Arbitrary Spatial Distribution Research Articles

Universal simulation of absorption effects for X-ray diffraction in reflection geometry.

Analytical calculations of absorption corrections for X-ray powder diffraction experiments on non-ideal samples with surface roughness, porosity or absorption contrasts from multiple phases require complex mathematical models to represent their material distribution. In a computational approach to this problem, a practicable ray-tracing algorithm is formulated which is capable of simulating angle-dependent absorption corrections in reflection geometry for any given rasterized sample model. Single or multiphase systems with arbitrary surface roughness, porosity and spatial distribution of the phases in any combination can be modeled on a voxel grid by assigning respective values to each voxel. The absorption corrections are calculated by tracing the attenuation of X-rays along their individual paths via a modified shear-warp algorithm. The algorithm is presented in detail and the results of simulated absorption corrections on samples with various surface modulations are discussed in the context of published experimental results.

Additively manufactured structures with powder inclusions for controllable dissipation: The critical influence of packing density

Particle dampers represent a simple yet effective means to reduce unwanted oscillations when attached to structural components. Powder bed fusion additive manufacturing of metals allows to integrate particle inclusions of arbitrary shape, size, and spatial distribution directly into bulk material, giving rise to novel metamaterials with controllable dissipation without the need for additional external damping devices. At present, however, it is not well understood how the degree of dissipation is influenced by the properties of the enclosed powder packing. In the present work, a two-way coupled discrete element - finite element model is proposed allowing for the first time to consistently describe the interaction between oscillating deformable structures and enclosed powder packings, while existing works have only considered rigid enclosures so far. As fundamental test case, the free oscillations of a hollow cantilever beam filled with various powder packings differing in packing density, particle size, and surface properties are considered to systematically study these factors of influence. Critically, it is found that the damping characteristics strongly depend on the packing density of the enclosed powder and that an optimal packing density exists at which the dissipation is maximized. Moreover, it is found that the influence of (absolute) particle size on dissipation is rather small. First-order analytical models for different deformation modes of such powder cavities are derived to shed light on this observation.

Fast Algorithm for Full-Wave EM Scattering Analysis of Large-Scale Chaff Cloud With Arbitrary Orientation, Spatial Distribution, and Length

Fast Algorithm for Full-Wave EM Scattering Analysis of Large-Scale Chaff Cloud With Arbitrary Orientation, Spatial Distribution, and Length

A Model for Evaluating the Visual Perception of an Arbitrary Distribution of Luminance in Indoor Lighting Installations

How to assess what kind of feeling the lighting scene causes? A new level of computer graphics visualization makes it possible to think about real image through synthetic images from one hand, and from other hand, today the HDRi method allows fixing luminance with an accuracy of up to 10 % in a wide range. Therefore, assessing the lighting quality of designed and existing lighting installations in terms of luminance reaches a new level. It brings the creating of psychophysical model of lighting quality assessment through photometric quantities closer. The structure of the model can be represented in two parts: the calculation equation and the psychophysical scale. This work considers the issue of choosing categories of the psychophysical scale, the method of creating of luminance maps for scene with an arbitrary spatial angle luminance distribution, and the method for evaluating scenes using a new gradient criterion Q based on these maps. An analysis of HDRi images of workplaces based on the experimental setup and scenes in a cafe showed that the Q criterion depends on the type of scene and on the number of light sources in the field of view. One could suggest that it is impossible to create one single psychophysical scale for the Q criterion. However, one can use this new criterion to evaluate the same scenes with different lighting options or similar scenes in terms of spatial luminance distribution and glare. Despite of the luminance map values have an error of about 30 % the using HDRi image of scene allows to calculate Q criterion with an accuracy of about 10 %.

Flow field disturbance due to point viscosity variations in a heterogeneous fluid

A fluid can be heterogeneous in either its density or viscosity - its two basic material properties. In this Letter, we ask how an ambient flow field is disturbed due to a point viscosity variation in the fluid. If we are able to answer this question, we can create an arbitrary spatial distribution of viscosity discretely by placing viscosity sources and sinks of appropriate strength, allowing us to model complex fluids. As an example, we show how the hydrodynamics of a rigid particle is altered due to the presence of point viscosity variations.

