Bulk and Interfacial Shear Thinning of Immiscible Polymers

Nonequilibrium molecular dynamics simulations are used to study the shear thinning behavior of immiscible symmetric polymer blends. The phase separated polymers are subjected to a simple shear flow imposed by moving a wall parallel to the fluid-fluid interface. The viscosity begins to shear thin at much lower rates in the bulk than at the interface. The entire shear rate dependence of the interfacial viscosity is consistent with a shorter effective chain length $s^*$ that also describes the width of the interface. This $s^*$ is independent of chain length $N$ and is a function only of the degree of immiscibility of the two polymers. Changes in polymer conformation are studied as a function of position and shear rate.Shear thinning correlates more closely with a decrease in the component of the radius of gyration along the velocity gradient than with elongation along the flow. At the interface, this contraction of chains is independent of $N$ and consistent with the bulk behavior for chains of length $s^*$. The distribution of conformational changes along chains is also studied. Central regions begin to stretch at a shear rate that decreases with increasing $N$, while shear induced changes at the ends of chains are independent of $N$.Comment: 8 pages, 8 figure

Random solids and random solidification: What can be learned by exploring systems obeying permanent random constraints?

In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this random solid state, particles are permanently but randomly localized in space, and a rigidity to shear deformations emerges. Owing to the permanence of the random constraints, this phase transition is an equilibrium transition, which confers on it a simplicity (at least relative to the conventional glass transition) in the sense that it is amenable to established techniques of equilibrium statistical mechanics. In this Paper I shall review recent developments in the theory of random solidification for systems obeying permanent random constraints, with the aim of bringing to the fore the similarities and differences between such systems and those exhibiting the conventional glass transition. I shall also report new results, obtained in collaboration with Weiqun Peng, on equilibrium correlations and susceptibilities that signal the approach of the random solidification transition, discussing the physical interpretation and values of these quantities both at the Gaussian level of approximation and, via a renormalization-group approach, beyond.Comment: Paper presented at the "Unifying Concepts in Glass Physics" workshop, International Centre for Theoretical Physics, Trieste, Italy (September 15-18, 1999

Universality and its Origins at the Amorphous Solidification Transition

Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling functions that describe the order parameter and (equivalently) the statistical distribution of localization lengths for these localized particles. The purpose of this Paper is to discuss the origins and consequences of this universality, and in doing so, three themes are explored. First, a replica-Landau-type approach is formulated for the universality class of systems that are composed of extended objects connected by permanent random constraints and undergo amorphous solidification at a critical density of constraints. This formulation generalizes the cases of randomly cross-linked and end-linked macromolecular systems, discussed previously. The universal replica free energy is constructed, in terms of the replica order parameter appropriate to amorphous solidification, the value of the order parameter is obtained in the liquid and amorphous solid states, and the chief universal characteristics are determined. Second, the theory is reformulated in terms of the distribution of local static density fluctuations rather than the replica order parameter. It is shown that a suitable free energy can be constructed, depending on the distribution of static density fluctuations, and that this formulation yields precisely the same conclusions as the replica approach. Third, the universal predictions of the theory are compared with the results of extensive numerical simulations of randomly cross-linked macromolecular systems, due to Barsky and Plischke, and excellent agreement is found.Comment: 10 pages, including 3 figures (REVTEX

The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion

For independent nearest-neighbour bond percolation on Z^d with d >> 6, we prove that the incipient infinite cluster's two-point function and three-point function converge to those of integrated super-Brownian excursion (ISE) in the scaling limit. The proof is based on an extension of the new expansion for percolation derived in a previous paper, and involves treating the magnetic field as a complex variable. A special case of our result for the two-point function implies that the probability that the cluster of the origin consists of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic, and xr package

AlGaN/GaN HEMTs - Operation in the K-Band and Above

We report on the power and microwave noise performance of AlGan/GaN high electron-mobility transistors (HEMTs) at frequencies f \u3e 18 GHz (K- and Ka-bands). At 20 GHz, a record continuous-wave output power of 1.6 W has been achieved on an eight-finger 500-mum total gate-periphery device. At 29 GHz, a 120-mum gate-periphery device showed a pulsed output density of 1.6 W/mm with an associated gain of 6.7 dB and power-added efficiency of 26%. Minimum noise figure of 1.5 dB has been achieved on a 0.2 mum x 200 mum device at 26 GHz. The data demonstrate the viability of AlGan/GaN HEMTs for high-frequency power and low-noise amplifier applications

