Geometry Of Proline And Hydroxyproline .1. An Analysis Of X-Ray Crystal-Structure Data

We have carried out an analysis of crystal structure data on prolyl and hydroxyprolyl moieties in small molecules. The flexibility of the pyrrolidine ring due to the pyramidal character of nitrogen has been defined in terms of two projection angles δ1 and δ2. The distribution of these parameters in the crystal structures is found to be consistent with results of the energy calculations carried out on prolyl moieties in our laboratory.

The mean geometry of the peptide unit from crystal structure data

The average dimensions of the peptide unit have been obtained from the data reported in recent crystal structure analyses of di- and tripeptides. The bond lengths and bond angles agree with those in common use, except for the bond angle C---N---H, which is about 4° less than the accepted value, and the angle C2α---N---H which is about 4° more. The angle τ (Cα) has a mean value of 114° for glycyl residues and 110° for non-glycyl residues. Attention is directed to these mean values as observed in crystal structures, as they are relevant for model building of peptide chain structures.

Geometry of the de-Sitter universe

By making use of the fact that the de-Sitter metric corresponds to a hyperquadric in a five-dimensional flat space, it is shown that the three Robertson-Walker metrics for empty spacetime and positive cosmological constant, corresponding to 3-space of positive, negative and zero curvative, are geometrically equivalent. The 3-spaces correspond to intersections of the hyperquadric by hyperplanes, and the time-like geodesics perpendicular to them correspond to intersections by planes, in all three cases.

Lattice embedding and equilibrium geometry of metal-halogen chains in the two-band extended Hubbard model

Two-band extended Hubbard model studies show that the shift in optical gap of the metal-halogen (MX) chain upon embedding in a crystalline environment depends upon alternation in the site-diagonal electron-lattice interaction parameter (epsilon(M)) and the strength of electron-electron interactions at the metal site (U(M)). The equilibrium geometry studies on isolated chains show that the MX chains tend to distort for alternating epsilon(M) and small U(M) values.

Geometry of proline-containing alpha-helices in proteins

Crystal structure analysis of proline-containing alpha-helices in proteins has been carried out. High resolution crystal structures were selected from the Protein Data Bank. Apart from the standard internal parameters, some parameters which are specifically related to the bend in the helix due to proline have been developed and analyzed. Finally the position and nature of these helices and their interactions with the rest of the protein have been analyzed.

Geometry of sand-bed channels with seepage

Literature suggests that apart from a significant percentage of water loss from seepage, downward seepage from the channel causes an increase in the mobility of channel bed materials and thus changes the channel stability. Consequently, regime conditions (which provide the relationship among hydraulic parameters) should also be revised by incorporating downward seepage as an additional parameter. In the present work, regime conditions for the prediction of channel geometry in alluvial channels affected by downward seepage have been formulated on the basis of experimental observations. (C) 2011 Elsevier B.V. All rights reserved.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Helical structures: The geometry of protein helices and nanotubes

In nature, helical structures arise when identical structural subunits combine sequentially, the orientational and translational relation between each unit and its predecessor remaining constant. A helical structure is thus generated by the repeated action of a screw transformation acting on a subunit. A plane hexagonal lattice wrapped round a cylinder provides a useful starting point for describing the helical conformations of protein molecules, for investigating the geometrical properties of carbon nanotubes, and for certain types of dense packings of equal spheres.

Geometry of static balancing during posture transition

The interaction between the digital human model (DHM) and environment typically occurs in two distinct modes; one, when the DHM maintains contacts with the environment using its self weight, wherein associated reaction forces at the interface due to gravity are unidirectional; two, when the DHM applies both tension and compression on the environment through anchoring. For static balancing in first mode of interaction, it is sufficient to maintain the projection of the centre of mass (COM) inside the convex region induced by the weight supporting segments of the body on a horizontal plane. In DHM, static balancing is required while performing specified tasks such as reach, manipulation and locomotion; otherwise the simulations would not be realistic. This paper establishes the geometric relationships that must be satisfied for maintaining static balance while altering the support configurations for a given posture and altering the posture for a given support condition. For a given location of the COM for a system supported by multiple point contacts, the conditions for simultaneous withdrawal of a specified set of contacts have been determined in terms of the convex hulls of the subsets of the points of contact. When the projection of COM must move beyond the existing support for performing some task, new supports must be enabled for maintaining static balance. This support seeking behavior could also manifest while planning for reduction of support stresses. Feasibility of such a support depends upon the availability of necessary features in the environment. Geometric conditions necessary for selection of new support on horizontal,inclined and vertical surfaces within the workspace of the DHM for such dynamic scenario have been derived. The concepts developed are demonstrated using the cases of sit-to-stand posture transition for manipulation of COM within the convex supporting polygon, and statically stable walking gaits for support seeking within the kinematic capabilities of the DHM. The theory developed helps in making the DHM realize appropriate behaviors in diverse scenarios autonomously.

