A rheological investigation of solid soap

Summary The rheological behaviour of solid soaps has been investigated over several orders in time and shear by means of creep experiments, measurement of stressstrain curves at constant shear rate and dynamic experiments. The modulus at small deformations is almost constant over a frequency range of 10^–3–10³ Hz; a transition from linear to non-linear behaviour has been observed at a strain of about 10^–3. The results suggest that some kind of network structure is responsible for the rheological behaviour of soap.

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Zusammenfassung Das Theologische Verhalten von Hartseifen wurde für mehrere Größenordnungen von Zeit und Schubgeschwindigkeit untersucht mittels Kriechversuche, Messung der Spannungs-Deformationskurven bei konstanter Schubgeschwindigkeit und dynamischer Experimente. Der Modul bei geringen Deformationen ist fast konstant im Frequenzbereich von 10^–3–10³ Hz; ein Übergang von linear zu nicht-linear wurde bei einer Deformation von etwa 10^–3 beobachtet. Die Ergebnisse lassen auf eine netzartige Struktur schließen, die für das Theologische Verhalten der Seife verantwortlich ist.

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The authors are indebted to Mr.C. J. Nederveen of the Central Laboratory T. N. O., Delft for the dynamic measurements, and thank Mr.D. W. Brinkman of the Unilever Research Laboratory, Vlaardingen for experimental assistance.     

Subgraph statistics in subcritical graph classes

Let H be a fixed graph and a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in of order n, chosen uniformly at random, follows a normal limiting distribution with linear expectation and variance. The main ingredient in our proof is the analytic framework developed by Drmota, Gittenberger and Morgenbesser to deal with infinite systems of functional equations [Drmota, Gittenberger, and Morgenbesser, Submitted]. As a case study, we obtain explicit expressions for the number of triangles and cycles of length 4 in the family of series‐parallel graphs. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 631–673, 2017     

Massenspektren von cyclischen Polyethern mit O bzw. O und N als Heteroatom im Etherring

Zusammenfassung Die Massenspektren von cyclischen Polyethern, die nur O als Heteroatom im Etherring enthalten, zeigen ein übersichtliches Fragmentierungsschema, welches die Deutung neuer analoger Massenspektren erleichtert. Bei cyclischen Polyethern mit O und N als Heteroatom dagegen findet eine zu starke Fragmentierung durch die Elektronenstoßionisation statt. Daher ist kein Fragmentierungsschema erkennbar und es werden nur die Massenspektren wiedergegeben.

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Mass spectra of cyclic polyethers with O or O and N as hetero-atom in the ether ring

Summary Mass spectra of cyclic polyethers containing only O as hetero-atom in the ether ring, show a well-arranged fragmention pattern, which facilitates the interpretation of similar new mass spectra, whereas electron impact ionization causes a too strong fragmentation of cyclic polyethers with O and N as hetero-atom. Hence, it follows that a fragmentation pattern cannot be verified and only mass spectra are given.

     

Internalization and end flux in morphogen gradient formation

Two simple reaction–diffusion systems of partial differential equations and auxiliary conditions governing the activities of diffusible ligands such as Dpp in anterior–posterior axis of Drosophila wing imaginal discs were previously formulated and investigated by numerical simulations in [Developmental Cell 2 (2002) 785–796]. System B focuses on diffusion, reversible binding with receptors and ligand-mediated degradation for a fixed receptor concentration uniform in time and space. System C extended this basic but meaningful model to allow for endocytosis, exocytosis and receptor synthesis and degradation. The present paper provides a mathematical underpinning for the computational studies of these two systems and some insight gained from our analysis. We will see for instance that the two boundary value problems governing the steady state for the two systems are identical in form. This result will enable us to avoid dealing with internalization explicitly when we investigate other complex morphogen activities such as the effects of (1) feedback and (2) diffusible and non-diffusible molecules competing for ligands and receptors to inhibit cell signaling and pattern formation. The principal contribution of the present work pertains to the extension of System C to allow for a ligand flux at the source end. The more general model has many significant consequences including the removal of a limitation of previous models on ligand synthesis rate for the existence of steady state behavior. Linear stability of the corresponding steady state behavior is established. While the actual decay rate of transients is less accessible in this new model, it is possible to obtain tight upper and lower bounds for the decay rate in terms of the (effective) degradation rate of the receptors and that of the ligand-receptor complexes.     

Localized Ectopic Expression of Dpp Receptors in a Drosophila Embryo

Receptor-mediated bone morphogeneric protein (BMP) degradation has been seen to play an important role in allowing for the formation of relatively stable morphogen signaling patterns. To the extent that receptors act as a "sink" for BMPs, one would predict that the localized over-expression of signaling receptors would cause a net flux of freely diffusing BMPs toward the  ectopic , i.e., abnormally high concentration, receptor site. One possible consequence would be a depression of BMP signaling in adjacent areas because less BMPs are now available for binding with the same normal concentration of receptors at the adjacent areas. However, recent experiments designed to examine this possible effect were inconclusive. In this paper, we investigate the possibility of depression of BMP signaling outside the area of elevated receptor level in a  Drosophila  embryo by modeling mathematically the basic biological processes at work in terms of a system of nonlinear reaction-diffusion equations with spatially varying (and possibly discontinuous) system properties. The steady-state signaling morphogen gradient is investigated by the method of matched asymptotic expansions and by numerical simulations.     

Neutron scattering investigation of the magnetic ground state of PrO2

We report on a series of neutron experiments on stoichiometric PrO₂. The material, which has the cubic CaF₂ structure, orders antiferromagnetically at 14 K with a type I magnetic structure as found in UO₂. The ordered moment is 0.6 ± 0.1 μ_B/Pr atom. No lattice distortion has been observed below T_N with a high-resolution neutron-diffraction experiment. Neutron inelastic scattering at the Intense Pulsed Neutron Source, Argonne National Laboratory, has been used to determine the crystal-field splitting of 130 ± 5 meV between the Γ₈ ground state and the Γ₇ excited state of the $\text{J =}\text{5}\text{2}$ multiplet. This represents the first direct observation of a crystal-field splitting in the rare-earth or actinide dioxides, and the largest such electronic splitting ever observed by neutron scattering. We propose that the ground state of PrO₂ is the Γ₈ quartet with the degeneracy lifted by a dynamic Jahn-Teller effect. The A₄〈r⁴〉 crystal field potential term for PrO₂ is - (57 ± 3) meV, and the significance of this determination for other oxides is discussed.     

Atomic displacements in the incommensurable charge-density wave in alpha-uranium

We present a detailed examination of the incommensurable charge-density wave (ICDW) in α-uranium below 43 K. We have measured the q vectors as a function of temperature and the structure factors of a large number of first-order satellites with neutron diffraction. From the structure factors the atomic displacements that occur at the onset of the CDW have been determined in all three independent crystallographic directions. Uniaxial stress up to 3.5 kbar has been applied along 2 directions but does not change the satellite intensities, thus leaving ambiguity whether the structure is single or multi q. We discuss the relationship between the present results and the observations of Smith et al.