A new class of three dimensional D-pi-A trigonal cryptand derivatives for second-order nonlinear optics

Synthesis, crystal structures, linear and nonlinear optical properties of tris D-pi-A cryptand derivatives with C-3 symmetry are reported. Three fold symmetry inherent in the cryptand molecules has been utilized for designing these molecules. Molecular nonlinearities have been measured by hyper-Rayleigh scattering (HRS) experiments. Among the compounds studied, L-1 adopts non-centrosymmetric crystal structure. Compounds L-1, L-2, L-3 and L-4 show a measurable SHG powder signal. These molecules are more isotropic and have significantly higher melting points than the classical p-nitroaniline based dipolar NLO compounds, making them useful for further device applications. Besides, different acceptor groups can be attached to the cryptand molecules to modulate their NLO properties.

Autoignition in a non-premixed medium: DNS studies on the effects of three-dimensional turbulence

Direct numerical simulation (DNS) results of autoignition in anon-premixed medium under an isotropic, homogeneous, and decaying turbulence are presented. The initial mixture consists of segregated fuel parcels randomly distributed within warm air, and the entire medium is subjected to a three-dimensional turbulence. Chemical kinetics is modeled by a four-step reduced reaction mechanism for autoignition of n-heptane/air mixture. Thus, this work overcomes the principal limitations of a previous contribution of the authors on two-dimensional DNS of autoignition with a one-step reaction model. Specific attention is focused on the differences in the effects of two- and three-dimensional turbulence on autoignition characteristics. The three-dimensional results show that ignition spots are most likely to originate at locations jointly corresponding to the most reactive mixture fraction and low scalar dissipation rate. Further, these ignition spots are found to originate at locations corresponding to the core of local vortical structures, and after ignition, the burning gases move toward the vortex periphery Such a movement is explained as caused by the cyclostrophic imbalance developed when the local gas density is variable. These results lead to the conclusion that the local ignition-zone structure does not conform to the classical stretched flamelet description. Parametric studies show that the ignition delay time decreases with an increase in turbulence intensity. Hence, these three-dimensional simulation results resolve the discrepancy between trends in experimental data and predictions from DNSs of two-dimensional turbulence. This qualitative difference between DNS results from three- and two-dimensional simulations is discussed and attributed to the effect of vortex stretching that is present in the former, but not in the latter.

Three-dimensional computational modeling of momentum, heat, and mass transfer in a laser surface alloying process

A three- dimensional, transient model is developed for studying heat transfer, fluid flow, and mass transfer for the case of a single- pass laser surface alloying process. The coupled momentum, energy, and species conservation equations are solved using a finite volume procedure. Phase change processes are modeled using a fixed-grid enthalpy-porosity technique, which is capable of predicting the continuously evolving solid- liquid interface. The three- dimensional model is able to predict the species concentration distribution inside the molten pool during alloying, as well as in the entire cross section of the solidified alloy. The model is simulated for different values of various significant processing parameters such as laser power, scanning speed, and powder feedrate in order to assess their influences on geometry and dynamics of the pool, cooling rates, as well as species concentration distribution inside the substrate. Effects of incorporating property variations in the numerical model are also discussed.

Transformations of two-dimensional layered zinc phosphates to three-dimensional and one-dimensional structures

Transformations of the layered zinc phosphates of the compositions [C6N4H22](0.5) [Zn-2 (HPO4)(3)], I, [C3N2H12][Zn-2 (HPO4)(3)], II and [C3N2OH12][Zn-2 (HPO4)(3)], III, containing triethylenetetramine, 1,3-diaminopropane, and 1,3-diamino-2-hydroxypropane, respectively, have been investigated under different conditions. On heating in water, I transforms to a one-dimensional (1-D) ladder and a three-dimensional (3-D) structure, while II gives rise to only a two-dimensional (2-D) layered structure. In the transformation reaction of I with zinc acetate, the same ladder and 3-D structures are obtained along with a tubular layer. Under similar conditions II gives a layered structure formed by the joining of two ladder motifs. III, on the other hand, is essentially unreactive when heated with water and zinc acetate, probably because the presence of the hydroxy group in the amine which hydrogen bonds to the framework. In the presence of piperazine, I, II and III give rise to a four-membered, corner-shared linear chain which is likely to be formed via the ladder structure. In addition, 2-D and 3-D structures derived from the 1-D linear chain or ladder structures are also formed. The primary result from the study is that the layers produce 1-D ladders, which then undergo other transformations. It is noteworthy that in the various transformations carried out, most of the products are single-crystalline.

Thermal instability in a three-dimensional rigid container with prescribed heat flux at lower boundary

The Bénard–Marangoni convection is studied in a three-dimensional container with thermally insulated lateral walls and prescribed heat flux at lower boundary. The upper surface of the incompressible, viscous fluid is assumed to be flat with temperature dependent surface tension. A Galerkin–Tau method with odd and even trial functions satisfying all the essential boundary conditions except the natural boundary conditions at the free surface has been used to solve the problem. The critical Marangoni and Rayleigh numbers are determined for the onset of steady convection as a function of aspect ratios x0 and y0 for the cases of Bénard–Marangoni, pure Marangoni and pure Bénard convections. It is observed that critical parameters are decreasing with an increase in aspect ratios. The flow structures corresponding to the values of the critical parameters are presented in all the cases. It is observed that the critical parameters are higher for case with heat flux prescribed than those corresponding to the case with prescribed temperature. The critical Marangoni number for pure Marangoni convection is higher than critical Rayleigh number corresponding to pure Bénard convection for a given aspect ratio whereas the reverse was observed for two-dimensional infinite layer.