Breast tumour cell-induced down-regulation of type I collagen mRNA in fibroblasts

This study investigated the modulation of type I collagen gene expression in normal fibroblasts by breast tumour cells. Northern analysis of total RNA extracted from stages I, II and III breast tumour tissue revealed that collagen mRNA levels were elevated in stage I tumours compared to the adjacent normal breast tissues, whereas they were decreased in stages II and III breast tumours. This aberrant collagen gene expression was confirmed by non-radioactive RNA:RNA in situ hybridization analysis of 30 breast carcinomas which localized the production of type I collagen mRNA to the stromal fibroblasts within the vicinity of the tumour cells. In order to determine whether the tumour cells were directly responsible for this altered collagen production by the adjacent fibroblasts, breast tumour cell lines were co-cultured with normal fibroblasts for in vitro assessment of collagen and steady-state collagen RNA levels. Co-culture of tumour cells and normal fibroblasts in the same dish resulted in down-regulation of collagen mRNA and protein. Treatment of the fibroblasts with tumour-cell conditioned medium also resulted in decreased collagen protein levels but the mRNA levels, however, remained unaltered. These results suggested that the tumour cells either secrete a labile ‘factor’, or express a cell surface protein requiring direct contact with the fibroblasts, resulting in down-regulation of collagen gene expression. Modulation of the ECM is a common characteristic of invading tumour cells and usually involves increased production of collagenases by the tumour cells or stromal fibroblasts. This study showed that tumour cells were also able to modulate collagen mRNA production by stromal fibroblasts, which may facilitate tumour cell invasion and metastasis. © 1999 Cancer Research Campaig

CHAMP: Cognitive behaviour therapy for health anxiety in medical patients, a randomised controlled trial

BACKGROUND: Abnormal health anxiety, also called hypochondriasis, has been successfully treated by cognitive behaviour therapy (CBT) in patients recruited from primary care, but only one pilot trial has been carried out among those attending secondary medical clinics where health anxiety is likely to be more common and have a greater impact on services. The CHAMP study extends this work to examine both the clinical and cost effectiveness of CBT in this population. METHOD/DESIGN: The study is a randomized controlled trial with two parallel arms and equal randomization of 466 eligible patients (assuming a 20% drop-out) to an active treatment group of 5-10 sessions of cognitive behaviour therapy and to a control group. The aim at baseline, after completion of all assessments but before randomization, was to give a standard simple explanation of the nature of health anxiety for all participants. Subsequently the control group was to receive whatever care might usually be available in the clinics, which is normally a combination of clinical assessment, appropriate tests and reassurance. Those allocated to the active treatment group were planned to receive between 5 and 10 sessions of an adapted form of cognitive behaviour therapy based on the Salkovskis/Warwick model, in which a set of treatment strategies are chosen aimed at helping patients understand the factors that drive and maintain health anxiety. The therapy was planned to be given by graduate research workers, nurses or other health professionals trained for this intervention whom would also have their competence assessed independently during the course of treatment. The primary outcome is reduction in health anxiety symptoms after one year and the main secondary outcome is the cost of care after two years. DISCUSSION: This represents the first trial of adapted cognitive behaviour therapy in health anxiety that is large enough to test not only the clinical benefits of treatment but also whether the cost of treatment is offset by savings from reduced use of other health services in comparison to the control group.Cognitive behaviour therapy for Health Anxiety in Medical Patients (CHAMP) TRIAL REGISTRATION: Current Controlled Trials ISRCTN14565822

Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State

As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equi- librium phase transition, the liquid state, in which all macromolecules are delocalised, is transformed into a solid state, in which a nonzero fraction of macromolecules have spontaneously become localised. This solid state is a most unusual one: localisation occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanisation transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter. In this review we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanisation transition.Comment: Review Article, REVTEX, 58 pages, 3 PostScript figure

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR(∞) Models *

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/101814/1/1468-2354.t01-1-00016.pd