Coupled Solution for Forced Recharge in Confined Aquifers

Analytical solutions for forced well recharge currently in use were initially developed for pumping scenarios and applied for recharge cases assuming that radial flow in the recharge well replicates a mirror image of that in to a pumping well. Moreover these solutions were not extended to multiaquifer systems. Well bore numerical solutions were generally not considering the effect of well bore interaction, which has a significant effect in the case of a recharge well. In the present paper, improved analytical solutions are developed for a well fully penetrating either single or multiaquifers in respect.to of well storage, well loss, and interactions between the individual aquifers through well bore. The solution developed for constant and variable rates of injection and well loss is applied to the experimental data of the Hansol well injection project near the city of Ahmedabad in the Gujarat state in India. The paper also discusses the difference in well hydraulics of recharge and recovery wells.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

A New Threshold Voltage Model for Omega Gate Cylindrical Nanowire Transistor

In this work, for the first time, we present a physically based analytical threshold voltage model for omega gate silicon nanowire transistor. This model is developed for long channel cylindrical body structure. The potential distribution at each and every point of the of the wire is derived with a closed form solution of two dimensional Poisson's equation, which is then used to model the threshold voltage. Proposed model can be treated as a generalized model, which is valid for both surround gate and semi-surround gate cylindrical transistors. The accuracy of proposed model is verified for different device geometry against the results obtained from three dimensional numerical device simulators and close agreement is observed.

An asymptotic analysis for the coupled dispersion characteristics of a structural acoustic waveguide

Analytical expressions are derived, using asymptotics, for the fluid-structure coupled wavenumbers in a one-dimensional (1-D) structural acoustic waveguide. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation with an added term due to the fluid-structure coupling. As a result of this coupling, the prior uncoupled structural and acoustic wavenumbers, now become coupled structural and acoustic wavenumbers. A fluid-loading parameter e, defined as the ratio of mass of fluid to mass of the structure per unit area, is introduced which when set to zero yields the uncoupled dispersion equation. The coupled wavenumber is then expressed in terms of an asymptotic series in e. Analytical expressions are found as e is varied from small to large values. Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. This systematic derivation helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Though the asymptotic expansion used is limited to the first-order correction factor, the results are close to the numerical results. A general trend is that a given wavenumber branch transits from a rigid-walled solution to a pressure-release solution with increasing E. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an-intersection in the coupled case, but a gap is created at that frequency. (c) 2007 Elsevier Ltd. All rights reserved.

Critical lattice size limit for synchronized chaotic state in one- and two-dimensional diffusively coupled map lattices

We consider diffusively coupled map lattices with P neighbors (where P is arbitrary) and study the stability of the synchronized state. We show that there exists a critical lattice size beyond which the synchronized state is unstable. This generalizes earlier results for nearest neighbor coupling. We confirm the analytical results by performing numerical simulations on coupled map lattices with logistic map at each node. The above analysis is also extended to two-dimensional P-neighbor diffusively coupled map lattices.

Modeling and analysis of a tunable piezoelectric structure for transverse shear wave generation

An analytical investigation of the transverse shear wave mode tuning with a resonator mass (packing mass) on a Lead Zirconium Titanate (PZT) crystal bonded together with a host plate and its equivalent electric circuit parameters are presented. The energy transfer into the structure for this type of wave modes are much higher in this new design. The novelty of the approach here is the tuning of a single wave mode in the thickness direction using a resonator mass. First, a one-dimensional constitutive model assuming the strain induced only in the thickness direction is considered. As the input voltage is applied to the PZT crystal in the thickness direction, the transverse normal stress distribution induced into the plate is assumed to have parabolic distribution, which is presumed as a function of the geometries of the PZT crystal, packing mass, substrate and the wave penetration depth of the generated wave. For the PZT crystal, the harmonic wave guide solution is assumed for the mechanical displacement and electric fields, while for the packing mass, the former is solved using the boundary conditions. The electromechanical characteristics in terms of the stress transfer, mechanical impedance, electrical displacement, velocity and electric field are analyzed. The analytical solutions for the aforementioned entities are presented on the basis of varying the thickness of the PZT crystal and the packing mass. The results show that for a 25% increase in the thickness of the PZT crystal, there is ~38% decrease in the first resonant frequency, while for the same change in the thickness of the packing mass, the decrease in the resonant frequency is observed as ~35%. Most importantly the tuning of the generated wave can be accomplished with the packing mass at lower frequencies easily. To the end, an equivalent electric circuit, for tuning the transverse shear wave mode is analyzed.

Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport

A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications.

One-dimensional zig-zag type coordination polymers of Ni(II) and Cu(II) containing 1,3-benzenedicarboxylate and 1,3-diaminopropane: Structural, spectral and thermal studies

Two coordination polymers [Ni(ipt)(dap)(2)](n) (1) and [Cu(ipt)(dap)H2O](n) center dot nH(2)O (2) with an overall one-dimensional arrangement and having isophthalate (ipt) as bridging moieties and chelating 1,3-diaminopropane (dap) as structure modulating units have been prepared and characterized by crystallographic, spectroscopic and thermo-analytical studies. Both have an overall one-dimensional zig-zag nature but with a distorted octahedral NiN4O2 chromophore for 1 and a distorted square pyramidal CuN2O3 chromophore for 2. Even though the ipt units are acting as bridging units through mono-dentatively coordinating carboxylate functions in both polymers, compound 1 has the carboxylate oxygen linkages at the trans positions, while in 2 the oxygen linkages occur at the cis positions leading to a different type of zig-zag arrangement. Relevant spectral and bonding parameters also could be evaluated for the compounds using UV-Vis and EPR spectra. Thermal stability and possible structural modifications on thermal treatment of the compounds were also investigated and the relevant thermodynamic and kinetic parameters evaluated from the thermal data. (C) 2007 Elsevier B.V. All rights reserved.

