Straight-line Approximation Research Articles

Influence of nano-sized horizontal inhomogeneities on surface profiling by means of XPS

Quantitative analysis of thin films surface is performed by means of X-ray electron spectroscopy (XPS) according to a calculation model assuming surface layers of the target to be homogeneous and parallel. However, almost every surface of an ultra-thin film is rough. A study of such surface using the plane-parallel layer model will lead to incorrect results. This work proposes to use the model of inhomogeneous stochastic nano-structured surface layer for ultra-thin film profiling. Surface stochastic nano-structured inhomogeneities are described by the normal Gauss distribution function. To determine these inhomogeneities, three parameters are specified: dispersion (spread of thicknesses by the layer), mean and maximal thickness of the surface layer. For the first time, the type of X-ray photoelectron spectrum of an inhomogeneous stochastic nano-structured surface is found that is determined by functions of photoelectron production and transmission through that surface layer. The designed model is based on the following assumptions: photoelectrons are produced in substance and travel straight-forward (Straight Line Approximation) along the surface, photoelectron flux density decreases in the layer according to the Bouguer–Lambert law, photoelectrons of different energies lose energy differently, photoelectron energy losses in bulk and on surface differ. Modeling of X-ray photoelectron spectra of an oxidized metal film is performed using different models: homogeneous plane-parallel layers, an island nano-structured surface layer and an inhomogeneous stochastic nano-structured surface layer. Ranges of applicability of plane-parallel layer models and simple periodical nano-structured island surface layer for inhomogeneous stochastic nano-structured surface profiling are determined. The model of homogeneous plane-parallel layers shows satisfactory profiling results by some values of parameters of an inhomogeneous stochastic surface layer. It is shown that the model of a simple periodically nano-structured island layer leads to inadequate results by profiling of an inhomogeneous stochastic surface. The investigation shows that for more accurate profiling of an inhomogeneous ultra-thin film, it is necessary to consider inhomogeneity of a real surface, otherwise the calculated results would not match the true profile.

Precise and analytical calculation of interface surface area in sharp interfaces and multiphase modeling

Various kinds of Piecewise Linear Interface Calculations (PLIC) are commonly used in Computational Fluid Dynamics (CFD) for multiphase flows. Here, a new method is proposed to calculate the interface size for CFD simulations. This PLIC method with the modifier, Analytic Size Based [method], (PLIC-ASB), being that the calculation requires a symbolic equation and no approximation or numerical methods. The primary advantage of the PLIC-ASB is maintaining a sharp interface and providing for physics-based (not iterative or empirically derived factors) mass transfer due to the cell-by-cell accuracy. Along with the sharp interface, this method leads to precise interface displacements and suppresses parasitic velocities; altogether, this means an accurate model of the temperature distribution near the interface can be achieved. The PLIC-ASB method was compared directly against the VOF gradient method (most prevalent PLIC in multiphase simulations). Static testing for accuracy on various geometric shapes expressed as the color function on representative grids of cells. The PLIC-ASB had a better result than the VOF gradient method, with an average relative error of 3% and 13%, respectively. Spherical bubble growth simulations were performed with customized ANSYS-Fluent. Both interface calculation methods were tested. Foremost, the PLIC-ASB method produced experimentally and theoretically anticipated results. Parasitic velocities were problematic in the VOF gradient method simulations but only minor with the use of PLIC-ASB. Further, a trend of accuracy improving with reduced cell size was found with the PLIC-ASB, whereas no trend was present with the VOF-gradient method. The PLIC-ASB method has the characteristic limitations of any PLIC method, most notably requiring a straight-line approximation to suitably represent the multiphase interface; however, the straightforward implementation and accuracy make broad adoption reasonable.

