Phase structure of the generalized two dimensional Yang-Mills theories on sphere

We find a general expression for the free energy of $G(\phi)=\phi^{2k}$ generalized 2D Yang-Mills theories in the strong ($A>A_c$) region at large $N$. We also show that in this region, the density function of Young tableau of these models is a three-cut problem. In the specific $\phi^6$ model, we show that the theory has a third order phase transition, like $\phi^2$ (YM_2) and $\phi^4$ models. We have some comments for $k \geq 4$ cases. At the end, we study the phase structure of $\phi^2 + g \phi^4$ model for $g \leq A/4$ region.Comment: 13 pages, LaTex,the introduction section was changed,will be appeared in: Eur. Phys. J. C (1999

Denosing Using Wavelets and Projections onto the L1-Ball

Both wavelet denoising and denosing methods using the concept of sparsity are based on soft-thresholding. In sparsity based denoising methods, it is assumed that the original signal is sparse in some transform domains such as the wavelet domain and the wavelet subsignals of the noisy signal are projected onto L1-balls to reduce noise. In this lecture note, it is shown that the size of the L1-ball or equivalently the soft threshold value can be determined using linear algebra. The key step is an orthogonal projection onto the epigraph set of the L1-norm cost function.Comment: Submitted to Signal Processing Magazin

Electroweak Phase Transition, Gravitational Waves and Dark Matter in Two Scalar Singlet Extension of The Standard Model

In this paper, the electroweak phase transition, the gravitational waves and the dark matter issues are investigated in two scalar singlet extension of the standard model. The detectability of the gravitational wave signals are discussed by comparing the results with the sensitivity curves of $\mathbf{eLISA}$, $\mathbf{ALIA}$, $\mathbf{DECIGO}$ and $\mathbf{BBO}$ detectors. It is shown that the results support the recent reports on the dark matter relic density by $\mathbf{Planck}$ $\mathbf{2018}$ collaboration and the direct detection experiment by $\mathbf{XENON1T}$ $\mathbf{2018}$ collaboration.Comment: 18 pages, 2 figures (4 subfigures), 4 tables, final version to match the published versio

Mass of the Stabilized Radion in the Limit of Finite Quartic Coupling

We present an exact treatment of the modulus stabilization condition with the general boundary conditions of the bulk scalar field in the Randall-Sundrum model. We find analytical expressions for the value of the modulus and the mass of the radion.Comment: 11 pages, 3 figures, Accepted for publication in AHE

Numerical simulation of single droplet dynamics in three-phase flows using ISPH

In this study, a new surface tension formulation for modeling incompressible, immiscible three-phase fluid flows in the context of incompressible smoothed particle hydrodynamics (ISPH) in two dimensions has been proposed. A continuum surface force model is employed to transform local surface tension force to a volumetric force while physical surface tension coefficients are expressed as the sum of phase specific surface tension coefficients, facilitating the implementation of the proposed method at triple junctions where all three phases are present. Smoothed color functions at fluid interfaces along with artificial particle displacement throughout the computational domain are combined to increase accuracy and robustness of the model. In order to illustrate the effectiveness of the proposed method, several numerical simulations have been carried out and results are compared to analytical data available in literature. Results obtained by simulations are compatible with analytical data, demonstrating that the ISPH scheme proposed here is capable of handling three-phase flows accurately