Thermal Conductivity of Soils at Very Low Moisture Content and Moderate Temperatures

An analysis of soil thermal conductivity data shows that, at very low moisture content, this property first varies insignificantly and then begins to increase from a certain critical moisture content, whose value tends to depend on clay mass fraction. Two simple models evaluating the critical moisture content were developed; the first one is a fraction of the permanent wilting point; the second one is a simple linear function dependent on clay mass fraction. An insignificant variation of soil thermal conductivity is observed at 20°C, within a water pressure head ranging from 1×10³ to 1×10³m, while for higher temperatures (45–50°C) from 5000 to 100000m. Three extensions of the enhanced thermal conductivity model by Sundberg, namely SUN-1, SUN-2 and SUN-3, were proposed and tested. They produce an average root mean square error of 27%, 24% and 30%, respectively, with respect to experimental data. SUN-1and SUN-2 predictions could be further improved if better estimates of thermal conductivity at the dry state and the permanent wilting point were provided. SUN-3 is a simple model which does not require information about the PWP and critical moisture content. All SUN models have a potential for implementing the latent heat transfer component.     

Constant factor approximation for ATSP with two edge weights

We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor approximation was given recently by Svensson. This was accomplished by introducing an easier problem called Local-Connectivity ATSP and showing that a good solution to this problem can be used to obtain a constant factor approximation for ATSP. In this paper, we solve Local-Connectivity ATSP for two different edge weights. The solution is based on a flow decomposition theorem for solutions of the Held–Karp relaxation, which may be of independent interest.     

Über den Einfluß des Lösungsmittels auf organische Reaktionen

Zusammenfassung Es wurde Phenol mit gasförmigem NO₂ in organischen Lösungsmitteln und wäßrigen Lösungen mit verschiedenen Dielektrizitätskonstanten nitriert. Es wurde festgestellt, daß mit Ansteigen der Dielektrizitätskonstante die relative Menge an Paraisomerem in den Reaktionsprodukten zunimmt. Ferner versuchte man, die funktionelle Abhängigkeit zwischen dem summarischen Dipolmoment der Reaktionsprodukte und der Dielektrizitätskonstante des Lösungsmittels festzustellen.     

Änderungen des Dipolmomentes von Phenol in verschiedenen Lösungsmitteln

Zusammenfassung Auf Grund des Mengenverhältnisses der bei Nitrierung von Phenol in verschiedenen Lösungsmitteln entstehenden Ortho-und Para-Isomeren wurden die Dipolmomente von Phenol berechnet. Es wurde die funktionelle Abhängigkeit dieser Momente von der Dielektrizitätskonstante der Lösungsmittel bestimmt.Mit 2 Abbildungen     

Magnetic AC susceptibility of stoichiometric and low zinc doped magnetite single crystals

Systematic studies of AC susceptibility in a stoichiometric magnetite single crystal, in a series of low zinc doped magnetite (xZn < 0.04) and in nonstoichiometric magnetite samples (both single crystals and pellets) in the temperature range 4–300 K are presented. Measurements were performed in several AC fields ( Oe) and at different frequencies (15–6000 Hz). It is suggested that the signal is primarily due to magnetic domain wall movement, strongly influenced by structural domains (twins). Two sets of anomalies were found: the first is associated with the Verwey transition and the second involves two different effects, one at 28 K, observed only in stoichiometric magnetite, and the other at 50 K. While the temperature position of the first anomaly (28 K) does not depend on frequency, the effect at 50 K is associated with an activation process, shifting to higher temperatures with increasing frequency. This last effect may be linked to the low temperature magnetoelectric effects terminating approximately at those temperatures. Qualitatively similar results have been observed by the Magnetic After Effect technique presented in the literature, that is associated with relaxation times that are 104 higher than those characteristic of our technique.     

Preconditioned conjugate gradient algorithms for nonconvex problems with box constraints

The paper describes new conjugate gradient algorithms for large scale nonconvex problems with box constraints. In order to speed up convergence the algorithms employ scaling matrices which transform the space of original variables into the space in which Hessian matrices of the problem’s functionals have more clustered eigenvalues. This is done by applying limited memory BFGS updating matrices. Once the scaling matrix is calculated, the next few conjugate gradient iterations are performed in the transformed space. The box constraints are treated efficiently by the projection. We also present a limited memory quasi-Newton method which is a special version of our general algorithm. The presented algorithms have strong global convergence properties, in particular they identify constraints active at a solution in a finite number of iterations. We believe that they are competitive to the L-BFGS-B method and present some numerical results which support our claim.     

An order-by-order construction of low-temperature phase diagrams for classical lattice systems

An inductive algorithm is presented for the construction of phase diagrams by means of the low-temperature expansion technique. First the phase diagram is studied in the set of formal series. In each step, properties of this phase diagram are related to extremal elements of some family of convex sets. Approximations of the phase diagram in orderN are obtained by truncating all formal series at theNth term.This paper was presented at the Trebon, Czechoslovakia, Symposium September 1–6, 1986.