Conformationally restricted formyl methionyl tripeptide chemoattractants: a three-dimensional structure-activity study of analogs incorporating a C alpha,alpha-dialkylated glycine at position 2

The conformationally restricted CHO-L-Met-Xxx-L-Phe-OY (where Xxx = Aib, Ac3c, Ac5c, Ac6c, and Ac7c; Y = H, Me) tripeptides, analogs of the chemoattractant CHO-L-Met-L-Leu-L-Phe-OH, have been synthesized in solution by classical methods and fully characterized. Compounds were compared to determine the combined effect of backbone conformational preferences and side-chain bulkiness on the relation of three-dimensional structure to biological activity. Each peptide was tested for its ability to induce granule enzyme secretion from rabbit peritoneal polymorphonuclear leukocytes. In parallel, a conformational analysis on the CHO-blocked peptide and their tertbutyloxycarbonylated synthetic precursors was performed in the crystal state and in solution using X-ray diffraction, infrared absorption, and 1H nuclear magnetic resonance. The biological and conformational data are discussed in relation to the proposed model of the chemotactic peptide receptor of rabbit neutrophils.

Solution-Combustion Synthesized Nanocrystalline Li4Ti5O12 As High-Rate Performance Li-Ion Battery Anode

Nanocrystalline Li4Ti5O12 (LTO) crystallizing in cubic spinel-phase has been synthesized by single-step-solution-combustion method in less than one minute. LTO particles thus synthesized are flaky and highly porous in nature with a surface area of 12 m(2)/g. Transmission electron micrographs indicate the primary particles to be agglomerated crystallites of varying size between 20 and 50 nm with a 3-dimensional interconnected porous network. During their galvanostatic charge-discharge at varying rates, LTO electrodes yield a capacity value close to the theoretical value of 175 mA h/g at C/2 rate. The electrodes also exhibit promising capacity retention with little capacity loss over 100 cycles at varying discharge rates together with attractive discharge-rate capabilities yielding capacity values of 140 mA h/g and 70 mA h/g at 10 and 100 C discharge rates, respectively. The ameliorated electrode-performance is ascribed to nano and highly porous morphology of the electrodes that provide short diffusion-paths for Li in conjunction with electrolyte percolation through the electrode pores ensuring a high flux of Li.

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Solution structure of O-glycosylated C-terminal leucine zipper domain of human salivary mucin (MUC7)

Solution structures of a 23 residue glycopeptide II (KIS* RFLLYMKNLLNRIIDDMVEQ, where * denotes the glycan Gal-beta-(1-3)-alpha-GalNAc) and its deglycosylated counterpart I derived from the C-terminal leucine zipper domain of low molecular weight human salivary mucin (MUC7) were studied using CD, NMR spectroscopy and molecular modeling. The peptide I was synthesized using the Fmoc chemistry following the conventional procedure and the glycopeptide II was synthesized incorporating the O-glycosylated building block (N alpha-Fmoc-Ser-[Ac-4,-beta-D-Gal-(1,3)-Ac(2)alpha-D-GalN(3)]-OPfp) at the appropriate position in stepwise assembly of peptide chain. Solution structures of these glycosylated and nonglycosylated peptides were studied in water and in the presence of 50% of an organic cosolvent, trifluoroethanol (TFE) using circular dichroism (CD), and in 50% TFE using two-dimensional proton nuclear magnetic resonance (2D H-1 NMR) spectroscopy. CD spectra in aqueous medium indicate that the apopeptide I adapts, mostly, a beta-sheet conformation whereas the glycopeptide II assumes helical structure. This transition in the secondary structure, upon glycosylation, demonstrates that the carbohydrate moiety exerts significant effect on the peptide backbone conformation. However, in 50% TFE both the peptides show pronounced helical structure. Sequential and medium range NOEs, C alpha H chemical shift perturbations, (3)J(NH:C alpha H) couplings and deuterium exchange rates of the amide proton resonances in water containing 50% TFE indicate that the peptide I adapts alpha-helical structure from Ile2-Val21 and the glycopeptide II adapts alpha-helical structure from Ser3-Glu22. The observation of continuous stretch of helix in both the peptides as observed by both NMR and CD spectroscopy strongly suggests that the C-terminal domain of MUC7 with heptad repeats of leucines or methionine residues may be stabilized by dimeric leucine zipper motif. The results reported herein may be invaluable in understanding the aggregation (or dimerization) of MUC7 glycoprotein which would eventually have implications in determining its structure-function relationship.

Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface

A numerical solution of the unsteady boundary layer equations under similarity assumptions is obtained. The solution represents the three-dimensional unsteady fluid motion caused by the time-dependent stretching of a flat boundary. It has been shown that a self-similar solution exists when either the rate of stretching is decreasing with time or it is constant. Three different numerical techniques are applied and a comparison is made among them as well as with earlier results. Analysis is made for various situations like deceleration in stretching of the boundary, mass transfer at the surface, saddle and nodal point flows, and the effect of a magnetic field. Both the constant temperature and constant heat flux conditions at the wall have been studied.

A two-dimensional model for crack closure effect in plates under bending

A two-dimensional model is proposed for taking into account the establishment of contact on the compression side of crack faces in plates under bending. An approximate but simple method is developed for evaluating reduction of stress intensity factor due to such ‘crack closure’. Analysis is first carried out permitting interference of the crack faces. Contact forces are then introduced on the crack faces and their magnitudes determined from the consideration that the interference is just eliminated. The method is based partly on finite element analysis and partly on a continuum analysis using Irwin's solution for point loads on the crack line.