Diffraction errors in micromirror-array based wavefront generation

Using Laser-based Speckle-Interferometers, the shape of optically rough surfaces can be measured precisely and contactlessly from variable measuring distances even in regions of difficult access. This work is concerned with the integration of a micromirror array (MMA) into an electronic Speckle-Pattern-Interferometer. With the adaptive optics, it is intended to adapt the phasefront of a reference wave to critical surface areas of the measurement object. Yet, due to the topography of the MMA, diffraction effects occur which affect the phase and intensity of the generated wavefront. We demonstrate how these diffraction effects can be efficiently modelled by a Fraunhofer diffraction method. We compare the results of this model to theoretical data obtained by a numerical Fresnel diffraction model and to measurement data obtained from a measurement setup incorporating a multi mirror array.     

Determination of depth-of-focus in lensless in-line digital particle holography

Lensless in-line digital particle holography (DPH) can be thought of as a special case of photography, and its depth of focus (DoF) characteristics combine those of both photography and holography. The effect of important parameters such as the pixel size and the number of pixels in a charge-coupled device (CCD), the object's distance, the wavelength of the laser, and the particle diameter on the DoF of a reconstruction image in lensless in-line DPH was investigated using simulation holograms. The DoF is directly proportional to the object distance and the particle size. As the wavelength of the laser increases, the DoF decreases. The DoF is inversely proportional to the pixel size and to the number of pixels in a CCD. Instead of expressing nonspecific proportional relationships for DoF, the DoF prediction equations for typical CCD cameras were obtained using DoF data from many simulation holograms and efficient data-fitting software. Finally, the DoF prediction equations were verified using real holograms from a calibration target for several cases. Good agreement between measured and predicted values was confirmed.     

Fast and accurate algorithm for the simulation of NMR spectra of large spin systems

The computational cost for the simulation of NMR spectra grows exponentially with the number of nuclei. Today, the memory available to store the Hamiltonian limits the size of the system that can be studied. Modern computers enable to tackle systems containing up to 13 spins [1], which obviously does not allow to study most molecules of interest in research. This issue can be addressed by identifying groups of spins or fragments that are not or only weakly interacting together, i.e., that only share weakly coupled spin pairs. Such a fragmentation is only permitted in the weak coupling regime, i.e., when the coupling interaction is weak compared to the difference in chemical shift of the coupled spins. Here, we propose a procedure that removes weak coupling interactions in order to split the spin system efficiently and to correct a posteriori for the effect of the neglected couplings. This approach yields accurate spectra when the adequate interactions are removed, i.e., between spins only involved in weak coupling interactions, but fails otherwise. As a result, the computational time for the simulation of 1D spectra grows linearly with the size of the spin system.     

Spinach--a software library for simulation of spin dynamics in large spin systems

We introduce a software library incorporating our recent research into efficient simulation algorithms for large spin systems. Liouville space simulations (including symmetry, relaxation and chemical kinetics) of most liquid-state NMR experiments on 40+ spin systems can now be performed without effort on a desktop workstation. Much progress has also been made with improving the efficiency of ESR, solid state NMR and Spin Chemistry simulations. Spinach is available for download at http://spindynamics.org.     

Analysis of two stacked cylindrical dielectric resonators in a TE₁₀₂ microwave cavity for magnetic resonance spectroscopy

The frequency, field distributions and filling factors of a DR/TE??? probe, consisting of two cylindrical dielectric resonators (DR1 and DR2) in a rectangular TE??? cavity, are simulated and analyzed by finite element methods. The TE(+++) mode formed by the in-phase coupling of the TE??(δ)(DR1), TE??(δ)(DR2) and TE??? basic modes, is the most appropriate mode for X-band EPR experiments. The corresponding simulated B(+++) fields of the TE(+++) mode have significant amplitudes at DR1, DR2 and the cavity's iris resulting in efficient coupling between the DR/TE??? probe and the microwave bridge. At the experimental configuration, B(+++) in the vicinity of DR2 is much larger than that around DR1 indicating that DR1 mainly acts as a frequency tuner. In contrast to a simple microwave shield, the resonant cavity is an essential component of the probe that affects its frequency. The two dielectric resonators are always coupled and this is enhanced by the cavity. When DR1 and DR2 are close to the cavity walls, the TE(+++) frequency and B(+++) distribution are very similar to that of the empty TE??? cavity. When all the experimental details are taken into account, the agreement between the experimental and simulated TE(+++) frequencies is excellent. This confirms that the resonating mode of the spectrometer's DR/TE??? probe is the TE(+++) mode. Additional proof is obtained from B?(x), which is the calculated maximum x component of B(+++). It is predominantly due to DR2 and is approximately 4.4 G. The B?(x) maximum value of the DR/TE??? probe is found to be slightly larger than that for a single resonator in a cavity because DR1 further concentrates the cavity's magnetic field along its x axis. Even though DR1 slightly enhances the performance of the DR/TE??? probe its main benefit is to act as a frequency tuner. A waveguide iris can be used to over-couple the DR/TE??? probe and lower its Q to ≈150. Under these conditions, the probe has a short dead time and a large bandwidth. The DR/TE??? probe's calculated conversion factor is approximately three times that of a regular cavity making it a good candidate for pulsed EPR experiments.     

