A geometric mass‐preserving redistancing scheme for the level set function

In this paper we describe and evaluate a geometric mass‐preserving redistancing procedure for the level set function on general structured grids. The proposed algorithm is adapted from a recent finite element‐based method and preserves the mass by means of a localized mass correction. A salient feature of the scheme is the absence of adjustable parameters. The algorithm is tested in two and three spatial dimensions and compared with the widely used partial differential equation (PDE)‐based redistancing method using structured Cartesian grids. Through the use of quantitative error measures of interest in level set methods, we show that the overall performance of the proposed geometric procedure is better than PDE‐based reinitialization schemes, since it is more robust with comparable accuracy. We also show that the algorithm is well‐suited for the highly stretched curvilinear grids used in CFD simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

Heat conduction in a cylinder crossed by an electric current with skin effect

The steady periodic temperature distribution in an infinitely long solid cylinder crossed by an alternating current is evaluated. First, the time dependent and non-uniform power generated per unit volume by Joule effect within the cylinder is determined. Then, the dimensionless temperature distribution is obtained by analytical methods in steady periodic regime. Dimensionless tables which yield the amplitude and the phase of temperature oscillations both on the axis and on the surface of copper or nichrome cylindrical electric resistors are presented.

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Wärmeleitung in einem stromdurchflossenen Zylinder unter Berücksichtigung des Skin-Effektes

Zusammenfassung Es wird die periodische Temperaturverteilung für den eingeschwungenen Zustand in einem unendlich langen, von Wechselstrom durchflossenen Vollzylinder ermittelt. Zuerst erfolgt die Bestimmung der zeitabhängigen, nichgleichförmigen Energiefreisetzung pro Volumeneinheit des Zylinders infolge Joulescher Wärmeentwicklung und anschließend die Ermittlung der quasistationären Temperaturverteilung auf analytischem Wege. Amplitude und Phasenverzögerung der Temperaturschwingungen werden für die Achse und die Oberfläche eines Kupfer- oder Nickelchromzylinders tabellarisch in dimensionsloser Form mitgeteilt.

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Nomenclature A integration constant introduced in Eq. (2) - ber, bei Thomson functions of order zero - Bi Biot numberhr ₀/ - c speed of light in empty space - c ₁,c ₂ integration constants introduced in Eq. (46) - c _p specific heat at constant pressure - E electric field - E _z component ofE alongz - E time independent part ofE, defined in Eq. (1) - f function ofs and defined in Eq. (11) - g function ofs and defined in Eq. (37) - h convection heat transfer coefficient - H magnetic field - i imaginary uniti=(–1)^1/2 - I electric current - I _eff effective electric currentI _eff=I/2^1/2 - Im imaginary part of a complex number - J _n Bessel function of first kind and ordern - J electric current density - q _g power generated per unit volume - time average of the power generated per unit volume - time averaged power per unit length - r radial coordinate - R electric resistance per unit length - r ₀ radius of the cylinder - Re real part of a complex number - s dimensionless radial coordinates=r/r ₀ - s, s integration variables - t time - T temperature - time averaged temperature - T _f fluid temperature outside the boundary layer - time average of the surface temperature of the cylinder - u, functions ofs, and defined in Eqs. (47) and (48) - W Wronskian - x position vector - x real variable - Y _n Bessel function of second kind and ordern - z unit vector parallel to the axis of the cylinder - z axial coordinate - · modulus of a complex number - equal by definition Greek symbols amplitude of the dimensionless temperature oscillations - electric permittivity - dimensionless temperature defined in Eq. (16) - ₀, ₁, ₂ functions ofs defined in Eq. (22) - thermal conductivity - dimensionless parameter=(2)^1/2 - magnetic permeability - ₀ magnetic permeability of free space - function of defined in Eq. (59) - dimensionless parameter=c _p/() - mass density - electric conductivity - dimensionless time=t - phase of the dimensionless temperature oscillations - function ofs:= ₁+i ₂ - angular frequency - dimensionless parameter=()^1/2 r ₀     

The effect of buoyancy forces on laminar convection with viscous dissipation in a vertical channel

The interaction of the viscous dissipation effect with the presence of buoyancy forces is investigated for laminar-flow heat transfer in a parallel-plate vertical channel. One of the channel walls is considered as isothermal with a prescribed temperature, while the other wall is considered as insulated. The velocity field is assumed to be parallel. The velocity field, the temperature field and the Nusselt number are obtained by a perturbation series method which employs the ratio between the Grashof number and the Reynolds number as the perturbation parameter. The radius of convergence of the perturbation series is estimated. Received on 10 December 1997     

