The leaking soft stadium

We soften the non zero y-boundary on a Bunimovich like quarter-stadium. The smoothing procedure is performed via an exponent monomial potential, the system becomes partially reflective, preserving the particle’s translation and rotational motion. By increasing the exponent value, the stadium’s boundaries become rigid and the system’s dynamics reaches a chaotic regime. We set a leaking soft stadium family by opening a limited region located at some place of its basis’s boundary, throughout which the particles can leak out. This work is an extension of our recently reported paper on this matter. We chase the particle’s trajectory and focus on the stadium transient behavior by means of the statistical analysis of the survival probability on the marginal orbits that never leave the system, the so called bouncing ball orbits. We compare these family orbits with the billiard’s transient chaos orbits.

Edge-Preserving Denoising of Image Sequences

To monitor the Earth’s surface, the satellite of the NASA Landsat program provides us image sequences of any region on the Earth constantly over time. These image sequences give us a unique resource to study the Earth’s surface, changes of the Earth resource over time, and their implications in agriculture, geology, forestry, and more. Besides natural sciences, image sequences are also commonly used in functional magnetic resonance imaging (fMRI) of medical studies for understanding the functioning of brains and other organs. In practice, observed images almost always contain noise and other contaminations. For a reliable subsequent image analysis, it is important to remove such contaminations in advance. This paper focuses on image sequence denoising, which has not been well-discussed in the literature yet. To this end, an edge-preserving image denoising procedure is suggested. The suggested method is based on a jump-preserving local smoothing procedure, in which the bandwidths are chosen such that the possible spatio-temporal correlations in the observed image intensities are accommodated properly. Both theoretical arguments and numerical studies show that this method works well in the various cases considered.

On the Consequences of Using Moving Window Segmentation to Analyze the Structural Stand Heterogeneity and Debatable Patchiness of Old-Growth Temperate Forests

(1) Background: Early research in natural forests on decennia implanted conviction concerning the patchy patterns of their structural heterogeneity. Due to the variety of methodological approaches applied, verification of this fundamental assumption remains open. The aim of this study was to discuss the methodological limitations associated with the use of moving windows with overlap for the delineation of homogeneous patch mosaics in forest ecosystems. (2) Methods: The “patchiness” hypothesis was tested in six old-growth forests formed by Abies alba Mill., Fagus sylvatica L., and Picea abies (L.) H. Karst. localized in Bosnia and Herzegovina and southern Poland. In each stand, the tree diameter at breast height (dbh) was recorded on circular sample plots of 154 m2 regularly distributed in a 20 × 20 m lattice over an area of 10 ha. (3) Results: Computer simulations showed that patch classification based on overlapping windows results in apparent patchiness, even for completely randomized tree distributions. Analyses carried out on the empirical data indicated prevalent random patterns of structural heterogeneity. (4) Conclusions: Patchiness is not a universal feature of the investigated forest communities. The size of the moving window and the noise-smoothing procedure exert strong effects on the biasedness of patch classification, the frequency of structural types, and the mean patch size.

ANALYSIS OF FINITE ELEMENT SOLUTION CONSERVATIVE SMOOTHING INFLUENCE ON THE ZERO ENERGY MODES SUPPRESSION

The problem of high-speed penetration of a non-deformable cylinder into a steel plate is considered. The defining system of equations is formulated in Lagrange variables in a three-dimensional formulation. The equation of motion is derived from virtual work capacities balance. Kinematic relations are recorded in the metric of the current state. The relations of the flow theory with kinematic and isotropic hardening are used as equations of state. The contact interaction of the cylinder and the plate is modeled by non-penetration conditions. The numerical solution of the problem under given boundary and initial conditions is based on the moment scheme of the finite element method and “cross” type explicit time integration scheme. To discretize the defining system of equations with respect to spatial variables, 8-node isoparametric finite elements with multilinear form functions are used. To suppress the high-frequency oscillations of the numerical solution, the procedure of nodal displacement velocities conservative smoothing is used. The smoothing algorithm is based on the momentum conservation law, focused on finite element grids consisting of blocks that are mutually unambiguously mapped to a unit cube. To analyze the nodal displacement velocities monotonicity, the numerical solution splitting in the directions of the finite element grid lines is used. As the results of computer modeling have shown, the finite elements of the plate are exposed large deformations and rotation angles as a rigid whole during local intense dynamic loading. The conservative smoothing procedure influence on the numerical solution stability is analyzed. It is shown that in the problem under consideration, without applying the conservative smoothing procedure, zero-energy modes develop in the contact zone in the finite-element grid of the plate (an hourglass-type instability) and the collision process cannot be modeled before the cylinder rebounds.

