A comparison of spin relaxation and local motion between symmetrically and asymmetrically ring-substituted bisphenol units in dissolved polycarbonates

Carbon-13 and proton spin-lattice relaxation times were measured at two field strengths on solutions 10% by weight of two polycarbonates in C₂D₂Cl₄ from ?20 to +120°C. The first polycarbonate is an asymmetrically substituted form with one chlorine on one of the two phenylene aromatic rings of the bisphenol unit, whereas the second polycarbonate is symmetrically substituted with two chlorines on each of the two rings. The nuclear spin relaxation data are interpreted in terms of several local motions likely in these polymers. Segmental motion was described by the Hall–Helfand correlation function. Segmental motion in the monosubstituted polycarbonate is somewhat slower than in unsubstituted polycarbonate, whereas segmental motion in the tetrasubstituted polycarbonate is considerably slower. Phenylene ring rotation is observed in unsubstituted polycarbonate and in the monosubstituted polycarbonate above 40°C. Below 40°C in the monosubstituted species, and at all temperatures in the tetrasubstituted species, ring rotation is replaced by ring libration as the predominant motion contributing to spin lattice relaxation. In addition, the rotational motion of the two types of rings in the asymmetric monosubstituted form are very similar although not identical. The substituted ring is slightly less mobile than the rings of unsubstituted polycarbonate. This indicates a strong coupling of ring motion, although the coupling leads to less than synchronous motion. Methyl group rotation is present in both polymers and is little affected by the various structural modifications.     

Multiple crossover phenomena and scale hopping in two dimensions

We study the renormalization group for nearly marginal perturbations of a minimal conformal field theory M_p with p 1. To leading order in perturbation theory, we find a unique one-parameter family of “hopping trajectories” that is characterized by a staircase-like renormalization group flow of the C-function and the anomalous dimensions and that is related to a factorizable scattering theory recently solved by Al. B. Zamolodchikov. We argue that this system is described by interactions of the form . As a function of the relevant parameter t, it undergoes a phase transition with new critical exponents simultaneously governed by all fixed points M_p, M_p−1,…, M₃. Integrable lattice models represent different phases of the same integrable system that are distinguished by the sign of the irrelevant parameter .     

Intramolecular motion and isotope effects in muonium‐substituted chloroalkyl radicals

Muon irradiation of pure liquid 3‐chloropropene, CH₂=CH-CH₂Cl, yields a primary radical, \dot\mboxCH₂-CHMu-CH₂Cl, and a secondary radical, MuCH₂-\rm\dot\mboxCH-CH₂Cl. 2‐methyl‐3‐chloropropene yields only the tertiary radical, MuCH₂-\rm\dot\mboxC(CH₃)-CH₂Cl. These three chloroalkyl radicals have been characterized by μSR and μLCR, and the hyperfine coupling constants (hfcs) have been determined over a range of temperatures, either in the pure liquid precursor or in concentrated solution. The temperature variation of the hfcs has been analyzed to obtain estimates of the barrier to internal rotation about the C_\alpha-C_\beta axis for various alkyl groups, and also their minimum energy conformations, i.e. their orientations with respect to the axis of the 2p_z orbital of the unpaired electron. The tertiary radical is particularly interesting because all three methyl‐like groups, -CH₃,-CH₂Cl and -CH₂Mu, are represented. The results can be compared to electron spin resonance data for analogous radicals, to provide information on the effects of Mu substitution for H. This revised version was published online in August 2006 with corrections to the Cover Date.     

Laser-induced breakdown of soda-lime glass microspheres using Nd:YAG laser

The Nd:YAG laser-induced breakdown of 20 μm glass microspheres was investigated using time-resolved optical shadow and Schlieren images. Time-resolved imaging showed the location of the initial breakdown and the shockwave motion over its first 400 μm of expansion. Measured shockwave velocities were in the range of 1–10 km/s and showed a linear dependency on laser fluence within 30 ns.     

On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models?

