Half-Monopole in the Weinberg-Salam Model

We present new axially symmetric half-monopole configuration of the SU(2)$\times$U(1) Weinberg-Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge $2\pi/e$ which is half the magnetic charge of a Cho-Maison monopole. The electromagnetic gauge potential is singular along the negative $z$-axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant $\lambda^{1/2}$ at $\sin^2\theta_W=0.2312$. In the U(1) magnetic field, the half-monopole is just a one dimensional finite length line magnetic charge extending from the origin $r=0$ and lying along the negative $z$-axis. In the SU(2) 't Hooft magnetic field, it is a point magnetic charge located at $r=0$. The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant $\lambda^{1/2}$ at $\sin^2\theta_W=0.2312$.Comment: 14 pages, 3 Figure

Monopole Solutions of the Massive SU(2) Yang-Mills-Higgs Theory

Monopoles in topologically massive gauge theories in 2+1 dimensions with a Chern-Simon mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang-Mills-Higgs model with an additional Chern-Simon mass term in the action. Pisarski argued that there is a monopole solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern-Simon term strength and for several fixed values of Higgs field strength.Comment: 10, pages, 5 figure

Monopole-Antimonopole Pair Dyons

Monopole-antimonopole pair (MAP) with both electric and magnetic charges are presented. The MAP possess opposite magnetic charges but they carry the same electric charges. These stationary MAP dyon solutions possess finite energy but they do not satisfy the first order Bogomol'nyi equations and are not BPS solutions. They are axially symmetric solutions and are characterized by a parameter, $-1\leq\eta\leq 1$ which determines the net electric charges of these MAP dyons. These dyon solutions are solved numerically when the magnetic charges of the dipoles are $n=\pm 1, \pm 2$ and when the strength of the Higgs field potential $\lambda=0, 1$. When $\lambda=0$, the time component of the gauge field potential is parallel to the Higgs field in isospin space and the MAP separation distance, total energy and net electric charge increase exponentially fast to infinity when $\eta$ approaches $\pm 1$. However when $\lambda=1$, all these three quantities approach a finite critical value as $\eta$ approaches $\pm 1$.Comment: 20 pages, 9 figures, 2 table

MAP, MAC, and Vortex-rings Configurations in the Weinberg-Salam Model

We report on the presence of new axially symmetric monopoles, antimonopoles and vortex-rings solutions of the SU(2)$\times$U(1) Weinberg-Salam model of electromagnetic and weak interactions. When the $\phi$-winding number $n=1$, and 2, the configurations are monopole-antimonopole pair (MAP) and monopole-antimonopole chain (MAC) with poles of alternating sign magnetic charge arranged along the $z$-axis. Vortex-rings start to appear from the MAP and MAC configurations when the winding number $n=3$. The MAP configurations possess zero net magnetic charge whereas the MAC configurations possess net magnetic charge of $4\pi n/e$. In the MAP configurations, the monopole-antimonopole pair is bounded by the ${\cal Z}^0$ field flux string and there is an electromagnetic current loop encircling it. The monopole and antimonopole possess magnetic charges $\pm\frac{4\pi n}{e}\sin^2\theta_W$ respectively. In the MAC configurations there is no string connecting the monopole and the adjacent antimonopole and they possess magnetic charges $\pm\frac{4\pi n}{e}$ respectively. The MAC configurations possess infinite total energy and zero magnetic dipole moment whereas the MAP configurations which are actually sphalerons possess finite total energy and magnetic dipole moment. The configurations were investigated for varying values of Higgs self-coupling constant $0\leq \lambda\leq 40$ at Weinberg angle $\theta_W=\frac{\pi}{4}$.Comment: 31 pages, 10 figures, 2 table

Electrically Charged One and a Half Monopole Solution

Recently, we have discussed the coexistence of a finite energy one-half monopole and a 't Hooft-Polyakov monopole of opposite magnetic charges. In this paper, we would like to introduce electric charge into this new monopoles configuration, thus creating a one and a half dyon. This new dyon possesses finite energy, magnetic dipole moment and angular momentum and is able to precess in the presence of an external magnetic field. Similar to the other dyon solutions, when the Higgs self-coupling constant, $\lambda$, is nonvanishing, this new dyon solution possesses critical electric charge, total energy, magnetic dipole moment, and dipole separation as the electric charge parameter, $\eta$, approaches one. The electric charge and total energy increase with $\eta$ to maximum critical values as $\eta\rightarrow1$ for all nonvanishing $\lambda$. However, the magnetic dipole moment decreases with $\eta$ when $\lambda\geq0.1$ and the dipole separation decreases with $\eta$ when $\lambda\geq1$ to minimum critical values as $\eta\rightarrow1$.Comment: 24 pages, 7 figures. arXiv admin note: text overlap with arXiv:1208.4893, arXiv:1112.149

Mixing effect on chemical reaction in liquid phase

Mathematical models for the mixing phenomenon are proposed in this study. First model deals Newtonian and non-Newtonian fluid without chemical reaction. The new terminology degree of mixing is define in this model for the time-dependency of mixing toward its completeness. The velocity profile and boundary conditions are given, then the degree of mixing can be calculated by the mathematical model. The degree of mixing is influenced by fluid motion and it is function of time. Second model deals with first-order reaction effected by mixing. A mean fractional conversion is defined to investigate the rate of bhemical reaction. Results from numerical method indicate the rate of chemical reaction is greatly influenced by mixing , especially when the reaction rate is fast. Finally, a mathematical model based on microscopic collision theory is developed for the estimation of chemical reaction rate constant in this study

Conceptual definition of a high voltage power supply test facility

NASA Lewis Research Center is presently developing a 60 GHz traveling wave tube for satellite cross-link communications. The operating voltage for this new tube is - 20 kV. There is concern about the high voltage insulation system and NASA is planning a space station high voltage experiment that will demonstrate both the 60 GHz communications and high voltage electronics technology. The experiment interfaces, requirements, conceptual design, technology issues and safety issues are determined. A block diagram of the high voltage power supply test facility was generated. It includes the high voltage power supply, the 60 GHz traveling wave tube, the communications package, the antenna package, a high voltage diagnostics package and a command and data processor system. The interfaces with the space station and the attached payload accommodations equipment were determined. A brief description of the different subsystems and a discussion of the technology development needs are presented

Dyons of One Half Monopole Charge

We would like to present some exact SU(2) Yang-Mills-Higgs dyon solutions of one half monopole charge. These static dyon solutions satisfy the first order Bogomol'nyi equations and are characterized by a parameter, $m$. They are axially symmetric. The gauge potentials and the electromagnetic fields possess a string singularity along the negative z-axis and hence they possess infinite energy density along the line singularity. However the net electric charges of these dyons which varies with the parameter $m$ are finite.Comment: 16 pages, 7 figure

Screening Solutions Of Multimonopole By Unit Charge Antimonopoles.

We would like to show in this paper that there exist a whole range of screening solutions of multirnonopole by unit charge antimonopoles in the SU(2) Yang-Mills-Higgs theory