A Proton Computed Tomography Demonstrator for Stopping Power Measurements

Particle therapy is an established method to treat deep-seated tumours using accelerator-produced ion beams. For treatment planning, the precise knowledge of the relative stopping power (RSP) within the patient is vital. Conversion errors from x-ray computed tomography (CT) measurements to RSP introduce uncertainties in the applied dose distribution. Using a proton computed tomography (pCT) system to measure the SP directly could potentially increase the accuracy of treatment planning. A pCT demonstrator, consisting of double-sided silicon strip detectors (DSSD) as tracker and plastic scintillator slabs coupled to silicon photomultipliers (SiPM) as a range telescope, was developed. After a significant hardware upgrade of the range telescope, a 3D tomogram of an aluminium stair phantom was recorded at the MedAustron facility in Wiener Neustadt, Austria. In total, 80 projections with 6.5 × 105 primary events were acquired and used for the reconstruction of the RSP distribution in the phantom. After applying a straight-line approximation for the particle path inside the phantom, the most probable value (MPV) of the RSP distribution could be measured with an accuracy of 0.59%. The RSP resolution inside the phantom was only 9.3% due to a limited amount of projections and measured events per projection.

Diffeomorphic Particle Image Velocimetry

The existing particle image velocimetry (PIV) do not consider the curvature effect of the non-straight particle trajectory, because it seems to be impossible to obtain the curvature information from a pair of particle images. As a result, the computed vector underestimates the real velocity due to the straight-line approximation, that further causes a systematic error for the PIV instrument. In this work, the particle curved trajectory between two recordings is firstly explained with the streamline segment of a steady flow (diffeomorphic transformation) instead of a single vector, and this idea is termed as diffeomorphic PIV. Specifically, a deformation field is introduced to describe the particle displacement, i.e., we try to find the optimal velocity field, of which the corresponding deformation vector field agrees with the particle displacement. Because the variation of the deformation function can be approximated with the variation of the velocity function, the diffeomorphic PIV can be implemented as iterative PIV. That says, the diffeomorphic PIV warps the images with deformation vector field instead of the velocity, and keeps the rest as same as iterative PIVs. Two diffeomorphic deformation schemes -- forward diffeomorphic deformation interrogation (FDDI) and central diffeomorphic deformation interrogation (CDDI) -- are proposed. Tested on synthetic images, the FDDI achieves significant accuracy improvement across different one-pass displacement estimators (cross-correlation, optical flow, deep learning flow). Besides, the results on three real PIV image pairs demonstrate the non-negligible curvature effect for CDI-based PIV, and our FDDI provides larger velocity estimation (more accurate) in the fast curvy streamline areas. The accuracy improvement of the combination of FDDI and accurate dense estimator means that our diffeomorphic PIV paves a new way for complex flow measurement.

Effect of nanocoating morphology on the signal of X-ray Photoelectron Spectroscopy

The paper considers the application of the traditional X-ray photoelectron spectroscopy (XPS) methodology: the Overlayer Thickness Determination for the analysis of coating parameters. In particular situations considered in this work, it is energetically favorable for the atoms of the coating to form clusters, but not be evenly distributed on the surface of the substrate material. The change in the XPS signal is analyzed in situations when the coating is not a plane-parallel homogeneous layer, but an island (cluster) structure. The mathematical model of the XPS signal formation is considered for the case of the cluster covering in the form of parallelepipeds. Photoelectron path distributions (in the coating material) analysis indicated a strong dependence of the signal on the viewing angle. For the purpose of analysis, experimental spectra were obtained for several samples: gold depositions of various thicknesses on a silicon substrate. The spectra were measured for different viewing angles of photoelectrons and interpreted within the Straight Line Approximation (SLA). It is shown that proposed simplest model of an island coating allows to describe the effect of a decrease in the value of the effective average coating thickness, determined in plane-parallel geometry, with an increase in the viewing angle, observed in XPS experiments with angular resolution.

