Improvement of the Cascadic Multigrid Algorithm with a Gauss Seidel Smoother to Efficiently Compute the Fiedler Vector of a Graph Laplacian

In this paper, we detail the improvement of the Cascadic Multigrid algorithm with the addition of the Gauss Seidel algorithm in order to compute the Fiedler vector of a graph Laplacian, which is the eigenvector corresponding to the second smallest eigenvalue. This vector has been found to have applications in graph partitioning, particularly in the spectral clustering algorithm. The algorithm is algebraic and employs heavy edge coarsening, which was developed for the first cascadic multigrid algorithm. We present numerical tests that test the algorithm against a variety of matrices of different size and properties. We then test the algorithm on a range of square matrices with uniform properties in order to prove the linear complexity of the algorithm

Possibility of ρ\rho Meson Condensation in Neutron Star: Unified Approach of Chiral SU(3) Model and QCD Sum Rules

In the present work the conjunction of chiral SU(3) model with QCD sum rules is employed to explore the possibility of $\rho$ meson condensation in neutron stars. The quark and gluon condensates in terms of which the in-medium masses of $\rho$ mesons can be expressed are calculated using the chiral SU(3) model in the charge neutral matter which is relevant for neutron stars. It is observed that condition of $\rho$ meson condensation is satisfied for the density of about 7$\rho_{0}$, where $\rho_{0}$ is the nuclear saturation density. In the end, a brief qualitative discussion of the magnetic field is also involved to check out for the further possibility of $\rho$ meson condensation.Comment: 21 pages, 5 figure

External-strain-induced semimetallic and metallic phase of chlorographene

To overcome the limitations of graphene due to lack of intrinsic band gap, it is generally functionalized with hydrogen or halogen atoms such as fluorine and chlorine. Generally, such functionalization yields a moderate- to high-band-gap material in case of 100% coverage, for example ~1.5 eV in graphene functionalized with chlorine atoms or chlorographene. In this paper, using ab initio calculations, we report very interesting transformations observed in chlorographene under external strain, driving it to a state with nearly vanishing band gap (under tensile strain) and even converting it to a metal (under compressive strain). We also show the importance of spin-orbit coupling, responsible for the few meV band gap of chlorographene observed under high tensile strain, which would have been a gapless semimetal otherwise.Comment: 7 pages, 6 figure

z-Classes in finite groups of conjugate type (n,1)

Two elements in a group $G$ are said to $z$-equivalent or to be in the same $z$-class if their centralizers are conjugate in $G$. In \cite{kkj}, it was proved that a non-abelian $p$-group $G$ can have at most $\frac{p^k-1}{p-1} +1$ number of $z$-classes, where $|G/Z(G)|=p^k$. In this note, we characterize the $p$-groups of conjugate type $(n,1)$ attaining this maximal number. As a corollary, we characterize $p$-groups having prime order commutator subgroup and maximal number of $z$-classes.Comment: 6 page

Slant H-Toeplitz Operators on the Hardy space

The notion of slant H-Toeplitz operator $V_\phi$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. We have shown that an operator on the space $H^2$ is slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained

Inverse approximation and GBS of bivariate Kantorovich type sampling series

In this paper, we derive an inverse result for bivariate Kantorovich type sampling series for the space of all continuous functions with upto second order partial derivatives are continuous and bounded on $R^2.$ Further, we prove the rate of approximation in the Bogel space of continuous functions for the GBS (Generalized Boolean Sum) of these operators. Finally, we give some examples for the kernel to which the theory can be applie

Detecting qubit entanglement : an alternative to the PPT test

We propose a Partial Lorentz Transformation (PLT) test for detecting entanglement in a two qubit system. One can expand the density matrix of a two qubit system in terms of a tensor product of $(\mathbb{I}, \vec{\sigma})$. The matrix $A$ of the coefficients that appears in such an expansion can be "squared" to form a $4\times4$ matrix $B$. It can be shown that the eigenvalues $\lambda_0, \lambda_1, \lambda_2, \lambda_3$ of $B$ are positive. With the choice of $\lambda_0$ as the dominant eigenvalue, the separable states satisfy $\sqrt{\lambda_1}+\sqrt{\lambda_2}+\sqrt{\lambda_3}\leq \sqrt{\lambda_0}$. Violation of this inequality is a test of entanglement. Thus, this condition is both necessary and sufficient and serves as an alternative to the celebrated Positive Partial Transpose (PPT) test for entanglement detection. We illustrate this test by considering some explicit examples.Comment: three pages, two figure

Decoupling of Self Diffusion from Viscosity of Supercooled Water: Role of Translational Jump-diffusion

Some experiments have witnessed increasing decoupling of viscosity from the translational self-diffusion of supercooled water with decreasing temperature. While theory and computer simulation studies indicated the jump translation of the molecules as a probable origin of the above decoupling, a precise quantitative estimation is still lacking. Through a molecular dynamics (MD) simulation study, along with careful consideration of translational jump motion, we have found the most definite proof of increasing relevance of translational jump diffusion in the above decoupling phenomena. By separating out the jump-only diffusion contribution from the overall diffusion of the water, we obtain the residual diffusion coefficient, which remains strongly coupled with the viscosity of the medium at the whole temperature range, including supercooled regime. These new findings can help to elucidate many experimental studies featuring molecular transport properties, where strong diffusion-viscosity decoupling comes into the picture

SIMPler realisation of Scalar Dark Matter

With growing agony of not finding a dark matter (DM) particle in direct search experiments so far (for example in XENON1T), frameworks where the freeze-out of DM is driven by number changing processes within the dark sector itself and do not contribute to direct search, like Strongly Interacting Massive Particle (SIMP) are gaining more attention. In this analysis, we ideate a simple scalar DM framework stabilised by $Z_3$ symmetry to serve with a SIMP-like DM ($\chi$) with additional light scalar mediation ($\phi$) to enhance DM self interaction. We identify that a large parameter space for such DM is available from correct relic density and self interaction constraints coming from Bullet or Abell cluster data. We derive an approximate analytic solution for freeze-out of the SIMP like DM in Boltzmann Equation describing $3 \to 2$ number changing process within the dark sector. We also provide a comparative analysis of the SIMP like solution with the Weakly Interacting Massive Particle (WIMP) realisation of the same model framework here.Comment: 43 pages, 24 figures, 2 tables, Version published in JCA

The Effects of Protostellar Jet Feedback on Turbulent Collapse

We present results of hydrodynamic simulations of massive star forming regions with and without protostellar jets. We show that jets change the normalization of the stellar mass accretion rate, but do not strongly affect the dynamics of star formation. In particular, $M_*(t) \propto f^2 (t-t_*)^2$ where $f = 1 - f_{\rm jet}$ is the fraction of mass accreted onto the protostar, $f_{\rm jet}$ is the fraction ejected by the jet, and $(t-t_*)^2$ is the time elapsed since the formation of the first star. The star formation efficiency is nonlinear in time. We find that jets have only a small effect (of order 25\%) on the accretion rate onto the protostellar disk (the "raw" accretion rate). We show that the small scale structure -- the radial density, velocity, and mass accretion profiles are very similar in the jet and no-jet cases. Finally, we show that the inclusion of jets does drive turbulence but only on small (parsec) scales.Comment: 15 pages, 14 figure