Summarizing complexity in high dimensions

High-dimensional, multispectral data on complex physical systems are increasingly common. As the amount of information in data sets increases, the difficulty of effectively utilizing it also increases. For such data, summary information is required for understanding and modeling the underlying dynamics. It is here proposed to use an extension of computational mechanics [C. R. Shalizi and J. P. Crutchfield, J. Stat. Phys. 104, 817 (2001)] to arbitrary spatiotemporal and spectral dimension, for providing such summary information. An example of the use of these tools to identify state evolution in the brain, an archetypal, complex biophysical system, serves as an illustration.     

On the changes in the microwave dielectric spectrum of aqueous phospholipid bilayer solutions at the ordered-fluid phase transition

The microwave part of the dielectric spectrum (ν ? 1 GHz) is considered of aqueous phospholipid solutions in the limit of high water content. A continuum model is presented which allows to calculate in the water relaxation region the frequency-dependent complex permittivity of solutions in which the bilayers form globular single-walled vesicles as well as multilamellar liposomes. The model is not only capable of explaining the strikingly small values of the extrapolated static permittivity and of the main dielectric relaxation time which became evident in many measurements on colloidal aqueous solutions of phospholipids. It also allows the positive and negative step-like changes in the dielectric properties of solutions, which have been found at the main (order-disorder) phase transition temperature of the bilayers, to be explained by dimensional changes as resulting from vesicle growth and fusion.     

Low energy positron scattering from atoms in and on solids observed with low energy positron diffraction and reemission microscopy

The present status of low energy positron diffraction (LEPD) and positron reemission microscopy (PRM) is reviewed in the context of unanswered questions regarding the elastic scattering of positrons in the 1–300 eV energy range from atoms in solids and at solid surfaces. Recent LEPD studies yield an agreement between theoretical and experimental diffraction intensities for semiconductors that has never been equalled in electron diffraction studies. This situation is discussed in terms of the repulsive interaction between the positron and the embedded atomic potential and the lack of exchange with the nonspherically distributed valence electrons. The scattering of re-emitted positrons in PRM from atoms chemisorbed or physisorbed on the re-emitting surface has not yet received the same theoretical attention as scattering from embedded atoms in LEPD. Possible ways in which positron scattering from overlying atomic structures manifests itself in PRM as well as positron re-emission holography are discussed, both from the practical viewpoint of observing these structures and in the context of fundamental questions regarding the positron re-emission process itself.     

Detection of tobacco smoke deposition by hyperpolarized krypton-83 MRI

Despite the importance of the tobacco smoke particulate matter in the lungs to the etiology of pulmonary disease in cigarette smokers, little is currently known about the spatial distribution of particle deposition or the persistence of the resulting deposits in humans, and no satisfactory technique currently exists to directly observe tobacco smoke condensate in airways. In this proof-of-principle work, hyperpolarized (hp) 83Kr MRI and NMR spectroscopy are introduced as probes for tobacco smoke deposition in porous media. A reduction in the hp-83Kr longitudinal (T1) relaxation of up to 95% under near-ambient humidity, pressure and temperature conditions was observed when the krypton gas was brought into contact with surfaces that had been exposed to cigarette smoke. This smoke-induced acceleration of the 83Kr self-relaxation was observed for model glass surfaces that, in some experiments, were coated with bovine lung surfactant extract. However, a similar effect was not observed with hp-(129)Xe indicating that the 83Kr sensitivity to smoke deposition was not caused by paramagnetic species but rather by quadrupolar relaxation due to high adsorption affinity for the smoke deposits. The 83Kr T1 differences between smoke-treated and untreated surfaces were sufficient to produce a strong contrast in variable flip angle FLASH hp-83Kr MRI, suggesting that hp-83Kr may be a promising contrast agent for in vivo pulmonary MRI.     

Continuum limit of overlap valence quarks on a twisted mass sea

We study a lattice QCD mixed action with overlap valence quarks on two flavours of Wilson maximally twisted mass sea quarks. Employing three different matching conditions to relate both actions to each other, we investigate the continuum limit by using three values of the lattice spacing ranging from a≈0.05 fm$a\approx 0.05\text{fm}$ to 0.08 fm$0.08\text{fm}$. A particular emphasis is put on the effect on physical observables of the topological zero modes appearing in the valence overlap operator. We estimate the region of parameter space where the contribution from these zero modes is sufficiently small such that their effects can be safely controlled and a restoration of unitarity of the mixed action in the continuum limit is reached.     

Driven depinning of strongly disordered media and anisotropic mean-field limits

Extended systems driven through strong disorder are modeled generically using coarse-grained degrees of freedom that interact elastically in the directions parallel to the drive and slip along at least one of the directions transverse to the motion. In the limit of infinite-range elastic and viscous coupling this model has a tricritical point separating a region where the depinning is continuous, in the universality class of elastic depinning, from a region where depinning is hysteretic. Many of the collective transport models discussed in the literature are special cases of the generic model.     

Molekülstruktur in der Theorie der Spinvalenz I

Zusammenfassung Wie in der Theorie der Valenzstrukturen (Kimball 1940), so kann man auch in der Theorie der Spinvalenz ohne Rechnung, d. h. nur mit den Mitteln der Gruppen- und Darstellungstheorie, zu Aussagen über die Molekülstruktur von Verbindungen des Typs ML _n kommen. Die Ergebnisse für sog. ¹ A ₁-Moleküle werden angegeben und mit denen von Kimball verglichen.

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Spin valence theory provides a basis for the group theoretical derivation of the structure of ML _n -molecules. Results for molecules in a totally symmetrical ground state are compared with predictions of the valence bond method (Kimball 1940).

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Résumé La théorie de la valence de spin permet de dériver les structures de molécules du type ML _n á l'aide de la théorie des groupes. Des résultats pour de molécules en état ¹ A ₁ (totalement symétrique) sont comparés á ceux de la méthode de mésomérie (Kimball 1940).

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Auszugsweise vorgetragen auf der Westdeutschen Chemiedozententagung, Freiburg i. Brsg., 27.–30. 4. 1964 und der 8. I. C. C. C., Wien, 7.–11. 9. 1964.