On determinism and well-posedness in multiple time dimensions

We study the initial value problem for the wave equation and the ultrahyperbolic equation for data posed on initial surface of mixed signature (both spacelike and timelike). Under a nonlocal constraint, we show that the Cauchy problem on codimension-one hypersurfaces has global unique solutions in the Sobolev spaces $H^{m}$, thus it is well-posed. In contrast, we show that the initial value problem on higher codimension hypersurfaces is ill-posed, at least when specifying a finite number of derivatives of the data, due to the failure of uniqueness. This is in contrast to a uniqueness result which Courant and Hilbert deduce from Asgeirsson's mean value theorem, for which we give an independent derivation. The proofs use Fourier synthesis and the Holmgren-John uniqueness theorem

Objectivity, Information, and Maxwell\u27s Demon

This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information‐content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwell\u27s Demon

A morphing algorithm for generating near optimal grids: applications in computational medicine

Journal ArticleWe apply morphing to t h e problem of generating the initial mesh for finite element simulations. This algorithm reduces mesh adaptation time by integrating physical and geometric constraints to provide a near optimal initial mesh. We apply this method to large-scale bioelectric field problems involving the complex geometries of the human body