Fractional Klein–Gordon Equations and Related Stochastic Processes

This paper presents finite-velocity random motions driven by fractional Klein–Gordon equations of order $\alpha \in (0,1]$ . A key tool in the analysis is played by the McBride’s theory which converts fractional hyper-Bessel operators into Erdélyi–Kober integral operators. Special attention is payed to the fractional telegraph process whose space-dependent distribution solves a non-homogeneous fractional Klein–Gordon equation. The distribution of the fractional telegraph process for $\alpha = 1$ coincides with that of the classical telegraph process and its driving equation converts into the homogeneous Klein–Gordon equation. Fractional planar random motions at finite velocity are also investigated, the corresponding distributions obtained as well as the explicit form of the governing equations. Fractionality is reflected into the underlying random motion because in each time interval a binomial number of deviations $B(n,\alpha )$ (with uniformly-distributed orientation) are considered. The parameter $n$ of $B(n,\alpha )$ is itself a random variable with fractional Poisson distribution, so that fractionality acts as a subsampling of the changes of direction. Finally the behaviour of each coordinate of the planar motion is examined and the corresponding densities obtained. Extensions to $N$ -dimensional fractional random flights are envisaged as well as the fractional counterpart of the Euler–Poisson–Darboux equation to which our theory applies.     

Nanoparticle microinjection and Raman spectroscopy as tools for nanotoxicology studies

Microinjection techniques and Raman spectroscopy have been combined to provide a new methodology to investigate the cytotoxic effects due to the interaction of nanomaterials with cells. In the present work, this novel technique has been used to investigate the effects of Ag and Fe(3)O(4) nanoparticles on Hela cells. The nanoparticles are microinjected inside the cells and these latter ones are probed by means of Raman spectroscopy after a short incubation time, in order to highlight the first and impulsive mechanisms developed by the cells to counteract the presence of the nanoparticles. The results put in evidence a different behaviour of the cells treated with nanoparticles in comparison with the control cells; these differences are supposed to be generated by an emerging oxidative stress due to the nanoparticles. The achieved results demonstrate the suitability of the proposed method as a new tool for nanotoxicity studies.     

1,10-(1-H-IMIDAZOL-5-YL)DECANEPHOSPHONIC ACID: A NEW COMPOUND WITH BASIC AND ACIDIC SITES TO FABRICATE PROTON-CONDUCTING SOLID ELECTROLYTES

2-(tert-butyldimethylsilyl)-5-(10-bromodecyl)-1-(N,N-dimethylsulfamoyl)-imidazole and NaPO₃ Et₂ react at room temperature to yield the corresponding imidazole diethyl phosphonate, which when refluxed with concentrated HBr yields 1,10-(1-H-imidazol-5-yl)decanephosphonic acid hydrobromide (VI). Compound VI titrated with the required mole equivalents of NaOH yields 1,10-(1-H-imidazol-5-yl)decanephosphonic acid (VII) and 1,10-(1-H-imidazol-5-yl)decane (sodium)phosphonates (VIII). CP-MAS NMR (¹³C, ³¹P, and ¹⁵N) and IR spectroscopy indicate that only compound VII is likely to yield a polymeric structure where each phosphonic acid group is H bonded to the imidazole ring of the same molecule and to the imidazole ring of another molecule. For this reason, solid-state proton conductivity in VII is likely to be favored.     

Multiscale entanglement in ring polymers under spherical confinement

The interplay of geometrical and topological entanglement in semiflexible knotted polymer rings confined inside a spherical cavity is investigated by using advanced numerical methods. By using stringent and robust algorithms for locating knots, we characterize how the knot length l(k) depends on the ring contour length L(c) and the radius of the confining sphere R(c). In the no- and strong-confinement cases, we observe weak knot localization and complete knot delocalization, respectively. We show that the complex interplay of l(k), L(c), and R(c) that seamlessly bridges these two limits can be encompassed by a simple scaling argument based on deflection theory. The same argument is used to rationalize the multiscale character of the entanglement that emerges with increasing confinement.     

Preparation of N-Alkylphtalimides Assisted by Solid-Liquid Phase-Transfer Systems

N-Alkylphtalimides are intermediates in the synthesis of primary amines¹ and are generally prepared from potassium phtalimide and alkyl halides in anhydrous polar aprotic solvents such as dimethylformamide.² Recently, N-alkylation of potassium phtalimide has been achieved from alkyl halides and methanesulfonates in toluene in the presence of hexadecyltributylphosphonium bromide³.     

Assembled systems [X-azolopyridine][quinoline]. Bases and salts

A series of bases containing X-azolopyridines (X = O, NH) and methylquinolines, assembled in different ways, was prepared by reaction of methylquinolinecarboxylic acids (or carboxamides) with diamino (or hydroxyamino) pyridines. The bases were quaternized with methyl iodide. The physical and spectroscopic data of both the bases and the salts were correlated and compared with those of [X-azolopyridine][pyridine] systems previously studied. The structure of the salts was markedly influenced by a balance of basicity-hindrance factors in the heteroaromatic substrates.