Generation and Optimization of interpolation approximation algorithm based on Laser Icon Contour Generation

Point-by-point comparison interpolation is a widely used algorithm in laser marking system. This algorithm plays a very important role in controlling the laser trajectory and fitting the image trajectory. Because the point-by-point comparison interpolation method has the characteristics of intuitive operation, uniform pulse output and convenient adjustment, it is a kind of interpolation algorithm which is more suitable for the application of marking machine system. In order to improve the marking efficiency of vector text in laser marking system, by analyzing the outline structure of TrueType font and the properties of Bezier curve, an optimization algorithm for straight line approximation of TrueType font outline is presented, and the theoretical analysis and experimental verification are carried out. Firstly, the Bezier curve in the TrueType font outline is segmented according to the deCasteljau recursive algorithm, and then the curve is replaced by the connection of the head and tail control points. Finally, the approximate line segment is interpolated to generate marking data, and the straight line approximation outline is compared with the standard TrueType font outline. The results show that under the condition of satisfying the accuracy, the algorithm has the advantages of simple calculation process and a small number of nodes, and improves the marking efficiency of vector text. The traditional point-by-point comparison interpolation algorithm has some problems such as low precision and slow speed. In order to improve the performance of the algorithm, the traditional point-by-point comparison interpolation algorithm is improved, and the calculation and simulation are carried out. The results show that the accuracy and speed of the improved interpolation algorithm are obviously improved. The patch is extracted from the point cloud data, and the feature patch is generated by patch growth and fusion, and the feature line is constructed quickly according to the proposed patch two-way index method, and finally the point cloud plane contour is generated. Experiments show that this algorithm can generate point cloud contours quickly, accurately and effectively.

First application of the GPU-based software framework TIGRE for proton CT image reconstruction.

In proton therapy, the knowledge of the proton stopping power, i.e. the energy deposition per unit length within human tissue, is essential for accurate treatment planning. One suitable method to directly measure the stopping power is proton computed tomography (pCT). Due to the proton interaction mechanisms in matter, pCT image reconstruction faces some challenges: the unique path of each proton has to be considered separately in the reconstruction process adding complexity to the reconstruction problem. This study shows that the GPU-based open-source software toolkit TIGRE, which was initially intended for X-ray CT reconstruction, can be applied to the pCT image reconstruction problem using a straight line approach for the proton path. This simplified approach allows for reconstructions within seconds. To validate the applicability of TIGRE to pCT, several Monte Carlo simulations modeling a pCT setup with two Catphan® modules as phantoms were performed. Ordered-Subset Simultaneous Algebraic Reconstruction Technique (OS-SART) and Adaptive-Steepest-Descent Projection Onto Convex Sets (ASD-POCS) were used for image reconstruction. Since the accuracy of the approach is limited by the straight line approximation of the proton path, requirements for further improvement of TIGRE for pCT are addressed.

Investigation of monolayer and submonolayer films using X-ray photoelectron spectroscopy

A method of layer thickness determination by X-ray photoelectron spectroscopy (XPS) is analyzed. Angle-resolved XPS spectra measured for three samples (gold films of different thicknesses located on top of silicon substrates) have been interpreted by the straight line approximation (SLA) model. Two configurations of films were considered: (i) a flat surface of a semi-infinite layer (substrate) is covered with a flat homogeneous layer, (ii) coating constitutes an island (cluster) structure. It is shown that the simplest model of an island coating makes it possible to qualitatively explain the effect of decreasing of the effective average coating thickness observed in the angle-resolved XPS experiments.

Method for solving plane unsteady contact problems for rigid stamp and elastic half-space with a cavity of arbitrary geometry and location

In the work, the process of unsteady contact interaction of rigid stamp and elastic half-space having a recessed cavity of arbitrary geometry and location with a smooth boundary was investigated. Three variants of contact conditions are considered: free slip, rigid coupling, and bonded contact. The method for solving the problem is constructed using boundary integral equations. To obtain boundary integral equations, the dynamic reciprocal work theorem is used. The kernels of integral operators are bulk Green functions for the elastic plane. Because of straight-line approximations of the domain boundaries with respect to the spatial variable and straight-line approximations of the boundary values of the desired functions with respect to time, the problem is reduced to solving a system of algebraic equations with respect to the pivotal values of the desired displacements and stresses at each time interval. One of the axes is directed along the regular boundary of half-space, the second - deep into half-space.

