Approximate controllability of impulsive fractional evolution equations of order 1<α<2$$ 1&amp;lt;\alpha &amp;lt;2 $$ with state-dependent delay in Banach spaces

This article deals with the approximate controllability problem for fractional evolution equations involving noninstantaneous impulses and state-dependent delay. In order to derive sufficient conditions for the approximate controllability of our problem, we first consider the linear-regulator problem and find the optimal control in the feedback form. By using this optimal control, we develop the approximate controllability of the linear fractional control system. Further, we obtain sufficient conditions for the approximate controllability of the nonlinear problem. In the end, we provide a concrete example to support the applicability of the derived results.     

Surfactant-induced effects on turbulent swirling flows

 We employ digital particle imaging velocimetry (DPIV) to investigate the influence of a drag reducing cationic surfactant additive, cetyltrimethyl-ammonium chloride (CTAC), on turbulent swirling flows generated in a cylindrical vessel either by a rotating disk or a rotating disk fitted with vertical flat blades. The largest concentration of CTAC used in this study (0.05 ≤ C ≤ 0.5 mmol/l) is an order of magnitude smaller than those used in experimental investigations of surfactant induced drag reduction in turbulent pipe/channel flows. Even for such dilute systems, a number of dramatic and intriguing effects are observed. In the case of disk-driven flow, it is shown that the surfactant has a non-monotonic influence on turbulence intensity: both radial and axial root mean square velocity fluctuations first increase with increasing surfactant concentration C, reach a maximum and decrease upon further increase in C. Moreover, the maximum intensity is attained at a concentration that is practically independent of the angular frequency Ω of the disk. For the flow driven by bladed impeller, the introduction of the surfactant leads to flow reversal at the impeller plane for low concentrations. Enhancement in the radial and azimuthal mean velocities is also observed. For relatively larger concentrations (=0.5 mmol/l), a mean flow field that consists of multiple transient mixing pockets emerges as Ω exceeds a critical value. Plausible mechanisms are proposed to explain these observations. Received: 11 September 2000 Accepted: 10 April 2001     

Analytical and numerical solutions of inward spherical solidification of a superheated melt with radiative-convective heat transfer and density jump at freezing front

Analytical and numerical solutions of a general problem related to the radially symmetric inward spherical solidification of a superheated melt have been studied in this paper. In the radiation-convection type boundary conditions, the heat transfer coefficient has been taken as time dependent which could be infinite, at time,t=0. This is necessary, for the initiation of instantaneous solidification of superheated melt, over its surface. The analytical solution consists of employing suitable fictitious initial temperatures and fictitious extensions of the original region occupied by the melt. The numerical solution consists of finite difference scheme in which the grid points move with the freezing front. The numerical scheme can handle with ease the density changes in the solid and liquid states and the shrinkage or expansions of volumes due to density changes. In the numerical results, obtained for the moving boundary and temperatures, the effects of several parameters such as latent heat, Boltzmann constant, density ratios, heat transfer coefficients, etc. have been shown. The correctness of numerical results has also been checked by satisfying the integral heat balance at every timestep.Die analytische und numerische Lösung des Problems der symmetrischen radialen kugelförmigen Erstarrung einer ultrahocherhitzten Schmelze wurden in dieser Arbeit untersucht. Bei den Randbedingungen für Strahlung und Konvektion wurde der Wärmeübergangskoeffizient als zeitabhängig angenommen, welcher für die Zeitt=0 als unendlich betrachtet werden konnte. Dies ist notwendig für das Einsetzen des sofortigen Erstarrens der Schmelze über der gesamten Oberfläche. Die analytische Lösung besteht aus dem Verwenden geeigneter fiktiver Anfangstemperaturen und fiktiver Ausdehnungen des durch die Schmelze besetzten Anfangsbereiches. Die numerische Lösung besteht aus der Methode der finiten Differenzen, bei der die Gitterpunkte mit der Erstarrungsfront voranschreiten. Die numerische Methode kann ohne Probleme die Dichteänderungen in der flüssigen und festen Phase sowie das dadurch hervorgerufene Schrumpfen oder Expandieren des Volumens behandeln. Bei den für die sich ändernden Grenzen und Temperaturen erhaltenen numerischen Ergebnissen werden die Einflüsse der verschiedenen Parameter wie latente Wärme, Boltzmannkonstante, Dichteverhältnisse, Wärmeübergangskoeffizienten usw. gezeigt. Die Gültigkeit der numerischen Lösungen wurde zu jedem Zeitpunkt untersucht, indem die Erfüllung der Energiegleichung überprüft wurde.     

