A fourth-order parabolic equation modeling epitaxial thin film growth

We study the continuum model for epitaxial thin film growth from Phys. D 132 (1999) 520-542, which is known to simulate experimentally observed dynamics very well. We show existence, uniqueness and regularity of solutions in an appropriate function space, and we characterize the existence of nontrivial equilibria in terms of the size of the underlying domain. In an investigation of asymptotical behavior, we give a weak assumption under which the ω-limit set of the dynamical system consists only of steady states. In the one-dimensional setting we can characterize the set of steady states and determine its unique asymptotically stable element. The article closes with some illustrative numerical examples.     

Flow equations and the strong-coupling expansion for the Hubbard model

Applying the method of continuous unitary transformations to a class of Hubbard models, we reexamine the derivation of thet/U expansion for the strong-coupling case. The flow equations for the coupling parameters of the higher order effective interactions can be solved exactly, resulting in a systematic expansion of the Hamiltonian in powers oft/U, valid for any lattice in arbitrary dimension and for general band filling. The expansion ensures a correct treatment of the operator products generated by the transformation, and only involves the explicit recursive calculation of numerical coefficients. This scheme provides a unifying framework to study the strong-coupling expansion for the Hubbard model, which clarifies and circumvents several difficulties inherent to earlier approaches. Our results are compared with those of other methods, and it is shown that the freedom in the choice of the unitary transformation that eliminates interactions between different Hubbard bands can affect the effective Hamiltonian only at ordert ³/U² or higher.     

Zur Plattenberechnung mittels finiter Elemente

Übersicht Vermehrt man die Freiheitsgrade eines Rechteckelements dadurch, daß man anstelle einer Vergrößerung der Knotenzahl an den vier Eckknoten zusätzlich höhere Verschiebungs- und damit auch Kraftgrößen vorsieht, so ist eine geometrische Kontinuität erreichbar. Es wird gezeigt, daß auch in diesem Fall das übliche Vorgehen — Berechnung der Elementsteifigkeitsmatrizen und Aufstellung der Knotengleichgewichtsbedingungen — formal beibehalten werden kann. Numerische Ergebnisse werden mitgeteilt.

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Summary If one increases the number of freedoms of a rectangular element by means of additional (higher) displacement- and therefore also force-quantities at the four edge-nodes instead of enlarging the number of nodes, one can receive a geometric continuity. It is shown that in this case the usual proceeding — evaluation of the element-stiffness-matrices and stating the conditions of equilibrium at the nodes — may formally be retained. Numerical examples are presented.

     

Tangentiale Steifigkeitsmatrizen bei Anwendung von Projektionsverfahren in der Elastoplastizitätstheorie

übersicht Die klassische PlastizitÄtstheorie mit einer Flie\bedingung nach v. Mises und assoziierter Flie\regel erfordert die Zeitintegration der plastischen Verzerrungsraten. Die hier verwendete Radial-return-Methode ist ein Projektionsverfahren zur Berechnung der inelastischen Spannungen und kann als implizite Integration der Flie\regel angesehen werden. Die Anwendung der Finite-Element-Methode zur numerischen Lösung nichtlinearer Probleme geht von der schwachen Form des Gleichgewichts aus (Prinzip der virtuellen Arbeit). Die entstehenden nichtlinearen Gleichungssysteme können mit dem Newton-Raphson-Verfahren iterativ gelöst werden. Um die quadratische Konvergenz zu sichern, mu\ ein Tangentenoperator berechnet werden, der mit dem verwendeten Projektionsverfahren konsistent ist.

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Tangent stiffness matrices for projection methods in elasto-plasticity

Summary In classical elastoplasticity with v. Mises yield condition and associate flow rule it is necessary to integrate the plastic strain rate. The radial return integration algorithm is employed to calculate elastoplastic stresses. In the context of the finite element method, the formulation and numerical solution of nonlinear problems in continuum mechanics is based on the weak form of the momentum balance equation (principle of virtual work). The solution of the nonlinear equations is achieved by the Newton-Raphson method in which a sequence of linear problems is solved. If the linear problem is obtained by consistent linearization one gets a quadratic rate of convergence.

     

Measurement of the mass of110Pd and114Pd using the (14C,16O) reaction

A measurement of the mass excess of¹¹⁰Pd and¹¹⁴Pd has been made by detecting emergent¹⁶O ions in aQ3D magnetic spectrometer using the¹¹²Cd(¹⁴C,¹⁶O)¹¹⁰Pd and¹¹⁶Cd(¹⁴C,¹⁶O)¹¹⁴Pd reactions at 60 MeV. The results are compared with theoretical predictions.     

The elongation and time dependence of the crystallinity of low-density polyethylene

It has been presumed in studies of the orientation of low-density polyethylene and its time dependence that the degree of crystallinity remained constant with elongation and did not vary with time following elongation. This paper represents a test of this hypothesis by several methods. The change in crystallinity accompanying stretching has been followed by a modification of an x-ray method for uniaxial orientation proposed by Ruland in which diffraction peaks are resolved into crystalline and amorphous components and their respective areas are determined by two-dimensional integration over both the Bragg angle and the azimuthal angle of diffraction. The weight-fraction crystallinity is then determined from the ratio of the weighted crystalline area to the total area. There appears to be no significant variation in crystallinity up to 50% sample elongation for both slowly and rapidly stretched samples at room temperature. The dynamic crystallinity change accompanying small amplitude vibration has also been determined by the dynamic x-ray diffraction technique and found to be negligible over a wide range of frequency. The degree of crystallinity has also been evaluated from the absolute infrared absorbance of crystallinity-sensitive bands and has also been found to be independent of elongation at room temperature up to 80% elongation. Changes have also been observed by this method during relaxation at constant length following rapid extension and have also been found to be negligible. These results also indicate negligible changes in rotational isomer population. Consequently, we conclude that changes observed during relaxation and vibration arise from orientational changes rather than changes in the degree of crystallinity.     

Fuzzy probability vectors

Several recent papers have discussed an extension of decision analysis: both the rewards and probabilities are modelled using fuzzy sets. However, arbitrary specification of the membership functions of the fuzzy probabilities in these models may lead to internal inconsistencies. To avoid this, the fuzzy beta possibility distribution is introduced.