Finite-element EM modelling on hexahedral grids with an FD solver as a pre-conditioner

SUMMARY The finite-element (FE) method is one of the most powerful numerical techniques for modelling 3-D electromagnetic fields. At the same time, there still exists the problem of efficient and economical solution of the respective system of FE equations in the frequency domain. In this paper, we concentrate on modelling with adapted hexahedral or logically rectangular grids. These grids are easy to generate, yet they are flexible enough to incorporate real topography and seismic horizons. The goal of this work is to show how a finite-difference (FD) solver can be used as a pre-conditioner for hexahedral FE modelling. Applying the lowest order Nédélec elements, we present a novel pre-conditioned iterative solver for the arising system of linear equations that combines an FD solver and simple smoothing procedure. The particular FD solver that we use relies on the implicit factorization of the horizontally layered earth matrix. We assessed runtime and accuracy of the presented approach on synthetic and real resistivity models (topography of the Black Sea continental slope). We further compared performance of our program versus publicly available Mare2DEM, ModEM and MUMPS programs/libraries. Our examples involve plane-wave and controlled source modelling. The numerical examples demonstrate that the presented approach is fast and robust for models with moderate contrast, supports highly deformed cells, and is quite memory-economical.

Modelling the basal hydrology under the Greenland Ice Sheet

<p>Subglacial hydrology plays an important role in the evolution of ice dynamics. Primarily, it affects basal processes such as basal sliding. Further, subglacial water exiting a calving front incites submarine melt, increasing calving, resulting in a thinning of the interior ice sheet. Knowledge of it is therefore crucial towards the development and improvement of ice sheet models. We implement a model representing the routing of subglacial water below the Greenland ice sheet in either a one, four or eight directional manner. Due to its computational efficiency, the model is suited for coupling with continental scale ice sheet models on very high resolutions (e.g. 150 m).</p><p>Routing depends on the hydraulic potential of individual grid cells which is therefore heavily dependent on accurate estimates of the ice thickness as well as the grid utilized. Sensitivity analyses brought to life that the routing exhibits artefacts resulting in significant flow diversions on high resolutions if the gradients are only considered over the distance of a single grid cell, this is overcome by incorporating a smoothing procedure.</p><p>With the basal water model in place and input of the basal melt rate from the VUB Greenland Ice Sheet Model (GISM) as well as runoff input from the Modèle Athmospherique Régional (MAR), we calculate the inflow of freshwater to several reference fjords for the last thirty years and investigate its temporal and spatial patterns. Jakobshavn Isbrae experiences by far the most freshwater inflow compared to the other reference fjords. Despite limited runoff in the northeast of Greenland, high basal melt rates and a significant catchment area provide the outlets of the Northeast Greenland Ice Stream (NEGIS) with substantial inflow too.</p>