Three-dimensional numerical analysis of geocell-reinforced soft clay beds by considering the actual geometry of geocell pockets

Due to its complex honeycomb structure, the numerical modeling of the geocell has always been a big challenge. Generally, the equivalent composite approach is used to model the geocells. In the equivalent composite approach, the geocellsoil composite is treated as the soil layer with improved strength and stiffness values. Though this approach is very simple, it is unrealistic to model the geocells as the soil layer. This paper presents a more realistic approach of modeling the geocells in three-dimensional (3D) framework by considering the actual curvature of the geocell pocket. A square footing resting on geocell reinforced soft clay bed was modeled using the ``fast Lagrangian analysis of continua in 3D'' (FLAC(3D)) finite difference package. Three different material models, namely modified Cam-clay, Mohr-Coulomb, and linear elastic were used to simulate the behaviour of foundation soil, infill soil and the geocell, respectively. It was found that the geocells distribute the load laterally to the wider area below the footing as compared to the unreinforced case. More than 50% reduction in the stress was observed in the clay bed in the presence of geocells. In addition to geocells, two other cases, namely, only geogrid and geocell with additional basal geogrid cases were also simulated. The numerical model was systematically validated with the results of the physical model tests. Using the validated numerical model, parametric studies were conducted to evaluate the influence of various geocell properties on the performance of reinforced clay beds.

Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization

In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry when the assumed layout contains more links than are necessary for optimality.

Geometry and quadratic nonlinearity of charge transfer complexes in solution using depolarized hyper-Rayleigh scattering

We report large quadratic nonlinearity in a series of 1:1 molecular complexes between methyl substituted benzene donors and quinone acceptors in solution. The first hyperpolarizability, beta(HRS), which is very small for the individual components, becomes large by intermolecular charge transfer (CT) interaction between the donor and the acceptor in the complex. In addition, we have investigated the geometry of these CT complexes in solution using polarization resolved hyper-Rayleigh scattering (HRS). Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D = I-2 omega,I-X,I-X/I-2 omega,I-Z,I-X and D' = I-2 omega,I-X,I-C/I-2 omega,I-Z,I-C in the laboratory fixed XYZ frame by detecting the second harmonic scattered light in a polarization resolved fashion. The experimentally obtained first hyperpolarizability, beta(HRS), and the value of macroscopic depolarization ratios, D and D', are then matched with the theoretically deduced values from single and double configuration interaction calculations performed using the Zerner's intermediate neglect of differential overlap self-consistent reaction field technique. In solution, since several geometries are possible, we have carried out calculations by rotating the acceptor moiety around three different axes keeping the donor molecule fixed at an optimized geometry. These rotations give us the theoretical beta(HRS), D and D' values as a function of the geometry of the complex. The calculated beta(HRS), D, and D' values that closely match with the experimental values, give the dominant equilibrium geometry in solution. All the CT complexes between methyl benzenes and chloranil or 1,2-dichloro-4,5-dicyano-p-benzoquinone investigated here are found to have a slipped parallel stacking of the donors and the acceptors. Furthermore, the geometries are staggered and in some pairs, a twist angle as high as 30 degrees is observed. Thus, we have demonstrated in this paper that the polarization resolved HRS technique along with theoretical calculations can unravel the geometry of CT complexes in solution. (C) 2011 American Institute of Physics. doi:10.1063/1.3514922]

Geometry and quadratic nonlinearity of charge transfer complexes in solution: A theoretical study

In this paper, we have computed the quadratic nonlinear optical (NLO) properties of a class of weak charge transfer (CT) complexes. These weak complexes are formed when the methyl substituted benzenes (donors) are added to strong acceptors like chloranil (CHL) or di-chloro-di-cyano benzoquinone (DDQ) in chloroform or in dichloromethane. The formation of such complexes is manifested by the presence of a broad absorption maximum in the visible range of the spectrum where neither the donor nor the acceptor absorbs. The appearance of this visible band is due to CT interactions, which result in strong NLO responses. We have employed the semiempirical intermediate neglect of differential overlap (INDO/S) Hamiltonian to calculate the energy levels of these CT complexes using single and double configuration interaction (SDCI). The solvent effects are taken into account by using the self-consistent reaction field (SCRF) scheme. The geometry of the complex is obtained by exploring different relative molecular geometries by rotating the acceptor with respect to the fixed donor about three different axes. The theoretical geometry that best fits the experimental energy gaps, beta(HRS) and macroscopic depolarization ratios is taken to be the most probable geometry of the complex. Our studies show that the most probable geometry of these complexes in solution is the parallel displaced structure with a significant twist in some cases. (C) 2011 American Institute of Physics. doi:10.1063/1.3526748]

On the evidence for the effect of bubble interference on cavitation noise

Cavitation-noise measurements from an axisymmetric body with ‘controlled’ generation of cavitation are reported. The control was achieved by seeding artificial nuclei in the boundary layer by electrolysis. It was possible to alter the number density of nuclei by varying the electrolysis voltage, polarity and the geometry of the electrode. From the observed trend of cavitation-noise data it is postulated that there exists an ‘interference effect’ which influences cavitation noise. When the nucleus-number density is high and cavitation numbers are low this effect is strong. Under these conditions the properties of cavitation noise are found to differ considerably from those expected based on theories concerning noise from single-spherical-bubble cavitation.