Another Proof of Born’s Rule on Arbitrary Cauchy Surfaces

In 2017, Lienert and Tumulka proved Born’s rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born’s rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolution between any two Cauchy surfaces, satisfying that there is no interaction faster than light and no propagation faster than light. Here, we prove Born’s rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set of assumptions. The conclusion is that if detectors are placed along any Cauchy surface $$\Sigma $$ Σ , then the observed particle configuration on $$\Sigma $$ Σ is a random variable with distribution density $$|\Psi _\Sigma |^2$$ | Ψ Σ | 2 , suitably understood. The main different assumption is that the Born and collapse rules hold on any spacelike hyperplane, i.e., at any time coordinate in any Lorentz frame. Heuristically, this follows if the dynamics of the detectors is Lorentz invariant.

A Grain-Scale Study of Mojave Mars Simulant (MMS-1)

Space exploration has attracted significant interest by government agencies and the scientific community in recent years in an attempt to explore possible scenarios of settling of facilities on the Moon and Mars surface. One of the important components in space exploration is related with the understanding of the geophysical and geotechnical characteristics of the surfaces of planets and their natural satellites and because of the limitation of available extra-terrestrial samples, many times researchers develop simulants, which mimic the properties and characteristics of the original materials. In the present study, characterization at the grain-scale was performed on the Mojave Mars Simulant (MMS-1) with emphasis on the frictional behavior of small size samples which follow the particle-to-particle configuration. Additional characterization was performed by means of surface composition and morphology analysis and the crushing behavior of individual grains. The results from the study present for the first time the micromechanical tribological response of Mars simulant, and attempts were also made to compare the behavior of this simulant with previously published results on other types of Earth and extra-terrestrial materials. Despite some similarities between Mars and Moon simulants, the unique characteristics of the MMS-1 samples resulted in significant differences and particularly in severe damage of the grain surfaces, which was also linked to the dilation behavior at the grain-scale.

Research on the Effect of Particle Distribution on the Crack Propagation in Shaped Energy Blasting Based on the Smoothed Particle Hydrodynamics

Conventional smoothed particle hydrodynamics (SPH) methods suffer from disadvantages, such as difficult initial particle configuration, uneven distribution of generated particles, and low computational efficiency when applied to numerical simulation of shaped charge blasting. In this research, to overcome these problems, a modified SPH method that generates the particle configuration through self-adaptive optimization is developed by the combined application of MATLAB and LS-DYNA. The results presented in this paper demonstrate that the modified configuration method solves the problem of uneven distribution of particles in complex geometry domains by providing a more uniform smoothed particle distribution than the conventional SPH method. Furthermore, the results from the application of these two methods to the bidirectional-shaped charge blasting problem reveal that the defects in the particle configuration in the conventional SPH method lead to the development of main cracks in both the shaped and the unshaped directions. However, with the self-adaptive optimization method, the main cracks develop only in the shaped direction. In addition, the equivalent stress difference between the shaped and unshaped directions, 0.7 ms after detonation, is 120 MPa with the modified method. This is 85 MPa more than that with the conventional method.

The effect of clay water content in the Jet Erosion Test

The understanding of the onset of breaching induced by surface erosion is fundamental to enable definition of the level of protection afforded by embankments and provision of standards for the design of new structures and the upgrading of existing ones. Compacted embankment materials are generally partially saturated due to seasonal variation in the water content. At the onset of the overflow process embankments undergo to a wetting process due to the changes at the outer surface boundary conditions (i.e. overflow). Erosion behaviour is known to be a counterbalance between gravity forces and shear erosion forces. However, as the particle size decreases (i.e. clayey soils), gravitational forces become negligible and electrochemical interaction between particles play a dominant role. Clay microstructure (e.g. particle configuration and inter-particle forces) changes with the hydro-mechanical stresses history. Thus, it is necessary to consider the microstructural changes in particle configuration to understand the influence of microstructure on the macroscopic behaviour of clay during erosion. Upon wetting, clay have a swelling/collapse behaviour. This research presents experimental results on erosion of clay samples compacted at the same initial dry density but with different compaction water content. The influence of different wetting times on erosion is also investigated. We show that for a given as-compacted water content, the longer the wetting stage, and hence the higher the sample water content, the more erodible the samples. Additionally, for samples compacted at the same dry density, the ones compacted on the dry side of optimum are more erodible than samples compacted at the optimum water content, despite the lower water content at formation. We hypothesise that this may be due to the formation of a different initial microstructure in sample on the dry side of optimum (i.e. bi-modal pore size distribution). Our results contribute to the fundamental understanding of time-dependent mechanisms that influence erosion of clay embankments during overflow and, hence, to embankment failure. In addition, these tests show how basic concepts of unsaturated soil mechanics can serve as a guide to ‘design’ the compaction conditions of embankment material.

In-situ poling and structurization of piezoelectric particulate composites

Composites of lead zirconate titanate particles in an epoxy matrix are prepared in the form of 0–3 and quasi 1–3 with different ceramic volume contents from 10% to 50%. Two different processing routes are tested. Firstly a conventional dielectrophoretic structuring is used to induce a chain-like particle configuration, followed by curing the matrix and poling at a high temperature and under a high voltage. Secondly a simultaneous combination of dielectrophoresis and poling is applied at room temperature while the polymer is in the liquid state followed by subsequent curing. This new processing route is practiced in an uncured thermoset system while the polymer matrix still possess a relatively high electrical conductivity. Composites with different degrees of alignment are produced by altering the magnitude of the applied electric field. A significant improvement in piezoelectric properties of quasi 1–3 composites can be achieved by a combination of dielectrophoretic alignment of the ceramic particles and poling process. It has been observed that the degree of structuring as well as the functional properties of the in-situ structured and poled composites enhance significantly compared to those of the conventionally manufactured structured composites. Improving the alignment quality enhances the piezoelectric properties of the particulate composites.