Three-dimensional laminar compressible boundary layers with large injection

The effect of large mass injection on the following three-dimensional laminar compressible boundary-layer flows is investigated by employing the method of matched asymptotic expansions: (i) swirling flow in a laminar compressible boundary layer over an axisymmetric surface with variable cross-section and (ii) laminar compressible boundary-layer flow over a yawed infinite wing in a hypersonic flow. The resulting equations are solved numerically by combining the finite-difference technique with quasi-linearization. An increase in the swirl parameter, the yaw angle or the wall temperature is found to be capable of bringing the viscous layer nearer the surface and reducing the effects of massive blowing.

Three-dimensional double-diffusive convection and macrosegregation during non-equilibrium solidification of binary mixtures

A three-dimensional transient mathematical model (following a fixed-grid enthalpy-based continuum formulation) is used to study the interaction of double-diffusive natural convection and non-equilibrium solidification of a binary mixture in a cubic enclosure cooled from a side. Investigations are carried out for two separate test systems, one corresponding to a typical model "metal-alloy analogue" system and other corresponding to a real metal-alloy system. Due to stronger effects of solutal buoyancy in actual metal-alloy systems than in corresponding analogues, the convective transport mechanisms for the two cases are quite different. However, in both cases, similar elements of three-dimensionality are observed in the curvature and spacing of the projected streamlines. As a result of three-dimensional convective flow patterns, a significant solute macrosegregation is observed across the transverse sections of the cavity, which cannot be captured by two-dimensional simulations. (C) 2003 Elsevier Science Ltd. All rights reserved.

Understanding the building-up process of three dimensional open-framework metal phosphates: Acid degradation of the 3D structures to lower dimensional structures

Acid degradation of 3D zinc phosphates primarily yields a one-dimensional ladder compound, an observation that is significant considering that the latter forms 3D structures on heating in water.

Real-time Computer Simulation of Three Dimensional Elastostatics using the Finite Point Method

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

New Concepts for Three-Dimensional Shape Analysis

A new approach to machine representation and analysis of three-dimensional objects is presented. The representation, based on the notion of "skeleton" of an object leads to a scheme for comparing two given object views for shape relations. The objects are composed of long, thin, rectangular prisms joined at their ends. The input picture to the program is the digitized line drawing portraying the three-dimensional object. To compare two object views, two characteristic vertices called "cardinal point" and "end-cardinal point," occurring consistently at the bends and open ends of the object are detected. The skeletons are then obtained as a connected path passing through these points. The shape relationships between the objects are then obtained from the matching characteristics of their skeletons. The method explores the possibility of a more detailed and finer analysis leading to detection of features like symmetry, asymmetry and other shape properties of an object.

Experiments on three-dimensional wire-frame object recognition

Some experimental results on the recognition of three-dimensional wire-frame objects are presented. In order to overcome the limitations of a recent model, which employs radial basis functions-based neural networks, we have proposed a hybrid learning system for object recognition, featuring: an optimization strategy (simulated annealing) in order to avoid local minima of an energy functional; and an appropriate choice of centers of the units. Further, in an attempt to achieve improved generalization ability, and to reduce the time for training, we invoke the principle of self-organization which utilises an unsupervised learning algorithm.

A Numerical Scheme for Three-Dimensional Front Propagation and Control of Jordan Mode

As an example of a front propagation, we study the propagation of a three-dimensional nonlinear wavefront into a polytropic gas in a uniform state and at rest. The successive positions and geometry of the wavefront are obtained by solving the conservation form of equations of a weakly nonlinear ray theory. The proposed set of equations forms a weakly hyperbolic system of seven conservation laws with an additional vector constraint, each of whose components is a divergence-free condition. This constraint is an involution for the system of conservation laws, and it is termed a geometric solenoidal constraint. The analysis of a Cauchy problem for the linearized system shows that when this constraint is satisfied initially, the solution does not exhibit any Jordan mode. For the numerical simulation of the conservation laws we employ a high resolution central scheme. The second order accuracy of the scheme is achieved by using MUSCL-type reconstructions and Runge-Kutta time discretizations. A constrained transport-type technique is used to enforce the geometric solenoidal constraint. The results of several numerical experiments are presented, which confirm the efficiency and robustness of the proposed numerical method and the control of the Jordan mode.

Sequence-Structure Similarity: Do Sequentially Identical Peptide Fragments have Similar Three-Dimensional Structures?

The rapidly growing structure databases enhance the probability of finding identical sequences sharing structural similarity. Structure prediction methods are being used extensively to abridge the gap between known protein sequences and the solved structures which is essential to understand its specific biochemical and cellular functions. In this work, we plan to study the ambiguity between sequence-structure relationships and examine if sequentially identical peptide fragments adopt similar three-dimensional structures. Fragments of varying lengths (five to ten residues) were used to observe the behavior of sequence and its three-dimensional structures. The STAMP program was used to superpose the three-dimensional structures and the two parameters (Sequence Structure Similarity Score (Sc) and Root Mean Square Deviation value) were employed to classify them into three categories: similar, intermediate and dissimilar structures. Furthermore, the same approach was carried out on all the three-dimensional protein structures solved in the two organisms, Mycobacterium tuberculosis and Plasmodium falciparum to validate our results.