Asymptotic behaviour of point processes with Markov-dependent intervals

This splitting techniques for MARKOV chains developed by NUMMELIN (1978a) and ATHREYA and NEY (1978b) are used to derive an imbedded renewal process in WOLD's point process with MARKOV-correlated intervals. This leads to a simple proof of renewal theorems for such processes. In particular, a key renewal theorem is proved, from which analogues to both BLACKWELL's and BREIMAN's forms of the renewal theorem can be deduced.

Asymptotic behaviour and boundedness of linear systems with time varying coefficients

Motivated by developments in spacecraft dynamics, the asymptotic behaviour and boundedness of solution of a special class of time varying systems in which each term appears as the sum of a constant and a time varying part, are analysed in this paper. It is not possible to apply standard textbook results to such systems, which are originally in second order. Some of the existing results are reformulated. Four theorems which explore the relations between the asymptotic behaviour/boundedness of the constant coefficient system, obtained by equating the time varying terms to zero, to the corresponding behaviour of the time varying system, are developed. The results show the behaviour of the two systems to be intimately related, provided the solutions of the constant coefficient system approach zero are bounded for large values of time, and the time varying terms are suitably restrained. Two problems are tackled using these theorems.

Some recent results on the stability of linear time varying systems

Some theorems derived recently by the authors on the stability of multidimensional linear time varying systems are reported in this paper. To begin with, criteria based on Liapunov�s direct method are stated. These are followed by conditions on the asymptotic behaviour and boundedness of solutions. Finally,L 2 andL ? stabilities of these systems are discussed. In conclusion, mention is made of some of the problems in aerospace engineering to which these theorems have been applied.

On the solution of the equation ut+unux+H(x, t, u)=0

We consider the equation u(t) + u(n)u(x) + H(x, t, u) = 0 and derive a transformation relating it to u(t) + u(n)u(x) = 0. Special cases of the equation appearing in applications are discussed. Initial value problems and asymptotic behaviour of the solution are studied.

Common underlying steering curves for motorcycles in steady turns

We study the steady turn behaviours of some light motorcycle models on circular paths, using the commercial software package ADAMS-Motorcycle. Steering torque and steering angle are obtained for several path radii and a range of steady forward speeds. For path radii much greater than motorcycle wheelbase, and for all motorcycle parameters including tyre parameters held fixed, dimensional analysis can predict the asymptotic behaviour of steering torque and angle. In particular, steering torque is a function purely of lateral acceleration plus another such function divided by path radius. Of these, the first function is numerically determined, while the second is approximated by an analytically determined constant. Similarly, the steering angle is a function purely of lateral acceleration, plus another such function divided by path radius. Of these, the first is determined numerically while the second is determined analytically. Both predictions are verified through ADAMS simulations for various tyre and geometric parameters. In summary, steady circular motions of a given motorcycle with given tyre parameters can be approximately characterised by just one curve for steering torque and one for steering angle.

Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

An unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid over a rotating infinite disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The magnetic field is applied normal to the disk surface. The new self-similar solution of the Navier-Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier-Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation-point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large magnetic field or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also the surface shear stress in the radial direction and the surface heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction increases. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Homogenization of eigenvalue problems in perforated domains

In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet: λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in the case of Neumann eigenvalue problem.

First passage distributions for long memory processes

We study the distribution of first passage time for Levy type anomalous diffusion. A fractional Fokker-Planck equation framework is introduced.For the zero drift case, using fractional calculus an explicit analytic solution for the first passage time density function in terms of Fox or H-functions is given. The asymptotic behaviour of the density function is discussed. For the nonzero drift case, we obtain an expression for the Laplace transform of the first passage time density function, from which the mean first passage time and variance are derived.

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements m in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes' theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito-Taylor's discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplifiedmby considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations. (C) 2010 Elsevier Ltd. All rights reserved.

Solute induced liquid crystalline behaviour of a quaternary ammonium salt and its application to structure determination

A new liquid crystalline phase, induced by the addition of small amounts of a non-mesogenic solute (such as dimethyl sulphoxide or methyl iodide) to a quaternary ammonium salt, N-methyl-N,N,N-trioctadecylammonium iodide (MTAI), has been detected by NMR and optical microscopic studies. In some cases, there is a coexistence of nematic and smectic phases. Information on the ordering of the phases in the magnetic field of the spectrometer has been derived from NMR spectra of a dissolved molecule, C-13-enriched methyl iodide. The low order parameter of the pure thermotropic nematic phase of the salt provides first-order spectra of the dissolved oriented molecules. Analyses of spectra of cis,cis-mucononitrile exemplifies the utility of the MTAI nematic phase in the determination of structural parameters of the solute.

Swelling behaviour of soil-bentonite mixtures

Studies on the swelling behaviour of mixtures of bentonite clay and nonswelling coarser fractions of different sizes and shapes reveal that observed swelling occurs only after the voids of the nonswelling particles are filled up with swollen clay particles. The magnitude of the swell within the voids, called intervoid swelling is large when the size and percentage of the nonswelling coarser fraction is large. The observable swell, after intervoid swelling, is called primary swelling and follows a rectangular hyperbolic relationship with time. The total swell per gram of the clay decreases with an increase in the size of the nonswelling fraction and with a decrease in the percentage of swelling clay. Time-swell relationships show that swelling continues to occur for a long time after the primary swelling, and this is called secondary swelling.

