An Estimate for the Morse Index of a Stokes Wave

Stokes waves are steady periodic water waves on the free surface of an infinitely deep irrotational two-dimensional flow under gravity without surface tension. They can be described in terms of solutions of the Euler–Lagrange equation of a certain functional; this allows one to define the Morse index of a Stokes wave. It is well known that if the Morse indices of the elements of a set of non-singular Stokes waves are bounded, then none of them is close to a singular one. The paper presents a quantitative variant of this result.     

Numerical analysis of the stress concentration near holes originating in previously loaded viscoelastic bodies at finite strains

The state of stress and strain of previously loaded viscoelastic bodies with holes originating in them, successively or simultaneously, is analyzed under finite plane deformations. The problem statement and solution are based on the theory of repeatedly superimposed large deformations. The material mechanical properties are described using integral relations of the convolution type over time with a weakly singular kernel. The problem solving is based on the finite-element method. To calculate the integral of the convolution type, a recurrence formula is used that can be obtained by approximating the initial kernel with a linear combination of exponential functions (the truncated Prony’s series). The nonlinear effects and the effect of the interaction between holes on the stress concentration are analyzed. For the dynamic problems, the results for incompressible and weakly compressible materials are compared.     

Characterization of microholograms recorded in a thermoplastic medium for three-dimensional optical data storage

A three-dimensional optical data storage system that combines a new recording material with a microholographic data format in which data are stored as single-bit microholograms is presented. This format offers less sensitivity to environmental conditions than the page-based holographic approach in addition to an increased compatibility with current storage technologies. The new recording material is based on a thermoplastic material. The results presented indicate that the dimensions of the microholograms are larger than those calculated by use of simple laser beam waist approximations and that multiple layers of microholograms would significantly affect signal levels. Data densities achievable with the microholographic format will likely be limited by those effects.     

Notes on equivalent stationary policies in Markov decision processes with total rewards

We construct examples of Markov Decision Processes for which, for a given initial state and for a given nonstationary transient policy, there is no equivalent (randomized) stationary policy, i.e. there is no stationary policy which occupation measure is equal to the occupation measure of a given policy. We also investigate the relation between the existence of equivalent stationary policies in special models and the existence of equivalent strategies in various classes of nonstationary policies in general models.     

Design and fabrication of subwavelength nanogratings based light-emitting diodes

Linearly polarized light from InGaN green light emitting diode grown on (0001) oriented sapphire is demonstrated by using subwavelength metallic nanogratings. Polarization ratio can reach 7:1 (∼88%), the highest ever reported from a single light emitting device. We discuss the design and fabrication of this device in detail.     

Rheological characterization of well-defined tetrafluoroethylene/hexafluoropropylene copolymers

The rheology of tetrafluoroethylene/hexafluoropropylene (TFE/HFP) copolymers, also known as Teflon FEP polymers, having different molecular weight and composition (HFP content) was studied by means of a parallel-plate rheometer. Two groups of polymers having different molecular weights with nearly constant polydispersity (around 2.5) were considered; namely, one group having a relatively low melting temperature (amorphous with a high content of HFP) and a second group having a higher melting point (semi-crystalline with a lower content of HFP). The relaxation time spectrum, H(λ), calculated by use of the BSW model (developed for monodisperse linear polymers) followed a scaling relationship in the terminal zone with scaling exponent of 0.13. However, at higher frequencies the model fails to predict adequately the experimental data. The longest relaxation time calculated from both the BSW model and discrete relaxation spectra (λ _i ,g _i ), which was determined by use of a parsimonious fitting software, depends on the molecular weight in a similar way as the zero-shear viscosity does with the well-established scaling factor of 3.4. The critical molecular weight for the onset of entanglements, M _c , was found to be about 100000, a value much higher than those previously reported in literature for other polymers. The rheology of resins in the second group (higher melting point) was found to exhibit a strong dependence on thermal history during oscillatory-shear measurements. The data obtained in experiments at different temperatures without a preheating to a certain value (330°C) exhibited a violation of the time-temperature superposition principle and no well-defined values of the zero-shear viscosity. This is attributed to residual crystallinity even at temperatures well above their melting point (260°C). However, the same experiments with preheating and subsequent cooling to desired temperature resulted into a very good time-temperature scaling. Received: 13 January 1998 Accepted: 6 April 1998     

Optimal boundary discretization by variational data assimilation

A variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow water model. The advantage of controlling the discretization of operators near the boundary rather than boundary conditions is shown. Assimilating data that have been produced by the same model on a finer grid, in a model on a coarse grid, we have shown that optimal discretization allows us to correct such errors of the numerical scheme as under‐resolved boundary layer and wrong wave velocity. Copyright © 2010 John Wiley & Sons, Ltd.     

Computerized Developments in Design,Generation, Simulation of Meshing,and Stress Analysis of Gear Drives

The paper represents new computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives. The main contents of the paper are: (i) application of a predesigned parabolic function of transmission errors for reduction of noise, (ii) computerized simulation of noise caused by transmission errors, (iii) modification of the basic algorithm of tooth contact analysis, and (iv) application of approaches developed for enhanced design and simulation of meshing of the following gear drives: (a) spiral bevel gear drives, (b) face-gear drives (including an approach for grinding), and (c) modified helical gear drives. The developed theory is illustrated with numerical examples.