Integrability and singularity structure of predator‐prey system

The ‘‘extended’’ ARS (Ablowitz, Ramani, and Segur) algorithm is introduced to characterize a dynamical system as Painlevé or otherwise; to that end, it is required that the formal series—the Laurent series, logarithmic, algebraic psi series about a movable singularity—are shown to converge in the deleted neighborhood of the singularity. The determinations thus obtained are compared with those following from the α method of Painlevé. An attempt is made to relate the structure of solutions about a movable singularity with that of first integrals (when they exist). All these ideas are illustrated by a comprehensive analysis of the general two‐dimensional predator‐prey system.

Phase nonequilibrium effects on the gain of a two-phase flow gasdynamic laser

Analysis of gas-particle nozzle flow is carried out with attention to the effect of dust particles on the vibrational relaxation phenomena and consequent effects on the gain of a gasdynamic laser. The phase nonequilibrium between the gas mixture and the particles during the nozzle expansion process is taken into account simultaneously. The governing equations of the two-phase nozzle flow have been transformed into similar form, and general correlating parameters have been obtained. It is shown from the present analysis that the particles present in the mixture affect the optimum gain obtainable from a gasdynamic laser adversely, and the effect depends on the size and loading of the particles in the mixture.

Solubility of sulfur dioxide at low partial pressures in dilute sulfuric acid solutions

Equilibrium of dissolution of sulfur dioxide at ppm levels in aqueous solutions of dilute sulfuric acid is analyzed, and a general expression is derived relating the total concentration of sulfur dioxide in the liquid phase to the partial pressure of SO2 in the gas and to the concentration of sulfuric acid in the solution. The equation is simplified for zero and high concentrations of the acid. Experiments at high concentrations of sulfuric acid have enabled the direct determination of Henry’s constant and its dependency on temperature. Heat of dissolution is -31.47 kJ/mol. Experiments in the absence of sulfuric acid and the related simplified expression have led to the determination of the equilibrium constant of the hydrolysis of aqueous sulfur dioxide and its temperature dependency.The heat of hydrolysis is 15.69 kJ/mol. The model equation with these parameters predicts the experimental data of the present work as well as the reported data very well.

Bearing capacity factors of circular foundations for a general c-phi soil using lower bound finite elements limit analysis

By using the lower bound limit analysis in conjunction with finite elements and linear programming, the bearing capacity factors due to cohesion, surcharge and unit weight, respectively, have been computed for a circular footing with different values of phi. The recent axisymmetric formulation proposed by the authors under phi = 0 condition, which is based on the concept that the magnitude of the hoop stress (sigma(theta)) remains closer to the least compressive normal stress (sigma(3)), is extended for a general c-phi soil. The computational results are found to compare quite well with the available numerical results from literature. It is expected that the study will be useful for solving various axisymmetric geotechnical stability problems. Copyright (C) 2010 John Wiley & Sons, Ltd.

A canonical formulation of the direct position kinematics problem for a general 6-6 stewart platform

This paper deals with the direct position kinematics problem of a general 6-6 Stewart platform, the complete solution of which is not reported in the literature until now and even establishing the number of possible solutions for the general case has remained an unsolved problem for a long period. Here a canonical formulation of the direct position kinematics problem for a general 6-6 Stewart platform is presented. The kinematic equations are expressed as a system of six quadratic and three linear equations in nine unknowns, which has a maximum of 64 solutions. Thus, it is established that the mechanism, in general, can have up to 64 closures. Further reduction of the system is shown arriving at a set of three quartic equations in three unknowns, the solution of which will yield the assembly configurations of the general Stewart platform with far less computational effort compared to earlier models.

A formula for the solution of general Abel integral equation

A new formula for the solution of the general Abel Integral equation is derived, and an important special case is checked with the known result.

A general procedure for modified crack closure integral in 3D problems with cracks

In linear elastic fracture mechanics (LEFM), Irwin's crack closure integral (CCI) is one of the signficant concepts for the estimation of strain energy release rates (SERR) G, in individual as well as mixed-mode configurations. For effective utilization of this concept in conjunction with the finite element method (FEM), Rybicki and Kanninen [Engng Fracture Mech. 9, 931 938 (1977)] have proposed simple and direct estimations of the CCI in terms of nodal forces and displacements in the elements forming the crack tip from a single finite element analysis instead of the conventional two configuration analyses. These modified CCI (MCCI) expressions are basically element dependent. A systematic derivation of these expressions using element stress and displacement distributions is required. In the present work, a general procedure is given for the derivation of MCCI expressions in 3D problems with cracks. Further, a concept of sub-area integration is proposed which facilitates evaluation of SERR at a large number of points along the crack front without refining the finite element mesh. Numerical data are presented for two standard problems, a thick centre-cracked tension specimen and a semi-elliptical surface crack in a thick slab. Estimates for the stress intensity factor based on MCCI expressions corresponding to eight-noded brick elements are obtained and compared with available results in the literature.

