Maximization of entropy for an elastic body free of surface traction

Communicated by C. Dafermos     

Capillary gravity waves on the free surface of an inviscid fluid of infinite depth. Existence of solitary waves

Permanent capillary gravity waves on the free surface of a two dimensional inviscid fluid of infinite depth are investigated. An application of the hodograph transform converts the free boundary-value problem into a boundary-value problem for the Cauchy-Riemann equations in the lower halfplane with nonlinear differential boundary conditions. This can be converted to an integro-differential equation with symbol –k ²+4|k|–4(1+), where is a bifurcation parameter. A normal-form analysis is presented which shows that the boundary-value problem can be reduced to an integrable system of ordinary differential equations plus a remainder term containing nonlocal terms of higher order for || small. This normal form system has been studied thoroughly by several authors (Iooss &Kirchgässner [8],Iooss &Pérouème [10],Dias &Iooss [5]). It admits a pair of solitary-wave solutions which are reversible in the sense ofKirchgässner [11]. By applying a method introduced in [11], it is shown that this pair of reversible solitary waves persists for the boundary-value problem, and that the decay at infinity of these solitary waves is at least like 1/|x|.     

On the cross flow through in-line tube banks with regard to the effect of surface roughness

The behaviour of the flow through an in-line tube bank is studied at variable roughness conditions of the surface. The total pressure loss, the local static pressure and the skin friction distribution were measured in the range of Reynolds numbers 4·10⁴<Re<10⁷. Opposing to the staggered arrangement the drag coefficient of an in-line bundle diminishes in the transcritical flow range with increasing roughness parameters. As at the same time heat transfer is improved the in-line bundle is of great practical interest. By means of the local flow parameters the interaction of the point of impact, separation point of the boundary layer and wake width can be pointed out.

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Zusammenfassung Die Strömung durch ein fluchtendes Rohrbündel glatter und rauher Oberfläche wird untersucht. Der Gesamtdruckverlust sowie die örtliche Druck- und Wandschubspannungsverteilung wurden im Bereich der ReynoldsZahlen 4·10⁴<Re<10⁷ gemessen. Im Gegensatz zum versetzten Wärmetauscher verringert sich bei der fluchtenden Anordnung im transkritischen Strömungsbereich der Widerstandsbeiwert mit zunehmender Oberflächenrauhigkeit. Da gleichzeitig eine Verbesserung des Wärmeüberganges beobachtet wird, kommt dem fluchtenden Bündel große praktische Bedeutung zu. Anhand der experimentell gewonnenen örtlichen Strömungsparameter wird die Wechselwirkung von Auftreffpunkt der Strömung, Grenzschichtablösung und Nachlauf breite verdeutlicht.

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Nomenclature D m tube diameter - k _s m sand grain roughness - L m tube length - p N/m₂ pressure - s ₁ m longitudinal pitch - s _tm transversal pitch - U _c m/s velocity in the smallest cross section between the tubes - z number of rows Greek symbols pressure drop coefficient (index t=total, index f=friction) - kg/sm fluid viscosity - kg/m³ fluid density - ₀ N/m² wall shear stresses - grd angle of circumference Characteristics Reynolds number - pressure drop coefficient The investigations have been carried out in the Institut für Reaktorbauelemente der Kernforschungsanlage Jülich GmbH The author wishes to thank Dr.von der Decken, new director of the institute, who supported the already started work in its final stages with great interest. He also expresses his gratitude to his co-workers H.Gillessen, F.Hoffmanns, H.Reger, W.Schmidt and G.Türk for their activity and engagement to bring these investigations to a successful end.     

On strain and straining

Communicated by K. R. Rajagopal For Máirín and Siobhán     

The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations

We prove that viscosity solutions in W ^1, of the second order, fully nonlinear, equation F(D ² u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) F is uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions, respectively. This method is completely different from that used in Lions [8, 9] for second order problems with F convex in D ² u and from that used by Crandall & Lions [3] and Crandall, Evans & Lions [2] for fully nonlinear first order problems.The research reported here was supported in part by grants from the Alfred P. Sloan Foundation and the National Science Foundation.     

Quasiconformal mappings as a tool to study certain two-dimensional G-closure problems

A recent theorem due to Astala establishes the best exponent for the area distortion of planar K-quasiconformal mappings. We use a refinement of Astala's theorem due to Eremenko and Hamilton to prove new bounds on the effective conductivity of two-dimensional composites. The bounds are valid for composites made of an arbitrary finite number n of possibly anisotropic phases in prescribed volume fractions. For n= 2 we prove the optimality of the bounds under certain additional assumptions on the G-closure parameters.     

