An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

Spontaneous self-assembly of designed cyclic dipeptide (Phg-Phg) into two-dimensional nano- and mesosheets

In this study, we present the spontaneous self-assembly of designed simplest aromatic cyclic dipeptides of (L-Phg-L-Phg) and (D-Phg-L-Phg) to form highly stable two-dimensional (2D) nano- and mesosheets with large lateral surface area. Various microscopy data revealed that the morphology of 2D mesosheets resembles the hierarchical natural materials with layered structure. Solution and solid-state NMR studies on cyclo(L-Phg-L-Phg) revealed the presence of strong (N-H-O) hydrogen-bonded molecular chains supported by aromatic pi-pi interactions to form 2D mesosheets. Interestingly, cyclo(D-Phg-L-Phg) self-assembles to form single-crystalline as well as non-crystalline 2D rhomboid sheets with large lateral dimension. X-ray diffraction analysis revealed the stacking of (N-H-O) hydrogen-bonded molecular layers along c-axis supported by aromatic pi-pi interactions. The thermogravimetric analysis shows two transitions with overall high thermal stability attributed to layered hierarchy found in 2D mesosheets.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Combined Atomic Force Microscopy and Modeling Study of The Evolution of Octadecylamine Films on a Mica Surface

The time evolution of the film thickness and domain formation of octadecylamine molecules adsorbed oil a mica surface is investigated Using atomic force microscopy. The adsorbed Film thickness is determined by measuring the height profile across the mica-amine interface of a mica surface partially immersed in a 15 mM solution of octadecylamine in chloroform. Using this novel procedure, adsorption of amine on mica is found to occur in three distinct stages, with morphologically distinct domain Formation and growth occurring during each stage. In the first stage, where adsorption is primarily in the thin-film regime, all average Film thickness of 0.2 (+/- 0.3) nm is formed for exposure times below 30 s and 0.8 (+/- 0.2) nm for 60 s of immersion time. During this stage, large sample spanning domains are observed. The second stage, which occurs between 60-300 s, is associated with it regime of rapid film growth, and the film thickness increases from about 0.8 to 25 nm during this stage. Once the thick-film regime is established, further exposure to the amine solution results in all increase in the domain area, and it regime of lateral domain growth is observed. In this stage, the domain area coverage grows from 38 to 75%, and the FTIR spectra reveal an increased level of crystallinity in the film. Using it diffusion-controlled model and it two-step Langmuir isotherm, the time evolution of the film growth is quantitatively captured. The model predicts the time at which the thin to thick film transition occurs as well its the time required for complete film growth at longer times. The Ward-Tordai equation is also solved to determine the model parameters in the monolayer (thin-film) regime, which occurs during the initial stages of film growth.

Characterization of Clean and Fouled Rail Track Ballast Subsurface Using Seismic Surface Survey Method: Model and Field Studies

The efficiency of track foundation material gradually decreases due to insufficient lateral confinement, ballast fouling, and loss of shear strength of the subsurface soil under cyclic loading. This paper presents characterization of rail track subsurface to identify ballast fouling and subsurface layers shear wave velocity using seismic survey. Seismic surface wave method of multi-channel analysis of surface wave (MASW) has been carried out in the model track and field track for finding out shear wave velocity of the clean and fouled ballast and track subsurface. The shear wave velocity (SWV) of fouled ballast increases with increase in fouling percentage, and reaches a maximum value and then decreases. This character is similar to typical compaction curve of soil, which is used to define optimum and critical fouling percentage (OFP and CFP). Critical fouling percentage of 15 % is noticed for Coal fouled ballast and 25 % is noticed for clayey sand fouled ballast. Coal fouled ballast reaches the OFP and CFP before clayey sand fouled ballast. Fouling of ballast reduces voids in ballast and there by decreases the drainage. Combined plot of permeability and SWV with percentage of fouling shows that after critical fouling point drainage condition of fouled ballast goes below acceptable limit. Shear wave velocities are measured in the selected location in the Wollongong field track by carrying out similar seismic survey. In-situ samples were collected and degrees of fouling were measured. Field SWV values are more than that of the model track SWV values for the same degree of fouling, which might be due to sleeper's confinement. This article also highlights the ballast gradation widely followed in different countries and presents the comparison of Indian ballast gradation with international gradation standards. Indian ballast contains a coarser particle size when compared to other countries. The upper limit of Indian gradation curve matches with lower limit of ballast gradation curves of America and Australia. The ballast gradation followed by Indian railways is poorly graded and more favorable for the drainage conditions. Indian ballast engineering needs extensive research to improve presents track conditions.

