Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.

Structure-flexoelastic properties of bimesogenic liquid crystals

In this paper, we report on the flexoelastic and viscoelastic ratios for a number of bimesogens compounds with the same generic structure. Values are obtained indirectly by measuring the flexoelectro-optic response in the chiral nematic phase. By varying the molecular structure we alter the bend angle, transverse dipole moment, and length of the molecule. First, to examine the influence of the bend angle we use a homologous series whereby the only alteration in the molecular structure is the number of methylene units in the aliphatic spacer, n. Results show that the flexoelastic ratio, e K, and the effective flexoelectric coefficient, e, both exhibit an odd-even effect with values for n=odd being greater than that for n=even. This is understood in terms of an increase in the bend angle of the molecule and an increase in the transverse dipole moment. Second, in order to investigate the impact of the dipole moment, we have altered the mesogenic units so as to vary the longitudinal dipole moment and used different linkages in the aliphatic spacer in an attempt to alter the transverse dipole moment. Qualitatively, the results demonstrate that the odd-spaced bimesogen with larger transverse dipole moments exhibit larger flexoelastic ratios. © 2007 The American Physical Society.

Structure-flexoelastic properties of bimesogenic liquid crystals.

In this paper, we report on the flexoelastic and viscoelastic ratios for a number of bimesogens compounds with the same generic structure. Values are obtained indirectly by measuring the flexoelectro-optic response in the chiral nematic phase. By varying the molecular structure we alter the bend angle, transverse dipole moment, and length of the molecule. First, to examine the influence of the bend angle we use a homologous series whereby the only alteration in the molecular structure is the number of methylene units in the aliphatic spacer, n . Results show that the flexoelastic ratio, e/K , and the effective flexoelectric coefficient, e , both exhibit an odd-even effect with values for n=odd being greater than that for n=even . This is understood in terms of an increase in the bend angle of the molecule and an increase in the transverse dipole moment. Second, in order to investigate the impact of the dipole moment, we have altered the mesogenic units so as to vary the longitudinal dipole moment and used different linkages in the aliphatic spacer in an attempt to alter the transverse dipole moment. Qualitatively, the results demonstrate that the odd-spaced bimesogen with larger transverse dipole moments exhibit larger flexoelastic ratios.

BEHAVIOUR OF FIXED CANTILEVER WALLS SUBJECT TO LATERAL SHAKING.

A programme of research on the seismic behaviour of retaining walls has been under way at Cambridge since 1981. Centrifuge tests have presently been conducted both on cantilever walls and isolated mass walls, retaining dry sands of varying grading and density. This paper is devoted to the modelling of fixed-base cantilever walls retaining Leighton Buzzard (14/25) sand of relative density 99% with a horizontal surface level with the crest of the wall. The base of the centrifuge container was used to fix the walls, and to provide a rigid lower boundary for the sand. No attempt was made to inhibit the propagation of compression waves from the side of the container opposite the inside face of the model wall. The detailed analysis of dynamic deflections and bending moments was made difficult by the anelastic nature of reinforced concrete, and the difficulty of measuring bending strains thereon. A supplementary programme of well-instrumented tests on Dural walls of similar stiffness, including the modelling of models, was therefore carried out. Refs.

Comment and reply on the 'assessment of combustion and submodels for turbulent nonpremixed hydrocarbon flames'

In deriving the flamelet model for nonpremixed combustion certain terms, but not the unsteady term, are assumed to be negligible. This results in a relation between all reacting scalars and the mixture fraction as independent variable. An ideal test of the flamelet assumption can be based on direct numerical simulation (DNS) data, if all reacting scalars are conditioned on mixture fraction and conditional moments are evaluated. The fundamental assumption of the flamelet model are unwillingly justified. The unsteady and steady formulations of the same equations are compared and found that unsteadiness is important in an unsteady simulation.

Seismic behaviour of anchored quay walls with dry backfill

The seismic behaviour of anchored sheet pile walls is a complex soil-structure interaction problem. Damaged sheet pile walls are very expensive to repair and their seismic behaviour needs to be investigated in order to understand their possible mechanisms of failure. The research described in this paper involves both centrifuge testing and Finite Element (FE) analyses aimed at investigating the seismic behaviour of an anchored sheet pile wall in dry sand. The model wall is tied to the backfill with two tie rods connected to an anchor beam. The accelerations of the sheet pile wall, the anchor beam and the soil around the wall were measured using miniature piezoelectric accelerometers. The displacement at the tip of the wall was also measured. Stain gauges at five different locations on the wall were used to measure the bending moments induced in the the wall. The anchor forces in the tie rods were also measured using load cells. The results from the centrifuge tests were compared with 2-D, plane strain FE analyses conducted using DIANA-SWANDYNE II and the observed seismic behaviour was explained in the light of these findings. © 2011 Taylor & Francis.