Impingement heat transfer from wedge surface

An experimental investigation is made to study the heat transfer characteristics of slot jet impingement on a wedge whose included angle is 90°. Local and average heat transfer rates from the wedge surfaces have been measured. The experiments have been conducted with isothermal wedge surface at Reynolds numbers ranging from 5 680 to 16 600. The effects of varying the flow rate, width of the nozzle, distance of the wedge vertex from the nozzle exit, eccentricity of the wedge vertex to the jet axis on the flow properties of the fluid have been investigated. A correlation has been proposed considering the relevant dimensionless parameters and then compared with experimental data.

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Wärmeübertragung einer Strömung, die auf einen Keil aufprallt

Zusammenfassung Ein experimenteller Versuch wurde durchgeführt, um die Wärmeübertragungseigenschaften bei der Spaltung eines Strahls, die beim Aufprall auf einen rechtwinkligen Keil entsteht, zu untersuchen. Gemessen wurde die lokale und mittlere Wärmeübertragungsrate der Keiloberfläche. Dieses Experiment wurde mit einer isothermen Keiloberfläche bei einer Reynolds-Zahl zwischen 5 680–16 600 durchgeführt. Untersucht wurden die Einwirkungen bei der Änderung der Strömungsrate, Düsenbreite, Abstand zwischen Keilscheitel und Düsenausgang, Exzentrizität von Keilscheitel und Strahlachse, sowie die Strömungseigenschaften des Fluids. Unter Betracht der maßgebenden dimensionslosen Parameter wurden Berechnungen durchgeführt und diese mit den experimentellen Daten verglichen.

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Nomenclature A surface area of the wedge - B breadth of the wedge or nozzle - C face length of the wedge - c _p specific heat at constant pressure - Gr _C Grashof number - H height of the wedge=C sin - h local heat transfer coefficient - average heat transfer coefficient - h _f free convective heat transfer coefficient - K thermal conductivity - L distance from the nozzle exit to the wedge vertex - Nu _f free convection Nusselt number - Nu _W local Nusselt number=hW/K - average Nusselt number= W/K - Pr Prandtl number=c _p /K - q heat loss due to forced convection - q _i heat input - q _f heat loss due to free convection - q _L heat loss due to conduction and radiation - Re _W Reynolds number=u _j W/ _a - average temperature in °C - T _j jet temperature in °C - T _a ambient air temperature in °C - T _m mean temperature=( +T _a )/2 - u mean velocity in m/s - u _j average jet exit velocity in m/s - W nozzle width - x distance measured from wedge vertex - angle between upper surface of the wedge and jet center line - angle between lower surface of the wedge and jet center line - eccentricity of the wedge vertex with the jet center line - absolute viscosity - kinematic viscosity     

Dielectric Studies in Solid Phase EBBA

Dielectric measurements have been made in the stable and metastable solid phases of EBBA in the frequency range 0.1 KHz to 100 KHz and in the temperature range - 170 to - 10°C. The dielectric dispersion was absent in the stable phase while in the metastable phase, obtained by rapid cooling, a clear dielectric dispersion was seen. In addition to the primary dispersion extending above about - 125°C there also appears a clear secondary dispersion region below - 125°C. The strength of the second dispersion is lower by one order of magnitude than the primary dispersion. The primary dispersion is of the Debye type with a symmetric distribution of relaxation times. The Cole-Cole distribution parameter varies with temperature and shows a maximum at about -64°C. The results in the primary dispersion region can be qualitatively explained by assuming the free rotation of dipoles above -64°C and a restricted rotation of dipoles at low temperatures.     

