Free scalar fields in de Sitter space have a one-parameter family of states invariant under the de Sitter group, including the standard thermal vacuum. We show that, except for the thermal vacuum, these states are unphysical when gravitational interactions are included. We apply these observations to the quantum state of the inflaton, and find that at best, dramatic fine tuning is required for ...

I discuss two case studies from classical electrodynamics challenging the distinction between laws that delineate physically possible words and initial conditions. First, for many reasonable initial conditions there exist no global solutions to the MaxwellLorentz equations for continuous charge distributions. Second, in deriving an equation of motion for a charged point particle one needs to in...

A resonant metasurface design based on boundary condition (BC) manipulation was recently established to control low-frequency Lamb waves in a plate. This study identifies the necessary BCs that forbid Rayleigh wave propagation order find rational methodology for an optimized BC-controlled meta-surface. An analytical of Mindlin BCs, type Cauchy shows promise surface control. The frequency-domain...

We propose an extended quantum theory, in which the number of degrees of freedom K behaves as fourth power the number N of distinguishable states. As the simplex of classical N–point probability distributions can be embedded inside a higher dimensional convex body M Q N of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embe...

We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N–point probability distributions can be embedded inside a higher dimensional convex body M Q N of mixed quantum states, one can further increase the dimensionality constructing the set...

Abstract We give a short proof of local well-posedness for the initial boundary value problem in general relativity with sole condition requirement that is umbilic. This includes as special case totally geodesic we had previously addressed [ 8]. The based on wave coordinates and key observation momentum constraint always valid umbilic boundaries. allows greater freedom choice conditions, since ...

Fixed and moving boundary problems for the one-dimensional heat equation are considered. A unified approach to solving such is proposed by embedding a given initial-boundary value problem into an appropriate initial on real line with arbitrary but functions, whose solution known. These functions determined imposing that of satisfies conditions. Exact analytical solutions some have not been prev...

One discrete problem of optimal population dynamics control with a controllable initial condition is considered. The process described by nonlinear system Fredholm-type difference equations. An analogue the L.S. Pontryagin’ maximum principle proved imposing series smoothness conditions on right side equation. linearized and Euler equation are for case convexity openness domain, which first-orde...

We study a multiple relaxation time lattice Boltzmann model for natural convection with moment–based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent wit...