Spatial Discretization Step Research Articles

Second-order correlations in single-particle interferometry

Interferometers with single particles are susceptible for dephasing perturbations from the environment, such as electromagnetic oscillations or mechanical vibrations. On the one hand, this limits sensitive quantum phase measurements as it reduces the interference contrast in the signal. On the other hand, it enables single-particle interferometers to be used as sensitive sensors for electromagnetic and mechanical perturbations. Recently, it was demonstrated experimentally, that a second-order correlation analysis of the spatial and temporal detection signal can decrease the electromagnetic shielding and vibrational damping requirements significantly. Thereby, the relevant matter-wave characteristics and the perturbation parameters could be extracted from the correlation analysis of a spatially ‘washed-out’ interference pattern and the original undisturbed interferogram could be reconstructed. This method can be applied to all interferometers that produce a spatial fringe pattern on a detector with high spatial and temporal single-particle resolution. In this article, we present and discuss in detail the used two-dimensional second-order correlation theory for multifrequency perturbations. The derivations of an explicit and approximate solution of the correlation function and corresponding amplitude spectra are provided. It is explained, how the numerical correlation function is extracted from the measurement data. Thereby, the influence of the temporal and spatial discretization step size on the extracted parameters, as contrast and perturbation amplitude, is analyzed. The influence of noise on the correlation function and corresponding amplitude spectrum is calculated and numerically cross-checked by a comparison of our theory with numerical single-particle simulations of a perturbed interference pattern. Thereby, an optimum spatial discretization step size is determined to achieve a maximum signal-to-noise ratio, which was used in former experiments to identify the perturbation caused by the electrical network. Our method can also be applied for the analysis of broad-band frequency noise, dephasing the interference pattern. Using Gaussian distributed noise in the simulations, we demonstrate that the relevant matter-wave parameters and the applied perturbation spectrum can be revealed by our correlation analysis.

Monte Carlo simulation of radiation transport in human skin with rigorous treatment of curved tissue boundaries.

In three-dimensional (3-D) modeling of light transport in heterogeneous biological structures using the Monte Carlo (MC) approach, space is commonly discretized into optically homogeneous voxels by a rectangular spatial grid. Any round or oblique boundaries between neighboring tissues thus become serrated, which raises legitimate concerns about the realism of modeling results with regard to reflection and refraction of light on such boundaries. We analyze the related effects by systematic comparison with an augmented 3-D MC code, in which analytically defined tissue boundaries are treated in a rigorous manner. At specific locations within our test geometries, energy deposition predicted by the two models can vary by 10%. Even highly relevant integral quantities, such as linear density of the energy absorbed by modeled blood vessels, differ by up to 30%. Most notably, the values predicted by the customary model vary strongly and quite erratically with the spatial discretization step and upon minor repositioning of the computational grid. Meanwhile, the augmented model shows no such unphysical behavior. Artifacts of the former approach do not converge toward zero with ever finer spatial discretization, confirming that it suffers from inherent deficiencies due to inaccurate treatment of reflection and refraction at round tissue boundaries.

NEW ALGORITHMS FOR THE SPECIFIC ABSORPTION RATE NUMERICAL EVALUATION BASED ON SPHERICAL AVERAGING VOLUMES

The numerical calculation of the Speciflc Absorption Rate (SAR) averaged over a certain tissue mass is a common practice when evaluating the potential health risk due to the human exposure to electromagnetic sources. Nevertheless, SAR values are strongly in∞uenced by many factors such as, for instance, the shape of the volume containing the reference mass, the spatial discretization step, or the treatment of internal air, just to mention some of them: difierent choices can induce signiflcant discrepancies. In this work, an overview on some of the most commonly adopted SAR algorithms is flrstly presented, and a discussion on their potential difierences reported. Then, based on a spherical volume approach, some new algorithms are proposed. All the algorithms are then used to evaluate the SAR both in artiflcially generated test cases and in some practical human-antenna interaction problems. The result comparison highlights relevant discrepancies and enforces the necessity of a reasoned standardization of the techniques for the SAR calculation.

Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations

A new two-equation model is proposed for large eddy simulations (LESs) using coarse grids. The modeled transport equations are obtained from a direct transposition of well-known statistical models by using multiscale spectrum splitting given by the filtering operation applied to the Navier–Stokes equations. The model formulation is compatible with the two extreme limits that are on one hand a direct numerical simulation and on the other hand a full statistical modeling. The characteristic length scale of subgrid turbulence is no longer given by the spatial discretization step size, but by the use of a dissipation equation. The proposed method is applied to a transposition of the well-known k-e statistical model, but the same method can be developed for more advanced closures. This approach is intended to contribute to non-zonal hybrid models that bridge Reynolds-averaged Navier–Stokes (RANS) and LES, by using a continuous change rather than matching zones. The main novelty in the model is the derivation of a new e equation for LES that is formally consistent with RANS when the filter width is very large. This approach is dedicated to applications to non-equilibrium turbulence and coarse grid simulations. An illustration is made of large eddy simulations of turbulence submitted to periodic forcing. The model is also an alternative approach to hybrid models.

An efficient solution procedure for the ONE-STEP experiment

The ONE-STEP experiment 1 describes an experimental procedure for determining the hydraulic properties of a soil sample. It involves measurements of cumulative outflow with time from a soil core placed in a pressure cell. The water flow in this soil core satisfies the classical Richards equation. The accuracy of numerical schemes for simulating this experiment strongly depends on experimental conditions. In case the pneumatic head applied to the pressure cell is high the solution is characterized by a “steep drying front”. A small spatial discretization step size is then required to obtain accurate solutions. To improve the efficiency of the procedure for determining soil hydraulic properties, we have studied the applicability of a simple variable step size scheme.