Extreme statistics of complex random and quantum chaotic states

Complex random states have the statistical properties of the Gaussian and circular unitary ensemble eigenstates of random matrix theory. Even though their components are correlated by the normalization constraint, it is nevertheless possible to derive compact analytic formulas for their extreme values' statistical properties for all dimensionalities. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulas.     

An embedded boundary framework for compressible turbulent flow and fluid–structure computations on structured and unstructured grids

The finite volume method with exact two‐phase Riemann problems (FIVER) is a two‐faceted computational method for compressible multi‐material (fluid–fluid, fluid–structure, and multi‐fluid–structure) problems characterized by large density jumps, and/or highly nonlinear structural motions and deformations. For compressible multi‐phase flow problems, FIVER is a Godunov‐type discretization scheme characterized by the construction and solution at the material interfaces of local, exact, two‐phase Riemann problems. For compressible fluid–structure interaction (FSI) problems, it is an embedded boundary method for computational fluid dynamics (CFD) capable of handling large structural deformations and topological changes. Originally developed for inviscid multi‐material computations on nonbody‐fitted structured and unstructured grids, FIVER is extended in this paper to laminar and turbulent viscous flow and FSI problems. To this effect, it is equipped with carefully designed extrapolation schemes for populating the ghost fluid values needed for the construction, in the vicinity of the fluid–structure interface, of second‐order spatial approximations of the viscous fluxes and source terms associated with Reynolds averaged Navier–Stokes (RANS)‐based turbulence models and large eddy simulation (LES). Two support algorithms, which pertain to the application of any embedded boundary method for CFD to the robust, accurate, and fast solution of FSI problems, are also presented in this paper. The first one focuses on the fast computation of the time‐dependent distance to the wall because it is required by many RANS‐based turbulence models. The second algorithm addresses the robust and accurate computation of the flow‐induced forces and moments on embedded discrete surfaces, and their finite element representations when these surfaces are flexible. Equipped with these two auxiliary algorithms, the extension of FIVER to viscous flow and FSI problems is first verified with the LES of a turbulent flow past an immobile prolate spheroid, and the computation of a series of unsteady laminar flows past two counter‐rotating cylinders. Then, its potential for the solution of complex, turbulent, and flexible FSI problems is also demonstrated with the simulation, using the Spalart–Allmaras turbulence model, of the vertical tail buffeting of an F/A‐18 aircraft configuration and the comparison of the obtained numerical results with flight test data. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of Isomerism in the Dipolar Interaction of Benzene with Butanol

Sound velocity, density, and viscosity values were measured at 303 K in four binary systems of benzene + 1-, 2-, tert-, or iso-butanol. From these data, acoustical parameters, such as adiabatic compressibility, free length, free volume, and internal pressure were estimated using the standard relations. The results are interpreted in terms of molecular interaction between the components of the mixtures. Observed excess value in all the mixture indicates that the molecular symmetry existing in the system is highly disturbed by the nonpolar benzene molecules. Interaction energy terms of the statistical mixing are also verified for these binary systems and the dipole-dipole interactions are found to be predominantly present and are sharply affected by the isomeric forms of butanol.     

Investigations into conformational transitions and solvation structure of a 7-piperidino-5,9-methanobenzo[8] annulene in water

Solvation shell structure of a 7-piperidino-5,9-methanobenzo[8] annulene (PMA) in water has been investigated in ambient conditions using both molecular dynamics (MD) and Car-Parrinello molecular dynamics (CPMD) calculations. From the MD calculations, we find that this molecule exists in three major conformational states out of which two are in twist-boat forms and one in chair form. Due to the limited time scale accessible in CPMD simulations, we have studied all the three conformational states separately using CPMD. The molecular geometry, electronic charge distribution and solvation structure for all three forms are investigated. The stability order of the chair and twist-boat conformations in water solvent has been reversed when compared to the gaseous phase results and in the case of polar aprotic solvents (J. Org. Chem., 1999, 61, 5979). From the radial distribution function, we find that the solvent density around the chair form is significantly lower, which has to be directly related to the smaller solvent accessible area for this conformation and this is in complete agreement with earlier reports. Among the findings are that the solvation shell structure around the nitrogen atom in the chair form of PMA is considerably different from the open conformational forms or the twist-boat forms. The dipole moment for the closed form is found to be significantly larger when compared to the twist-boat forms.     

