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Nucleic acids such as mRNA have emerged as a promising therapeutic modality with the capability of addressing a wide range of diseases. Lipid nanoparticles (LNPs) as a delivery platform for nucleic acids were used in the COVID-19 vaccines and have received much attention. While modern manufacturing processes which involve rapidly mixing an organic stream containing the lipids with an aqueous stream containing the nucleic acids are conceptually straightforward, detailed understanding of LNP formation and structure is still limited and scale-up can be challenging. Mathematical and computational methods are a promising avenue for deepening scientific understanding of the LNP formation process and facilitating improved process development and control. This article describes strategies for the mechanistic modeling of LNP formation, starting with strategies to estimate and predict important physicochemical properties of the various species such as diffusivities and solubilities. Subsequently, a framework is outlined for constructing mechanistic models of reactor- and particle-scale processes. Insights gained from the various models are mapped back to product quality attributes and process insights. Lastly, the use of the models to guide development of advanced process control and optimization strategies is discussed., Comment: 67 pages, 10 figures

A partial flag variety is a smooth projective homogeneous variety admitting an action of a maximal torus $T$. Schubert varieties are $T$-invariant subvarieties of the partial flag varieties. We study toric Schubert varieties in Grassmannian varieties with respect to the action of the torus $T$. Indeed, we present an explicit description of the fan of a Gorenstein toric Schubert variety in a Grassmannian, and we prove that any Gorenstein toric Schubert variety in a Grassmannian variety is Fano.

The double Cayley Grassmannian is a unique smooth equivariant completion with Picard number one of the 14-dimensional exceptional complex Lie group $G_2$, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bi-octonions. We show the rigidity of the double Cayley Grassmannian under K\"{a}hler deformations. This means that for any smooth projective family of complex manifolds over a connected base of which one fiber is biholomorphic to the double Cayley Grassmannian, all other fibers are biholomorphic to the double Cayley Grassmannian., Comment: 10 pages, 2 figures. arXiv admin note: text overlap with arXiv:1905.06490

We describe varieties of minimal rational tangents on the wonderful symmetric varieties by marked Dynkin diagrams. An irreducible component of a variety of minimal rational tangents is a rational homogeneous space, and hence, we have a corresponding marked Dynkin diagram expression. On the other hand, we have marked Dynkin diagrams from the marked Kac diagram of a irreducible symmetric space by marking adjacent nodes to the marked node. We note that the above two diagrams coincide when the restricted root system is not of type A., Comment: 12 page, 8 tables

We investigate double-strangeness exchange reactions, $K^-p\to K^+\Xi^-$ and $K^-p\to K^0\Xi^0$, using an effective Lagrangian approach based on a hybrid Regge-plus-resonance model involving rescattering diagrams. We consider the background processes that include $\Lambda$, $\Sigma$, and $\Sigma(1385)$ Regge trajectories in the $u$ channel and the $s$-channel Born-term diagrams. The $s$-channel hyperon resonances account for the bump structures in the total cross sections. The $s$-channel $\Lambda(2100,7/2^-)$ and $\Sigma(2030,7/2^+)$ resonances contribute significantly, and the $\Sigma(2250)$ resonance favors $J^P = 7/2^-$. The interference pattern between the $\Lambda(2100,7/2^-)$ and $\Sigma(2030,7/2^+)$ amplitudes is essential for describing forward differential cross sections in the resonance region $2.07 < \sqrt{s} < 2.15$ GeV. The absence of the $S=-2$ meson leads to the inclusion of the meson-baryon rescattering diagrams to describe the $K^- p \to K\Xi$ reaction data, proving the significant contribution of the $(\phi,\rho,\omega)$--$(\Lambda,\Sigma)$ rescattering diagrams.

