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This paper reviews particle packing models and explores their application in geotechnical engineering, specifically for sand-silt mixtures. The review covers key models, including limiting case, linear, and non-linear packing models, focusing on their mathematical structures, physical principles, assumptions, and limitations through the concept of excess free volume. The application of particle packing models in geotechnical engineering is explored in characterizing the properties of sand-silt mixtures, offering insights into maximum, minimum, and critical void ratios and inter-granular void ratio, and the prediction of mechanical properties. 

Centromeres reside in rapidly evolving, repeat-rich genomic regions, despite their essential function in chromosome segregation. Across organisms, centromeres are rich in selfish genetic elements such as transposable elements and satellite DNAs that can bias their transmission through meiosis. However, these elements still need to cooperate at some level and contribute to, or avoid interfering with, centromere function. To gain insight into the balance between conflict and cooperation at centromeric DNA, we take advantage of the close evolutionary relationships within theDrosophila simulansclade—D.simulans,D.sechellia, andD.mauritiana—and their relative,D.melanogaster. Using chromatin profiling combined with high-resolution fluorescence in situ hybridization on stretched chromatin fibers, we characterize all centromeres across these species. We discovered dramatic centromere reorganization involving recurrent shifts between retroelements and satellite DNAs over short evolutionary timescales. We also reveal the recent origin (<240 Kya) of telocentric chromosomes inD.sechellia, where the X and fourth centromeres now sit on telomere-specific retroelements. Finally, the Y chromosome centromeres, which are the only chromosomes that do not experience female meiosis, do not show dynamic cycling between satDNA and TEs. The patterns of rapid centromere turnover in these species are consistent with genetic conflicts in the female germline and have implications for centromeric DNA function and karyotype evolution. Regardless of the evolutionary forces driving this turnover, the rapid reorganization of centromeric sequences over short evolutionary timescales highlights their potential as hotspots for evolutionary innovation. 

We consider the time evolution in two spatial dimensions of a double vorticity layer consisting of two contiguous, infinite material fluid strips, each with uniform but generally differing vorticity, embedded in an otherwise infinite, irrotational, inviscid incompressible fluid. The potential application is to the wake dynamics formed by two boundary layers separating from a splitter plate. A thin-layer approximation is constructed where each layer thickness, measured normal to the common centre curve, is small in comparison with the local radius of curvature of the centre curve. The three-curve equations of contour dynamics that fully describe the double-layer dynamics are expanded in the small thickness parameter. At leading order, closed nonlinear initial-value evolution equations are obtained that describe the motion of the centre curve together with the time and spatial variation of each layer thickness. In the special case where the layer vorticities are equal, these equations reduce to the single-layer equation of Moore ( Stud. Appl. Math. , vol. 58, 1978, pp. 119–140). Analysis of the linear stability of the first-order equations to small-amplitude perturbations shows Kelvin–Helmholtz instability when the far-field fluid velocities on either side of the double layer are unequal. Equal velocities define a circulation-free double vorticity layer, for which solution of the initial-value problem using the Laplace transform reveals a double pole in transform space leading to linear algebraic growth in general, but there is a class of interesting initial conditions with no linear growth. This is shown to agree with the long-wavelength limit of the full linearized, three-curve stability equations. 

Y chromosomes across diverse species convergently evolve a gene-poor, heterochromatic organization enriched for duplicated genes, LTR retrotransposons, and satellite DNA. Sexual antagonism and a loss of recombination play major roles in the degeneration of young Y chromosomes. However, the processes shaping the evolution of mature, already degenerated Y chromosomes are less well-understood. Because Y chromosomes evolve rapidly, comparisons between closely related species are particularly useful. We generated de novo long-read assemblies complemented with cytological validation to reveal Y chromosome organization in three closely related species of the Drosophila simulans complex, which diverged only 250,000 years ago and share >98% sequence identity. We find these Y chromosomes are divergent in their organization and repetitive DNA composition and discover new Y-linked gene families whose evolution is driven by both positive selection and gene conversion. These Y chromosomes are also enriched for large deletions, suggesting that the repair of double-strand breaks on Y chromosomes may be biased toward microhomology-mediated end joining over canonical non-homologous end-joining. We propose that this repair mechanism contributes to the convergent evolution of Y chromosome organization across organisms. 

The Moore–Saffman–Tsai–Widnall (MSTW) instability is a parametric instability that arises in strained vortex columns. The strain is assumed to be weak and perpendicular to the vortex axis. In this second part of our investigation of vortex instability including density and surface tension effects, a linear stability analysis for this situation is presented. The instability is caused by resonance between two Kelvin waves with azimuthal wavenumber separated by two. The dispersion relation for Kelvin waves and resonant modes are obtained. Results show that the stationary resonant waves for $$m=\pm 1$$ are more unstable when the density ratio $$\rho_2/\rho_1$$ , the ratio of vortex to ambient fluid density, approaches zero, whereas the growth rate is maximised near $$\rho _2/\rho _1 =0.215$$ for the resonance $(m,m+2)=(0,2)$ . Surface tension suppresses the instability, but its effect is less significant than that of density. As the azimuthal wavenumber $$m$$ increases, the MSTW instability decays, in contrast to the curvature instability examined in Part 1 (Chang & Llewellyn Smith, J. Fluid Mech. vol. 913, 2021, A14). 

The curvature instability of thin vortex rings is a parametric instability discovered from short-wavelength analysis by Hattori & Fukumoto ( Phys. Fluids , vol. 15, 2003, pp. 3151–3163). A full-wavelength analysis using normal modes then followed in Fukumoto & Hattori ( J. Fluid Mech. , vol. 526, 2005, pp. 77–115). The present work extends these results to the case with different densities inside and outside the vortex core in the presence of surface tension. The maximum growth rate and the instability half-bandwidth are calculated from the dispersion relation given by the resonance between two Kelvin waves of $$m$$ and $m+1$ , where $$m$$ is the azimuthal wavenumber. The result shows that vortex rings are unstable to resonant waves in the presence of density and surface tension. The curvature instability for the principal modes is enhanced by density variations in the small axial wavenumber regime, while the asymptote for short wavelengths is close to the constant density case. The effect of surface tension is marginal. The growth rates of non-principal modes are also examined, and long waves are most unstable.