Semantic Perversity

This paper consists of two parts. In section I, I explore Christopher Hookway's proposal (1988) to elude a counterexample which Gareth Evans (Evans (1975)) offers against Quine's 'thesis of the inscrutability of reference'. Evans produced a line of argument which suggests that one of Quine's semantically perverse translation manuals is behaviorally incorrect. Hookway modifies the perverse manual to make it behaviorally correct. As we'll see in due course, Hookway's proposal fails to deliver the right satisfaction conditions. Fortunately, just a minor modification will suffice for Hookway to meet Evans's objection. In section II, I shall offer the Quinean a different strategy to bypass Evans's counter, a strategy which is not subject to certain criticisms which may put Hookway's own proposal in jeopardy

All‐hexahedral element meshing: automatic elimination of self‐intersecting dual lines

There has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed by the use of the combinatorial dual to the mesh in order to define the internal connectivities among elements. For all of the known methods using the dual concept, it is necessary to first prevent or eliminate self‐intersecting (SI) dual lines of the given quadrilateral mesh. The relevant features of SI lines are studied, giving a method to remove them, which avoids deforming the original geometry. Some examples of resulting meshes are shown where the current meshing method has been successfully applied.&nbsp

All-hexahedral element meshing: Generation of the dual mesh by recurrent subdivision

The domain geometry is defined by means of a closed all-quadrilateral mesh. The outer mesh imposes very strong restrictions on the possible connectivities between the inner hexahedral elements. Following the guidelines of the outer topology, the inner one is almost entirely defined. Several ways may be decided for certain configurations, some of them requiring special considerations in order to achieve a valid FEM mesh. The process is entirely performed by constructing the (graph theoretical) dual of the hexahedral mesh, this means no metric information is handled until the final (positioning and smoothing) steps. The essential steps of this scheme are described by means of examples

All‐hexahedral mesh smoothing with a node‐based measure of quality

This research work deals with the analysis and test of a normalized‐Jacobian metric used as a measure of the quality of all‐hexahedral meshes. Instead of element qualities, a measure of node quality was chosen. The chosen metric is a bound for deviation from orthogonality of faces and dihedral angles. We outline the main steps and algorithms of a program that is successful in improving the quality of initially invalid meshes to acceptable levels. For node movements, the program relies on a combination of gradient‐driven and simulated annealing techniques. Some examples of the results and speed are also shown

Exact time-reversal focusing of acoustic and quantum excitations in open cavities: The perfect inverse filter

The time-reversal mirror (TRM) prescribes the reverse playback of a signal to focalize an acoustic excitation as a Loschmidt echo. In the quantum domain, the perfect inverse filter (PIF) processes this signal to ensure an exact reversion provided that the excitation originated outside the cavity delimited by the transducers. We show that PIF takes a simple form when the initial excitation is created inside this cavity. This also applies to the acoustical case, where it corrects the TRM and improves the design of an acoustic bazooka. We solve an open chaotic cavity modeling a quantum bazooka and a simple model for a Helmholtz resonator, showing that the PIF becomes decisive to compensate the group velocities involved in a highly localized excitation and to achieve subwavelength resolution.Comment: 6 pages, 2 figure

Measuring two-photon orbital angular momentum entanglement

We put forward an approach to estimate the amount of bipartite spatial entanglement of down-converted photon states correlated in orbital angular momentum and the magnitude of the transverse (radial) wave vectors. Both degrees of freedom are properly considered in our framework, which only requires azimuthal local linear optical transformations and mode selection analysis with two fiber detectors. The coincidence distributions predicted by our approach give an excellent fit to the distributions measured in a recent experiment aimed to show the very high-dimensional transverse entanglement of twin photons from a down-conversion source. Our estimate for the Schmidt number is substantially lower but still confirms the presence of high-dimensional entanglement.Comment: Extended paper of a published version in PRA, with some extra appendice

Finite elements numerical solution of a coupled profile–velocity–temperature shallow ice sheet approximation model

AbstractThis work deals with the numerical solution of a complex mathematical model arising in theoretical glaciology. The global moving boundary problem governs thermomechanical processes jointly with ice sheet hydrodynamics. One major novelty is the inclusion of the ice velocity field computation in the framework of the shallow ice model so that it can be coupled with profile and temperature equations. Moreover, the proposed basal velocity and shear stress laws allow the integration of basal sliding effects in the global model. Both features were not taking into account in a previous paper (Math. Model. Methods Appl. Sci. 12 (2) (2002) 229) and provide more realistic convective terms and more complete Signorini boundary conditions for the thermal problem. In the proposed numerical algorithm, one- and two-dimensional piecewise linear Lagrange finite elements in space and a semi-implicit upwinding scheme in time are combined with duality and Newton's methods for nonlinearities. A simulation example involving real data issued from Antarctic shows the temperature, profile and velocity qualitative behaviour as well as the free boundaries and basal effects