Exact free-surface flows for shallow-water equations .1. - the incompressible case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.

Free vibration analysis Of stochastic strings

The free vibration of strings with randomly varying mass and stiffness is considered. The joint probability density functions of the eigenvalues and eigenfunctions are characterized in terms of the solution of a pair of stochastic non-linear initial value problems. Analytical solutions of these equations based on the method of stochastic averaging are obtained. The effects of the mean and autocorrelation of the mass process are included in the analysis. Numerical results for the marginal probability density functions of eigenvalues and eigenfunctions are obtained and are found to compare well with Monte Carlo simulation results. The random eigenvalues, when normalized with respect to their corresponding deterministic values, are observed to tend to become first order stochastically stationary with respect to the mode count.

Intracellular free calcium level and its response to cAMP stimulation in developing Dictyostelium cells transformed with jellyfish apoaequorin CDNA

A new method is described for measuring intracellular free calcium concentrations, [(Ca2+)(i)], in the cells of Dictyostelium discoideum transformed with apoaequorin cDNA of the jellyfish, Aequorea victoria. Aequorin, a calcium-specific indicator, was regenerated in vivo from apoaequorin produced in the cells by incubation with coelenterazine. The results showed that [(Ca2+)(i)] in developing cells markedly increases at the aggregation stage and again at the culmination stage after a temporary drop at the migration stage. Except for the vegetative stage, the cells al all stages of development exhibit a sharp transient increase in [(Ca2+)(i)] upon stimulation with a cAMP (50 nM) pulse, high responses being observed at the migration and culmination stages. Separated prestalk cells of migrating slugs contain more than twice as much [(Ca2+)(i)] and show three times as large a response to cAMP stimulation as prespore cells.

A critical assessment of the standard molar gibbs free energy of formation of NiWO4

Three independent studies have been reported on the free energy of formation of NiWO4. Results of these measurements are analyzed by the �third-law� method, using thermal functions for NiWO4 derived from both low and high temperature heat capacity measurements. Values for the standard molar enthalpy of formation of NiWO4 at 298·15 K obtained from �third-law� analysis are compared with direct calorimetric determinations. Only one set of free energy measurements is found to be compatible with calorimetric enthalpies of formation. The selected value for ?f H m 0 (NiWO4, cr, 298·15 K) is the average of the three calorimetric measurements, using both high temperature solution and combustion techniques, and the compatible free energy determination. A new set of evaluated data for NiWO4 is presented.

Wet chemical syntheses of ultrafine multicomponent ceramic powders through gel to crystallite conversion

Coarse (BOn/2)-O-n+/xH(2)O (10

Metal-Free Deprotection of Terminal Acetonides by Using tert-Butyl Hydroperoxide in Aqueous Medium

Employing aqueous tert-butyl hydroperoxide (70%) as an inexpensive reagent a useful methodology for the regioselective and chemoselective deprotection of terminal acetonide groups in aqueous medium is developed. A variety of acetonide derivatives on reaction with aqueous tert-butyl hydroperoxide in water:tert-butanol (1:1) furnish the corresponding acetonide deprotected diols in good yields. A large number of acid labile protecting functional groups and other functional moieties were found to be unaffected under the conditions employed for the present deprotection. This method has been successfully applied to sugar derivatives.

Characterization of lysozyme crystals with unusually low solvent content

Studies on the low-humidity (88%) forms of tetragonal and monoclinic lysozyme, resulting from water-mediated transformations, have provided a wealth of information on the variability in protein hydration, its structural consequences and the water structure associated with proteins, in addition to facilitating the delineation of the rigid and the flexible regions in the protein molecule and the invariant features in its hydration shell. Surprisingly, monoclinic lysozyme continues to diffract even when the environmental humidity is drastically reduced, thus permitting the structural study of the enzyme at different levels of hydration. As part of a study in this direction, three very low humidity forms, two of them occuring at a nominal relative humidity of 38% and the other at 5% relative humidity, have been characterized. These have unprecedented low solvent contents of 16.9, 17.6 and 9.4%, respectively, as determined by the Matthews method.

Quantum and non-Markovian effects in the electron transfer reaction dynamics in the Marcus inverted region

Electron transfer reactions in large molecules may often be coupled to both the polar solvent modes and the intramolecular vibrational modes of the molecule. This can give rise to a complex dynamics which may in some systems, like betaine, be controlled more by vibrational rather than by solvent effects. Additionally, a significant contribution from an ultrafast relaxation component in the solvation dynamics may enhance the complexity. To explain the wide range of behavior that has been observed experimentally, Barbara et al. recently proposed that a model of an electron transfer reaction should minimally consist of a low-frequency classical solvent mode (X), a low-frequency vibrational mode (Q), and a high-frequency quantum mode (q) (J. Phys. Chem. 1991, 96, 3728). In the present work, a theoretical study of this model is described. This study generalizes earlier work by including the biphasic solvent response and the dynamics of the low-frequency vibrational mode in the presence of a delocalized, extended reaction zone. A novel Green's function technique has been developed which allowed us to study the non-Markovian dynamics on a multidimensional surface. The contributions from the high-frequency vibrational mode and the ultrafast component in the non-Markovian solvent dynamics are found to be primarily responsible for the dramatic increase in charge transfer rate over the prediction of the classical theories that neglect both these factors. These, along with a large coupling between the reactant and the product states, may combine to render the electron transfer rate both very large and constant over a wide range of solvent relaxation rates. A study on the free energy gap dependence of the electron transfer rate reveals that the rates are sensitive to changes in the quantum frequency particularly when the free energy gap is very large.

