First passage time for a class of one-dimensional stochastic systems

We consider the time evolution of a class of stochastic systems of finite size with polynomial nearest neighbor transition rates. We obtain analytical expressions for the first passage time (FPT) and its moments. We show that the mean FPT, averaged over a uniform initial distribution, shows a simple asymptotoc behavior with the system size and the parameters of the transition rates.     

Some stability results in the theory of whirling

The whirling motion of a fixed-free viscoelastic shaft, whose model is based on the spring and dashpot (Kelvin element), is considered. We develop a precise determination of the system's stability by first obtaining its eigenvalues. It is shown that asymptotic stability exists as long as the angular speed of the shaft is below a certain critical value. On the other hand, the degree of stability first increases as the speed is increased but eventually decreases again.

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Zusammenfassung Es wird die Wirbelbewegung einer einseitig eingespannten Welle untersucht, deren Modell dem Kelvin-Element entspricht. Zur Beurteilung der Stabilität werden zunächst die Eigenwerte ermittelt. Dann wird gezeigt, dass asymptotische Stabilität besteht, solange die Winkelgeschwindigkeit unter einem kritischen Wert liegt. Der Stabilitätsgrad nimmt zuerst mit der Winkelgeschwindigkeit zu und schliesslich wieder ab.

     

Morphological explanation of the extraordinary fracture toughness of linear low density polyethylenes

The fracture toughness of commercial linear low-density polyethylenes (LLDPE) has been found to be extraordinarily high relative to commercial low-density (LDPE) and high-density (HDPE) polyethylenes in previously reported investigations. The present investigation shows that this extraordinary fracture toughness cannot be explained by differences in molecular structure variables, such as molecular weight, long-chain and short-chain branching, fractional crystallinity, and comonomer content. Instead, the presence of a second soft phase, which was extractable with a weak solvent, in a hard semicrystalline matrix was discovered by morphological investigations of LLDPE resins. This second phase arises from the extreme compositional heterogeneity of the copolymers which comprise these LLDPE resins. No evidence for a similar morphological entity was found in LDPE and HDPE resins. This finding provides persuasive evidence that this very-low-crystallinity second phase performs a function similar to that of the rubberlike second phase in other high impact resins and, thus, leads to the observed extraordinary fracture toughness of LLDPE resins. Evidence for the nature and existence of this second phase is given from temperature-rising elution fractionation and scanning electron microscopy investigations.     

An O(k2 + kh2 + h4) arithmetic average discretization for the solution of 1‐D nonlinear parabolic equations

This article develops a new two‐level three‐point implicit finite difference scheme of order 2 in time and 4 in space based on arithmetic average discretization for the solution of nonlinear parabolic equation ε u_xx = f(x, t, u, u_x, u_t), 0 < x < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where ε > 0 is a small positive constant. We also propose a new explicit difference scheme of order 2 in time and 4 in space for the estimates of (?u/?x). The main objective is the proposed formulas are directly applicable to both singular and nonsingular problems. We do not require any fictitious points outside the solution region and any special technique to handle the singular problems. Stability analysis of a model problem is discussed. Numerical results are provided to validate the usefulness of the proposed formulas. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Study of precipitation in NaCl:Pb2+ by light scattering and ultramicroscopy

The formation and dissolution behaviour of precipitates in NaCl : Pb²⁺ single crystals is studied by light scattering and ultramicroscopy. Measurements of Rayleigh ratio together with ultramicroscopic observations during isochronal annealing indicate the presence of two types of precipitates in as-grown crystals. Isochronal annealing after suitable thermal and thermomechanical treatments shows that precipitates of first type (I) which form and dissolve at lower temperatures, are due to homogeneous nucleation. Precipitates of the second category (II) which form and dissolve at higher temperatures are aligned along crystallographic directions and have their origin in stress-assisted processes. Isothermal annealing has been used to study the dissolution kinetics of the precipitated fraction, and it is found that the kinetics is of first order. The enthalpy of solution is determined from a study of the temperature dependence of the kinetic rate constant, in conjunction with available information on the migration energy of Pb²⁺ in NaCl. The enthalpy so deduced is in good agreement with the value as usually obtained from the concentration dependence of the dissolution temperature.     

High-field magnetoresistance and magnetothermal e.m.f. in many-valley semiconductors with ellipsoidal energy surface

Thermomagnetic coefficients appropriate to a many-valley model of a semiconductor of the n -Germanium type are evaluated in the framework of the density matrix formalism developed earlier. These coefficients are determined for arbitrary values of the magnetic field, within the effective mass approximation. The phonon-drag contribution is not included in this work. An application is made to the four-ellipsoidal model of n-Ge under the conditions where elastic-acoustic phonon scattering is the predominant mechanism of scattering and the high-temperature limit of the phonon distribution is valid. The thermoelectric power (magneto-Seebeck effect) is found to increase with increasing values of the magnetic field except for a small region of low magnetic field values where it decreases in the longitudinal configuration only.