Transverse Momentum Distribution and Elliptic Flow of Charged Hadrons in UU+UU collisions at sNN=193\sqrt{s_{NN}}=193 GeV using HYDJET++

Recent experimental observations of the charged hadron properties in $U+U$ collisions at $193$ GeV contradict many of the theoretical models of particle production including two-component Monte Carlo Glauber model. The experimental results show a small correlation between the charged hadron properties and the initial geometrical configurations (e.g. body-body, tip-tip etc.) of $U+U$ collisions. In this article, we have modified the Monte Carlo HYDJET++ model to study the charged hadron production in $U+U$ collisions at $193$ GeV center-of-mass energy in tip-tip and body-body initial configurations. We have modified the hard as well as soft production processes to make this model suitable for $U+U$ collisions. We have calculated the pseudorapidity distribution, transverse momentum distribution and elliptic flow distribution of charged hadrons with different control parameters in various geometrical configurations possible for $U+U$ collision. We find that HYDJET++ model supports a small correlation between the various properties of charged hadrons and the initial geometrical configurations of $U+U$ collision. Further, the results obtained in modified HYDJET++ model regarding $dn_{ch}/d\eta$ and elliptic flow ($v_{2}$) suitably matches with the experimental data of $U+U$ collisions in minimum bias configuration.Comment: 29 pages, 25 figures. Accepted for Publication in EPJ

On the relationship between the modifications to the Raychaudhuri equation and the canonical Hamiltonian structures

The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy condition, or more attractive than in the classical theory. Canonical structure of the modified theories is determined demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse trigonometric function of Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a `generalized polymerized' canonical phase space. Both of the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is non-trigonometric and singularities persist. Our results hint on connections between repulsive/attractive nature of modifications to gravity arising from gravitational sector and polymerized/non-polymerized gravitational phase space.Comment: 22 pages with two new plots. Discussion on uniqueness added, and possible links with existing models expanded. Periodicity for 'generalized polymerized' theory and its comparison with standard polymerization discussed. References added. To appear in CQ

Dual automorphism-invariant modules

A module $M$ is called an automorphism-invariant module if every isomorphism between two essential submodules of $M$ extends to an automorphism of $M$. This paper introduces the notion of dual of such modules. We call a module $M$ to be a dual automorphism-invariant module if whenever $K_1$ and $K_2$ are small submodules of $M$, then any epimorphism $\eta:M/K_1\rightarrow M/K_2$ with small kernel lifts to an endomorphism $\varphi$ of $M$. In this paper we give various examples of dual automorphism-invariant module and study its properties. In particular, we study abelian groups and prove that dual automorphism-invariant abelian groups must be reduced. It is shown that over a right perfect ring $R$, a lifting right $R$-module $M$ is dual automorphism-invariant if and only if $M$ is quasi-projective.Comment: To appear in Journal of Algebr