Acoustic full waveform inversion for 2-D ambient noise source imaging

SUMMARYWe present a method for estimating seismic ambient noise sources by acoustic full waveform inversion (FWI) of interstation cross-correlations. The method is valid at local scales for laterally heterogeneous media, and ambient noise sources confined to the Earth’s surface. Synthetic tests performed using an actual field array geometry, are used to illustrate three unique aspects of our work. First: the method is able to recover noise sources of arbitrary spatial distribution, both within and outside the receiver array, with high fidelity. This holds true for complex velocity models and does not require a good initial guess for inversion, thereby addressing an outstanding issue in the existing research literature. Second: we analyse the extent of biases in source inversion that arise due to inaccurate velocity models. Our findings indicate that source inversion using simplified (e.g. homogeneous) velocity models may work reliably when lateral variations in velocity structure are limited to 5 or 10 per cent in magnitude, but is vitiated by strong variations of 20 per cent or higher, wherein the effect of strong scattering and/or phase distortions become significant. Finally, our technique is implemented without the adjoint method, which is usually inextricably linked to FWI. Inversions are performed using source kernels computed for each receiver pair, and this approach is computationally tractable for real-world problems with small aperture seismic arrays.

SOME PROBLEMS OF OPTIMIZATION OF ROD SYSTEMS CONTAINING COMPRESSED ELEMENTS USING ADDITIONAL CONSTRAINTS

The article is devoted to the problem of increasing the stability of rod systems containing longitudinally compressed elements. The influence of the imposition of constraints on the behavior of such systems is investigated in order to determine such places for imposing constraints that provide the maximum stability of the system reinforced by the constraint. To get generality, the consideration includes such rod systems that allow various equilibrium configurations, for example, having internal ideal hinges, as well as an arbitrary distribution of longitudinal compressive forces, including leaving some areas free from compression. For the same purpose, the constraints are considered as generalized, producing a reaction with an arbitrary spatial distribution. The paper formulates some general results related to the influence of the introduction of generalized constraints on the critical forces of a rod system with some generalizations related to the extension of the class of rod systems under consideration. Particular attention is paid to the buckling modes in view of their important role as a basis for describing various configurations of the structure. It has been established that the shape of these modes, in particular, the position of their nodes, is essential for finding the optimal position of the constraint. For the case of constraint in the form of a concentrated hinged support, analytical expressions are obtained that represent the derivatives of the critical forces of the system with respect to the coordinate of the support. The case of a multiple critical force, when this derivative, generally speaking, does not exist, is especially considered. These expressions make it possible to qualitatively characterize the optimal position of the support. The application of some of the obtained results is demonstrated by the example of the problem of finding the optimal position of an intermediate hinged support of a two-span rod supported at the ends by elastic hinged supports. These positions are qualitatively described for various values of the stiffness coefficients of the end supports. It has been established that under certain conditions, the optimal positions of the intermediate support correspond to a special semi-curved mode of buckling, in which one of the spans does not bend, but retains its rectilinear equilibrium shape.

Generation of A Space-Variant Vector Beam with Catenary-Shaped Polarization States.

We demonstrate the generation of a space-variant vector beam with catenary-shaped polarization states based on the polarization interferometry. With a spatial light modulator and a common path interferometric configuration, two orthogonally circularly polarized beams with different phase modulation overlap each other, yielding the vector beams. In addition, the polarization states of this vector beam are scalable to the arbitrary spatial distribution because of its great flexibility and universal applicability. It is expected that this vector beam may have many potential and intriguing applications in the micro/nano material processing, liquid crystal elements fabrication and optical micro-manipulation, and so on.

Measuring the absorption coefficient of optical materials with arbitrary shape or distribution within an integrating sphere.