Lanthanide Luminescent Coordination Polymer Constructed from Unsymmetrical Dinuclear Building Blocks Based on 4-((1H-Benzod]imidazol-1-yl)methyl)benzoic Acid

Lanthanide coordination polymers of the general formula Ln(2)(L)(5)(NO3)(H2O)(4)](n) (Ln = Eu (1), Tb (2), Gd (3)) supported by a novel aromatic carboxylate ligand 4-((1H-benzod]imidazol-1-yl)methyl)benzoic acid (HL) have been synthesized, characterized, and their photoluminescence behavior is examined. The powder X-ray diffraction patterns of complexes 1-3 showed that 1-3 are isostructural; thus, 1 has been chosen as an example to discuss in detail about the molecular structure by single-crystal X-ray diffraction. Complex 1 is a one-dimensional (1D) helical chain-like coordination polymer consisting of unique unsymmetrical dinuclear lanthanide building blocks. The 1D chains are further linked by the significant intermolecular hydrogen-bonding interactions to form a two-dimensional supramolecular network. The Tb3+ complex exhibits bright green luminescence efficiency in the solid state with a quantum yield of 15%. On the other hand, poor luminescence efficiency has been noted for Eu3+-benzoate complex.

Distinct Allostery Induced in the Cyclic GMP-binding, Cyclic GMP-specific Phosphodiesterase (PDE5) by Cyclic GMP, Sildenafil, and Metal Ions

The activity of many proteins orchestrating different biological processes is regulated by allostery, where ligand binding at one site alters the function of another site. Allosteric changes can be brought about by either a change in the dynamics of a protein, or alteration in its mean structure. We have investigated the mechanisms of allostery induced by chemically distinct ligands in the cGMP-binding, cGMP-specific phosphodiesterase, PDE5. PDE5 is the target for catalytic site inhibitors, such as sildenafil, that are used for the treatment of erectile dysfunction and pulmonary hypertension. PDE5 is a multidomain protein and contains two N-terminal cGMP-specific phosphodiesterase, bacterial adenylyl cyclase, FhLA transcriptional regulator (GAF) domains, and a C-terminal catalytic domain. Cyclic GMP binding to the GAFa domain and sildenafil binding to the catalytic domain result in conformational changes, which to date have been studied either with individual domains or with purified enzyme. Employing intramolecular bioluminescence resonance energy transfer, which can monitor conformational changes both in vitro and in intact cells, we show that binding of cGMP and sildenafil to PDE5 results in distinct conformations of the protein. Metal ions bound to the catalytic site also allosterically modulated cGMP- and sildenafil-induced conformational changes. The sildenafil-induced conformational change was temperature-sensitive, whereas cGMP-induced conformational change was independent of temperature. This indicates that different allosteric ligands can regulate the conformation of a multidomain protein by distinct mechanisms. Importantly, this novel PDE5 sensor has general physiological and clinical relevance because it allows the identification of regulators that can modulate PDE5 conformation in vivo.

Dynamics of zeolite cage and its effect on the diffusion properties of sorbate: persistence of diffusion anomaly in NaA zeolite

Recent computer simulations on zeolites Y and A have found that the diffusion coefficient and the rate of intercage diffusion exhibit, apart from a linear dependence on the reciprocal of the square of the sorbate diameter, an anomalous peak as sorbate diameter approaches the window diameter. Here we report molecular dynamics simulations of zeolite NaA incorporating framework flexibility as a function of sorbate diameter in order to verify the existence of anomalous diffusion. Results suggest persistence of anomalous diffusion or ring effect. This suggests that the anomalous behavior is a general effect characteristic of zeolites Y and A. The barrier for diffusion across the eight-ring window is seen to be negative and is found to decrease with sorbate size. The effect of sorbate on the cage motion has also been investigated. Results suggest that the window expands during intercage migration only if the sorbate size is comparable to the window diameter. Flexible cage simulations yield a higher value for the diffusion coefficient and also the rate of intercage diffusion. This increase has been shown to be due to an increase in the intercage diffusions via the centralized diffusion mode rather than the surface-mediated mode. It is shown that this increase arises from an increase in the single particle density distribution in the region near the cage center.

Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

Ultrafast underdamped solvation: Agreement between computer simulation and various theories of solvation dynamics

A theoretical analysis of the three currently popular microscopic theories of solvation dynamics, namely, the dynamic mean spherical approximation (DMSA), the molecular hydrodynamic theory (MHT), and the memory function theory (MFT) is carried out. It is shown that in the underdamped limit of momentum relaxation, all three theories lead to nearly identical results when the translational motions of both the solute ion and the solvent molecules are neglected. In this limit, the theoretical prediction is in almost perfect agreement with the computer simulation results of solvation dynamics in the model Stockmayer liquid. However, the situation changes significantly in the presence of the translational motion of the solvent molecules. In this case, DMSA breaks down but the other two theories correctly predict the acceleration of solvation in agreement with the simulation results. We find that the translational motion of a light solute ion can play an important role in its own solvation. None of the existing theories describe this aspect. A generalization of the extended hydrodynamic theory is presented which, for the first time, includes the contribution of solute motion towards its own solvation dynamics. The extended theory gives excellent agreement with the simulations where solute motion is allowed. It is further shown that in the absence of translation, the memory function theory of Fried and Mukamel can be recovered from the hydrodynamic equations if the wave vector dependent dissipative kernel in the hydrodynamic description is replaced by its long wavelength value. We suggest a convenient memory kernel which is superior to the limiting forms used in earlier descriptions. We also present an alternate, quite general, statistical mechanical expression for the time dependent solvation energy of an ion. This expression has remarkable similarity with that for the translational dielectric friction on a moving ion.

Variations in the copper(I)-copper(I) distances in multinuclear clusters with identical coordination geometries. Short metal-metal contacts induced by oligomerization

Factors contributing to the variations in the Cu(I)-Cu(I) distances in two clusters with identical ligand and coordination geometries have been analyzed. While the hexamer, 4, exhibits metal-metal distances in the range 2.81-3.25 Angstrom, shorter contacts are found in the corresponding tetramer, 3 (2.60-2.77 Angstrom). EHT calculations reveal relatively little attractive interactions in the corresponding Cu-4(4+) and Cu-6(6+) cores. Introduction of the ligands lowers the reduced overlap populations between the metals further. MNDO calculations with model electrophiles have been carried out to determine the bite angle requirements of the ligands. These are satisfactorily met in the structures of both 3 and 4. The key geometric feature distinguishing 3 and 4 is the Cu-S-Cu angle involving the bridging S- unit. In 4, the corresponding angles are about 90 degrees, while the values in 3 are smaller (70-73 degrees). Wider angles are computed to be energetically favored and are characterized by an open three-center bond and a long Cu-Cu distance. The bridging angles are suggested to be primarily constrained by the mode of oligomerization. Implications of these results for the stability and reactivity of these clusters and for short metal-metal distances in d(10) systems in general are discussed.

3-D Warping in Four-Bar Laminated Linkages

This paper deals with the evaluation of the component-laminate load-carrying capacity, i.e., to calculate the loads that cause the failure of the individual layers and the component-laminate as a whole in four-bar mechanism. The component-laminate load-carrying capacity is evaluated using the Tsai-Wu-Hahn failure criterion for various layups. The reserve factor of each ply in the component-laminate is calculated by using the maximum resultant force and the maximum resultant moment occurring at different time steps at the joints of the mechanism. Here, all component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict more quickly and accurately than would otherwise be possible. Local 3-D stress, strain and displacement fields for representative sections in the component-bars are recovered, based on the stress resultants from the 1-D global beam analysis. A numerical example is presented which illustrates the failure of each component-laminate and the mechanism as a whole.

The Shannon Cipher System With a Guessing Wiretapper: General Sources

The Shannon cipher system is studied in the context of general sources using a notion of computational secrecy introduced by Merhav and Arikan. Bounds are derived on limiting exponents of guessing moments for general sources. The bounds are shown to be tight for i.i.d., Markov, and unifilar sources, thus recovering some known results. A close relationship between error exponents and correct decoding exponents for fixed rate source compression on the one hand and exponents for guessing moments on the other hand is established.