A Novel Module Independent Straight Line-Based Fast Maximum Power Point Tracking Algorithm for Photovoltaic Systems

The maximum power point tracking (MPPT) algorithm has become an integral part of many charge controllers that are used in photovoltaic (PV) systems. Most of the existing algorithms have a compromise among simplicity, tracking speed, ability to track accurately, and cost. In this work, a novel “straight-line approximation based Maximum Power Point (MPP) finding algorithm” is proposed where the intersections of two linear lines have been utilized to find the MPP, and investigated for its effectiveness in tracking maximum power points in case of rapidly changing weather conditions along with tracking speed using standard irradiance and temperature curves for validation. In comparison with a conventional Perturb and Observe (P&O) method, the Proposed method takes fewer iterations and also, it can precisely track the MPP s even in a rapidly varying weather condition with minimal deviation. The Proposed algorithm is also compared with P&O algorithm in terms of accuracy in duty cycle and efficiency. The results show that the errors in duty cycle and power extraction are much smaller than the conventional P&O algorithm.

Post-Born corrections to the one-point statistics of (CMB) lensing convergence obtained via large deviation theory

ABSTRACT Weak lensing of galaxies and cosmic microwave background (CMB) photons through the large-scale structure of the Universe is one of the most promising cosmological probes with upcoming experiments dedicated to its measurements such as Euclid/LSST and CMB Stage 4 experiments. With increasingly precise measurements, there is a dire need for accurate theoretical predictions. In this work, we focus on higher order statistics of the weak-lensing convergence field, namely its cumulants such as skewness and kurtosis and its one-point probability distribution function (PDF), and we quantify using perturbation theory the corrections coming from post-Born effects, meaning beyond the straight-line and independent lens approximations. At first order, two such corrections arise: lens–lens couplings and geodesic deviation. Though the corrections are small for low source redshifts (below a few per cent) and therefore for galaxy lensing, they become important at higher redshifts, notably in the context of CMB lensing, where the non-Gaussianities computed from tree-order perturbation theory are found to be of the same order as the signal itself. We include these post-Born corrections on the skewness in a prediction for the one-point convergence PDF obtained with large deviation theory and successfully test these results against numerical simulations. The modelled PDF is indeed shown to perform better than the per cent for apertures above ∼10 arcmin and typically in the 3σ region around the mean.

Finger Vein Recognition using Straight Line Approximation based on Ensemble Learning

Human identity recognition and protection of information security are current global concerns in this age of increasing information growth. Biometrics approach of defining identity is considered as one of the highly potential approaches due to its internal feature that is difficult to be artificially recreated, stolen and/or forgotten. The new recognition system based on finger vein is a unique method depending on physiological traits and parameters of the vein patterns for the human. Published works on finger vein identification have hitherto ignored the power of aggregating different types of features and classifiers in improving the performance of the biometric recognition system. In this paper, we developed a novel feature approach named as straight line approximator (SLA) for extending the feature space of vein pattern using a public data set SDUMLA-HMT comprising about 3,816 images of finger vein for 160 persons. Furthermore, we applied a set of extreme learning machine (ELM) and support vector machine (SVM) classifier in different kernels. Then, we used the combination rules to improve the performance of the system. The experiment result of the proposed method achieved an accuracy of 87% using (DS and GWAR) rules at rank 1, while the accuracy of DS rule 93% and GWAR rule 92% at rank 5.

Depth Profiling Using Reflected Electron Spectroscopy

Nondestructive depth profiling method based on reflected electron spectroscopy is presented. Large loss spectra of wide energy range is analyzed. Spectra analysis is performed using two approaches: boundary problem solution using invariant imbedding method and approximate interpretation based on Straight Line Approximation with correction coefficients, which depend on ration of evaporated layer thickness and transport mean free path. It is shown that the transport mean free path, not the inelastic mean free path, limits the information depth of the method in opposite of X-ray photoelectron spectroscopy, elastic peak electron spectroscopy. This fact significantly increase depths that can be analyzed using presented method. Thickness of the evaporated Nb layer on the Si substrate is determined.

