String Webs from Field Theory

The spectrum of stable electrically and magnetically charged supersymmetric particles can change discontinuously as one changes the vacuum on the Coulomb branch of gauge theories with extended supersymmetry in four dimensions. We show that this decay process can be understood and is well described by semiclassical field configurations purely in terms of the low energy effective action on the Coulomb branch even when it occurs at strong coupling. The resulting picture of the stable supersymmetric spectrum is a generalization of the ``string web'' picture of these states found in string constructions for certain theories.Comment: 53 pages, 6 figures; more references adde

Fuzzy Symmetric Solutions of Fuzzy Matrix Equations

The fuzzy symmetric solution of fuzzy matrix equation A X = B, in which A is a crisp m × m nonsingular matrix and B is an m × n fuzzy numbers matrix with nonzero spreads, is investigated. The fuzzy matrix equation is converted to a fuzzy system of linear equations according to the Kronecker product of matrices. From solving the fuzzy linear system, three types of fuzzy symmetric solutions of the fuzzy matrix equation are derived. Finally, two examples are given to illustrate the proposed method

Solution of arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations

Control system theory often involved the application of matrix equations and pair matrix equations where there are possibilities that uncertainty conditions can exist. In this case, the classical matrix equations and pair matrix equations are not well equipped to handle these conditions. Even though there are some previous studies in solving the matrix equations and pair matrix equations with uncertainty conditions, there are some limitations that include the fuzzy arithmetic operations, the type of fuzzy coefficients and the singularity of matrix coefficients. Therefore, this study aims to construct new methods for solving matrix equations and pair matrix equations with all the coefficients of the matrix equations are arbitrary left-right triangular fuzzy numbers (LR-TFN), which either positive, negative or near-zero. In constructing these methods, some modifications on the existing fuzzy subtraction and multiplication arithmetic operators are necessary. By modifying the existing fuzzy arithmetic operators, the constructed methods exceed the positive restriction to allow the negative and near-zero LR-TFN as the coefficients of the equations. The constructed methods also utilized the Kronecker product and Vec-operator in transforming the fully fuzzy matrix equations and pair fully fuzzy matrix equations to a simpler form of equations. On top of that, new associated linear systems are developed based on the modified fuzzy multiplication arithmetic operators. The constructed methods are verified by presenting some numerical examples. As a result, the constructed methods have successfully demonstrated the solutions for the arbitrary fully fuzzy matrix equations and pair fully fuzzy matrix equations, with minimum complexity of the fuzzy operations. The constructed methods are applicable for singular and non-singular matrices regardless of the size of the matrix. With that, the constructed methods are considered as a new contribution to the application of control system theory

Self-similar solutions for Fuzzy Dark Matter

Fuzzy Dark Matter (FDM) models admit self-similar solutions which are very different from their Cold Dark Matter (CDM) counterparts and do not converge to the latter in the semiclassical limit. In contrast with the familiar CDM hierarchical collapse, they correspond to an inverse-hierarchy blow-up. Constant-mass shells start in the nonlinear regime, at early times, with small radii and high densities, and expand to reach at late times the Hubble flow, up to small linear perturbations. Thus, larger masses become linear first. This blow-up approximately follows the Hubble expansion, so that the central density contrast remains constant with time, although the width of the self-similar profile shrinks in comoving coordinates. As in a gravitational cooling process, matter is ejected from the central peaks through successive clumps. As in wave systems, the velocities of the geometrical structures and of the matter do not coincide, and matter slowly moves from one clump to the next, with intermittent velocity bursts at the transitions. These features are best observed using the density-velocity representation of the nonrelativistic scalar field, or the mass-shell trajectories, than with the Husimi phase-space distribution, where an analogue of the Heisenberg uncertainty principle blurs the resolution in the position or velocity direction. These behaviours are due to the quantum pressure and the wavelike properties of the Schr\"odinger equation. Although the latter has been used as an alternative to N-body simulations for CDM, these self-similar solutions show that the semiclassical limit needs to be handled with care.Comment: 21 pages,10 figure