Exotic blow up solutions for the $\Box u^5$-focussing wave equation in $\mathbb{R}^3$
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We provide a common theoretical framework reuniting specific models for the Ca2+-alginate system and general reaction diffusion theory along with experimental validation on a microfluidic chip. As a starting point, we use a set of nonlinear, partial differ ...
Antidot lattices fabricated from permalloy thin films have been investigated by all-electrical spin-wave spectroscopy and Brillouin light scattering. Periodic arrays of 120-nm-diameter nanoholes have been prepared using focused ion beam etching. The period ...
The present invention discloses a method and an apparatus to compute a complex wavefield, referred to as the object wave o, by means of measuring the intensity signal resulting from the interference of the said object wave with a second wave termed the ref ...
Seemingly unrelated empirical hydrologic laws and several experimental facts related to the fractal geometry of the river basin are shown to find a natural explanation into a simple finite-size scaling ansatz for the power laws exhibited by cumulative dist ...
We want to extend the approximation of the error probability via a scaling approach from the BEC to general binary-input memoryless output-symmetric (BMS) channels. In particular, we consider such scaling laws for regular LDPC ensembles and message-passing ...
For a class of second order quasilinear elliptic equations we establish the existence of two non-negative weak solutions of the Dirichlet problem on a bounded domain, Omega. Solutions of the boundary value problem are critical points of C-1-functional on H ...
Meteorite showers are the remains of extraterrestrial objects which are captivated by the gravitational field of the Earth. We have analyzed the mass distribution of fragments from 16 meteorite showers for scaling. The distributions exhibit distinct scalin ...
We derive the behavior of the average exit time (i.e., the number of reflections before escape) of a ray path traveling between two perfect mirrors subject to dynamic random-tilt aberrations. Our calculation is performed in the paraxial approximation. When ...
We describe in this article two recent results [11], [12], obtained by the author jointly with W. Schlag and D. Tataru, about singular solutions for the critical wave maps equation, as well as the critical focussing semilinear wave equation. Specifically, ...
A nonlinear model is studied which describes the evolution of a landscape under the effects of erosion and regeneration by geologic uplift by mean of a simple differential equation. The equation, already in wide use among geomorphologists and in that conte ...