Criticality in Third Order Lovelock Gravity and the Butterfly effect

We study third order Lovelock Gravity in $D=7$ at the critical point which three (A)dS vacua degenerate into one. We see there is not propagating graviton at the critical point. And also we compute the butterfly velocity for this theory at the critical point by considering the shock wave solutions near horizon, this is important to note that although there is no propagating graviton at the critical point, due to boundary gravitons the butterfly velocity is non-zero. Finally we observe that the butterfly velocity for third order Lovelock Gravity at the critical point in $D=7$ is less than the butterfly velocity for Einstein-Gauss-Bonnet Gravity at the critical point in $D=7$ which is less than the butterfly velocity in D = 7 for Einstein Gravity, $v_{B}^{E.H}>v_{B}^{E.G.B}>v_{B}^{3rd\,\,Lovelock}$. Maybe we can conclude that by adding higher order curvature corrections to Einstein Gravity the butterfly velocity decreases.Comment: 10 pages, No figure, Minor correction

Mapping the solid-state properties of crystalline lysozyme during pharmaceutical unit-operations

Bulk crystallisation of protein therapeutic molecules towards their controlled drug delivery is of interest to the biopharmaceutical industry. The complexity of biotherapeutic molecules is likely to lead to complex material properties of crystals in the solid state and to complex transitions. This complexity is explored using batch crystallised lysozyme as a model. The effects of drying and milling on the solid-state transformations of lysozyme crystals were monitored using differential scanning calorimetry (DSC), X-ray powder diffraction (XRPD), FT-Raman, and enzymatic assay. XRPD was used to characterise crystallinity and these data supported those of crystalline lysozyme which gave a distinctive DSC thermogram. The apparent denaturation temperature (Tm) of the amorphous lysozyme was ∼201 °C, while the Tm of the crystalline form was ∼187 °C. Raman spectra supported a more α-helix rich structure of crystalline lysozyme. This structure is consistent with reduced cooperative unit sizes compared to the amorphous lysozyme and is consistent with a reduction in the Tm of the crystalline form. Evidence was obtained that milling also induced denaturation in the solid-state, with the denatured lysozyme showing no thermal transition. The denaturation of the crystalline lysozyme occurred mainly through its amorphous form. Interestingly, the mechanical denaturation of lysozyme did not affect its biological activity on dissolution. Lysozyme crystals on drying did not become amorphous, while milling-time played a crucial role in the crystalline-amorphous-denatured transformations of lysozyme crystals. DSC is shown to be a key tool to monitor quantitatively these transformations