Efficient techniques for Solving Electromagnetic Scattering by Electrically Large Arbitrarily Shaped Three-Dimensional Objects

The Method of Moments (MoM) is deeply described and used for the analysis of electromagnetic (EM) radiation and scattering problems involving arbitrarily shaped 3D targets. The proposed MoM formulation allows us to investigate perfect and imperfect conductor, and dielectric object. Next, a novel method for efficient MoM analysis of electrically large objects using Characteristic Basis Functions (CBFs) is proposed to reduce the matrix solution time. The CBFs are special types of high-level basis functions, defined over the domains that encompass a relatively large number of conventional sub-domain bases, e.g., triangular patches or rooftops. This technique differs from other similar approaches developed previously, in several aspects. First, it includes mutual coupling effects directly by using primary and secondary CBFs, which are then used to represent the unknown induced currents on the blocks, and solved via the Galerkin method rather than using iterative refinements. Second, the Characteristic Basis Function Method (CBFM) is more general, and can be applied to a wide class of electromagnetic problems

Semi-linear wave equations with effective damping

We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existence of small energy data solutions in the supercritical case.Comment: 28 page

Nonlinear Wave Equation with Vanishing Potential

We study the Cauchy problem for utt − ∆u + V (x)u^5 = 0 in 3–dimensional case. The function V (x) is positive and regular, in particular we are interested in the case V (x) = 0 in some points. We look for the global classical solution of this equation under a suitable hypothesis on the initial energy

Probing Dark Matter Long-lived Mediators with Solar γ\gamma rays

We show that solar $\gamma$-ray observations can provide a complementary probe of Dark Matter in scenarios where the interactions with the Standard Model proceed via long-lived mediators. For illustration we consider a simplified model which provides solar $\gamma$-ray fluxes observable with the next generation $\gamma$-ray telescopes, while complying with the existing experimental constraints. Our results suggest that solar $\gamma$-ray fluxes can be orders of magnitude larger than the ones from the Galactic center, while being subject to low backgrounds.Comment: 4 pages, 2 figures. To appear in the proceedings of The European Physical Society Conference on High Energy Physics, 5-12 July 2017 in Venice, Ital

From p0(n)p_0(n) to p0(n+2)p_0(n+2)

In this note we study the global existence of small data solutions to the Cauchy problem for the semi-linear wave equation with a not effective scale-invariant damping term, namely $$v_{tt}-\triangle v + \frac2{1+t}\,v_t = |v|^p, \qquad v(0,x)=v_0(x),\quad v_t(0,x)=v_1(x),$$ where $p>1$, $n\ge 2$. We prove blow-up in finite time in the subcritical range $p\in(1,p_2(n)]$ and an existence result for $p>p_2(n)$, $n=2,3$. In this way we find the critical exponent for small data solutions to this problem. All these considerations lead to the conjecture $p_2(n)=p_0(n+2)$ for $n\ge2$, where $p_0(n)$ is the Strauss exponent for the classical wave equation

Solar γ\gamma-rays as a Complementary Probe of Dark Matter

We show that observations of solar $\gamma$-rays offer a novel probe of dark matter in scenarios where interactions with the visible sector proceed via a long-lived mediator. As a proof of principle, we demonstrate that there exists a class of models which yield solar $\gamma$-ray fluxes observable with the next generation of $\gamma$-ray telescopes, while being allowed by a variety of current experimental constraints. The parameter space allowed by big bang nucleosynthesis and beam dump experiments naturally leads to mediator lifetimes sufficient to produce observable solar $\gamma$-ray signals. The model allows for solar $\gamma$-ray fluxes up to orders of magnitude larger compared to dwarf spheroidal galaxies, without reaching equilibrium between dark matter annihilation and capture rate. Our results suggest that solar $\gamma$-ray observations are complementary, and in some cases superior, to existing and future dark matter detection efforts.Comment: 15 pages + references, 7 figures, v3: Fermi-LAT and HERD sensitivity corrected, minor presentational improvements, matches journal versio