High temperature time-dependent low cycle fatigue behaviour of a type 316L(N) stainless steel

Total strain controlled low cycle fatigue tests on 316L(N) stainless steel have been conducted in air at various strain rates in the temperature range of 773-873 K to identify the operative time-dependent mechanisms and to understand their influence on the cyclic deformation and fracture behaviour of the alloy. The cyclic stress response at all the testing conditions was marked by an initial hardening followed by stress saturation. A negative strain rate stress response is observed under specific testing conditions which is attributed to dynamic strain ageing (DSA). Transmission electron microscopy studies reveal that there is an increase in the dislocation density and enhanced slip planarity in the DSA regime. Fatigue life is found to decrease with a decrease in strain rate. The degradation in fatigue resistance is attributed to the detrimental effects associated with DSA and oxidation. Quantitative measurement of secondary cracks indicate that both transgranular and intergranular cracking are accelerated predominantly under conditions conducive to DSA.

Influence of lanthanum doping on the dielectric, ferroelectric and relaxor behaviour of barium bismuth titanate ceramics

Barium lanthanum bismuth titanate (Ba1−(3/2)xLaxBi4Ti4O15, x = 0–0.4) ceramics were fabricated using the powders synthesized via the solid-state reaction route. X-ray powder diffraction analysis confirmed the above compositions to be monophasic and belonged to the m = 4 member of the Aurivillius family of oxides. The effect of the partial presence of La3+ on Ba2+ sites on the microstructure, dielectric and relaxor behaviour of BaBi4Ti4O15 (BBT) ceramics was investigated. For the compositions pertaining to x ≤ 0.1, the dielectric constant at both room temperature and in the vicinity of the temperature of the dielectric maximum (Tm) of the parent phase (BBT) increased significantly with an increase in x while Tm remained almost constant. Tm shifted towards lower temperatures accompanied by a decrease in the magnitude of the dielectric maximum (εm) with an increase in the lanthanum content (0.1 < x ≤ 0.4). The dielectric relaxation was modelled using the Vogel–Fulcher relation and a decrease in the activation energy for frequency dispersion with increasing x was observed. The frequency dispersion of Tm was found to decrease with an increase in lanthanum doping, and for compositions corresponding to x ≥ 0.3, Tm was frequency independent. Well-developed P(polarization)–E(electric field) hysteresis loops were observed at 150 °C for all the samples and the remanent polarization (2Pr) was improved from 6.3 µC cm−2 for pure BBT to 13.4 µC cm−2 for Ba0.7La0.2Bi4Ti4O15 ceramics. Dc conductivities and associated activation energies were evaluated using impedance spectroscopy.

Resolidification behaviour of laser surface-melted metals and alloys

The solidification behaviour is described of two pure metals (Bi and Ni) and two eutectic alloys (A1-Ge and AI-Cu) under nonequilibrium conditions, in particular the microsecond pulsed laser surface melting. The resolidification behaviour of bismuth shows that epitaxial regrowth is the dominant mechanism. For mixed grain size, regrowth of larger grains dominates the microstructure and can result in the development of texture. In the case of nickel, epitaxial growth has been noted. For lower energy pulse-melted pool, grain refinement takes place, indicating nucleation of fresh nickel grains. The A1-Ge eutectic alloy indicates the nucleation and columnar growth of a metastable monoclinic phase from the melt-substrate interface at a high power density laser irradiation. An equiaxed microstructure containing the same monoclinic phase is obtained at a lower power density laser irradiation. It is shown that the requirement of solution partition acts as a barrier to eutectic regrowth from the substrate. The laser-melted pool of A1-Cu eutectic alloy includes columnar growth of c~-A1 and 0-A12Cu phase followed by the dendritic growth of A12Cu phase with ct-Al forming at the interdendritic space. In addition, a banded microstructure was observed in the resolidified laser-melted pool.

Families of asymptotic tensile crack tip stress fields in elastic-perfectly plastic single crystals

In this work, two families of asymptotic near-tip stress fields are constructed in an elastic-ideally plastic FCC single crystal under mode I plane strain conditions. A crack is taken to lie on the (010) plane and its front is aligned along the [(1) over bar 01] direction. Finite element analysis is first used to systematically examine the stress distributions corresponding to different constraint levels. The general framework developed by Rice (Mech Mater 6:317-335, 1987) and Drugan (J Mech Phys Solids 49:2155-2176, 2001) is then adopted to generate low triaxiality solutions by introducing an elastic sector near the crack tip. The two families of stress fields are parameterized by the normalized opening stress (tau(A)(22)/tau(o)) prevailing in the plastic sector in front of the tip and by the coordinates of a point where elastic unloading commences in stress space. It is found that the angular stress variations obtained from the analytical solutions show good agreement with finite element analysis.