DYNGA: a general purpose QM-MM-MD program. I. Application to water

We present a general purpose QM-MM-MD engine (DYNGA) designed to test alternative hybrid Hamiltonians geared towards the treatment of problems of interest in structural biology including the use of experimental data constraints. In this first presentation we use DYNGA to explore the behaviour of a traditional QM-MM approach in the treatment of the water—water interaction. We find the potential energy hypersurface for the water dimer computed with the HF 4–31G*/TIP3P hybrid Hamiltonian tends to be too flat. We also explore the effect of using traditional QM-MM techniques on proton wires and conclude there is a need for improvement, possibly addressed by using polarizable force fields.     

Inflation, Bending and Torsion of Reinforced Elastic Tubes

Analysis is given for elastic tubes containing a number of surfacesof balanced-angleply fibre reinforcement when subjected to internaland external pressures and to large displacements and rotationsof the cross-sections. The strain is small, so that the firstapproximation to the stress and strain distributions over eachcross-section is found to be a superposition of the types analysedby Green & Nicol (1978) and Nicol (1978). The equilibriumequations for a length of tube undergoing combined extension,inflation, bending and torsion are derived and an expressionfor the maximum tensions arising in the reinforcing fibres isobtained. Numerical calculations for tubes having the same compositionas those of Green & Nicol show that the only rigidity parameterwhich is significantly affected by the reinforcement is thetorsional rigidity, even though the tensions developed in theindividual reinforcement layers depend on the elastic propertiesof the fibres. The influence of a large torsional rigidity on configurationsadopted by a tube loaded only at its ends and subjected to internaland external pressures is illustrated by considering deformationsin which the tube becomes helical, with an additional materialtwist about the helical line of centres.     

Coupled evolution equations for axially inhomogeneous optical fibres

At ‘monomode’ frequencies, a uniform axisymmetricoptical fibre can support left- and right-handed circularlypolarized modes having the same dispersion relation. Nonlinearityintroduces cubic terms into the evolution equations, which arecoupled nonlinear Schrdinger equations (Newboult, Parker, andFaulkner, 1989). This paper analyses signal propagation in axisymmetricfibres for which the distribution of dielectric properties variesgradually, but significantly, along the fibre. At each cross-section,left- and right-handed modal fields are defined, but their axialvariations introduce changes into the coupled evolution equations.Two regimes are identified. When axial variations occur on lengthscales comparable with nonlinear evolution effects, the governingequations are determined as coupled nonlinear Schrdinger equationswith variable coefficients. On the other hand, for more rapidaxial variations it is found that the evolution equations haveconstant coefficients, defined as appropriate averages of thoseassociated with each cross-section. Situations in which thevariable coefficient equations may be transformed into constantcoefficient equations are investigated. It is found that theonly possibilities are natural generalizations of thosefoundby Grimshaw (1979) for a single nonlinear Schrdinger equation.In such cases, suitable sech-envelope pulses will propagatewithout radiation. Numerical evidence is presented that, insome other cases with periodically varying coefficients, a sech-envelopepulse loses little amplitude even after propagating through40 periods of axial inhomogeneity of significant amplitude.