Anomalous Stark effect on excitonic states in a preionization electric field

The low-temperature (T=80 K) excitonic light reflection spectra of CdS crystals in the electric field of a Schottky barrier are investigated. An anomalous Stark shift of the hydrogen-like excitonic state in the preionization limit is recorded for the first time. The distribution of the subbarrier electric field is determined from an analysis of the spectra performed on the basis of the theory of nonlocal dielectric response in a spatially inhomogeneous medium. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 38–42 (10 July 1996)     

A linear time-varying model of force generation in skeletal muscle

A model of isometric force production by skeletal muscle was developed in which the response to each stimulus in a train was described by a critically damped, linear second-order system. The parameters describing the system were constrained to be constant within an interstimulus interval, but were allowed to vary between interstimulus intervals. The ability of this model to match experimental data, and the time variation in the parameters (low-frequency gain and natural frequency) required to do so were examined in soleus and plantaris muscles of the cat stimulated by synchronous whole-nerve stimulation. The model produced good fits across firing rates from twitch to tetanus for slow and fast muscle, rested and fatigued muscle, and maximal and submaximal stimulation. Both gain and natural frequency generally varied smoothly and predictably under all conditions. Gain increased at intermediate stimulation rates and in potentiated muscle, and decreased with fatigue and submaximal stimulation. Natural frequency was higher in fast muscle, and decreased with stimulation rate and fatigue. This modeling approach may provide a useful alternative to current models of skeletal muscle force, as its implementation is simple and it can describe force under conditions (fatigue, potentiation) where the muscle dynamics change with time     

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.

     

Bonding and thermal stability of implanted hydrogen in silicon

The behavior of implanted hydrogen in Si has been investigated by differential infrared transmittance measurements using multiple-internal-reflection (MIR) plates. Si-H bonding of implanted hydrogen is detected by seven absorption bands between 4.5 and 5.5 μm after implantation with 10¹⁶ H⁺/cm² at ion energies between 70 and 400 keV. The absorption bands are close in frequency to those for SiH stretching modes for silane, and they are produced only by hydrogen implantation. Implantation with deuterium gave absorption bands shifted to lower frequencies in accord with the square root of the reduced mass ratio for Si-H relative to Si-D. The multiplicity of hydrogen-associated bands is apparently a consequence of defects in the implanted layer. A dependence of the hydrogen-associated bands on the disorder is suggested by the annealing loss of five of the initial seven bands, and a growth of the other two, for the same temperatures (100–300°C) as those for annealing out the broad divacancy band at 1.8 μm. A disorder dependence of the Si-H vibrational frequencies is further demonstrated by a regeneration of the bands annealing below 300°C when a hydrogen-implanted MIR plate annealed at 300°C was subsequently bombarded with neon. In addition to the seven resolved bands after H⁺ implantation, five other bands in the same range of frequencies grow in and anneal out between 100 and 700°C. Annealing at 700°C eliminates all SiH bands, and they cannot be regenerated by bombardment with other ions. It is suggested that implanted hydrogen in Si is bonded at defect sites, and that a loss of an SiH band is caused by either a change in charge state of a defect or by the loss of a defect. This work was supported by the United States Atomic Energy Commission     

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.     

Prey?Predator?Protector Model for Cancer

This paper presents a simulation model of the disease cancer. Various aspects of the disease are noted and changes in these aspects are modeled to indicate their resemblance to real-life situations. As with any model, its validity depends on how well it conforms with experimental evidence, and how useful it is as a predictor of future events. It is hoped that the model will stimulate sufficient interest that such experiments will be conducted, with the ultimate goal being a better approach to the control of the disease.     

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.