Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Quasi-simple wave solutions for acoustic gravity waves

The special class of quasi-simple wave solutions is studied for the system of partial differential equations governing inviscid acoustic gravity waves. It is shown that these traveling wave solutions do not admit shocks. Periodic solutions are found to exist when there is no propagation in the vertical direction. The solutions for some particular cases are depicted graphically. Physics of Fluids is copyrighted by The American Institute of Physics.

Studies on transport phenomena during solidification of an aluminum alloy in the presence of linear electromagnetic stirring

Numerical and experimental studies on transport phenomena during solidification of an aluminum alloy in the presence of linear electromagnetic stirring are performed. The alloy is electromagnetically stirred to produce semisolid slurry in a cylindrical graphite mould placed in the annulus of a linear electromagnetic stirrer. The mould is cooled at the bottom, such that solidification progresses from the bottom to the top of the cylindrical mould. A numerical model is developed for simulating the transport phenomena associated with the solidification process using a set of single-phase governing equations of mass. momentum, energy. and species conservation. The viscosity variation of the slurry, used in the model, is determined experimentally using a rotary viscometer. The set of governing equations is solved using a pressure-based finite volume technique, along with an enthalpy based phase change algorithm. The numerical study involves prediction of temperature, velocity, species and solid fraction distribution in the mould. Corresponding solidification experiments are performed, with time-temperature history recorded at key locations. The microstructures at various temperature measurement locations in the solidified billet are analyzed. The numerical predictions of temperature variations are in good agreement with experiments, and the predicted flow field evolution correlates well with the microstructures observed at various locations.

Underwater Sustainability of the ``Cassie'' State of Wetting

A rough hydrophobic surface when immersed in water can result in a ``Cassie'' state of wetting in which the water is in contact with both the solid surface and the entrapped air. The sustainability of the entrapped air on such surfaces is important for underwater applications such as reduction of flow resistance in microchannels and drag reduction of submerged bodies such as hydrofoils. We utilize an optical technique based oil total internal reflection of light at the water-air interface to quantify the spatial distribution of trapped air oil such a surface and its variation with immersion time. With this technique, we evaluate the sustainability of the Cassie state on hydrophobic surfaces with four different kinds of textures. The textures studied are regular arrays of pillars, ridges, and holes that were created in silicon by a wet etching technique, and also a texture of random craters that was obtained through electrodischarge machining of aluminum. These surfaces were rendered hydrophobic with a self-assembled layer Of fluorooctyl trichlorosilane. Depending on the texture, the size and shape of the trapped air pockets were found to vary. However, irrespective of the texture, both the size and the number of air pockets were found to decrease with time gradually and eventually disappear, suggesting that the sustainability of the ``Cassie'' state is finite for all the microstructures Studied. This is possibly due to diffusion of air from the trapped air pockets into the water. The time scale for disappearance of air pockets was found to depend on the kind of microstructure and the hydrostatic pressure at the water-air interface. For the surface with a regular array of pillars, the air pockets were found to be in the form of a thin layer perched on top of the pillars with a large lateral extent compared to the spacing between pillars. For other surfaces studied, the air pockets are smaller and are of the same order as the characteristic length scale of the texture. Measurements for the surface with holes indicate that the time for air-pocket disappearance reduces as the hydrostatic pressure is increased.

Analysis of microstructure and texture evolution in pure magnesium during symmetric and asymmetric rolling

Asymmetric rolling of commercially pure magnesium was carried out at three different temperatures: room temperature, 200 degrees C and 350 degrees C. Systematic analysis of microstructures, grain size distributions, texture and misorientation distributions were performed using electron backscattered diffraction in a field emission gun scanning electron microscope. The results were compared with conventional (symmetric) rolling carried out under the same conditions of temperature and strain rate. Simulations of deformation texture evolution were performed using the viscoplastic self-consistent polycrystal plasticity model. The main trends of texture evolution are faithfully reproduced by the simulations for the tests at room temperature. The deviations that appear for the textures obtained at high temperature can be explained by the occurrence of dynamic recrystallization. Finally, the mechanisms of texture evolution in magnesium during asymmetric and symmetric rolling are explained with the help of ideal orientations, grain velocity fields and divergence maps displayed in orientation space.