On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

Processes of 30-90 days sea surface temperature variability in the northern Indian Ocean during boreal summer

During summer, the northern Indian Ocean exhibits significant atmospheric intraseasonal variability associated with active and break phases of the monsoon in the 30-90 days band. In this paper, we investigate mechanisms of the Sea Surface Temperature (SST) signature of this atmospheric variability, using a combination of observational datasets and Ocean General Circulation Model sensitivity experiments. In addition to the previously-reported intraseasonal SST signature in the Bay of Bengal, observations show clear SST signals in the Arabian Sea related to the active/break cycle of the monsoon. As the atmospheric intraseasonal oscillation moves northward, SST variations appear first at the southern tip of India (day 0), then in the Somali upwelling region (day 10), northern Bay of Bengal (day 19) and finally in the Oman upwelling region (day 23). The Bay of Bengal and Oman signals are most clearly associated with the monsoon active/break index, whereas the relationship with signals near Somali upwelling and the southern tip of India is weaker. In agreement with previous studies, we find that heat flux variations drive most of the intraseasonal SST variability in the Bay of Bengal, both in our model (regression coefficient, 0.9, against similar to 0.25 for wind stress) and in observations (0.8 regression coefficient); similar to 60% of the heat flux variation is due do shortwave radiation and similar to 40% due to latent heat flux. On the other hand, both observations and model results indicate a prominent role of dynamical oceanic processes in the Arabian Sea. Wind-stress variations force about 70-100% of SST intraseasonal variations in the Arabian Sea, through modulation of oceanic processes (entrainment, mixing, Ekman pumping, lateral advection). Our similar to 100 km resolution model suggests that internal oceanic variability (i.e. eddies) contributes substantially to intraseasonal variability at small-scale in the Somali upwelling region, but does not contribute to large-scale intraseasonal SST variability due to its small spatial scale and random phase relation to the active-break monsoon cycle. The effect of oceanic eddies; however, remains to be explored at a higher spatial resolution.

Generalized model predictive static programming and its application to 3D impact angle constrained guidance of air-to-surface missiles

A new `generalized model predictive static programming (G-MPSP)' technique is presented in this paper in the continuous time framework for rapidly solving a class of finite-horizon nonlinear optimal control problems with hard terminal constraints. A key feature of the technique is backward propagation of a small-dimensional weight matrix dynamics, using which the control history gets updated. This feature, as well as the fact that it leads to a static optimization problem, are the reasons for its high computational efficiency. It has been shown that under Euler integration, it is equivalent to the existing model predictive static programming technique, which operates on a discrete-time approximation of the problem. Performance of the proposed technique is demonstrated by solving a challenging three-dimensional impact angle constrained missile guidance problem. The problem demands that the missile must meet constraints on both azimuth and elevation angles in addition to achieving near zero miss distance, while minimizing the lateral acceleration demand throughout its flight path. Both stationary and maneuvering ground targets are considered in the simulation studies. Effectiveness of the proposed guidance has been verified by considering first order autopilot lag as well as various target maneuvers.

Evolution of Surface Roughness During Electropolishing

The characteristics of surface roughness span a range of length scales determined by the nature of the surface generation process. The mechanism by which material is removed at a length scale determines the roughness at that scale. Electropolishing preferentially reduces the peaks of surface protuberances at sub-micron length scales to produce smooth surfaces. The material removal in electropolishing occurs by two different mechanisms of anodic leveling and microsmoothing. Due to insufficient lateral resolution, individual contribution of these two mechanisms could not be measured by conventional roughness measurement techniques and parameters. In this work, we utilize the high lateral resolution offered by Atomic force microscopy along with the power spectral density method of characterization, to study the evolution of roughness during electropolishing. The power spectral density show two corner frequencies indicating the length scales over which the two mechanisms operate. These characteristic frequencies are found to be a function of the electropolishing time and hence can be used to optimize the electropolishing process.