We describe the families of minimal rational curves on any complete symmetric variety, and the corresponding varieties of minimal rational tangents (VMRT). In particular, we prove that these varieties are homogeneous and that for non-exceptional irreducible wonderful varieties, there is a unique family of minimal rational curves, and hence a unique VMRT. We relate these results to the restricted root system of the associated symmetric space. In particular we answer by the negative a question of Hwang: for certain Fano wonderful symmetric varieties, the VMRT has two connected components., Comment: 54 pages, 1 table

We examine the HI gas kinematics of galaxy pairs in two clusters and a group using Australian Square Kilometre Array Pathfinder (ASKAP) WALLABY pilot survey observations. We compare the HI properties of galaxy pair candidates in the Hydra I and Norma clusters, and the NGC 4636 group, with those of non-paired control galaxies selected in the same fields. We perform HI profile decomposition of the sample galaxies using a tool, {\sc baygaud} which allows us to de-blend a line-of-sight velocity profile with an optimal number of Gaussian components. We construct HI super-profiles of the sample galaxies via stacking of their line profiles after aligning the central velocities. We fit a double Gaussian model to the super-profiles and classify them as kinematically narrow and broad components with respect to their velocity dispersions. Additionally, we investigate the gravitational instability of HI gas disks of the sample galaxies using Toomre Q parameters and HI morphological disturbances. We investigate the effect of the cluster environment on the HI properties of galaxy pairs by dividing the cluster environment into three subcluster regions (i.e., outskirts, infalling and central regions). We find that the denser cluster environment (i.e., infalling and central regions) is likely to impact the HI gas properties of galaxies in a way of decreasing the amplitude of the kinematically narrow HI gas ($M_{\rm{narrow}}^{\rm{HI}}$/$M_{\rm{total}}^{\rm{HI}}$), and increasing the Toomre Q values of the infalling and central galaxies. This tendency is likely to be more enhanced for galaxy pairs in the cluster environment., Comment: Accepted for publication in MNRAS, 25 pages, 20 figures. Supplementary material included (20 pages)

The distribution of LIGO black hole binaries (BBH) shows an intermediate-mass range consistent with the Salpeter Initial Mass Function (IMF) in black hole formation by core-collapse supernovae, subject to preserving binary association. They are effectively parameterized by mean mass $\mu$ with Pearson correlation coefficient $r = 0.93\,\pm\,0.06$ of secondary to primary masses with mean mass-ratio $\bar{q}\simeq 0.67$, $q=M_2/M_1$, consistent with the paucity of intermediate-mass X-ray binaries. The mass-function of LIGO BBHs is well-approximated by a broken power-law with a tail $\mu\gtrsim 31.4M_\odot$ {in the mean binary mass $\mu=\left(M_1+M_2\right)/2$}. Its power-law index $\alpha_{B,true}=4.77\pm 0.73$ inferred from the tail of the observed mass-function is found to approach the upper bound $2\alpha_S=4.7$ of the uncorrelated binary initial mass-function, defined by the Salpeter index $\alpha_S=2.35$ of the Initial Mass Function of stars. The observed low scatter in BBH mass ratio $q$ evidences equalizing mass-transfer in binary evolution prior to BBH formation. At the progenitor redshift $z^\prime$, furthermore, the power-law index satisfies $\alpha_B^\prime>\alpha_B$ in a flat $\Lambda$CDM background cosmology. The bound $\alpha_{B,true}^\prime \lesssim 2\alpha_S$ hereby precludes early formation at arbitrarily high redshift $z^\prime \gg1$, that may be made more precise and robust with extended BBH surveys from upcoming LIGO O4-5 observations., Comment: 7 pages, 6 figures

Let $X$ be a smooth projective horospherical variety of Picard number one, of type $B_m$ for $m \geq 3$ or of type $F_4$. We show that any uniruled projective manifold with Picard number one is biholomorphic to $X$ if the variety of minimal rational tangents at a general point is projectively equivalent to that of $X$.

A horospherical variety is a normal $G$-variety such that a connected reductive algebraic group $G$ acts with an open orbit isomorphic to a torus bundle over a rational homogeneous manifold. The projective horospherical manifolds of Picard number one are classified by Pasquier, and it turned out that the automorphism groups of all nonhomogeneous ones are non-reductive, which implies that they admit no K\"{a}hler--Einstein metrics. As a numerical measure of the extent to which a Fano manifold is close to be K\"{a}hler--Einstein, we compute the greatest Ricci lower bounds of projective horospherical manifolds of Picard number one using the barycenter of each moment polytope with respect to the Duistermaat--Heckman measure based on a recent work of Delcroix and Hultgren. In particular, the greatest Ricci lower bound of the odd symplectic Grassmannian $\text{SGr}(n,2n+1)$ can be arbitrarily close to zero as $n$ grows., Comment: 22 pages, 1 figure, 3 tables