Crystallization of polyamide confined in sub‐micrometer droplets dispersed in a molten polyethylene matrix

The crystallization of submicrometer PA6 droplets dispersed in an ethylene‐1‐octene copolymer matrix, using PE‐g‐MA as a compatibilizer agent, is investigated. This system shows a nonconventional mechanical behavior at high temperatures. Up to ～100 °C above the final melting temperature of the ethylene‐1‐octene copolymer matrix, the system shows good thermal and mechanical properties including dimensional stability. Because of the dispersed phase morphology of the system, so‐called fractionated/homogeneous crystallization takes place leading to an extra supercooling of PA6: ～50 °C compared to the bulk PA6 crystallization temperature. Thus—though this is most probably just of interest for small‐scale research—the system can be processed at lowered temperatures while still providing exceptional high‐temperature properties. While the matrix is in the melt state when crystallization of the dispersed PA6 phase occurs, the possibility of matrix induced crystallization is absent, contrary to almost all of the ‘dispersed droplets in a matrix’ systems reported so far. The kinetics of this phenomenon is investigated in detail by DSC: the existence of fractionated/homogeneous crystallization is shown to be related to the lack of active nuclei in the dispersed droplets by means of self‐seeding experiments. The occurrence of extensive cold crystallization of PA6 in the confined environment is studied as is the crystallization kinetics, including the characterization of its time dependences showing its sporadic nature. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 815–825, 2006     

Unitary Orbits in a Full Matrix Algebra

The Hilbert manifold ∑ _∞ consisting of positive invertible (unitized) Hilbert-Schmidt operators has a rich structure and geometry. The geometry of unitary orbits Ω⊂∑ _∞ is studied from the topological and metric viewpoints: we seek for conditions that ensure the existence of a smooth local structure for the set Ω, and we study the convexity of this set for the geodesic structures that arise when we give ∑ _∞ different Riemannian metrics.     

What is wrong with the Hausdorff measure in Finsler spaces

We construct a class of Finsler metrics in three-dimensional space such that all their geodesics are lines, but not all planes are extremal for their Hausdorff area functionals. This shows that if the Hausdorff measure is used as notion of volume on Finsler spaces, then totally geodesic submanifolds are not necessarily minimal, filling results such as those of Ivanov [On two-dimensional minimal fillings, St. Petersburg Math. J. 13 (2002) 17-25] do not hold, and integral-geometric formulas do not exist. On the other hand, using the Holmes-Thompson definition of volume, we prove a general Crofton formula for Finsler spaces and give an easy proof that their totally geodesic hypersurfaces are minimal.     

Zur Jacobsthalschen transfiniten Arithmetik

Ohne Zusammenfassung     

Numerical simulations in granular matter: The discharge of a 2D silo

In this paper I give a short and elementary review of numerical simulations in granular assemblies, giving the process of discharge of a 2D silo as an example. The strengths and limitations of different approaches are discussed, together with some comments on the specific issues related to the numerics of discontinuous dissipative collisions.      

A remark about possible unity of the neutron star and black hole high frequency QPOs

In a series of papers it was discussed,on the basis of phenomenological arguments, whether the high frequency quasiperiodic oscillations (kHz QPOs)observed in the neutron-star and black-hole X-ray sources originate in the same physical mechanism. Recently it was suggested that a general trend seen in neutron star kHz QPOs instead excludes such a uniform origin. Using the example of the atoll source 4U 1636-53 we illustrate that this is not neccesarily true.      

The mechanism of neutral amino acid decomposition in the gas phase. The elimination kinetics of N,N‐dimethylglycine ethyl ester,ethyl 1‐piperidineacetate,and N,N‐dimethylglycine

The gas‐phase elimination kinetics of the ethyl ester of two α‐amino acid type of molecules have been determined over the temperature range of 360–430°C and pressure range of 26–86 Torr. The reactions, in a static reaction system, are homogeneous and unimolecular and obey a first‐order rate law. The rate coefficients are given by the following equations. For N,N‐dimethylglycine ethyl ester: log k₁(s^?1) = (13.01 ± 3.70) ? (202.3 ± 0.3)kJ mol^?1 (2.303 RT)^?1 For ethyl 1‐piperidineacetate: log k₁(s^?1) = (12.91 ± 0.31) ? (204.4 ± 0.1)kJ mol^?1 (2.303 RT)^?1 The decompositon of these esters leads to the formation of the corresponding α‐amino acid type of compound and ethylene. However, the amino acid intermediate, under the condition of the experiments, undergoes an extremely rapid decarboxylation process. Attempts to pyrolyze pure N,N‐dimethylglycine, which is the intermediate of dimethylglycine ethyl ester pyrolysis, was possible at only two temperatures, 300 and 310°C. The products are trimethylamine and CO₂. Assuming log A = 13.0 for a five‐centered cyclic transition‐state type of mechanism in gas‐phase reactions, it gives the following expression: log k₁(s^?1) = (13.0) ? (176.6)kJ mol^?1 (2.303 RT)^?1. The mechanism of these α‐amino acids differs from the decarbonylation elimination of 2‐substituted halo, hydroxy, alkoxy, phenoxy, and acetoxy carboxylic acids in the gas phase. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33:465–471, 2001     

A structure theorem for abelian quasi-ordered groups

We introduce a notion of compatible quasi-ordered groups which unifies valued and ordered abelian groups. It was proved by S.M. Fakhruddin that a compatible quasi-order on a field is always either an order or a valuation. We show here that the group case is more complicated than the field case and describe the general structure of a compatible quasi-ordered abelian group. We then define a notion of Hahn product of compatible quasi-ordered groups and generalize Hahn's embedding theorem to quasi-ordered groups. We also develop a notion of quasi-order-minimality and establish a connection with C-minimality, thus answering a question of F. Delon. Finally, we use compatible quasi-ordered groups to give an example of a C-minimal group which is neither an ordered nor a valued group.