increasing film thickness. A correlation between stress and crystallographic texture vis-a-vis the fcc-hcp phase transformation has been established. The total free energy change of the system upon phase transformation calculated using the experimental results shows that the fcc-hcp transformation is theoretically possible in the investigated film thickness regime (144-720 nm) and the hcp structure is stable for films thicker than 720 nm, whereas the fcc structure can be stabilized in Ti films much thinner than 144 nm. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Carbon-13 and proton relaxation study of backbone dynamics of poly(vinyl acetate) in solution

The dynamics of poly(vinyl acetate) in toluene solution has been examined by C-13 and proton relaxation. C-13 spin-lattice relaxation time and nuclear Overhauser enhancement measurements were carried out as a function of temperature at 50.3 and 100.6 MHz. The spin-lattice relaxation times for backbone protons were measured at different temperatures at 200 MHz. The relaxation data have been analyzed using the Hall-Weber-Helfand (HWH) model, which describes backbone dynamics in terms of conformational transitions and the Dejean-Laupretre-Monnerie (DLM) model, which includes bond librations in addition to conformational transitions. The parameters obtained from the analysis of C-13 relaxation data were utilized to predict the proton relaxation data. The DLM model was found to be more successful in reproducing the experimental results. To study the influence of libration further, proton relaxation data for poly(vinyl acetate) over a wider range of temperature reported in the literature were analyzed by these two models. The DLM model could reproduce the experimental data at all temperatures whereas the HWH model was found to be successful only in accounting for the experimental data at high temperatures. The results demonstrate the importance of including the librational mode in the description of the backbone dynamics in polymers.

Carbon-13 relaxation study of chain segmental motion and side-chain internal rotations of poly(isobutyl methacrylate) in solution

The dynamics of poly(isobutyl methacrylate) in toluene solution has been examined by C-13 spin-lattice relaxation time and NOE measurements as a function of temperature. The experiments were performed at 50.3 and 100.6 MHz. The backbone carbon relaxation data have been analyzed using the Dejean-Laupretre-Monnerie (DLM) model, which describes the dynamical processes in the backbone in terms of conformational transitions and bond librations. The relaxation data of the side chain nuclei have been analyzed by assuming different motional models, namely, unrestricted rotational diffusion, three site jumps, and restricted rotational diffusion. The different models have been compared for their ability to reproduce the experimental spin-lattice relaxation times and also to predict the behavior of NOE as a function of temperature. Conformational energy calculations have been carried out on a model compound by using the semiempirical quantum chemical method, AM1, and the results confirm the validity of the motional models used to describe the side-chain motion.

Concentration-dependent NMR and conductivity studies of (PEG)(x)NH4ClO4

Films of (PEG)(x)NH4ClO4 (x = 5 to 1000) were prepared and characterized. The physical properties are observed to be a sensitive function of concentration. Hygroscopicity increases as salt content increases. Conductivity peaks (sigma = 2.7 x 10(-6) S/cm) at x = 46. The H-1 NMR line width has a minimum at x = 46, while that of Cl-35 monotonically increases with salt concentration, indicating that the complex is essentially a protonic conductor.

Effect of thermal annealing on the dielectric properties of KTiOPO4 single crystals

Dielectric properties of potassium titanyl phosphate have been investigated as a function of thickness and frequency, as well as annealing treatment under various atmospheres. The low frequency dielectric constant of KTP crystals is shown to depend upon the sample thickness, and this feature is attributed to the existence of surface layers. The frequency-dependent dielectric response of KTP exhibits a non-Debye type relaxation, with a distribution of relaxation times. The dielectric behavior of KTP samples annealed in various atmospheres shows that the low frequency dielectric constant is influenced by the contribution from the space charge layers. Prolonged annealing of the samples leads to a surface degradation, resulting in the formation of a surface layer of lower dielectric constant. This surface degradation is least when annealed in the presence of dry oxygen. From the analysis of the dielectric data using complex electric modulus, alpha(m) has been evaluated for the virgin and annealed samples. (C) 1996 American Institute of Physics.

Electrical transport studies in alkali borovanadate glasses

The ac conductivity and dielectric behaviors of sodium borovanadate glasses have been studied over wide ranges of composition and frequency. The de activation energies calculated from the complex impedance plots decrease linearly with the Na2O concentration, indicating that ionic conductivity dominates in these glasses. The possible origin of low-temperature departures of conductivity curves (from linearity) of vanadium-rich glasses in log sigma versus 1/T plots is discussed. The ac conductivities have been fitted to the Almond-West type power law expression with use of a single value of s. It is found that in most of the glasses s exhibits a temperature-dependent minimum. The dielectric data are converted into moduli (M*) and are analyzed using the Kohlrausch-William-Watts stretched exponential function, The activation barriers, W, calculated from the temperature-dependent dielectric loss peaks compare well with the activation barriers calculated from the de conductivity plots. The stretching exponent beta is found to be temperature independent and is not likely to be related as in the equation beta = 1 - s, An attempt is made to elucidate the origin of the stretching phenomena. It appears that either a model of the increased contribution of polarization energy (caused by the increased modifier concentration) and hence the increased monopole-induced dipole interactions or a model based on increased intercationic interactions can explain the slowing down of the primitive relaxation in ionically conducting glasses.