A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation

A second-order splitting method is applied to a KdV-like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L² and L^∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin–Bona–Mahony) and BBMB (Benjamin–Bona–Mahony–Burgers) equations and the well-known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695–716, 1998     

Characterization of pure and urea-doped γ-glycine single crystals grown by solution method

Pure and urea-doped gamma-glycine (γ-glycine) single crystals were grown by solution method with slow evaporation technique. When urea was added as dopant, morphological alterations were noticed in γ-glycine crystals. Structural characterization of the grown crystals was carried out by single and powder X-ray diffraction (XRD) methods and it is observed that the samples crystallize in non-centrosymmetric space groups. UV-visible transmittance studies were performed to analyse optical transparency of pure and urea-doped γ-glycine crystals and found that the crystals were transparent in the entire visible-NIR region. Density and melting point of the grown crystals were measured. Second harmonic generation (SHG) for the grown crystals of this work was confirmed using Nd:YAG laser. Thermogravimetric and differential thermal analyses (TG/DTA) thermograms reveal that the materials have good thermal stability. From Microhardness studies, it is observed that urea-doped γ-glycine crystal is harder than pure (undoped) sample.     

Spectral, optical, and thermal studies of pure and Zn(II)-doped l-histidine hydrochloride monohydrate (LHHC) crystals

The influence of doping the transition metal Zn(II) on the growth, spectral, optical, and thermal properties of l-histidine hydrochloride monohydrate (LHHC) crystals grown by slow solvent evaporation method has been investigated. Structural characterizations of the grown crystals were carried out by single crystal X-ray diffraction analysis and it shows slight structural changes as a result of doping. The FT-IR spectral study reveals the presence of various functional groups and confirms the slight distortion of the structure of the crystals due to doping. The energy dispersive X-ray analysis reveals the incorporation of Zn(II) in the crystalline matrix of LHHC crystal. The UV?CVis spectral study was carried out to analyze the optical transmittance of the grown crystals and found that the transmittance is very high in the visible and UV regions for both pure and doped crystals. The second harmonic generation (SHG) for the grown crystals was confirmed by Nd:YAG laser. The scanning electron microscopy reveals the presence of defect centers and crystal voids. The thermal stability and purity of the grown crystals were analyzed by thermogravimetry, differential thermal analysis, and differential scanning calorimetry techniques.     

Crystallization,spectral, and thermal characterization of <Emphasis Type="SmallCaps">l</Emphasis>-histidine methyl ester dihydrochloride (LHMED)

A novel nonlinear optical semi-organic single crystal of l-histidine methyl ester dihydrochloride was grown by slow evaporation solution growth method at an ambient temperature. The grown crystal was characterized by single crystal X-ray diffraction. Functional groups and the modes of vibrations were identified by FT–IR spectroscopy. The chemical composition of the crystal was confirmed by Energy dispersive X-ray analysis. The optical behavior of the crystal was examined by UV spectral analysis, which shows the absence of absorption between the wavelengths ranging from 230 to 1000 nm. The optical band gap of the grown crystal was estimated and is found to be 5.35 eV. The thermal behavior of the crystal was investigated by thermogravimetric and differential thermal analyses. The nonlinear optical property of the grown crystal was confirmed by the powder technique of Kurtz and Perry.     

Synthesis,structure, characterization and biological evaluation of 3‐substituted 1‐pyridin‐2‐ylimidazo[1,5‐a]pyridine‐based copper(I)–phosphine complexes for anticancer drug screening

Copper(I) complexes of the types [Cu(N–N)(PPh₃)₂]NO₃ (LC41–LC44) and [Cu(N–N)(PPh₃)(NO₃)] (LC45) carrying 3‐substituted 1‐pyridine‐2‐ylimidazo[1,5‐a]pyridine (N–N) derivatives and triphenylphosphine (PPh₃) ligands have been prepared. The synthesized copper(I)–phosphine complexes were fully characterized by NMR, IR, ESI‐MS and UV–visible spectroscopy as well as by cyclic voltammetry. Selected structures such as LC42, LC43 and LC45 were additionally analysed by single‐crystal X‐ray method, which show that copper(I) centre adopts a highly distorted tetrahedral geometry. The ¹H and ¹³C NMR spectral data of the complexes throw light on the nature of metal–ligand bonding. They display dπ–π* metal‐to‐ligand charge transfer (MLCT) transition and show quasireversible Cu^I/Cu^II metal oxidation. Among the copper(I)–phosphine complexes, LC41–LC44 exhibit moderate cytotoxicity (IC₅₀: 24 h, 67–74 μM; 48 h, 58–70 μM) against human lung epithelial adenocarcinoma A549 cells, whereas LC45 displays the best activity (IC₅₀: 24 h, 42 μM; 48 h, 34 μM) for A549 cancer cell line, which is better than that of the commercial antitumor drug cisplatin. All the complexes also displayed excellent selectivity by being relatively inactive against the human lung epithelial L132 normal cell line with selectivity index (SI) values ranging from 3.4 to 7.4. The complexes block cell cycle progression of A549 cells in G₀/G₁ phase. FACSVerse analyses are suggestive of reactive oxygen species (ROS) generation and apoptotic cell death induced by the LC41, LC43 and LC45. The induction of apoptosis in A549 cells was shown by Annexin V with propidium iodide (PI) and 4′,6‐diamidino‐2‐phenylindole (DAPI) staining methods and established the ability of LC41, LC43 and LC45 to accumulate in the cell nuclei.