TDHF investigations of the U+U quasifission process

The use of actinide collisions have been suggested as a way to produce neutron rich isotopes of high Z nuclei. The collision dynamics of these reactions can be studied using unrestricted time-dependent Hartree-Fock (TDHF) calculations. Here, we report on the recent studies of quasifission for the $^{238}$U+$^{238}$U system.Comment: Presented at the XXXV Mazurian Lakes Conference on Physics, Piaski, Poland, September 3-9, 2017

U-operators

Inspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives and antiderivatives some kind of additive universality or multiplicative universality on certain compact subsets of the complex plane or of, respectively, the punctured complex plane, we introduce in this paper the new concept of U-operators, which are defined on the space of entire functions. Concrete examples, including differential and antidifferential operators, composition, multiplication and shift operators, are studied. A result due to Luh, Martirosian and Müller about the existence of universal entire functions with gap power series is also strengthened.Plan Andaluz de Investigación (Junta de Andalucía

U-Manifolds

We use non-perturbative U-duality symmetries of type II strings to construct new vacuum solutions. In some ways this generalizes the F-theory vacuum constructions. We find the possibilities of new vacuum constructions are very limited. Among them we construct new theories with N=2 supersymmetry in 3-dimensions and (1, 1) supersymmetry in 2-dimensions.Comment: 11 pages, minor changes in references and text (version to appear in Phys. Lett. B

The equation divuu+⟨a,u⟩=f\langle a, u \rangle=f

We study the solutions $u$ to the equation $$\begin{cases} \operatorname{div} u + \langle a , u \rangle = f & \textrm{ in } \Omega,\\ u=0 & \textrm{ on } \partial \Omega, \end{cases}$$ where $a$ and $f$ are given. We significantly improve the existence results of [Csat\'o and Dacorogna, A Dirichlet problem involving the divergence operator, \textit{Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire}, 33 (2016), 829--848], where this equation has been considered for the first time. In particular, we prove the existence of a solution under essentially sharp regularity assumptions on the coefficients. The condition that we require on the vector field $a$ is necessary and sufficient. Finally, our results cover the whole scales of Sobolev and H\"older spaces

Prospects for quarkonia production studies in U+U collisions

Collisions of deformed uranium nuclei provide a unique opportunity to study the spatial dependence of charmonium in-medium effects. By selecting the orientations of the colliding nuclei, different path lengths through the nuclear medium could be selected within the same experimental environment. In addition, higher energy densities can be achieved in U+U collisions relative to Au+Au collisions. In this paper, we investigate the prospects for charmonium studies with U+U collisions. We discuss the effects of shadowing and nuclear absorption on the J/\psi\ yield. We introduce a new observable which could help distinguish between different types of J/\psi\ interactions in hot and dense matter.Comment: 13 pages, 10 figure

Braided Weyl algebras and differential calculus on U(u(2))

On any Reflection Equation algebra corresponding to a skew-invertible Hecke symmetry (i.e. a special type solution of the Quantum Yang-Baxter Equation) we define analogs of the partial derivatives. Together with elements of the initial Reflection Equation algebra they generate a "braided analog" of the Weyl algebra. When $q\to 1$, the braided Weyl algebra corresponding to the Quantum Group $U_q(sl(2))$ goes to the Weyl algebra defined on the algebra \Sym((u(2)) or that $U(u(2))$ depending on the way of passing to the limit. Thus, we define partial derivatives on the algebra $U(u(2))$, find their "eigenfunctions", and introduce an analog of the Laplace operator on this algebra. Also, we define the "radial part" of this operator, express it in terms of "quantum eigenvalues", and sketch an analog of the de Rham complex on the algebra $U(u(2))$. Eventual applications of our approach are discussed.Comment: LaTex, 18 pages. Accepted in Journal of Geometry and Physic