Optimization of space-constrained micro-perforated absorbers by causality criteria

The problem of space-constrained absorbers in the low frequency range constitutes an area of continuous research. Micro-perforated panels are advantageous because they can be tuned by a proper selection of their constitutive physical parameters including the diameter of the perforations and their separation distance, their thickness and the length of the backing cavity. However, such optimal selection is not straightforward, especially when considering multi-layer partitions. Current optimization algorithms are based on the maximization of the total absorption coefficient averaged over a frequency band, that requires a compromise between the bandwidth and the thickness of the control device. In this work, the problem is analysed on the basis of a causality criterion. This principle is generalized from its formulation in the field of electromagnetism to obtain a relation that correlates the thickness-to-bandwidth performance of a micro-perforated absorber to its total absorption coefficient. Using this relation, an optimization procedure is presented for the sequential selection of the optimal physical parameters for single-layer partitions. An excellent agreement has been found between the optimal values obtained by the causality criterion and those achieved by critical coupling conditions.

Expanding, shearing and accelerating isotropic plane symmetric universe with conformal Kasner geometry

We construct a model of a universe filled with a perfect fluid with isotropic particle pressure. The anisotropic plane symmetric Kasner spacetime is used as a seed metric and through a conformal mapping a perfect fluid is generated. The model is inhomogeneous, irrotational, shearing and accelerating. For negative time, the universe is expanding, while for positive time, it is collapsing. With the aid of graphical three-dimensional plots, it is established that the density and pressure hypersurfaces are smooth and singularity free. Additionally, the sound-speed index is computed and the fluid obeys the causality criterion. The non-static exact solution found may prove useful in the study of gravitational waves.

Is a time symmetric interpretation of quantum theory possible without retrocausality?

Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called λ -mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time symmetric ontology.

Conformal Mappings in Relativistic Astrophysics

We describe the use of conformal mappings as a mathematical mechanism to obtain exact solutions of the Einstein field equations in general relativity. The behaviour of the spacetime geometry quantities is given under a conformal transformation, and the Einstein field equations are exhibited for a perfect fluid distribution matter configuration. The field equations are simplified and then exact static and nonstatic solutions are found. We investigate the solutions as candidates to represent realistic distributions of matter. In particular, we consider the positive definiteness of the energy density and pressure and the causality criterion, as well as the existence of a vanishing pressure hypersurface to mark the boundary of the astrophysical fluid.

Tentative Requiem for the M'Naghten Rule

The "knowledge of right and wrong" test of criminal responsi bility, as formulated in the M'Naghten Rule, should be aban doned, and the "causality" criterion, as expressed in the Pike and Durham cases, should be universally adopted. A fresh attack on the constitutionality of the M'Naghten Rule as a violation of the Eighth Amendment prohibition against cruel and unusual pun ishments may be timely and fruitful.