Existenzbeweis für cnoidal waves unter berücksichtigung der oberflächenspannung

Ohne ZusammenfassungHerrn Prof. Herbert Beckert zum 50. Geburtstag Vorgelegt von J. Serrin     

Fit regions and functions of bounded variation

Dedicated to James B. Serrin on the occasion of his sixtieth birthday     

The Bianchi identities in an explicit form

Dedicated to Professor Bernard D. Coleman     

Experimental investigation of the asymptotically approached Mach reflection over the second surface in a double wedge reflection

The assumption that the Mach reflection which is formed over the second surface of a double wedge with angles _w ¹ and kw/2 approaches asymptotically the Mach reflection which would have been obtained by an identical incident shock wave over a single wedge with an angle _w = _w ² was verified experimentally. The verification of this assumption supports the shock polar analysis suggested by Ben-Dor et al. (1987) for the study of the reflection process of a planar shock wave over a double wedge. Measurements of the rate of approach to the asymptotic value are also provided.     

Generalized characteristics in hyperbolic systems of conservation laws

In Memoriam Ronald J. DiPerna     

A group theoretical approach to a certain class of perturbations of the Kepler problem

We study a particular class of perturbations of the classical Kepler Hamiltonian, first in two, then in three and finally in n dimensions. At every stage of our investigation the group theoretical nature of our constructions is fully exposed.In particular we present a new regularization of the n-dimensional Kepler problem which is based on previous constructions of Guillemin & Sternberg (see [8]). This regularization is similarily related to Moser's (see [9]) as is Kustaanheimo-Stiefel's (see [4]) in three dimensions.     

Zur mathematischen theorie akustischer Wellenfelder

Ohne Zusammenfassung Vorgelegt von C. Müller Zur praktischen Berechnung von U können nach Satz 2 die numerischen Methoden zur Auflösung Fredholmscher Integralgleichungen, etwa das Verfahren von Cl. Müller [10], verwendet werden.     

Avere una memoria tenace crea gravi problemi

Dedicata a Clifford A. Truesdell nel Suo 60 compleanno     

On patches of uniform vorticity in a plane of irrotational flow

We derive an evolution equation for the motions of patches of vorticity (vortex). Steady state solutions of this equation that include those of Kirchhoff and Moore & Saffman are established. The m-fold symmetric, m3, hypotrochoid is an exact steady solution of this equation when rotation and strain are present. When strain is absent but rotation is present, the m-fold symmetric, m2, hypotrochoid is a perturbation solution with a dispersion relation extending that of Lamb. The case of m=2 is exact and is the Kirchhoff elliptical vortex.     

Convergence of Solutions to the Boltzmann Equation in the Incompressible Euler Limit

 We consider here the problem of deriving rigorously, for well-prepared initial data and without any additional assumption, dissipative or smooth solutions of the incompressible Euler equations from renormalized solutions of the Boltzmann equation. This completes the partial results obtained by Golse [B. Perthame and L. Desvillettes eds., Series in Applied Mathematics 4 (2000), Gauthier-Villars, Paris] and Lions & Masmoudi [Arch. Rational Mech. Anal. 158 (2001), 195–211]. (Accepted June 6, 2002) Published online December 3, 2002 Communicated by Y. BRENIER     

On the equilibrium of a cylindrical elastic solid: Comparisons with St. Venant's theory

Communicated by M. E. Gurtin &; C. Truesdell     

Über den Resonanz fall bei Systemen von n nichtlinearen gewöhnlichen Differentialgleichungen erster Ordnung

Ohne Zusammenfassung Vorgelegt von L. Collatz II. Teil einer bei der Naturwissenschaftlich-Philosophischen Fakultät der Technischen Hochschule zu Braunschweig eingereichten Dissertation. Referenten: Prof. Dr. R. Iglisch und Prof. Dr. H.-J. Kanold. Auch Herrn Dr. H. Eltermann bin ich für wertvolle Ratschläge zu großem Dank verpflichtet.     

Zur thermoelastostatik stückweise homogener Körper

Ohne Zusammenfassung Vorgelegt von H. Beckert Den Herren Professoren H. Beckert und R. Klötzler möchte ich an dieser Stelle für das Interesse am Entstehen dieser Arbeit herzlich danken.     

Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≧ 2. We address the question of the global existence of strong solutions for initial data close to a constant state having critical Besov regularity. First, this article shows the recent results of Charve and Danchin (Arch Ration Mech Anal 198(1):233–271, 2010) and Chen et al. (Commun Pure Appl Math 63:1173–1224, 2010) with a new proof. Our result relies on a new a priori estimate for the velocity that we derive via the intermediary of the effective velocity, which allows us to cancel out the coupling between the density and the velocity as in Haspot (Well-posedness in critical spaces for barotropic viscous fluids, 2009). Second, we improve the results of Charve and Danchin (2010) and Chen et al. (2010) by adding as in Charve and Danchin (2010) some regularity on the initial data in low frequencies. In this case we obtain global strong solutions for a class of large initial data which rely on the results of Hoff (Arch Rational Mech Anal 139:303–354, 1997), Hoff (Commun Pure Appl Math 55(11):1365–1407, 2002), and Hoff (J Math Fluid Mech 7(3):315–338, 2005) and those of Charve and Danchin (2010) and Chen et al. (2010). We conclude by generalizing these results for general viscosity coefficients.