FIRST RESULTSOF THESEISMICTOMOGRAPHICGEOTRAVERSE "VINNYTSIA – TAGANROG" RESEARCH

Methodological aspects and results of studying of the stratigraphic section of the upper mantle along the seismic tomographic geotraverse "Vinnytsia – Taganrog" are considered in the article. To localize mantle anomalies associated with changes in the composition, density of the substrate, temperature, etc., an analysis of the curves of the first and second velocity gradients was used to search for the inflection points of the vp curve. A velocity curve was obtained by constructing a seismotomographic model using the Taylor approximation method. Before the curvature analysis, a smoothing procedure was carried out in accordance with the wavelength. This procedure is important for screening false anomalies, the size of which is responsible for Fresnel zones, since the resolution of the seismic wave has the dimension of the Fresnel zones. According to this technique, the curves of the first and second velocity gradients vp were calculated for the upper mantle under the main tectonic structures of the Ukrainian Shield along the "Vinnytsia – Taganrog" geotraverse. The profile crosses the Podol, Bug megablocks, Golovanev suture zone, Ingul megablock, Kryvyy-Rig-Kremenchug suture zone, Middle-Dnipro megablock, Orekhovo-Pavlograd suture zone and Azov megablock. According to the results, the most significant features of the mantle structure were identified in the depth interval of 50–750 km. A transregional tectonic zone was distinguished (between points 30.0E, 49N and 32.0E, 48.25N), over which the Golovan suture zone (GSZ) and the eastern part of the Bug-Ros megablock and the western part of Ingul, where significant violations of the common mantle border of 660 km are observed – a border between the upper and middle mantle. Under the Podol megablock, this border is located at a depth of 550–560 km. Under GSZ it rises to 450–460 km, and to the east of the suture zone it drops sharply to 660-670 km, where it takes a subhorizontal position. A sharp jump to marks of 450–460 km shows the global breakdown zone and the nature of the contact between different geodynamic mantle regions under the modern platform.

Accurate Viscoelastic Large Deformation Analysis Using F-Bar Aided Edge-Based Smoothed Finite Element Method for 4-Node Tetrahedral Meshes (F-BarES-FEM-T4)

A state-of-the-art tetrahedral smoothed finite element method, F-barES-FEM-T4, is demonstrated on viscoelastic large deformation problems. The stress relaxation of viscoelastic materials brings near incompressibility when the long-term Poisson’s ratio is close to 0.5. The conventional hybrid 4-node tetrahedral (T4) elements cannot avoid the shear locking and pressure checkerboarding issues, meanwhile F-barES-FEM-T4 can suppress these issues successfully by adopting the edge-based smoothed finite element method (ES-FEM) with the aid of the F-bar method and the cyclic smoothing procedure. A few examples of analyses verify that F-barES-FEM-T4 is locking-free and pressure oscillation-free in viscoelastic analyses as well as in nearly incompressible hyperelastic or elastoplastic analyses.

Identification of Spikes in Time Series

Researchers interested in the effects of exposure spikes on an outcome need tools to identify unexpectedly high values in a time series. However, the best method to identify spikes in time series is not known. This paper aims to fill this gap by testing the performance of several spike detection methods in a simulation setting. We created simulations parameterized by monthly violence rates in nine California cities that represented different series features, and randomly inserted spikes into the series. We then compared the ability to detect spikes of the following methods: ARIMA modeling, Kalman filtering and smoothing, wavelet modeling with soft thresholding, and an iterative outlier detection method. We varied the magnitude of spikes from 10 to 50 % of the mean rate over the study period and varied the number of spikes inserted from 1 to 10. We assessed performance of each method using sensitivity and specificity. The Kalman filtering and smoothing procedure had the best overall performance. We applied each method to the monthly violence rates in nine California cities and identified spikes in the rate over the 2005–2012 period.

SEPARATION OF DIFFRACTION SPECTRA BY PRINCIPAL COMPONENT METHOD BY THE EXAMPLE OF ARIFON DRUG

The article deals with the results of experimental studies on statistical processing of diffraction spectra of solid drugs for the purpose of their separation and identification. Diffractograms of the original and falsified drugs Arifon were used for the study. They were obtained on a desktop diffractometer Difray 401 produced by Scientific Instruments Inc. (Saint Petersburg, Russia). The research was conducted in the Scilab environment distributed under a free license. The captured diffraction spectra were processed using a smoothing procedure that eliminated the influence of a random component in the original data. Analysis of the results of smoothing by the moving average method showed that the smoothing algorithm with the window 41 point is most preferable. The results of statistical processing of diffractograms of the drugs investigated by the principal component analysis (PCA) in graphical and numerical form, which showed good convergence and efficiency of this method in the separation of diffraction spectra, are presented. The conducted studies make it possible to create a technique that allows identifying solid drugs by X-ray diffraction.