Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

The relationship between radiation-induced chemical processes and transverse relaxation times in polymer gel dosimeters

The effects of ionizing radiation in different compositions of polymer gel dosimeters are investigated using FT-Raman spectroscopy and NMR T-2 relaxation times. The dosimeters are manufactured from different concentrations of comonomers (acrylamide and N,N'-methylene-bis-acrylamide) dispersed in different concentrations of an aqueous gelatin matrix. Results are analysed using a model of fast exchange of magnetization between three proton pools. The fraction of protons in each pool is determined using the known chemical composition of the dosimeter and FT-Raman spectroscopy. Based on these results, the physical and chemical processes in interplay in the dosimeters are examined in view of their effect on the changes in T-2 The precipitation of growing macroradicals and the scavenging of free radicals by gelatin are used to explain the rate of polymerization. The model describes the changes in T-2 as a function of the absorbed dose up to 50 Gy for the different compositions. This is expected to aid the theoretical design of new, more efficient dosimeters, since it was demonstrated that the optimum dosimeter (i.e, with the lowest dose resolution) must have a range of relaxation times which match the range of T-2 values which can be determined with the lowest uncertainty using an MRI scanner.

Folding processes and solitary waves in structural geology

Evolution of localized folding patterns in layered elastic and visco-elastic materials is reviewed in the context of compressed geological systems. The thin strut or plate embedded in a visco-elastic medium is used as an archetypal example to describe localized buckles which, in contrast to those from earlier formulations, appear in the absence of triggering imperfections. Structural and material effects are surveyed and important nonlinear characteristics are identified. A brief review of possible methods of analysis is conducted.

Regulation and properties of KCNQ1 (K(v)LQT1) and impact of the cystic fibrosis transmembrane conductance regulator

The K+ channel KCNQ1 (K(V)LQT1) is a voltage-gated K+ channel, coexpressed with regulatory subunits such as KCNE1 (IsK, mink) or KCNE3, depending on the tissue examined. Here, we investigate regulation and properties of human and rat KCNQ1 and the impact of regulators such as KCNE1 and KCNE3. Because the cystic fibrosis transmembrane conductance regulator (CFTR) has also been suggested to regulate KCNQ1 channels we studied the effects of CFTR on KCNQ1 in Xenopus oocytes, Expression of both human and rat KCNQ1 induced time dependent K+ currents that were sensitive to Ba2+ and 293B. Coexpression with KCNE1 delayed voltage activation, while coexpression with KCNE3 accelerated current activation. KCNQ1 currents were activated by an increase in intracellular cAMP, independent of coexpression with KCNE1 or KCNE3. cAMP dependent activation was abolished in N-terminal truncated hKCNQ1 but was still detectable after deletion of a single PKA phosphorylation motif. In the presence but not in the absence of KCNE1 or KCNE3, K+ currents were activated by the Ca2+ ionophore ionomycin. Coexpression of CFTR with either human or rat KCNQ1 had no impact on regulation of KCNQ1 K+ currents by cAMP but slightly shifted the concentration response curve for 293B. Thus, KCNQ1 expressed in Xenopus oocytes is regulated by cAMP and Ca2+ but is not affected by CFTR.

Free radical copolymerization of methyl methacrylate and allyl acetate Part 2 structure and properties

The structure of the product from the free radical bulk copolymerization of methyl methacrylate (MMA) and allyl acetate (AAc) was investigated. The mole fraction of AAc plays an important role in the copolymerization of these two monomers. Molecular weight (MW) and molecular weight distribution (MWD) are completely altered when the feed composition is dominantly AAc. NMR spectroscopy confirmed the incorporation of AAc into the polymer. However, no allyl-allyl linkages were observed at low conversions. T-g was found to be affected by the incorporation of AAc into the polymer. (C) 2001 Society of Chemical Industry.

Non-Markovian quantum optical processes and pseudomodes

Non-Markovian behaviour in atomic systems coupled to a structured reservoir of quantum EM field modes, such as in high Q cavities, is treated using a quasimode description, and the pseudo mode theory for single quantum reservoir excitations is obtained via Fano diagonalisation. The atomic transitions are coupled to a discrete set of (cavity) quasimodes, which are also coupled to a continuum set of (external) quasimodes with slowly varying coupling constants. Each pseudomode corresponds to a cavity quasimode, and the original reservoir structure is obtained in expressions for the equivalent atom-true mode coupling constants. Cases of multiple excitation of the reservoir are now treatable via Markovian master equations for the atom-discrete quasimode system.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

The downsides of downsizing: Communication processes and information needs in the aftermath of a workforce reduction strategy

This study explored the impact of downsizing on levels of uncertainty, coworker and management trust, and communicative effectiveness in a health care organization downsizing during a 2-year period from 660 staff to 350 staff members. Self-report data were obtained from employees who were staying (survivors), from employees were being laid off (victims), and from employees with and without managerial responsibilities. Results indicated that downsizing had a similar impact on the amount of trust that survivors and victims had for management. However, victims reported feeling lower levels of trust toward their colleagues compared with survivors. Contrary to expectations, survivors and victims reported similar perceptions of job and organizational uncertainty and similar levels of information received about changes. Employees with no management responsibilities and middle managers both reported lower scores than did senior managers on all aspects of information received. Implications for practice and the management of the communication process are discussed.

Morphology and properties of thermoplastic polyurethane nancomposites incorporating hydrophilic layered silicates

Hydrophilic layered silicate/polyurethane nanocomposites were prepared via twin screw extrusion and solvent casting. Good dispersion and delamination was achieved-regardless of processing route, illustrating that the need for optimised processing conditions diminishes when there is a strong driving for de for intercalation between the polymer and organosilicate. Evidence for altered polyurethane microphase morphology in the nanocomposites was provided by DMTA and DSC. WAXD results suggested that the appearance of an additional high temperature melting endotherm in some melt-compounded nanocomposites was not due to the formation of a second crystal polymorph, but rather due to more well-ordered hard microdomains. Solvent casting was found to be the preferred processing route due to the avoidance of polyurethane and surfactant degradation associated with melt processing. While tensile strength and elongation were not improved on organosilicate addition, large increases in stiffness were observed. At a 7 wt% organosilicate loading, a 3.2-fold increase in Young's modulus was achieved by solvent casting. The nanocomposites also displayed higher hysteresis and permanent set. (C) 2004 Elsevier Ltd. All rights reserved.