EPR and optical absorption study of Cr-doped tetramethyl ammonium cadmium chloride single crystals

EPR study of Cr³⁺-doped tetramethyl cadmium chloride (TMCC) single crystals is carried out at room temperature. The crystal field and spin-Hamiltonian parameters are evaluated from the resonance line positions of different lines observed in the EPR spectra. The g and D parameter values are found to be g=1.9741±0.0002 and D=553±2×10⁻⁴ cm⁻¹, respectively. EPR data indicate that the site symmetry of Cr³⁺ ion in the crystal is distorted octahedron. Cr³⁺ ions enter the lattice substitutionally replacing Cd²⁺ sites and bind to the neighboring extra Cd vacancies necessary for charge compensation. The optical absorption spectra are measured in 195–925 nm wavelength range at room temperature. From optical study the energy values of different orbital levels are estimated. Further, the bonding parameters are obtained by correlating optical and EPR data and the nature of bonding in the crystal is discussed. The values of Racah parameters (B and C), crystal field parameter (Dq) and nephelauxetic parameters (h and k) are obtained to be B=722, C=2845, Dq=2043 cm⁻¹, h=1.015 and k=0.21.     

Synthesis and evaluation of multitopic bisbenzothiazolyl calix[4]arenes for ionic toxicants

Abstract

Two new benzothiazolyl calix[4]arene-based multitopic molecular receptors L-1 and L-2 have been synthesised and evaluated for recognition of ionic toxicants. The receptors selectively interact with copper, silver and fluoride ion toxicants as assessed through UV-visible, NMR and colorimetric techniques. The stability of L-1:Cu⁺² and L-2:Cu⁺² complexes was found to be higher than that of complexes formed with Ag⁺ and F^– complexes in the presence of trifluoroacetic acid. Superiority of L-1 over L-2 for analysis of identified toxicants has been determined by measurement of binding constants.     

Octahedral titanium(IV) complexes with five novel hydroximic acid ligands: Synthesis,spectroscopic characterization,and <Emphasis Type="Italic">in vitro</Emphasis> activities on IMR-32 and CHO cell lines and ten bacterial strains

Complexes with the composition TiCl₄L₂ where L = benzohydroxamic acid, 2-hydroxybenzo-hydroxamic acid, acetohydroxamic acid, hydroxyurea, and N-hydroxy-N-phenylbenzamide have been synthesized by reaction of titanium tetrachloride with 2 equiv of the corresponding hydroxamic acids. The structure of these complexes has been studied by analytical and spectroscopic (FT-IR, UV-Vis, MS, ¹H and ¹³C NMR) techniques. The free ligands and the complexes have been tested in vitro to evaluate their activities against IMR-32 (neuroblastoma) cancer cell line, CHO p-40 (Chinese hamster ovary) normal cells, and ten pathogenic bacterial strains.     

Macrocyclic β-Sheets Stabilized by Hydrogen Bond Surrogates

Mimics of protein secondary and tertiary structure offer rationally-designed inhibitors of biomolecular interactions. β-Sheet mimics have a storied history in bioorganic chemistry and are typically designed with synthetic or natural turn segments. We hypothesized that replacement of terminal inter-β-strand hydrogen bonds with hydrogen bond surrogates (HBS) may lead to conformationally-defined macrocyclic β-sheets without the requirement for natural or synthetic β-turns, thereby providing a minimal mimic of a protein β-sheet. To access turn-less antiparallel β-sheet mimics, we developed a facile solid phase synthesis protocol. We surveyed a dataset of protein β-sheets for naturally observed interstrand side chain interactions. This bioinformatics survey highlighted an over-abundance of aromatic–aromatic, cation-π and ionic interactions in β-sheets. In correspondence with natural β-sheets, we find that minimal HBS mimics show robust β-sheet formation when specific amino acid residue pairings are incorporated. In isolated β-sheets, aromatic interactions endow superior conformational stability over ionic or cation-π interactions. Circular dichroism and NMR spectroscopies, along with high-resolution X-ray crystallography, support our design principles.     

Fréchet Embeddings of Negative Type Metrics

We show that every n-point metric of negative type (in particular, every n-point subset of L ₁) admits a Fréchet embedding into Euclidean space with distortion , a result which is tight up to the O(log log n) factor, even for Euclidean metrics. This strengthens our recent work on the Euclidean distortion of metrics of negative into Euclidean space. S. Arora supported by David and Lucile Packard Fellowship and NSF grant CCR-0205594. J.R. Lee supported by NSF grant CCR-0121555, NSF 0514993, NSF 0528414 and an NSF Graduate Research Fellowship.