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.

Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V-0, our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V-0; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

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.

Anode Phenomena in Triggered Vacuum Gaps

Arc voltage - current characteristics and threshold current densities occuring during the formation of anode spots in triggered vacuum gaps are reported. Single pulses of 1.65 ms arcing time, which correspond to switching surge currents, are used in the study with copper and aluminum anodes. The threshold values are 1.75 times the values reported earlier using the longer, 8 mis, arcing time. They are found to depend upon the duration of arcing time as well as upon electrode material, surface conditions, electrode size and contact separation. Lateral inhomogenity in the electrode geometry appears to reduce the threshold value by promoting early formation of anode spots.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

Modeling of Freezing Phenomena Induced by Chemical Reactions

Spatial variations in the concentration of a reactive solute in solution are often encountered in a catalyst particle, and this leads to variation in the freezing point of the solution. Depending on the operating temperature, this can result in freezing of the solvent oil a portion of catalyst, rendering that part of the active area ineffective Freezing call occur by formation of a sharp front or it mush that separates the solid and fluid phases. In this paper, we model the extent of reduction in the active area due to freezing. Assuming that the freezing point decreases linearly with solute concentration, conditions for freezing to occur have been derived. At steady state, the ineffective fraction of catalyst pellet is found to be the same irrespective of the mode of freezing. Progress of freezing is determined by both the heat of reaction and the latent heat of fusion Unlike in freezing of alloys where the latter plays a dominant role, the exothermicity of the reaction has a significant effect on freezing in the presence of chemical reactions. A dimensionless group analogous to the Stefan number could be defined to capture the combined effect of both of these.

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.

Modeling of heat and mass transfer for solid state fermentation process in tray bioreactor

A mathematical model is developed to simulate oxygen consumption, heat generation and cell growth in solid state fermentation (SSF). The fungal growth on the solid substrate particles results in the increase of the cell film thickness around the particles. The model incorporates this increase in the biofilm size which leads to decrease in the porosity of the substrate bed and diffusivity of oxygen in the bed. The model also takes into account the effect of steric hindrance limitations in SSF. The growth of cells around single particle and resulting expansion of biofilm around the particle is analyzed for simplified zero and first order oxygen consumption kinetics. Under conditions of zero order kinetics, the model predicts upper limit on cell density. The model simulations for packed bed of solid particles in tray bioreactor show distinct limitations on growth due to simultaneous heat and mass transport phenomena accompanying solid state fermentation process. The extent of limitation due to heat and/or mass transport phenomena is analyzed during different stages of fermentation. It is expected that the model will lead to better understanding of the transport processes in SSF, and therefore, will assist in optimal design of bioreactors for SSF.

Suppression of the zero-order term in off-axis digital holography through nonlinear filtering

We present experimental validation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object autocorrelation,namely, the zero-order term,from holographic data,thereby improving the reconstruction bandwidth of complex wavefronts. The algorithm is based on nonlinear filtering and can be applied to standard DHM setups with realistic recording conditions.We study the robustness of the technique under different experimental configurations,and quantitatively demonstrate its enhancement capabilities on phase signals.

Development of Very High Frequency Damped Sine Wave Generator

In order to protect the critical electronic equipment/system against damped sine transient currents induced into its cables due to transient electromagnetic fields, switching phenomena, platform resonances, etc. it is necessary to provide proper hardening. The hardness assurance provided can be evaluated as per the test CS 116 of MIL STD 461E/F in laboratory by generating & inducing the necessary damped sine currents into the cables of the Equipment Under Test (EUT). The need and the stringent requirements for building a damped sine wave current generator for generation of damped sine current transients of very high frequencies (30 MHz & 100 MHz) have been presented. A method using LC discharge for the generation has been considered in the development. This involves building of extremely low & nearly loss less inductors (about 5 nH & 14 nH) as well as a capacitor & a switch with much lower inductances. A technique for achieving this has been described. Two units (I No for 30 MHz. & 100 MHz each) have been built. Experiments to verify the output are being conducted.