Hybrid magnetic field formulation based on the losses separation method for modified dynamic inverse Jiles-Atherton model

Dynamic formulation based on the losses separation method in conducting media for the inverse Jiles-Atherton model is proposed. This formulation is based on the concept of the Hybrid Magnetic Field model (HMF). The HMF consists of the modification of the effective field by introducing two counter-fields associated, respectively, with the eddy current and excess losses. Such a formulation is characterized by seven parameters with five parameters issued from the quasi-static Jiles-Atherton model. Thus, two new parameters related to these fields are added to that defined in the quasi-static model. The identification of these new parameters is based on the measurements of the volumetric energy density. To validate this formulation, measurements are carried out on grain non-oriented Fe-Si 3% electrical sheets.     

Classical Molecular Dynamics Model for Coupled Two‐Component Plasmas – Ionization Balance and Time Considerations

The dynamic properties of ion‐electron two‐component plasmas (TCP) are studied by using classical molecular dynamics (MD) simulations. There is a variety of time dependent and structural results that MD is able to provide in complement to other methods, e.g., useful micro‐field sequences can be generated. The method deals with some specific difficulties: the mass ratio between ions and electrons enforces very small time‐steps appropriate to follow electrons motion while, ions must move significantly in order to build, self consistently, their spatial structure. This results in expensive simulations. Electron trajectories are trapped and de‐trapped with multiple electron collisions around ions resulting in the occurrence of quasi metastable bound electron states. An analysis of micro‐fields at neutral in a hydrogen plasma reveals the need to consider a complete hierarchy of time scales extended typically over 7 order of magnitude, i.e., from a time‐step: ～10^‐19s, to a time required to obtain statistical averages, ～10^‐11s. In order to extend the MD capabilities in representing real coupled plasmas a classical ionization/recombination process has been implemented allowing to follow the evolution of plasmas involving several ion stages and model the ionization balance. Here again TCP simulations deal with extended time‐scale providing information about relaxation of non equilibrium plasma states (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A symmetric BEM–FEM method for an axisymmetric eddy current problem

This paper deals with the numerical solution of the time-harmonic eddy current model in an axisymmetric unbounded domain. To this end, a new symmetric BEM–FEM formulation is derived and also analyzed. Moreover, error estimates for the corresponding discretization are proven.     

Genetic-algorithm-based simulation optimization considering a single stochastic constraint

In this paper, we consider the discrete optimization via simulation problem with a single stochastic constraint. We present two genetic-algorithm-based algorithms that adopt different sampling rules and searching mechanisms, and thus deliver different statistical guarantees. The first algorithm offers global convergence as the simulation effort goes to infinity. However, the algorithm’s finite-time efficiency may be sacrificed to maintain this theoretically appealing property. We therefore propose the second heuristic algorithm that can take advantage of the desirable mechanics of genetic algorithm, and might be better able to find near-optimal solutions in a reasonable amount of time. Empirical studies are performed to compare the efficiency of the proposed algorithms with other existing ones.     

The analytic hierarchy process with stochastic judgements

The analytic hierarchy process (AHP) is a widely-used method for multicriteria decision support based on the hierarchical decomposition of objectives, evaluation of preferences through pairwise comparisons, and a subsequent aggregation into global evaluations. The current paper integrates the AHP with stochastic multicriteria acceptability analysis (SMAA), an inverse-preference method, to allow the pairwise comparisons to be uncertain. A simulation experiment is used to assess how the consistency of judgements and the ability of the SMAA-AHP model to discern the best alternative deteriorates as uncertainty increases. Across a range of simulated problems results indicate that, according to conventional benchmarks, judgements are likely to remain consistent unless uncertainty is severe, but that the presence of uncertainty in almost any degree is sufficient to make the choice of best alternative unclear.