Ethanol-dependent oxygen consumption and acetaldehyde formation during vanadyl oxidation by H2O2

Sequential addition of vanadyl sulfate to a phosphate-buffered solution of H2O2 released oxygen only after the second batch of vanadyl. Ethanol added to such reaction mixtures progressively decreased oxygen release and increased oxygen consumption during oxidation of vanadyl by H2O2. Inclusion of ethanol after any of the three batches of vanadyl resulted in varying amounts of oxygen consumption, a property also shared by other alcohols (methanol, propanol and octanol). On increasing the concentration of ethanol, vanadyl sulfate or H2O2, both oxygen consumption and acetaldehyde formation increased progressively. Formation of acetaldehyde decreased with increase in the ratio of vanadyl:H2O2 above 2:1 and was undetectable with ethanol at 0.1 mM. The reaction mixture which was acidic in the absence of phosphate buffer (pH 7.0), released oxygen immediately after the first addition of vanadyl and also in presence of ethanol soon after initial rapid consumption of oxygen, with no accompanying acetaldehyde formation. The results underscore the importance of some vanadium complexes formed during vanadyl oxidation in the accompanying oxygen-transfer reactions.

Temperature-dependent photoluminescence of GaN grown on beta-Si3N4/Si (111) by plasma-assisted MBE

Photoluminescence (PL) of high quality GaN epitaxial layer grown on beta-Si3N4/Si (1 1 1) substrate using nitridation-annealing-nitridation method by plasma-assisted molecular beam epitaxy (PA-MBE) was investigated in the range of 5-300 K. Crystallinity of GaN epilayers was evaluated by high resolution X-ray diffraction (HRXRD) and surface morphology by Atomic Force Microscopy (AFM) and high resolution scanning electron microscopy (HRSEM). The temperature-dependent photoluminescence spectra showed an anomalous behaviour with an `S-like' shape of free exciton (FX) emission peaks. Distant shallow donor-acceptor pair (DAP) line peak at approximately 3.285 eV was also observed at 5 K, followed by LO replica sidebands separated by 91 meV. The activation energy of the free exciton for GaN epilayers was also evaluated to be similar to 27.8 +/- 0.7 meV from the temperature-dependent PL studies. Low carrier concentrations were observed similar to 4.5 +/- 2 x 10(17) Cm-3 by measurements and it indicates the silicon nitride layer, which not only acts as a growth buffer layer, but also effectively prevents Si diffusion from the substrate to GaN epilayers. The absence of yellow band emission at around 2.2 eV signifies the high quality of film. The tensile stress in GaN film calculated by the thermal stress model agrees very well with that derived from Raman spectroscopy. (C) 2010 Elsevier B.V. All rights reserved.

Spatially dependent zero-frequency response functions and correlation functions in the Kondo model

We present the details of a formalism for calculating spatially varying zero-frequency response functions and equal-time correlation functions in models of magnetic and mixed-valence impurities of metals. The method is based on a combination of perturbative, thermodynamic scaling theory [H. R. Krishna-murthy and C. Jayaprakash, Phys. Rev. B 30, 2806 (1984)] and a nonperturbative technique such as the Wilson renormalization group. We illustrate the formalism for the spin-1/2 Kondo problem and present results for the conduction-spin-density�impurity-spin correlation function and conduction-electron charge density near the impurity. We also discuss qualitative features that emerge from our calculations and discuss how they can be carried over to the case of realistic models for transition-metal impurities.

The concentration dependent cooperative friction coefficient of dilute polymer solutions at the theta point

We combine multiple scattering and renormalization group methods to calculate the leading order dimensionless virial coefficient k(s) for the friction coefficient of dilute polymer solutions under conditions where the osmotic second virial coefficient vanishes (i.e., at the theta point T-theta). Our calculations are formulated in terms of coupled kinetic equations for the polymer and solvent, in which the polymers are modeled as continuous chains whose configurations evolve under the action of random forces in, the velocity field of the solvent. To lowest order in epsilon=4-d, we find that k(s) = 1.06. This result compares satisfactorily with existing experimental estimates of k(s), which are in the range 0.7-0.8. It is also in good agreement with other theoretical results on chains and suspensions at T-theta. Our calculated k(s) is also found to be identical to the leading order virial coefficient of the tracer friction coefficient at the theta point. We discuss possible reasons for the difficulties encountered when attempting to evaluate k(s) by extrapolating prior renormalization group calculations from semidilute concentrations to the infinitely dilute limit. (C) 1996 American Institute of Physics.

