Bifurcation contrasts between plane Poiseuille flow and plane Magnetohydrodynamic flow

The stability characteristics of an incompressible viscous pressure-driven flow of an electrically conducting fluid between two parallel boundaries in the presence of a transverse magnetic field are compared and contrasted with those of Plane Poiseuille flow (PPF). Assuming that the outer regions adjacent to the fluid layer are perfectly electrically insulating, the appropriate boundary conditions are applied. The eigenvalue problems are then solved numerically to obtain the critical Reynolds number Rec and the critical wave number ac in the limit of small Hartmann number (M) range to produce the curves of marginal stability. The non-linear two-dimensional travelling waves that bifurcate by way of a Hopf bifurcation from the neutral curves are approximated by a truncated Fourier series in the streamwise direction. Two and three dimensional secondary disturbances are applied to both the constant pressure and constant flux equilibrium solutions using Floquet theory as this is believed to be the generic mechanism of instability in shear flows. The change in shape of the undisturbed velocity profile caused by the magnetic field is found to be the dominant factor. Consequently the critical Reynolds number is found to increase rapidly with increasing M so the transverse magnetic field has a powerful stabilising effect on this type of flow.

ProxiMAX randomisation:a new technology for non-degenerate saturation mutagenesis of contiguous codons

Back in 2003, we published ‘MAX’ randomisation, a process of non-degenerate saturation mutagenesis using exactly 20 codons (one for each amino acid) or else any required subset of those 20 codons. ‘MAX’ randomisation saturates codons located in isolated positions within a protein, as might be required in enzyme engineering, or else on one face of an alpha-helix, as in zinc finger engineering. Since that time, we have been asked for an equivalent process that can saturate multiple, contiguous codons in a non-degenerate manner. We have now developed ‘ProxiMAX’ randomisation, which does just that: generating DNA cassettes for saturation mutagenesis without degeneracy or bias. Offering an alternative to trinucleotide phosphoramidite chemistry, ProxiMAX randomisation uses nothing more sophisticated than unmodified oligonucleotides and standard molecular biology reagents. Thus it requires no specialised chemistry, reagents nor equipment and simply relies on a process of saturation cycling comprising ligation, amplification and digestion for each cycle. The process can encode both unbiased representation of selected amino acids or else encode them in pre-defined ratios. Each saturated position can be defined independently of the others. We demonstrate accurate saturation of up to 11 contiguous codons. As such, ProxiMAX randomisation is particularly relevant to antibody engineering.

ProxiMAX Randomisation:a new technology for non-degenerate saturation mutagenesis of contiguous codons

ProxiMAX randomisation achieves saturation mutagenesis of contiguous codons without degeneracy or bias. Offering an alternative to trinucleotide phosphoramidite chemistry, it uses nothing more sophisticated than unmodified oligonucleotides and standard molecular biology reagents and as such, requires no specialised chemistry, reagents nor equipment. When particular residues are known to affect protein activity/specificity, their combinatorial replacement with all 20 amino acids, or a subset thereof, can provide a rapid route to generating proteins with desirable characteristics. Conventionally, saturation mutagenesis replaced key codons with degenerate ones. Although simple to perform, that procedure resulted in unnecessarily large libraries, termination codons and inherent uneven amino acid representation. ProxiMAX randomisation is an enzyme-based technique that can encode unbiased representation of all or selected amino acids or else can provide required codons in pre-defined ratios. Each saturated position can be defined independently of the others. ProxiMAX randomisation is achieved via saturation cycling: an iterative process comprising blunt end ligation, amplification and digestion with a Type IIS restriction enzyme. We demonstrate both unbiased saturation of a short 6-mer peptide and saturation of a hypervariable region of a scfv antibody fragment, where 11 contiguous codons are saturated with selected codons, in pre-defined ratios. As such, ProxiMAX randomisation is particularly relevant to antibody engineering. The development of ProxiMAX randomisation from concept to reality is described.

Bifurcation study for a vertical channel with constant flux and large aspect ratio

Using suitable coupled Navier-Stokes Equations for an incompressible Newtonian fluid we investigate the linear and non-linear steady state solutions for both a homogeneously and a laterally heated fluid with finite Prandtl Number (Pr=7) in the vertical orientation of the channel. Both models are studied within the Large Aspect Ratio narrow-gap and under constant flux conditions with the channel closed. We use direct numerics to identify the linear stability criterion in parametric terms as a function of Grashof Number (Gr) and streamwise infinitesimal perturbation wavenumber (making use of the generalised Squire’s Theorem). We find higher harmonic solutions at lower wavenumbers with a resonance of 1:3exist, for both of the heating models considered. We proceed to identify 2D secondary steady state solutions, which bifurcate from the laminar state. Our studies show that 2D solutions are found not to exist in certain regions of the pure manifold, where we find that 1:3 resonant mode 2D solutions exist, for low wavenumber perturbations. For the homogeneously heated fluid, we notice a jump phenomenon existing between the pure and resonant mode secondary solutions for very specific wavenumbers .We attempt to verify whether mixed mode solutions are present for this model by considering the laterally heated model with the same geometry. We find mixed mode solutions for the laterally heated model showing that a bridge exists between the pure and 1:3 resonant mode 2D solutions, of which some are stationary and some travelling. Further, we show that for the homogeneously heated fluid that the 2D solutions bifurcate in hopf bifurcations and there exists a manifold where the 2D solutions are stable to Eckhaus criterion, within this manifold we proceed to identify 3D tertiary solutions and find that the stability for said 3D bifurcations is not phase locked to the 2D state. For the homogeneously heated model we identify a closed loop within the neutral stability curve for higher perturbation wavenumubers and analyse the nature of the multiple 2D bifurcations around this loop for identical wavenumber and find that a temperature inversion occurs within this loop. We conclude that for a homogeneously heated fluid it is possible to have abrup ttransitions between the pure and resonant 2D solutions, and that for the laterally heated model there exist a transient bifurcation via mixed mode solutions.

ProxiMAX randomisation:a new technology for non-degenerate saturation mutagenesis of contiguous codons

Back in 2003, we published ‘MAX’ randomisation, a process of non-degenerate saturation mutagenesis using exactly 20 codons (one for each amino acid) or else any required subset of those 20 codons. ‘MAX’ randomisation saturates codons located in isolated positions within a protein, as might be required in enzyme engineering, or else on one face of an alpha-helix, as in zinc finger engineering. Since that time, we have been asked for an equivalent process that can saturate multiple, contiguous codons in a non-degenerate manner. We have now developed ‘ProxiMAX’ randomisation, which does just that: generating DNA cassettes for saturation mutagenesis without degeneracy or bias. Offering an alternative to trinucleotide phosphoramidite chemistry, ProxiMAX randomisation uses nothing more sophisticated than unmodified oligonucleotides and standard molecular biology reagents. Thus it requires no specialised chemistry, reagents nor equipment and simply relies on a process of saturation cycling comprising ligation, amplification and digestion for each cycle. The process can encode both unbiased representation of selected amino acids or else encode them in pre-defined ratios. Each saturated position can be defined independently of the others. We demonstrate accurate saturation of up to 11 contiguous codons. As such, ProxiMAX randomisation is particularly relevant to antibody engineering.

Bifurcation and stability in a low-dimensional model for multiple-frequency mode-locked lasers

Recent theoretical investigations have demonstrated that the stability of mode-locked solutions of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this article, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and the existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for the existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple-frequency channels. © 2010 The American Physical Society.