An investigation of first-order transition across charge ordered and ferromagnetic phases in Gd0.5Sr0.5MnO3 single crystals by magnetic and magnetotransport studies

Gadolinium strontium manganite single crystals of the composition Gd0.5Sr0.5MnO3 were grown using the optical float zone method. We report here the magnetic and magnetotransport properties of these crystals. A large magnetoresistance similar to 10(9)% was observed at 45 K under the application of a 110 kOe field. We have observed notable thermomagnetic anomalies such as open hysteresis loops across the broadened first-order transition between the charge order insulator and the ferromagnetic metallic phase while traversing the magnetic field-temperature (H-T) plane isothermally or isomagnetically. In order to discern the cause of these observed anomalies, the H-T phase diagram for Gd0.5Sr0.5MnO3 is formulated using the magnetization-field (M-H), magnetization-temperature (M-T) and resistance-temperature (R-T) measurements. The temperature dependence of the critical field (i.e. H-up, the field required for transformation to the ferromagnetic metallic phase) is non-monotonic. We note that the non-monotonic variation of the supercooling limit is anomalous according to the classical concepts of the first-order phase transition. Accordingly, H-up values below similar to 20 K are unsuitable to represent the supercooling limit. It is possible that the nature of the metastable states responsible for the observed open hysteresis loops is different from that of the supercooled ones.

Charge-order-driven multiferroic properties of Y1-xCaxMnO3

Dielectric measurements on the charge-ordered insulators, Y1-xCaxMnO3 (x = 0.4. 0.45 and 0.5), show maxima in the dielectric constant around the charge ordering transition temperature while magnetic measurements show the presence of weak ferromagnetic interactions at low temperatures. Besides the magnetic field dependence of the dielectric constant, these manganites also exhibit second harmonic generation. Thus, the charge-ordered Y1-xCaxMnO3 compositions are multiferroic and magnetoelectric, in accordance with theoretical predictions. Magnetoelectric properties are retained in small particles of Y0.5Ca0.5MnO3. (C) 2008 Elsevier Ltd. All rights reserved.

A Combinatorial Optimization Problem for High Order PODs with Few Sensors

Experimental characterization of high dimensional dynamic systems sometimes uses the proper orthogonal decomposition (POD). If there are many measurement locations and relatively fewer sensors, then steady-state behavior can still be studied by sequentially taking several sets of simultaneous measurements. The number required of such sets of measurements can be minimized if we solve a combinatorial optimization problem. We aim to bring this problem to the attention of engineering audiences, summarize some known mathematical results about this problem, and present a heuristic (suboptimal) calculation that gives reasonable, if not stellar, results.

Disorder Induced Concomitant Polymorphism in 3-Fluoro-N-(3-fluorophenyl)benzamide

The occurrence of concomitant polymorphism in 3-fluoro-N-(3-fluorophenyl) benzamide has been identified to be due to the disorder in the crystal structure. Of the two modifications, the plate form (Form I) crystallizes in the monoclinic centrosymmetric space group C2/c with Z = 4, and the needle form (Form II) crystallizes in the noncentrosymmetric space group P21 with Z = 2. An interesting positional disorder at the bridging atoms in both forms holds the molecular conformation identical, while subtle variations brought by N−H···O hydrogen bonds along with weak C−H···F and F···F interactions result in packing polymorphism.

Critical test for Altshuler-Aronov theory: Evolution of the density of states singularity in double perovskite Sr2FeMoO6 with controlled disorder

With high-resolution photoemission spectroscopy measurements, the density of states (DOS) near the Fermi level (E-F) of double perovskite Sr2FeMoO6 having different degrees of Fe/Mo antisite disorder has been investigated with varying temperature. The DOS near E-F showed a systematic depletion with increasing degree of disorder, and recovered with increasing temperature. Altshuler-Aronov (AA) theory of disordered metals well explains the dependences of the experimental results. Scaling analysis of the spectra provides experimental indication for the functional form of the AA DOS singularity.