Quaternionic Root Systems and Subgroups of the Aut(F4)Aut(F_{4})

Cayley-Dickson doubling procedure is used to construct the root systems of some celebrated Lie algebras in terms of the integer elements of the division algebras of real numbers, complex numbers, quaternions and octonions. Starting with the roots and weights of SU(2) expressed as the real numbers one can construct the root systems of the Lie algebras of SO(4),SP(2)= SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the division algebras. The roots themselves display the group structures besides the octonionic roots of E_{8} which form a closed octonion algebra. The automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the largest crystallographic group in 4-dimensional Euclidean space, is realized as the direct product of two binary octahedral group of quaternions preserving the quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192 with different conjugacy classes occur as maximal subgroups in the finite subgroups of the Lie group $G_{2}$ of orders 12096 and 1344 and proves to be useful in their constructions. The triality of SO(8) manifesting itself as the cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and F_{4} respectively

Non-Isothermal Model for Nematic Spherulite Growth

A computational study of the growth of two-dimensional nematic spherulites in an isotropic phase was performed using a Landau-de Gennes type quadrupolar ensor order parameter model for the first-order isotropic/nematic transition of 5CB (pentyl-cyanobiphenyl). An energy balance, taking anisotropy into account, was derived and incorporated into the time-dependent model. Growth laws were determined for two different spherulite morphologies of the form tn, with and without the inclusion of thermal effects. Results show that incorporation of the thermal energy balance correctly predicts the transition of the growth law exponent from the volume driven regime (n=1) to the thermally limited regime (approaching n=0.5), agreeing well with experimental observations. An interfacial nemato-dynamic model is used to gain insight into the interactions that result in the progression of different spherulite growth regimes

Dry Formulation of Virus-Like Particles in Electrospun Nanofibers

Biologics can be combined with liquid polymer materials and electrospun to produce a dry nanofibrous scaffold. Unlike spray-drying and freeze-drying, electrospinning minimizes the physiological stress on sensitive materials, and nanofiber mat properties such as hydrophobicity, solubility, and melting temperature can be tuned based on the polymer composition. In this study, we explored the dry formulation of a virus-like particle (VLP) vaccine by electrospinning VLP derived from rabbit hemorrhagic disease virus modified to carry the MHC-I gp100 tumor-associated antigen epitope. VLP were added to a polyvinylpyrrolidone (PVP) solution (15% w/v) followed by electrospinning at 24 kV. Formation of a nanofibrous mat was confirmed by scanning electron microscopy, and the presence of VLP was confirmed by transmission electron microscopy and Western blot. VLP from the nanofibers induced T-cell activation and interferon- (IFN-) γ production in vitro. To confirm in vivo cytotoxicity, Pmel mice treated by injection with gp100 VLP from nanofibers induced a gp100 specific immune response, lysing approximately 65% of gp100-pulsed target cells, comparable to mice vaccinated with gp100 VLP in PBS. VLP from nanofibers also induced an antibody response. This work shows that electrospinning can be used to dry-formulate VLP, preserving both humoral and cell-mediated immunity