Surface chemical studies of Thiobacillus ferrooxidans with reference to copper tolerance

A strain of Thiobacillus ferrooxidans was adapted to grow at higher concentrations of copper by single step culturing in the presence of 20 g/L (0.314 mol/L) cupric ions added to 9K medium. Exposure to copper results in change in the surface chemistry of the microorganism. The isoelectric point of the adapted strain (pI=4.7) was observed to be at a higher pH than that of the wild unadapted strain(pI=2.0). Compared to the wild strain, the copper adapted strain was found to be more hydrophobic and showed enhanced attachment efficiency to the pyrite mineral. The copper adsorption ability of the adapted strain was also found to be higher than that of the wild strain. Fourier transform infrared spectroscopy of adapted cells suggested that a proteinaceous new cell surface component is synthesized by the adapted strain. Treatment of adapted cells with proteinase-K, resulted in complete loss of tolerance to copper, reduction in copper adsorption and hydrophobicity of the adapted cells. These observations strongly suggest a role played by cell surface modifications of Thiobacillus ferrooxidans in imparting the copper tolerance to the cells and bioleaching of sulphide minerals.

On the measurement of the surface energy budget over a land surface during the summer monsoon

The measurement of surface energy balance over a land surface in an open area in Bangalore is reported. Measurements of all variables needed to calculate the surface energy balance on time scales longer than a week are made. Components of radiative fluxes are measured while sensible and latent heat fluxes are based on the bulk method using measurements made at two levels on a micrometeorological tower of 10 m height. The bulk flux formulation is verified by comparing its fluxes with direct fluxes using sonic anemometer data sampled at 10 Hz. Soil temperature is measured at 4 depths. Data have been continuously collected for over 6 months covering pre-monsoon and monsoon periods during the year 2006. The study first addresses the issue of getting the fluxes accurately. It is shown that water vapour measurements are the most crucial. A bias of 0.25% in relative humidity, which is well above the normal accuracy assumed the manufacturers but achievable in the field using a combination of laboratory calibration and field intercomparisons, results in about 20 W m(-2) change in the latent heat flux on the seasonal time scale. When seen on the seasonal time scale, the net longwave radiation is the largest energy loss term at the experimental site. The seasonal variation in the energy sink term is small compared to that in the energy source term.

Surface chemical studies on mica and galena using dextrin

The interactions of dextrin with biotite mica and galena have been investigated through adsorption, flotation, and electrokinetic measurements. The adsorption densities of dextrin onto mica continuously increase with increase of pH, while those onto galena show a maximum at pH 11.5. It is observed that the adsorption density of dextrin onto galena is quite high compared to that on mica. Both the adsorption isotherms exhibit Langmuirian behavior. Electrokinetic measurements portray conformational rearrangements of macromolecules with the loading, resulting in a shift of the shear plane, further away from the interface. Dissolution experiments indicate release of the lattice metal ions from mica and galena. Coprecipitation tests confirm polymer-metal ion interaction in the bulk solution. Dextrin does not exhibit any depressant action toward mica, whereas, with galena, the flotation recovery is decreased with an increase in pH beyond 9, in the presence of dextrin, complementing the adsorption results. Differential flotation results on a synthetic mixture of mica and galena show that mica can be selectively separated from galena using dextrin as a depressant for galena above pH 10. Possible mechanisms of interaction between dextrin and mica/galena are discussed.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time-dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier-Stokes equations and the energy equation governing the flow and the heat transfer admit a self-similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses dong the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Supramolecular control of the magnetic anisotropy in two-dimensional high-spin Fe arrays at a metal interface

Magnetic atoms at surfaces are a rich model system for solid-state magnetic bits exhibiting either classical(1,2) or quantum(3,4) behaviour. Individual atoms, however, are difficult to arrange in regular patterns(1-5). Moreover, their magnetic properties are dominated by interaction with the substrate, which, as in the case of Kondo systems, often leads to a decrease or quench of their local magnetic moment(6,7). Here, we show that the supramolecular assembly of Fe and 1,4-benzenedicarboxylic acid molecules on a Cu surface results in ordered arrays of high-spin mononuclear Fe centres on a 1.5nm square grid. Lateral coordination with the molecular ligands yields unsaturated yet stable coordination bonds, which enable chemical modification of the electronic and magnetic properties of the Fe atoms independently from the substrate. The easy magnetization direction of the Fe centres can be switched by oxygen adsorption, thus opening a way to control the magnetic anisotropy in supramolecular layers akin to that used in metallic thin films.