Colour in visualisation for computational fluid dynamics

Colour is used in computational fluid dynamic (CFD) simulations in two key ways. First it is used to visualise the geometry and allow the engineer to be confident that the model constructed is a good representation of the engineering situation. Once an analysis has been completed, colour is used in post-processing the data from the simulations to illustrate the complex fluid mechanic phenomena under investigation. This paper describes these two uses of colour and provides some examples to illustrate the key visualisation approaches used in CFD.     

Domains containing the field of values of a matrix

Two groups of estimates are given for the field of values of a general complex matrix. The first group gives a domain containing both the field of values and the convex hull of the diagonal elements, while the second group gives a domain containing both the field of values and the convex hull of the eigenvalues. The domain given by the second group reduces to the smallest domain possible if the matrix is normal. The results have useful applications in control theory and in stability theory for differential equations.     

Rates and mechanisms of the intermolecular cation-exchange reactions of sodium tetraphenylboron with sodium–nitrobenzene and with sodium–p-nitrobenzonitrile

The rates of the exchange of sodium ions between sodium tetraphenylborate and sodium–nitrobenzene or sodium–p-nitrobenzonitrile were measured from analysis of the line broadening effect on the ESR spectra off the paramagnetic ion pairs. The rate is significantly lower for the substituted nitro compound, and it is suggested that this reflects a difference in mechanism for the two systems.     

Direct measurement of the lifetime of the neutral pion

The lifetime of the neutral pion (π⁰) has been directly measured. The lifetime has been found to be τ_π⁰ = (0.897±0.022±0.017) × 10^?16 s. The systematic error results from uncertainties in the momentum spectrum of the π⁰ used for the measurement. This measurement yields a decay width of the π⁰ of (7.34±0.18±0.11) eV. An axial anomaly calculation, which neglects the finite mass of the π⁰, predicts a value of 7.87 eV.     

The four-pion final state in pp annihilations at 5.7 GeV/c

577 events from $\text{p}\text{p}\text{→2π}{}^{\mathrm{+}}\text{2π}{}^{\mathrm{?}}$ annihilations at 5.7 GeV/c are analyzed. Single-particle spectra are studied and an effective matrix element in the form Π_i=1⁴ exp(?Bp_Ti²) is determined. The rates for production of ?° and f⁰ mesons are estimated and the influence of resonances on the angular distributions of pions and dipions is investigated. Transverse momenta correlations can be explained using peripheral phase space.     

Controlled transport and focusing of laser-accelerated protons with miniature magnetic devices

This Letter demonstrates the transporting and focusing of laser-accelerated 14 MeV protons by permanent magnet miniature quadrupole lenses providing field gradients of up to 500 T/m. The approach is highly reproducible and predictable, leading to a focal spot of (286 x 173) microm full width at half maximum 50 cm behind the source. It decouples the relativistic laser-proton acceleration from the beam transport, paving the way to optimize both separately. The collimation and the subsequent energy selection obtained are perfectly applicable for upcoming high-energy, high-repetition rate laser systems.     

Observation of faraday waves in a Bose-Einstein condensate

Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.