We demonstrate that many collective phenomena in multi-cellular systems can be explained by models in which cells, despite their complexity, are represented as simple particles which are parameterized mainly by their physical properties. We mainly focus on two examples that nevertheless span a wide range of biological sub-disciplines: Unstructured cell populations growing in cell culture and growing cell layers in early animal development. While cultured unstructured cell populations would apriori been classified as particularly suited for a biophysical approach since the degree to which they are committed to a genetic program is expected to be modest, early animal development would be expected to mark the other extreme—here the degree of determinism according to a genetic program would be expected to be very high. We consider a number of phenomena such as the growth kinetics and spatial structure formation of monolayers and multicellular spheroids, the effect of the presence of another cell type surrounding the growing cell population, the effect of mutations and the critical surface dynamics of monolayers. Different from unstructured cell populations, cells in early development and at tissue interfaces usually form highly organized structures. An example are tissue layers. Under certain circumstances such layers are observed to fold. We show that folding pattern again can largely be explained by physical mechanisms either by a buckling instability or active cell shape changes. The paper combines new and published material and aims at an overview of a wide range of physical aspects in unstructured populations and growing tissue layers.     

A Metropolis Monte Carlo Implementation of Bayesian Time-Domain Parameter Estimation: Application to Coupling Constant Estimation from Antiphase Multiplets

The Bayesian perspective on statistics asserts that it makes sense to speak of a probability of an unknown parameter having a particular value. Given a model for an observed, noise-corrupted signal, we may use Bayesian methods to estimate not only the most probable value for each parameter but also their distributions. We present an implementation of the Bayesian parameter estimation formalism developed by G. L. Bretthorst (1990,J. Magn. Reson.88, 533) using the Metropolis Monte Carlo sampling algorithm to perform the parameter and error estimation. This allows us to make very few assumptions about the shape of the posterior distribution, and allows the easy introduction of prior knowledge about constraints among the model parameters. We present evidence that the error estimates obtained in this manner are realistic, and that the Monte Carlo approach can be used to accurately estimate coupling constants from antiphase doublets in synthetic and experimental data.     

Determination of the Tolman cone angle from crystallographic parameters and a statistical analysis using the crystallographic data base

Summary A new method of evaluating the Tolman cone angle from X-ray structural data available from the Cambridge Crystallographic Data Base has been developed and a statistical analysis of the cone angles of the phosphines PPh₃, PMe₂Ph, PMePh₂, PMe₃, PEt₃ and PCy₃ (Cy = cyclohexyl) in transition metal complexes has been completed.     

A goal programming approach to strategic resource allocation in acute care hospitals

This paper describes a methodology for allocating resources in hospitals. The methodology uses two linear goal-programming models. One model sets case mix and volume for physicians, while holding service costs fixed; the other translates case mix decisions into a commensurate set of practice changes for physicians. The models allow decision makers to set case mix and case costs in such a way that the institution is able to break even, while preserving physician income and minimizing disturbance to practice. The models also permit investigation of trade-offs between case mix and physician practice parameters. Results are presented from a decision-making scenario facing the surgical division of Toronto's Mount Sinai Hospital after the announcement of a 3-year, 18% reduction in funding.     

Modeling synchronization and suppression of spontaneous otoacoustic emissions using Van der Pol oscillators: effects of aspirin administration

Many of the aspects of the interaction of spontaneous otoacoustic emissions with external tones (suppression and synchronization) can be qualitatively simulated by the behavior of a single driven Van der Pol oscillator. Analytical and numerical investigations of a model of spontaneous otoacoustic emissions based on such an oscillator (with appropriate parametric changes in the nonlinear and negative damping components) lead to predictions of the nature of the changes in suppression and synchronization (frequency-locking) tuning curves when the levels of spontaneous otoacoustic emissions are modified. Observations of the suppression and synchronization of spontaneous otoacoustic emissions by external tones of different frequencies and levels were obtained while the levels of spontaneous emissions were altered by aspirin administration. Modeling an emission as a single Van der Pol oscillator qualitatively accounts for: (1) the reduction of the level of an external tone required to suppress the emission by a decibel amount equivalent to the level reduction induced by aspirin administration; (2) the broadening of the frequency-locking tuning curve of an emission whose level is reduced; and (3) the pulling of the emission frequency by an external tone. It does not account for: (1) the observed asymmetry in the slopes of the external-tone suppression curves (more gradual for frequencies of the suppressor tone higher, rather than lower, than that of the emission); and (2) the frequency pushing of the emission by an external tone.