The density of emission current by a rough surface with fractal structure is analyzed. A possible experimental setup is modeled by an irregular emitting surface, iteratively generated by a fractional Brownian motion FBM algorithm with roughness or Hurst exponent H=0.3 and a far away plane representing the anode. The boundaries are held at a fixed potential difference and the Laplace’s equation,...

V L Katkov and V A Osipov Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, 141980 Dubna, Moscow region, Russia Abstract The field emission of crystalline AAA graphite is studied within a simple analytical approach with account of the exact dispersion relation near the Fermi level. The emission current is calculated for two crystal orientations with respect to ...

arises in the study of gas dynamics and fluids mechanics, and in the study of relativistic mechanics, nuclear physics, and chemically reacting system see, e.g., 1 and the references therein for the continuous model. The negative exponent Emden-Fowler equation α < 0 has been used in modeling non-Newtonian fluids such as coal slurries 2 . The physical interest lies in the existence of positive so...

We study the Emden-Fowler equation −∆u = |u|u on the hyperbolic space H . We are interested in radial solutions, namely solutions depending only on the geodesic distance from a given point. The critical exponent for such equation is p = (n + 2)/(n − 2) as in the Euclidean setting, but the properties of the solutions show striking differences with the Euclidean case. While the papers [23, 4] con...

The present paper is concerned with the asymptotic behavior of solutions to a class noncanonical third-order Emden–Fowler delay differential equations superlinear neutral term. Using Riccati-type transformation as well integral criteria, we establish some new sufficient conditions guaranteeing that every solution equation considered either oscillates or converges zero asymptotically. results ar...

We welcome the opportunity to clarify issues raised by Gualda & Ghiorso (G&G, hereafter) on our 2010 paper, ‘A metamodel for crustal magmatism: phase equilibria of giant ignimbrites’. Voluminous (V 100^1000 km) explosive eruption of silicic magma, accompanied by eruption columns that may empty into the stratosphere, has environmental consequences of planetary significance and represents an impo...