Thermodynamic properties of liquid mixtures of carbon monoxide and methane

The equations of state of liquid methane at 125.00 K and of six liquid mixtures of carbon monoxide and methane at 116.30, 120.00 and 125.00 K have been measured from just above the saturation vapour pressure to the freezing pressure of methane. The results show that the excess volume V^E is large and negative at low pressures but becomes less negative as the pressure is increased, being almost zero at the highest pressures. The curve of V^E against the mole fraction x is very asymmetrical at low pressures, but becomes more symmetrical with rising pressure.The effect of pressure on the excess functions G^E, H^E and T·S^E has been calculated. H^E and T·S^E prove to be much more sensitive to pressure than G^E.Conformal solution theory, in the van der Waals one-fluid form, reproduces the experimental results very successfully.     

Black hole formation in c=1 string field theory

A suggestion on how black holes may appear in Das-Jevicki collective field theory is given. We study the behaviour of a “test” particle when energy is sent into the system. A perturbation moving near the potential barrier can create a large-distance black hole geometry where the seeming curvature singularity is at the position of the barrier. In the simplest “static” case the exact D=2 black hole metric emerges.     

Incoherent recovering of the spatial resolution in digital holography

We report on a technique to recover the spatial resolution of digitally recorded and reconstructed holograms of large objects. Due to the high-contrast speckle noise diminishes the spatial resolution in coherent imaging systems our proposal is based on the reduction of the contrast of it. This aim is achieved through the superposition on an intensity basis of digitally reconstructed holograms of the same static scene. We show a theoretical justification of the procedure and experimentally-obtained results of applying the technique with digitally reconstructed holograms of an object with very poor optical contrast.     

Topological invariants in forced piecewise-linear FitzHugh–Nagumo-like systems

Mathematical models for periodically-forced excitable systems arise in many biological and physiological contexts. Chaotic dynamics of a forced piecewise-linear Fitzhugh–Nagumo-like system under large-amplitude forcing was identified by Othmer and Xie in their work [J. Math. Biol. 39 (1999) 139]. Using kneading theory we study the topological entropy of some chaotic return maps associated with a singular system. Finally we introduce a new topological invariant to distinguish isentropic dynamics and we exhibit numerical results about maps with the same topological entropy, that suggest the existence of a relation between the parameters A and θ, when T is fixed.     

Kinetics and mechanism of the thermal decomposition reaction of acetone cyclic diperoxide in methyl tert‐butyl ether solution

The thermal decomposition reaction of acetone cyclic diperoxide (3,3,6,6‐tetramethyl‐1,2,4,5‐tetroxane, ACDP), in the temperature range of 130.0–166.0°C and initial concentrations range of 0.4–3.1 × 10^?2 mol kg^?1 has been studied in methyl t‐butyl ether solution. The thermolysis follows first‐order kinetic laws up to at least ca 60% ACDP conversion. Under the experimental conditions, the activation parameters of the initial step of the reaction (ΔH^# = 33.6 ± 1.1 kcal mol^?1; ΔS^# = ?4.1 ± 0.7 cal mol^?1 K^?1; ΔG^# = 35.0 ± 1.1 kcal mol^?1) and acetone, as the only organic product, support a stepwise reaction mechanism with the homolytic rupture of one of its peroxidic bond. Also, participation of solvent molecules in the reaction is postulated given an intermediate diradical, which further decomposes by C? O bond ruptures, yielding a stoichiometric amount of acetone (2 mol per mole of ACDP decomposed). The results are compared with those obtained for the above diperoxide thermolysis in other solvents. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 302–307, 2004     

The dynamical origin of physiological instructions used in birdsong production

In this work we report experimental measurements of pressure patterns used in canary song. We find that these patterns are qualitatively similar to the subharmonic solutions of a simple dynamical system. This is built to account for the activities of subpopulations of neurons arranged in a simple architecture compatible with anatomical observations. The consequences of Hebbian plasticity in the coupling between the driving and the driven systems are outlined.      

Very Colorful Theorems

We prove several colorful generalizations of classical theorems in discrete geometry. Moreover, the colorful generalization of Kirchberger’s theorem gives a generalization of the theorem of Tverberg on non-separated partitions.     

Copper(II)-methylmalonate complexes with unidentate N-donor ligands: Syntheses,structural characterization and magnetic properties

Two new methylmalonate-bridged copper(II) complexes with the formulas [Cu(3-Ipy)(Memal)(H₂O)] (1) and [Cu(2,4′-bpy)(Memal)(H₂O)] · 3H₂O (2) [Memal = methylmalonate dianion, 3-Ipy = 3-iodopyridine, 2,4′-bpy = 2,4′-bipyridine] have been synthesized and characterized by X-ray diffraction. Both compounds crystallize in the monoclinic space group P2₁/n and Z = 4, with unit cell parameters a = 8.5874(13) Å, b = 7.1738(14) Å, c = 19.093(5) Å, β = 99.509(15)° in 1 and a = 17.375(4) Å, b = 7.3305(14) Å, c = 14.247(3) Å, β = 111.409(15)° in 2. The structures of 1 and 2 consist of zigzag chains of anti-syn carboxylate-bridged copper(II) ions running along the b direction. The pyridine-like ligands occupy one equatorial position of the copper environment avoiding the formation of the sheet-like arrangement observed in previously reported Memal complexes. The chains are grouped together in hydrophilic layers through hydrogen bonds and the layers are pillared through the 3-Ipy (1) and 2,4′-bpy (2) ligands which are stacked through π–π interactions involving alternatively aromatic ligands from two adjacent chains. Magnetic susceptibility measurements of both compounds in the temperature range 2–290 K show the occurrence of intrachain ferromagnetic interactions between the copper(II) ions [J = +2.66(2) cm^?1 (1) and J = +2.62(2) cm^?1 (2)].