Large Low-Frequency Fluctuations in the Velocity of a Driven Vortex Lattice in a Single Crystal of 2H-NbSe2 Superconductor

The driven state of a well-ordered flux line lattice in a single crystal of 2H-NbSe2 in the time domain has revealed the presence of substantial fluctuations in velocity, with large and distinct time periods (similar to seconds). A superposition of a periodic drive in the driven vortex lattice causes distinct changes in these fluctuations. We propose that prior to the onset of the peak effect there exists a heretofore unexplored regime of coherent dynamics, with unexpected behavior in velocity fluctuations.

Surface Proteins of Lactobacillus crispatus: Adhesive Properties and Cell Wall Anchoring

Bacterial surface-associated proteins are important in communication with the environment and bacteria-host interactions. In this thesis work, surface molecules of Lactobacillus crispatus important in host interaction were studied. The L. crispatus strains of the study were known from previous studies to be efficient in adhesion to intestinal tract and ECM. L. crispatus JCM 5810 possess an adhesive surface layer (S-layer) protein, whose functions and domain structure was characterized. We cloned two S-layer protein genes (cbsA; collagen-binding S-layer protein A and silent cbsB) and identified the protein region in CbsA important for adhesion to host tissues, for polymerization into a periodic layer as well as for attachment to the bacterial cell surface. The analysis was done by extensive mutation analysis and by testing His6-tagged fusion proteins from recombinant Escherichia coli as well as by expressing truncated CbsA peptides on the surface of Lactobacillus casei. The N-terminal region (31-274) of CbsA showed efficient and specific binding to collagens, laminin and extracellular matrix on tissue sections of chicken intestine. The N-terminal region also contained the information for formation of periodic S-layer polymer. This region is bordered at both ends by a conserved short region rich in valines, whose substitution to leucines drastically affected the periodic polymer structure. The mutated CbsA proteins that failed to form a periodic polymer, did not bind collagens, which indicates that the polymerized structure of CbsA is needed for collagen-binding ability. The C-terminal region, which is highly identical in S-layer proteins of L. crispatus, Lactobacillus acidophilus and Lactobacillus helveticus, was shown to anchor the protein to the bacterial cell wall. The C-terminal CbsA peptide specifically bound to bacterial teichoic acid and lipoteichoic acids. In conclusion, the N-terminal domain of the S-layer protein of L. crispatus is important for polymerization and adhesion to host tissues, whereas the C-terminal domain anchors the protein to bacterial cell-wall teichoic acids. Lactobacilli are fermentative organisms that effectively lower the surrounding pH. While this study was in progress, plasminogen-binding proteins enolase and glyceraldehyde-3-phosphate dehydrogenase (GAPDH) were identified in the extracellular proteome of L. crispatus ST1. In this work, the cell-wall association of enolase and GAPDH were shown to rely on pH-reversible binding to the cell-wall lipoteichoic acids. Enolase from L. crispatus was functionally compared with enolase from L. johnsonii as well as from pathogenic streptococci (Streptococcus pneumoniae, Streptococcus pyogenes) and Staphylococcus aureus. His6-enolases from commensal lactobacilli bound human plasminogen and enhanced its activation by human plasminogen activators similarly to, or even better than, the enolases from pathogens. Similarly, the His6-enolases from lactobacilli exhibited adhesive characteristics previously assigned to pathogens. The results call for more detailed analyses of the role of the host plasminogen system in bacterial pathogenesis and commensalism as well of the biological role and potential health risk of the extracellular proteome in lactobacilli.

Spinodal Decomposition in Tellurite-Based Glasses Induced by Excimer Laser Irradiation

Tellurite-based glasses in the TeO2-K3Li2Nb5O15, TeO2-Ba5Li2Ti2Nb8O30, and V2Te2O9 were fabricated by the conventional melt-quenching technique. Amorphous and glassy characteristics of the as-quenched samples were established via the X-ray powder diffraction technique and differential thermal analysis, respectively. The as-quenched samples were irradiated by an excimer laser (248 nm). The effect of laser power, duration of irradiation, and the frequency of the laser pulses on the surface features of the above glasses were studied. The optical microscopic studies carried out on the above systems revealed the presence of quasi-periodic and periodic structures on their surfaces. The local compositional variations of these structures were confirmed by back-scattered electron imaging using scanning electron microscope accompanied by energy-dispersive X-ray analysis. These results were convincing enough to state that the glasses in the present investigations had undergone spinodal decomposition on laser irradiation. The incidence of the interconnected texture of two different phases was observed owing to the quenching effect produced by the heating and cooling cycle of the successive laser pulses. Ring- and line-shaped patterns were also observed, respectively, when the pulse frequency of the laser and the duration of irradiation were increased.