Role of free valences and spin densities on the migrating atom in location of saddle points in radical-exchange reactions

The principle of the conservation of bond orders during radical-exchange reactions is examined using Mayer's definition of bond orders. This simple intuitive approximation is not valid in a quantitative sense. Ab initio results reveal that free valences (or spin densities) develop on the migrating atom during reactions. For several examples of hydrogen-transfer reactions, the sum of the reaction coordinate bond orders in the transition state was found to be 0.92 +/- 0.04 instead of the theoretical 1.00 because free valences (or spin densities) develop on the migrating atom during reactions. It is shown that free valence is almost equal to the square of the spin density on the migrating hydrogen atom and the maxima in the free valence (or spin density) profiles coincide (or nearly coincide) with the saddle points in the corresponding energy profiles.

Solubilization of n-decane into n-decyl-polyoxyethylene surfactants: A cavity forming free energy based model

The present paper reports the results of a theoretical study of the forces and factors driving the solubilization of n-alkane solubilizates into the micellar core of some non-ionic surfactants, based on a micellar model which includes the cavity forming free energy as a component of micellization. The solubilizate is n-decane and the non-ionic surfactants considered are n-decyl-polyoxyethylene surfactants. The extent of solubilization, i.e. the mole fraction of the solubilizate within the core has been calculated. The results indicate that the incorporated solubilizate has more translational and rotational degrees of freedom as compared to those of the tail parts of the surfactants present in the core. This drives the total free energy of aggregation after solubilization into a more favourable direction. The results are in fair agreement with the experimental results.

Time scales for transitions between free-energy minima of a dense hard-sphere system

Time scales associated with activated transitions between glassy metastable states of a free-energy functional appropriate for a dense hard-sphere system are calculated by using a new Monte Carlo method for the local density variables. In particular, we calculate the time the system, initially placed in a shallow glassy minimum of the free-energy, spends in the neighborhood of this minimum before making a transition to the basin of attraction of another free-energy minimum. This time scale is found to increase as the average density is increased. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This time scale does not show any evidence of increasing with sample size

Role of Water in the Enzymatic Catalysis: Study of ATP plus AMP -> 2ADP Conversion by Adenylate Kinase

The catalytic conversion ATP + AMP -> 2ADP by the enzyme adenylate kinase (ADK) involves the binding of one ATP. molecule to the LID domain and one AMP molecule to the NMP domain. The latter is followed by a. phosphate transfer and then the release of two ADP molecules. We have computed a novel two-dimensional configurational free energy surface (2DCFES), with one reaction coordinate each for the LID and the NMP domain motions, while considering explicit water interactions. Our computed 2DCFES clearly reveals the existence of a stable half-open half-closed (HOHC) intermediate stale of the enzyme. Cycling of the enzyme through the HOHC state reduces the conformational free energy barrier for. the reaction by about 20 kJ/mol. We find that the stability of the HOHC state (missed in all earlier studies with implicit solvent model) is largely because of the increase of specific interactions of the polar amino acid side chains with water, particularly with the arginine and the histidine residues. Free energy surface of the LID domain is rather rugged, which can conveniently slow down LID's conformational motion, thus facilitating a new substrate capture after the product release in the catalytic cycle.

Exact free-surface flows for shallow-water equations .2. the compressible case

Exact free surface flows with shear in a compressible barotropic medium are found, extending the authors' earlier work for the incompressible medium. The barotropic medium is of finite extent in the vertical direction, while it is infinite in the horizontal direction. The ''shallow water'' equations for a compressible barotropic medium, subject to boundary conditions at the free surface and at the bottom, are solved in terms of double psi-series, Simple wave and time-dependent solutions are found; for the former the free surface is of arbitrary shape while for the latter it is a damping traveling wave in the horizontal direction, For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed. In the case of an isothermal medium, when gamma = 1, we again find simple wave and time-dependent solutions.

Free convection in power-law fluids near a three-dimensional stagnation point

Numerical results are presented for the free-convection boundary-layer equations of the Ostwald de-Waele non-Newtonian power-law type fluids near a three-dimensional (3-D) stagnation point of attachment on an isothermal surface. The existence of dual solutions that are three-dimensional in nature have been verified by means of a numerical procedure. An asymptotic solution for very large Prandtl numbers has also been derived. Solutions are presented for a range of values of the geometric curvature parameter c, the power-law index n, and the Prandtl number Pr.