The absorption coefficient of a material is classically determined by measuring the transmittance of a homogeneous sample contained within flat optical faces and under collimated illumination. For arbitrary shapes this method is impracticable. The characterization of inhomogeneous or randomly distributed samples such as granules, powders or fibers suffers the same problem. Alternatively, an integrating cavity permits us to illuminate a sample under a homogenous and isotropic light field where the analysis simplifies. We revisit this strategy and present a new formal basis based on simple radiometric laws and principles. We introduce a new concept to describe the absorption: the optical form factor. We tackle a rigorous treatment of several regular forms, including full absorption range and the reflection at its surfaces. We also model and improve an integrating sphere setup to perform reliable measurements. Altogether, it permits achieving simple but general conclusions for samples with arbitrary shape or spatial distribution, from weak to highly absorbing, expanding the applicability of quantitative absorption spectroscopy. Finally, we validate it by measuring different sample formats made of PMMA: a cube, groups of granules and injection molding loose parts. The absorption coefficient of PMMA varies near three orders of magnitude in the explored range (380-1650 nm).

Semi-analytical source (SAS) method for 3-D transient heat conduction problems with moving heat source of arbitrary shape

In this study, the semi-analytical source method, which has recently developed by the authors, is implemented for a 3-D fully-transient heat conduction problem with a moving heat source. The method utilizes the exact Green’s function for a diffusion problem with a piecewise constant heat source meaning that the heat source term is defined as the superposition of piece-wise constant contributions in each time interval and in each spatial interval. This approach allows the modeling of any arbitrary spatial distribution of heating with time varying power. Moreover, the method is not limited to straight-line motion of the heat source, and can include internal heating as well as surface heating. One important aspect of the method is that spatial discretization is required only on the path of the heating source and at the observation locations of interest, consequently the discretization of the entire domain is not required as in the case of fully-numerical methods. To verify the semi-analytical source method, an experimental setup was constructed and experiments were conducted with a fiber laser, and satisfactory agreement is achieved. Several case studies are also demonstrated with a Gaussian heat source. The semi-analytical source method is particularly well-suited for parallel computing. To explore this aspect, the parallelization of the method is explored using the Message Passing Interface (MPI) and domain decomposition with up to 800 processors on Stampede2. The parallelization results reveal that semi-analytical method is very suitable for parallel computation. For a strong scaling, the method shows an ideal linear scaling with increasing number of processors with a proper load balance. The weak scaling reveals that the parallelization performance exponentially increases with the increasing time domain due to convolution nature of the method in time.

Magnetoelastic parametric instabilities of localized spin waves induced by traveling elastic waves

A theory of parametric interaction between spin waves localized in a waveguide and traveling elastic waves is developed for ferromagnetic thin films. The presented theoretical formalism takes into account an arbitrary spatial distribution of the displacement field in the acoustic waves and an arbitrary magnetization in spin waves. Using the theory, we examine interaction of forward-volume spin waves (FVSW) localized in a narrow waveguide and Rayleigh surface acoustic waves traveling in a substrate underneath the waveguide. We show that, in contrast to classical electromagnetic pumping, the symmetry of the magnetoelastic interaction allows for the generation of first-order parametric instabilities in spin waves with circular precession, such as FVSW. At the same time the localization of spin waves modifies the momentum conservation law for the parametric process to include the transfer of momentum to the waveguide, which allows for a frequency separation of the interacting counterpropagating spin waves. The frequency separation enables amplification of a localized spin wave without generation of a traveling idler wave, which results in a greater amplification efficiency.

Quantitative lock-in thermography imaging of thermal-wave spatial profiles and thermophysical property measurements in solids with inner corner geometries using thermal-wave field theory

In this study, we established a theoretical photothermal model and its experimental validation for an infinitely long solid with an inner corner of arbitrary opening angle, with the solid being irradiated photothermally by a modulated laser beam of arbitrary spatial intensity distribution directed to the corner. The thermal-wave field distribution on the flat surfaces of the solid centered at the corner was obtained using the Green function method. Experimental results based on quantitative thermographic imaging were obtained and used to validate the theoretical model in which thermal diffusivity of an inner cornered stainless steel was measured. The thermal-wave theory based lock-in thermography imaging technique provides a quantitative tool for thermal property measurement and/or non-destructive evaluation of non-flat structures. It also generates valuable physical insights into the spatial distribution of the thermal-wave field in the neighborhood of geometric discontinuities such as inner corners in solids.

