A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

A bio-mechanical model for coupling cell contractility with focal adhesion formation

Focal adhesions (FAs) are large, multi-protein complexes that provide a mechanical link between the cytoskeletal contractile machinery and the extracellular matrix. They exhibit mechanosensitive properties; they self-assemble upon application of pulling forces and dissociate when these forces are decreased. We rationalize this mechano-sensitivity from thermodynamic considerations and develop a continuum framework in which the cytoskeletal contractile forces generated by stress fibers drive the assembly of the FA multi-protein complexes. The FA model has three essential features: (i) the low and high affinity integrins co-exist in thermodynamic equilibrium, (ii) the low affinity integrins within the plasma membrane are mobile, and (iii) the contractile forces generated by the stress fibers are in mechanical equilibrium and change the free energies of the integrins. A general two-dimensional framework is presented and the essential features of the model illustrated using one-dimensional examples. Consistent with observations, the coupled stress fiber and FA model predict that (a) the FAs concentrate around the periphery of the cell; (b) the fraction of the cell covered by FAs increases with decreasing cell size while the total FA intensity increases with increasing cell size; and (c) the FA intensity decreases substantially when cell contractility is curtailed.     

The effect of dipole-dipole interaction on zero-THz frequency polarisation

The effect of intramolecular dipole-dipole interaction on polarisation at frequencies from 0 – 10¹² Hz in dipolar media is investigated using a numerical solution of the Sturm-Liouville eigenvalue problem to which the governing Smoluchowski equation reduces. The results of Budó for the long-wavelength limit are extended to all frequencies up to the far infrared, where the predominant inertial effects are treated using a preliminary first-order correction. The numerical method of Pryce may be used to investigate much more realistic interaction potentials than the simple harmonic and cosine form considered by Budó. These simple forms are, however, sufficient to indicate that the integrated absorption intensity per molecule in the far infrared is very sensitive to dipole-dipole interaction and relative hydrodynamic drag on both interacting groups. Applications of the theory to the disordered solid and nematic phases are considered.     

A generalised friction model for the evaluation of angular momentum auto correlation functions

A theory of brownian motion where the friction coefficient is a finite correlation function of molecular torque is used to derive an expression for the angular velocity autocorrelation function, ψ(r). This is related to the orientational a.c.f., φ(t), using an analysis of bandshapes due to Kubo and extended by Shimizu. Both functions φ(t) and ψ(t) contain inherent weaknesses since ψ(t) has a MacLaurin expansion even up to t⁴ only, and π(t) does not reduce to the Kummer function for an ensemble of free rotors in the so-called limit of vanishing friction. Reasons for this behaviour are discussed.     

Methyl displacements from cyclopentadienyl ring planes in sterically crowded (C5Me5)3M complexes

The displacements of the methyl substituents away from the metal and out of the cyclopentadienyl ring plane are compared in sterically crowded (C(5)Me(5))(3)M complexes vs sterically normal f-element complexes in an attempt to evaluate the utility of this parameter in predicting unusual (C(5)Me(5))(1-) ring reactivity. The out-of-plane displacements of 16 sterically crowded tris(cyclopentadienyl) complexes of general formula (C(5)Me(5))(3)M, (C(5)Me(4)R)(3)M (R = Et, (i)Pr, (t)()Bu, SiMe(3)), (C(5)Me(5))(3)MX (X = anion), and (C(5)Me(5))(3)ML (L = neutral ligand) are compared with [(C(5)Me(5))(2)U](2)(C(6)H(6)), (C(5)Me(5))(2)Sm(PC(4)H(2)(t)Bu(2)), and 33 representative examples of f-element bis(cyclopentadienyl) complexes with normal cyclopentadienyl behavior and coordination numbers ranging from 6 to 10. In general, the methyl displacement values of sterically crowded complexes overlap with those in the other complexes, which demonstrates that the basis of the structural distortions is complex. However, if the most extreme out-of-plane displacement in each of the sterically crowded complexes is examined vs the analogous maximum out-of-plane displacement in less crowded systems, there appears to be a basis for predicting cyclopentadienyl reactivity.     

Critical micelle concentrations for alkyltrimethylammonium bromides in water from 25 to 160°C

Critical micelle concentrations were determined by conductance measurements for decyl-, dodecyl-, tetradecyl- and hexadecyltrimethylammonium bromide in water at 25, 60, 95, 130, and 160°C. The results are discussed in terms of the equilibrium model and the nonlinear Poisson-Boltzmann model for micelle formation. The free energies of transferring a methylene group from water to the oil-like interior of the micelle are found to be –781 at 25°C, –796 at 60°C, –819 at 95°C, –815 at 130°C, and –787 at 160°C cal-mol^–1.     

Dual analyte flow injection fluorescence immunoassays using thiophilic gel reactors and synchronous scanning detection

Heterogeneous fluorescence immunoassays have been automated using flow injection manifolds incorporating thiophilic gel solid phase reactors to separate antibody-bound and unbound analyte molecules. Antibody elution is achieved by changes in ionic strength, thus allowing the use of pH sensitive fluorescent labels. This facilitates the development of dual analyte systems, in which two competitive immunoassays with separate labels are monitored in parallel. Detection of the fluorophores by high speed synchronous fluorescence scanning while the flow is briefly stopped utilises either one synchronous interval which detects both fluorophores, or two separate scans at different wavelength intervals, one for each fluorophore. Simultaneous analyses of serum albumin and transferrin exemplify these novel approaches. Spectroscopic interferences are very small, analyte recoveries are close to 100%, with a relative standard deviation of 5-6% and a sampling rate of 20 h-1.