False Vacuum Decay with Gravity in a Critical Case

The vacuum decay in a de Sitter universe is studied for the class of effective inflaton potentials that curvature at the top is less than as well as greater than a critical value determined previously. By comparing the actions of the Hawking - Moss instanton and the Coleman - de Luccia instanton(s) the mode of vacuum decay is determined in this critical situation.     

Homothetic self-similar solutions of three-dimensional Brans-Dicke gravity

All homothetic self-similar solutions of the Brans-Dicke scalar field in three-dimensional spacetime with circular symmetry are found in closed form.     

A Quantum-Like Description of the Planetary Systems

The Titius–Bode law for planetary distances is reviewed. A model describing the basic features of this rule in the “quantum-like” language of a wave equation is proposed. Some considerations about the ’t Hooft idea on the quantum behavior of deterministic systems with dissipation are discussed.     

Thermal behavior of the maleic anhydride modified poly(3-hydroxybutyrate)

Poly(3-hydroxybutyrate), PHB has been structurally modified through reaction with maleic anhydride, MA. Transesterification reaction was carried out fixing the PHB and MA and besides time and temperature the concentration of the triethylamine (used as catalyst) was changed. Glass transition, melting and crystallization temperature obtained from DSC curves and thermal degradation temperatures obtained from TG traces were used to evaluate the influence of the reaction conditions on the modification of PHB according to factorial design. On the base of the results the optimum conditions are to perform the PHB modification reaction with MA reaction at 110°C for 1 h with 5% v/v triethylamine.     

On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002     

Cost–benefit modelling for reliability growth

Decisions during the reliability growth development process of engineering equipment involve trade-offs between cost and risk. However slight, there exists a chance an item of equipment will not function as planned during its specified life. Consequently the producer can incur a financial penalty. To date, reliability growth research has focussed on the development of models to estimate the rate of failure from test data. Such models are used to support decisions about the effectiveness of options to improve reliability. The extension of reliability growth models to incorporate financial costs associated with ‘unreliability’ is much neglected. In this paper, we extend a Bayesian reliability growth model to include cost analysis. The rationale of the stochastic process underpinning the growth model and the cost structures are described. The ways in which this model can be used to support cost–benefit analysis during product development are discussed and illustrated through a simple case.     

Bis[μ‐1‐(1,10‐phenanthrolin‐2‐yl)‐2‐pyridone]bis{aqua[1‐(1,10‐phenanthrolin‐2‐yl)‐2‐pyridone]cadmium(II)} tetrakis(perchlorate)

In the title centrosymmetric binuclear complex, [Cd₂(C₁₇H₁₁N₃O)₄(H₂O)₂](ClO₄)₄, the Cd^II ion assumes a distorted octahedral geometry. There are π–π stacking interactions between the pyridine and 1,10‐phenanthroline ring systems of adjacent ligands at the same Cd^II centre. Intermolecular hydrogen bonds between the coordinated aqua ligand and the O atom of a keto group connect adjacent complex cations into extended chains. Hydrogen bonds also exist between the complex cations and the perchlorate anions. Compared with the fluorescence spectrum of the organic ligand, the complex displays strong fluorescent emission and an ipsochromic shift of the emission peaks, which may be attributed to the structural character.     

A semi-analytic meshfree method for Almansi–Michell problems of piezoelectric cylinders

Saint-Venant’s Problem, Almansi–Michell Problems, Meshfree Methods, Piezoelectricity. We present a semi-analytical method for analyzing prismatic nonhomogeneous piezoelectric cylinders with arbitrary cross-sectional geometry. The prescribed loads considered in this study include axial forces, torques, moments, and voltage resultants prescribed at the cylinder’s ends, as well as body forces, lateral surface shears, voltages, and pressures as long as they can be represented by a power series in the axial coordinate. This problem can be considered as an extension of Saint-Venant and Almansi–Michell problems for elastic bodies to piezoelectric bodies. In this computationally efficient method, the cross-sectional plane is discretized with a meshfree approach, and the solution is obtained analytically with respect to the axial coordinate. A number of examples are provided to demonstrate the veracity and utility of the proposed method.     

Atomistic phenomena in dense fluid shock waves

The shock structure problem is one of the classical problems of fluid mechanics and at least for non-reacting dilute gases it has been considered essentially solved. Here we present a few recent findings, to show that this is not the case. There are still new physical effects to be discovered provided that the numerical technique is general enough to not rule them out a priori. While the results have been obtained for dense fluids, some of the effects might also be observable for shocks in dilute gases.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.