Wireless Communication Using Unmanned Aerial Vehicles (UAVs): Optimal Transport Theory for Hover Time Optimization

In this paper, the effective use of flight-time constrained unmanned aerial vehicles (UAVs) as flying base stations that provide wireless service to ground users is investigated. In particular, a novel framework for optimizing the performance of such UAV-based wireless systems in terms of the average number of bits (data service) transmitted to users as well as the UAVs’ hover duration (i.e. flight time) is proposed. In the considered model, UAVs hover over a given geographical area to serve ground users that are distributed within the area based on an arbitrary spatial distribution function. In this case, two practical scenarios are considered. In the first scenario, based on the maximum possible hover times of UAVs, the average data service delivered to the users under a fair resource allocation scheme is maximized by finding the optimal cell partitions associated to the UAVs. Using the powerful mathematical framework of optimal transport theory, this cell partitioning problem is proved to be equivalent to a convex optimization problem. Subsequently, a gradient-based algorithm is proposed for optimally partitioning the geographical area based on the users’ distribution, hover times, and locations of the UAVs. In the second scenario, given the load requirements of ground users, the minimum average hover time that the UAVs need for completely servicing their ground users is derived. To this end, first, an optimal bandwidth allocation scheme for serving the users is proposed. Then, given this optimal bandwidth allocation, optimal cell partitions associated with the UAVs are derived by exploiting the optimal transport theory. Simulation results show that our proposed cell partitioning approach leads to a significantly higher fairness among the users compared with the classical weighted Voronoi diagram. Furthermore, the results demonstrate that the average hover time of the UAVs can be reduced by 64% by adopting the proposed optimal bandwidth allocation scheme as well as the optimal cell partitioning approach. In addition, our results reveal an inherent tradeoff between the hover time of UAVs and bandwidth efficiency while serving the ground users.

Optimal Transport Theory for Cell Association in UAV-Enabled Cellular Networks

In this letter, a novel framework for delay-optimal cell association in unmanned aerial vehicle (UAV)-enabled wireless cellular networks is proposed. In particular, to minimize the average network delay under any arbitrary spatial distribution of the ground users, the optimal cell partitions of the UAVs and terrestrial base stations are determined. To this end, using the powerful mathematical tools of optimal transport theory, the existence of the solution to the optimal cell association problem is proved and the solution space is completely characterized. The analytical and simulation results show that the proposed approach yields substantial improvements in terms of the average network delay.

Nonuniformity correction of infrared cameras by reading radiance temperatures with a spatially nonhomogeneous radiation source

We present a novel method of nonuniformity correction (NUC) of infrared cameras and focal plane arrays (FPA) in a wide optical spectral range by reading radiance temperatures and by applying a radiation source with an unknown and spatially nonhomogeneous radiance temperature distribution. The benefit of this novel method is that it works with the display and the calculation of radiance temperatures, it can be applied to radiation sources of arbitrary spatial radiance temperature distribution, and it only requires sufficient temporal stability of this distribution during the measurement process. In contrast to this method, an initially presented method described the calculation of NUC correction with the reading of monitored radiance values. Both methods are based on the recording of several (at least three) images of a radiation source and a purposeful row- and line-shift of these sequent images in relation to the first primary image. The mathematical procedure is explained in detail. Its numerical verification with a source of a predefined nonhomogeneous radiance temperature distribution and a thermal imager of a predefined nonuniform FPA responsivity is presented.

Incorporation of a spatial source distribution and a spatial sensor sensitivity in a laser ultrasound propagation model using a streamlined Huygens’ principle

The near-field, surface-displacement waveforms in plates are modeled using interwoven concepts of Green’s function formalism and streamlined Huygens’ principle. Green’s functions resemble the building blocks of the sought displacement waveform, superimposed and weighted according to the simplified distribution. The approach incorporates an arbitrary circular spatial source distribution and an arbitrary circular spatial sensitivity in the area probed by the sensor. The displacement histories for uniform, Gaussian and annular normal-force source distributions and the uniform spatial sensor sensitivity are calculated, and the corresponding weight distributions are compared. To demonstrate the applicability of the developed scheme, measurements of laser ultrasound induced solely by the radiation pressure are compared with the calculated waveforms. The ultrasound is induced by laser pulse reflection from the mirror-surface of a glass plate. The measurements show excellent agreement not only with respect to various wave-arrivals but also in the shape of each arrival. Their shape depends on the beam profile of the excitation laser pulse and its corresponding spatial normal-force distribution.