Simple theoretical analysis of the Einstein's photoemission from quantum confined superlattices

In this paper, we study the Einstein's photoemission from III-V, II-VI, IV-VI and HgTe/CdTe quantum well superlattices (QWSLs) with graded interfaces and quantum well effective mass superlattices in the presence of a quantizing magnetic field on the basis of newly formulated dispersion relations in the respective cases. Besides, the same has been studied from the afore-mentioned quantum dot superlattices and it appears that the photoemission oscillates with increasing carrier degeneracy and quantizing magnetic field in different manners. In addition, the photoemission oscillates with film thickness and increasing photon energy in quantum steps together with the fact that the solution of the Boltzmann transport equation will introduce new physical ideas and new experimental findings under different external conditions. The influence of band structure is apparent from all the figures and we have suggested three applications of the analyses of this paper in the fields of superlattices and microstructures.

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

Search for chaos in neutron star systems: Is Cyg X-3 a black hole?

The accretion disk around a compact object is a nonlinear general relativistic system involving magnetohydrodynamics. Naturally, the question arises whether such a system is chaotic (deterministic) or stochastic (random) which might be related to the associated transport properties whose origin is still not confirmed. Earlier, the black hole system GRS 1915+105 was shown to be low-dimensional chaos in certain temporal classes. However, so far such nonlinear phenomena have not been studied fairly well for neutron stars which are unique for their magnetosphere and kHz quasi-periodic oscillation (QPO). On the other hand, it was argued that the QPO is a result of nonlinear magnetohydrodynamic effects in accretion disks. If a neutron star exhibits chaotic signature, then what is the chaotic/correlation dimension? We analyze RXTE/PCA data of neutron stars Sco X-1 and Cyg X-2, along with the black hole Cyg X-1 and the unknown source Cyg X-3, and show that while Sco X-1 and Cyg X-2 are low dimensional chaotic systems, Cyg X-1 and Cyg X-3 are stochastic sources. Based on our analysis, we argue that Cyg X-3 may be a black hole.

Temperature dependent structural properties of nanocrystalline SnS structures

This letter explores the structural behavior of nanocrystalline tin mono sulfide (SnS) structures with respect to temperature (100-600 K). These studies emphasize that the structural properties of SnS nanocrystalline structures depend on the surrounding temperature. The lattice parameters of SnS nanocrystals slightly varied like their microstructures with the increase of temperature. These changes strongly influence the optical properties of SnS nanostructures. On the other hand, the structures exhibited higher strain (similar to 0.44%) than that of microstructured (0.3%) and bulk (0.12%) counterparts. The observed results are discussed under the light of existing concepts and reported.

Recent progress on synthesis, multi-scale structure, and properties of Y-Si-O oxides

Yttrium silicates (Y-Si-O oxides), including Y2Si2O7, Y2SiO5, and Y4·67(SiO4)3O apatite, have attracted wide attentions from material scientists and engineers, because of their extensive polymorphisms and important roles as grain boundary phases in improving the high-temperature mechanical/thermal properties of Si3N4and SiC ceramics. Recent interest in these materials has been renewed by their potential applications as high-temperature structural ceramics, oxidation protective coatings, and environmental barrier coatings (EBCs). The salient properties of Y-Si-O oxides are strongly related to their unique chemical bonds and microstructure features. An in-depth understanding on the synthesis - multi-scale structure-property relationships of the Y-Si-O oxides will shine a light on their performance and potential applications. In this review, recent progress of the synthesis, multi-scale structures, and properties of the Y-Si-O oxides are summarised. First, various methods for the synthesis of Y-Si-O ceramics in the forms of powders, bulks, and thin films/coatings are reviewed. Then, the crystal structures, chemical bonds, and atomic microstructures of the polymorphs in the Y-Si-O system are summarised. The third section focuses on the properties of Y-Si-O oxides, involving the mechanical, thermal, dielectric, and tribological properties, their environmental stability, and their structure-property relationships. The outlook for potential applications of Y-Si-O oxides is also highlighted.

A Compact Defected Ground Microstrip Device with Photonic Bandgap Effects

Filters and other devices using photonic bandgap (PBG) theory are typically implemented in microstrip lines by etching periodic holes on the ground plane of the microstrip. The period of such several holes corresponds to nearly half the guided wavelength of the transmission line. In this paper we study the effects of miniaturization of the PBG device by meandering the microstrip line about one single hole in the ground plane. A comparison of the S-parameters and dispersion behavior of the modified geometry and a conventional PBG device with a straight microstrip line shows that these devices have similar behaviors.