A DATA DRIVEN METHOD FOR FLAT ROOF BUILDING RECONSTRUCTION FROM LiDAR POINT CLOUDS

Abstract. 3D building modeling is one of the most important applications in photogrammetry and remote sensing. Airborne LiDAR (Light Detection And Ranging) is one of the primary information sources for building modeling. In this paper, a new data-driven method is proposed for 3D building modeling of flat roofs. First, roof segmentation is implemented using region growing method. The distance between roof points and the height difference of the points are utilized in this step. Next, the building edge points are detected using a new method that employs grid data, and then roof lines are regularized using the straight line approximation. The centroid point and direction for each line are estimated in this step. Finally, 3D model is reconstructed by integrating the roof and wall models. In the end, a qualitative and quantitative assessment of the proposed method is implemented. The results show that the proposed method could successfully model the flat roof buildings using LiDAR point cloud automatically.

Mutual effects of thermal radiations and thermal stratification on tangent hyperbolic fluid flow yields by both cylindrical and flat surfaces

The characteristics of tangent hyperbolic fluid flow in the presence of both thermal radiation and thermal stratification effects are not discussed until now especially by way of an inclined cylindrical surface. Therefore, an endeavour as a comparative study is reported to offered numerical solution for tangent hyperbolic fluid model towards both cylindrical and flat stretching surfaces. The physical situation which also includes the noteworthy effects namely, stagnation point region, mixed convection, magnetic field individualities and heat generation is translated in terms of partial differential equations and for solution purpose a computational algorithm is executed. The obtained results are provided by way of both graphical and tabular outcomes. It is observed that the temperature profile is an increasing function of thermal radiation parameter but opposite trends are noticed for positive values of thermal stratification parameter. In addition, straight line approximation is accomplished to scrutinize the impact of mixed convection and an inclination effects on skin friction coefficient while the impact of thermal radiation and thermal stratification parameters are provided on heat transfer rate.

Energy straggling cross section for antiproton-atom collisions

SynopsisWe present benchmark simulations of the energy straggling cross section for antiprotons colliding with hydrogen and helium. We solve the one- and two-particle Schrödinger equation numerically within the framework of the straight-line impact-parameter approximation. Our results provide first evidence for the convergence of the ab-initio simulation toward the classical Bohr straggling cross section proposed a century ago.

Measuring (subglacial) bedform orientation, length, and longitudinal asymmetry – Method assessment

Geospatial analysis software provides a range of tools that can be used to measure landform morphometry. Often, a metric can be computed with different techniques that may give different results. This study is an assessment of 5 different methods for measuring longitudinal, or streamlined, subglacial bedform morphometry: orientation, length and longitudinal asymmetry, all of which require defining a longitudinal axis. The methods use the standard deviational ellipse (not previously applied in this context), the longest straight line fitting inside the bedform footprint (2 approaches), the minimum-size footprint-bounding rectangle, and Euler’s approximation. We assess how well these methods replicate morphometric data derived from a manually mapped (visually interpreted) longitudinal axis, which, though subjective, is the most typically used reference. A dataset of 100 subglacial bedforms covering the size and shape range of those in the Puget Lowland, Washington, USA is used. For bedforms with elongation > 5, deviations from the reference values are negligible for all methods but Euler’s approximation (length). For bedforms with elongation < 5, most methods had small mean absolute error (MAE) and median absolute deviation (MAD) for all morphometrics and thus can be confidently used to characterize the central tendencies of their distributions. However, some methods are better than others. The least precise methods are the ones based on the longest straight line and Euler’s approximation; using these for statistical dispersion analysis is discouraged. Because the standard deviational ellipse method is relatively shape invariant and closely replicates the reference values, it is the recommended method. Speculatively, this study may also apply to negative-relief, and fluvial and aeolian bedforms.