Orientational relaxation in dipolar systems: How much do we understand the role of correlations

Dipolar systems, both liquids and solids, constitute a class of naturally abundant systems that are important in all branches of natural science. The study of orientational relaxation provides a powerful method to understand the microscopic properties of these systems and, fortunately, there are many experimental tools to study orientational relaxation in the condensed phases. However, even after many years of intense research, our understanding of orientational relaxation in dipolar systems has remained largely imperfect. A major hurdle towards achieving a comprehensive understanding is the long range and complex nature of dipolar interactions which also made reliable theoretical study extremely difficult. These difficulties have led to the development of continuum model based theories, which although they provide simple, elegant expressions for quantities of interest, are mostly unsatisfactory as they totally neglect the molecularity of inter-molecular interactions. The situation has improved in recent years because of renewed studies, led by computer simulations. In this review, we shall address some of the recent advances, with emphasis on the work done in our laboratory at Bangalore. The reasons for the failure of the continuum model, as revealed by the recent Brownian dynamics simulations of the dipolar lattice, are discussed. The main reason is that the continuum model predicts too fast a decay of the torque-torque correlation function. On the other hand, a perturbative calculation, based on Zwanzig's projection operator technique, provides a fairly satisfactory description of the single particle orientational dynamics for not too strongly polar dipolar systems. A recently developed molecular hydrodynamic theory that properly includes the effects of intermolecular orientational pair correlations provides an even better description of the single-particle orientational dynamics. We also discuss the rank dependence of the dielectric friction. The other topics reviewed here includes dielectric relaxation and solvation dynamics, as they are intimately connected with orientational relaxation. Recent molecular dynamics simulations of the dipolar lattice are also discussed. The main theme of the present review is to understand the effects of intermolecular interactions on orientational relaxation. The presence of strong orientational pair correlation leads to a strong coupling between the single particle and the collective dynamics. This coupling can lead to rich dynamical properties, some of which are detailed here, while a major part remains yet unexplored.

DNA Condensation by the Rat Spermatidal Protein TP2 Shows GC-Rich Sequence Preference and Is Zinc Dependent

Transition protein-2 (TP2), isolated from rat testes, was recently shown to be a zinc metalloprotein. We have now carried out a detailed analysis of the DNA condensing properties of TP2 with various polynucleotides using circular dichroism spectroscopy. The condensation of the alternating copolymers by TP2 (incubated with 10 mu M ZnSO4), namely, poly(dG-dC). poly(dG-dC) and poly(dA-dT). poly(dA-dT), was severalfold higher than condensation of either of the homoduplexes poly(dG). poly-(dC) and poly(dA). poly(dT) or rat oligonucleosomal DNA. Between the two alternating copolymers, poly(dG-dC). poly(dG-dC) was condensed 3.2-fold more effectively than poly(dA-dT). poly(dA-dT). Preincubation of TP2 with 5 mM EDTA significantly reduced its DNA-condensing property. Interestingly, condensation of the alternating copolymer poly(dI-dC). poly(dI-dC) by TP2 was much less as compared to that of poly(dG-dC). poly(dG-dC). The V8 protease-derived N-terminal fragment (88 aa) condensed poly(dA-dT). poly(dA-dT) to a very small extent but did not have any effect on poly(dG-dC). poly-(dG-dC). The C-terminal fragment (28 aa) was able to condense poly(dA-dT) . poly(dA-dT) more effectively than poly(dG-dC). poly(dG-dC). These results suggest that TP2 in its zinc-coordinated form condenses GC-rich polynucleotides much more effectively than other types of polynucleotides. Neither the N-terminal two-thirds of TP2 which is the zinc-binding domain nor the C-terminal basic domain are as effective as intact TP2 in bringing about condensation of DNA.

Dynamic Behavior of Poly(2-vinylpyridine) in Solution Studied by 13C Nuclear Magnetic Relaxation

Abstract: The dynamics of poly(2-vinylpyridine) in chloroform solution has been examined by C-13 spin-lattice relaxation time and NOE measurements as a function of temperature. The experiments were performed at 50.3 and 100.6 MHz. The backbone carbon relaxation data have been analyzed in terms of six motional models. Among these models, the models which consider conformational transitions and bond librations for the backbone were found to be more successful. Pyridyl ring motion has been modeled as a restricted rotation with the rotational amplitude varying with temperature. The activation energy parameters obtained from the relaxation data of the pyridyl ring carbon have been compared with the energy barrier for ring rotation estimated from conformational energy calculations using the AM1 semiempirical quantum chemical method. The results of the conformational energy calculations support the description of pyridyl ring motion as a restricted rotation.