Half-explicit Runge-Kutta methods for semi-explicit differential-algebraic equations of index 1

Summary For the numerical solution of non-stiff semi-explicit differentialalgebraic equations (DAEs) of index 1 half-explicit Runge-Kutta methods (HERK) are considered that combine an explicit Runge-Kutta method for the differential part with a simplified Newton method for the (approximate) solution of the algebraic part of the DAE. Two principles for the choice of the initial guesses and the number of Newton steps at each stage are given that allow to construct HERK of the same order as the underlying explicit Runge-Kutta method. Numerical tests illustrate the efficiency of these methods.     

Collapse of square and rectangular tubes in transverse loading

Summary Analysis of the in plane lateral collapse of square and rectangular cross-section tubes is presented by considering the out-of-straightness of horizontal and vertical arms, corner radius, friction between the platens and the deforming specimen and instability of vertical arms. Results of collapse load for tubes of aluminium and mild steel, thus computed, are presented for some typical tube geometrics, and influence thereon of various parameters considered is discussed. Experiments were conducted wherein tubes of square and rectangular cross-sections of both the materials were laterally compressed between two parallel platens in an Instron machine. The observed collapse loads compare very well with the corresponding computed values.

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Kollaps von vertikal belasteten Rohren mit quadratischem und rechteckigem Querschmitt

Übersicht Der Kollaps von Rohren mit quadratischem und rechteckigem Querschnitt, welche senkrecht zur Achse belastet werden, wird untersucht, wobei schiefe Vertikal- und Horizontalstege, gerundete Profilecken, Reibung zwischen Belastungsplatten und Rohr sowie die Stabilität der Vertikalstege brücksichtigt werden. Die Kollapslast wird für Aluminium und Weichstahl und einige typische Rohrgeometrien ermittelt und der Einfluß verschiedener Parameter wird untersucht. Die Experimente wurden auf einer Instron-Maschine durchgeführt, wobei Rohre mit quadratischem und rechteckigem Querschnitt aus beiden Werkstoffen zwischen zwei parallelen Platten quer zur Achse komprimiert wurden. Es konnte eine gute Übereinstimmung zwischen den Resultaten aus Experiment und Rechnung festgestellt werden.

     

Investigation by EPR and ENDOR spectroscopy of the novel 4Fe ferredoxin fromPyrococcus furiosus

The hyperthermophilic archaeonPyrococcus furiosus contains a four-Fe ferredoxin (Pf- Fd) that differs from most other 4Fe-Fd’s in that its [Fe₄S₄] cluster is anchored to protein by only three cysteinyl residues.Pf- Fd also is of interest because in its reduced form, [Fe₄S₄]⁺, the cluster exhibits bothS = 1/2 andS = 3/2 spin states. Addition of excess cyanide ion converts the cluster exclusively to anS = 1/2 state (g₁ = 2.09, g₂ = 1.95, g₃ = 1.92), however dialysis restores the EPR signal of native reduced protein indicating that the cluster is not irreversibly altered by cyanide. Both the native protein and protein in the presence of excess cyanide ion (Pf- Fd 4Fe-CN) were investigated here using the techniques of electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy. In particular,Pf- Fd 4Fe-CN was investigated using¹³CN^? and C¹⁵N^? ligands.¹³C and¹⁵N ENDOR indicated that a single cyanide ion bound directly, with the cluster showing an unusually small contact interaction (a_iso(¹³C)～ ?3 MHz, a_iso(¹⁵N) ～ 0). This is in contrast to cyanide bound to monomeric low-spin Fe(III)-containing proteins such as transferrin and myoglobin, for which the¹³C hyperfine coupling has a large isotropic component (a_iso(¹³C) ≈ ?30 MHz). This small contact interaction is not due to low spin density of Fe, as⁵⁷Fe ENDOR of the singly and triply labeledPf- Fd 4FeCN isotopologs, [⁵⁷FeFe₃S₄]⁺ and [Fe⁵⁷Fe₃S₄]⁺, show hyperfine coupling characteristic for [Fe₄S₄]⁺ clusters, particularly for the Fe to which cyanide binds. Thus, the low spin density on¹³C is not due to low spin density on the Fe ion to which it binds. Further theoretical work is needed to explain the contrast between the strong electronic effect of cyanide ion binding with the low spin density on the ligand.     

Calorimetric analysis of the ethanolysis of 1,2-epoxybutane

Polyethers, which are produced by alcoholysis of oxiranes, are often used as solvents in chemical plants. The spectra of the products can be influenced by the choice of the catalyst (acid or base). The results of the base-catalyzed ethanolysis of 1,2-epoxybutane are displayed. The reaction was investigated calorimetrically by varying the molar ratio between ethanol and 1,2-epoxybutane, the starting temperature and the concentration of the catalyst sodium hydroxide. Additionally, the influence of the used alcohol will be shown in one example. To determine the activation parameters, the experiments were evaluated by the nonlinear software package TA-kin v3.3.     

CONFLICT AND COOPERATION IN UTILIZING A COMMON PROPERTY RESOURCE

Noncooperative games are used to demonstrate that, while free riding is always an option, the “tragedy of the commons” is not inevitable. When the decision to cooperate or free ride is considered in a dynamic setting, there is no intermediate case where some cooperate and others free ride. The game is only stabilized in either full cooperation or full defection. The important factor in obtaining a cooperative outcome is the critical number of players that decide to cooperate. The concept of commitment is used to demonstrate the necessary and sufficient conditions for full cooperation. Although the analysis is based on a shared water resource, it can be extended to other natural resources with common costs and private benefits, especially in the cases where there are no international authorities or treaties that internalize the externalities involved in privatizing the resource.     

Superconductivity and normal state resistivity of Ba0.6K0.4BiO3: an optical phonon approach

We discuss the nature of the pairing mechanism and the physical properties associated with the normal as well as the superconducting state of cubic perovskites Ba_0.6K_0.4BiO₃using the strong coupling theory. An interaction potential which includes the Coulomb, electron–optical phonon and electron–plasmon interactions is developed to elucidate the superconducting state. A model dielectric function is constructed with these interactions fulfilling thef-sum rule. The screening parameter (μ^* = 0.26) infers the poor screening of charge carriers. The electron–optical phonon strength (λ) estimated as 0.98 is consistent with an attractive electron–electron interaction and supports the moderate to strong coupling theory. The superconducting transition temperature of Ba_0.6K_0.4BiO₃is then estimated as 32 K. Ziman's formula of resistivity is employed to analyse and compare this with the temperature-dependent resistivity of a single crystal. The estimated contribution from the electron–optical phonon together with the residual resistivity clearly infers a difference when a comparison is made with experimental data. The subtracted data infer a quadratic temperature dependence in the temperature domain (30 ≤ T ≤ 200 K). The quadratic temperature dependence of ρ [ = ρ_exp − (ρ₀ + ρ_e–ph)] is understood in terms of 3D electron–electron inelastic scattering. The presence of these el–el and el–ph interactions allows a coherent interpretation of the physical properties. Analysis reveals that a moderate to strong coupling exists in the Ba_0.6K_0.4BiO₃system and the coupling of electrons with the high-energy optical phonons of the oxygen breathing mode will be a reason for superconductivity. The implications of the above analysis are discussed.