Monomorphous decomposition method and its application for phase retrieval and phase-contrast tomography

We show that an arbitrary spatial distribution of complex refractive index inside an object can be exactly represented as a sum of two "monomorphous" complex distributions, i.e. the distributions with the ratios of the real part to the imaginary part being constant throughout the object. A priori knowledge of constituent materials can be used to estimate the global lower and upper boundaries for this ratio. This approach can be viewed as an extension of the successful phase-retrieval method, based on the Transport of Intensity equation, that was previously developed for monomorphous (homogeneous) objects, such as e.g. objects consisting of a single material. We demonstrate that the monomorphous decomposition can lead to more stable methods for phase retrieval using the Transport of Intensity Equation. Such methods may find application in quantitative in-line phase-contrast imaging and phase-contrast tomography.

Calculation of Mutual Inductance based on 3D Field and Circuit Coupling Analysis for WPT System

Determination of mutual inductance in the WPT system based on the electromagnetic coupling mode is crucial for system design and efficiency optimization. The analytic formulas and experimental methods which only aim at a coupling coil with a certain type of configuration and parameters are not universal approaches. Therefore they can’t serve as a design basis for the system optimization. This paper presents a novel method based on 3D field and circuit coupling analysis to calculate mutual inductance of coupling coils with arbitrary spatial distribution for WPT system. The method can obtain maximum efficiency under the condition that the spatial distribution of coupling coils are irregular and restrained in actual physical systems. The method has made a breakthrough and provided a powerful tool for the design and optimization of electromagnetic coupling power transmission system.

Optimization of spatial light distribution through genetic algorithms for vision systems applied to quality control

The paper presents an adaptive illumination system for image quality enhancement in vision-based quality control systems. In particular, a spatial modulation of illumination intensity is proposed in order to improve image quality, thus compensating for different target scattering properties, local reflections and fluctuations of ambient light. The desired spatial modulation of illumination is obtained by a digital light projector, used to illuminate the scene with an arbitrary spatial distribution of light intensity, designed to improve feature extraction in the region of interest. The spatial distribution of illumination is optimized by running a genetic algorithm. An image quality estimator is used to close the feedback loop and to stop iterations once the desired image quality is reached. The technique proves particularly valuable for optimizing the spatial illumination distribution in the region of interest, with the remarkable capability of the genetic algorithm to adapt the light distribution to very different target reflectivity and ambient conditions. The final objective of the proposed technique is the improvement of the matching score in the recognition of parts through matching algorithms, hence of the diagnosis of machine vision-based quality inspections. The procedure has been validated both by a numerical model and by an experimental test, referring to a significant problem of quality control for the washing machine manufacturing industry: the recognition of a metallic clamp. Its applicability to other domains is also presented, specifically for the visual inspection of shoes with retro-reflective tape and T-shirts with paillettes.

Simultaneous Control of Light Polarization and Phase Distributions Using Plasmonic Metasurfaces

Harnessing light for modern photonic applications often involves the control and manipulation of light polarization and phase. Traditional methods require a combination of multiple discrete optical components, each of which contributes to a specific functionality. Here, plasmonic metasurfaces are proposed that accomplish the simultaneous manipulation of polarization and phase of the transmitted light. Arbitrary spatial field distribution of the optical phase and polarization direction can be obtained. The multifunctional metasurfaces are validated by demonstrating a broadband near‐perfect anomalous refraction with controllable linear polarization through introducing a constant phase gradient along the interface. Furthermore, the power of the proposed metasurfaces is demonstrated by generating a radially polarized beam. The new degrees of freedom of metasurfaces facilitate arbitrary manipulation of light and will profoundly affect a wide range of photonic applications.