Expressing the Entropy of Lattice Systems as Sums of Conditional Entropies

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively taken into account. Compared to the traditional approach for estimating the entropy density, in which successive approximations build on step-wise extensions of blocks of symbols, we show that one can take larger steps when collecting the statistics necessary to calculate the entropy density of the system. In one dimension this means that, instead of a single sweep over the system in which states are read sequentially, one take several sweeps with larger steps so that eventually the whole lattice is covered. This means that the information in correlations is captured in a different way, and in some situations this will lead to a considerably much faster convergence of the entropy density estimate as a function of the size of the configurations used in the estimate. The formalism is exemplified with both an example of a free energy minimisation scheme for the two-dimensional Ising model, and an example of increasingly complex spatial correlations generated by the time evolution of elementary cellular automaton rule 60.     

Frequency response correction of hot-film measurements in a turbulent airflow

Turbulence measurements were performed in a fully developed turbulent pipe flow using a wedged-shaped hot-film probe. The dynamic sensitivity of hot-film probes is frequency dependent and cannot be obtained from static calibration. As it is complicated to make a dynamic calibration, a correction method for the turbulent energy spectrum is used instead. The measurements were compared with hot-wire turbulence measurements and show good agreement. Received: 28 May 1999/Accepted: 24 August 1999     

Shimura invariant differential operators and their eigenvalues

Let be the covariant Cauchy-Riemann operator and the covariant holomorphic differential operator on a line bundle over a Hermitian symmetric space . We study the Shimura invariant differential operators defined via and . We find the eigenvalues of a family of the Shimura operators and of the generators. Received October 2, 1999 / Published online October 30, 2000     

Extraction of Polonium from Aqueous Lactic Acid Solutions Using Dioctyl Sulphide, Cyanex 272, Cyanex 301 or Cyanex 302 in Toluene

The extraction of polonium from lactic acid (HLac) solutions has been studied with di-n-octyl sulphide (DOS), Cyanex 272, Cyanex 301 and Cyanex 302 extractants dissolved in toluene. For the extraction with DOS, the extracted species is most likely PoO(Lac)₂·3DOS. The results for Cyanex 272 also indicate extraction via a solvation mechanism rather than cation exchange. The extracted species is probably PoO(Lac)₂·2HA. The major species extracted with Cyanex 301 or Cyanex 302 do not contain any lactate molecules. The extracted species is most likely PoOA₂ at low extractant concentrations, while at higher concentrations an adduct complex of the type PoOA₂·2HA is formed. The extraction of polonium increases in the order Cyanex 272 < Cyanex 302 < DOS < Cyanex 301, which is the same order as the increase of the number of sulphur atoms in the reagents.     

Valuations and Dedekind's Prague Theorem

To any field K we associate an entailment relation in the sense of Scott (Proceedings of the Tarski Symposium, 1974, pp. 411–435). In this way we can interpret an abstract propositional theory representing a generic valuation ring of a field, and obtain a simple effective proof of Dedekind's Prague theorem (Edwards, Arch. Hist. Ex. Sci (1980) 321–378; Divisor Theory, Birkhäuser, Boston, 1990).     

Observation of the second harmonic in the phase dependence of a superconducting current in Nb/Au/YBCO heterojunctions

The second harmonic in the dependence of a superconducting current on the phase difference of superconducting wave functions of the electrodes was observed experimentally in Nb/Au/(001)YBa₂Cu₃O_x heterojunctions. Possible reasons for its appearance were discussed within the framework of a mixed (d±s) symmetry order parameter of YBa₂Cu₃O_x.     

Embedding Spacetime via a Geodesically Equivalent Metric of Euclidean Signature

Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This geodesically equivalent, or dual, metric can be embedded in ordinary Euclidean space. On the embedded surface freely falling particles move on the shortest path. Thus one can visualize how acceleration in a gravitational field is explained by particles moving freely in a curved spacetime. Freedom in the dual metric allows us to display, with substantial curvature, even the weak gravity of our earth. This may provide a nice pedagogical tool for elementary lectures on general relativity. I also study extensions of the dual metric scheme to higher dimensions.     

Permittivity of BaTiO3 epitaxial films grown on the YBa2Cu3O7−δ(001) surface

The epitaxial heterostructures YBa₂Cu₃O_7?δ and YBa₂Cu₃O_7?δ/(5 nm)SrTiO₃/BaTiO₃/(5 nm)SrTiO₃/YBa₂Cu₃O_7?δ are grown by the laser evaporation method on an LaAlO₃(100) substrate. The permittivity of a BaTiO₃ layer is approximately doubled (T=300 K) when a SrTiO₃ thin layer is inserted between a ferroelectric layer and superconducting cuprate electrodes. A maximum in the temperature dependence of the permittivity for a barium titanate layer in the YBa₂Cu₃O_7?δ/(5 nm)SrTiO₃/BaTiO₃/(5 nm)SrTiO₃/YBa₂Cu₃O_7?δ heterostructure is shifted by 70–80 K toward the low-temperature range with respect to its location in the corresponding dependence for the BaTiO₃ bulk single crystal. The bias voltage dependence of the permittivity for the BaTiO₃ grown layers exhibits a clearly pronounced hysteresis (T=300 K). The superconducting transition temperature for the lower YBa₂Cu₃O_7?δ electrode in a superconductor/ferroelectric/superconductor heterostructure considerably depends on the rate of its cooling after the completion of the formation process.     

One-nucleon removal cross-sections for 17, 19C and 8, 10B

One-neutron removal cross-sections ( ) of ^{17, 19}C in various targets at about 900 MeV/nucleon, and one-proton removal cross-sections ( ) of ^{8, 10}B at about 1400 MeV/nucleon were measured using the fragment separator FRS at GSI. A significant increase of for ¹⁹C compared to its neighbors was observed. The same behavior was found for for the neutron-deficient nucleus ⁸B compared to the stable isotope ¹⁰B. These results support a one-neutron halo structure in ¹⁹C and a one-proton halo in ⁸B. Received: 26 July 2000 / Accepted: 11 January 2001