The Melting Point of Palladium Using Miniature Fixed Points of Different Ceramic Materials: Part II—Analysis of Melting Curves and Long-Term Investigation

Fifteen miniature fixed-point cells made of three different ceramic crucible materials (\(\hbox {Al}_{2}\hbox {O}_{3}\), \(\hbox {ZrO}_{2}\), and \(\hbox {Al}_{2}\hbox {O}_{3}(86\,\%)+\hbox {ZrO}_{2}\)(14 %)) were filled with pure palladium and used to calibrate type B thermocouples (Pt30 %Rh/Pt6 %Rh). A critical point by using miniature fixed points with small amounts of fixed-point material is the analysis of the melting curves, which are characterized by significant slopes during the melting process compared to flat melting plateaus obtainable using conventional fixed-point cells. The method of the extrapolated starting point temperature using straight line approximation of the melting plateau was applied to analyze the melting curves. This method allowed an unambiguous determination of an electromotive force (emf) assignable as melting temperature. The strict consideration of two constraints resulted in a unique, repeatable and objective method to determine the emf at the melting temperature within an uncertainty of about \(0.1\,\upmu \hbox {V}\). The lifetime and long-term stability of the miniature fixed points was investigated by performing more than 100 melt/freeze cycles for each crucible of the different ceramic materials. No failure of the crucibles occurred indicating an excellent mechanical stability of the investigated miniature cells. The consequent limitation of heating rates to values below \({\pm }3.5\,\hbox {K}\,\hbox {min}^{-1}\) above \(1100\,{^{\circ }}\hbox {C}\) and the carefully and completely filled crucibles (the liquid palladium occupies the whole volume of the crucible) are the reasons for successfully preventing the crucibles from breaking. The thermal stability of the melting temperature of palladium was excellent when using the crucibles made of \(\hbox {Al}_{2}\hbox {O}_{3}(86\,\%)+\hbox {ZrO}_{2}(14\,\%)\) and \(\hbox {ZrO}_{2}\). Emf drifts over the total duration of the long-term investigation were below a temperature equivalent of about 0.1 K–0.2 K.

Histotripsy pulse-reflection for 3D image forming and bubble cloud localization in transcranial applications

Here, we present results from experiments using histotripsy pulses scattered off the surface of the skull, as well as bubble clouds generated within, to reconstruct 3D images of the exterior skull surface and localize bubbles within. These capabilities have the potential to provide image coregistration and real-time ultrasound monitoring for transcranial histotripsy treatment, without the need for MRI guidance. Histotripsy pulses were delivered to an ex vivo human skullcap mounted centrally within a 500 kHz, 256-element histotripsy transducer with transmit-receive capable elements. Straight-line ray tracing approximations based on the times-of-flight of the emitted pulses and the known geometry of the array were used to calculate points on the skull surface and to localize bubble clouds generated within. Using these methods, we were able to accurately locate and orient the skull within the array and generate a 3D map of its surface for coregistration with an a priori 3D scan. The points calculated based o...

Optimal placement of public-access AEDs in urban environments

Use of public-access Automated External Defibrillators (AEDs) is showing promising results in decreasing collapse-to-shock times among Sudden Cardiac Arrest (SCA) patients which is associated with improved patient outcomes. Bystander access to these medical devices ensure that the necessary care to victims of SCA is provided prior to arrival of emergency responders. Prior studies have suggested methods for deploying AEDs for public use by implementing mathematical optimization based on historic incidences of SCA. The purpose of this study is to improve upon these studies by developing a novel method for generating placement plans in urban environments. The novelty of this study is: (1) the use of route-based walking time instead of straight-line approximations; (2) introduction of temporal availability in deployed devices to account for location hours-of-operation; (3) use of a multi-objective optimization to balance decision-maker objectives; and (4) the implementation of an interactive decision-maker tool for observing effects on benefits and costs. The approach is deployed and evaluated for a case study in the city of Hoboken, New Jersey. This case study is simulated with a resulting average decrease of time-to-retrieve by 98.06s indicating an estimated 11.44–16.30% survival probability improvement using our optimization technique compared to a baseline optimization.