Evaluating the robustness of objective pilling classification with the two-dimensional discrete wavelet transform

Previously, we proposed a new method of frequency domain analysis based on the two-dimensional discrete wavelet transform to objectively measure pilling intensity in sample fabric images. We have further evaluated this method, and our results indicate that it is robust to small horizontal and/or vertical translations and to significant variations in the brightness of the image under analysis, and is sensitive to rotation and to dilation of the image. These results suggest that as long as precautions are taken to ensure fabric test samples are imaged under consistent conditions of weave/knit pattern alignment (rotation) and apparent interyarn pitch (dilation), the method will yield repeatable results. <br /

Optimisation of material properties for the modelling of large deformation manufacturing processes using a finite element model of the Gleeble compression test

The finite element modelling of manufacturing processes often requires a large amount of large plastic strain flow stress data in order to represent the material of interest over a wide range of temperatures and strain rates. Compression data generated using a Gleeble thermo-mechanical simulator is difficult to interpret due to the complex temperature and strain fields, which exist within the specimen during the test. In this study, a non-linear optimisation process is presented, which includes a finite element model of the compression process to accurately determine the constants of a five-parameter Norton–Hoff material model. The optimisation process is first verified using a reduced three-parameter model and then the full five-parameter model using a known set of constants to produce the target data, from which the errors are assessed. Following this, the optimisation is performed using experimental target data starting from a set of constants derived from the test data using an initial least-squares fit and also an arbitrary starting point within the parameter space. The results of these tests yield coefficients differing by a maximum of less than 10% and significantly improve the representation of the flow stress of the material

Integral transform solution of random coupled parabolic partial differential models

[EN] Random coupled parabolic partial differential models are solved numerically using random cosine Fourier transform together with non-Gaussian random numerical integration that captures the highly oscillatory behaviour of the involved integrands. Sufficient condition of spectral type imposed on the random matrices of the system is given so that the approximated stochastic process solution and its statistical moments are numerically convergent. Numerical experiments illustrate the results.Spanish Ministerio de Economia, Industria y Competitividad (MINECO); Agencia Estatal de Investigacion (AEI); Fondo Europeo de Desarrollo Regional (FEDER UE), Grant/Award Number: MTM2017-89664-PCasabán Bartual, MC.; Company Rossi, R.; Egorova, VN.; Jódar Sánchez, LA. (2020). Integral transform solution of random coupled parabolic partial differential models. Mathematical Methods in the Applied Sciences. 43(14):8223-8236. https://doi.org/10.1002/mma.6492S822382364314Bäck, J., Nobile, F., Tamellini, L., & Tempone, R. (2010). Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison. Spectral and High Order Methods for Partial Differential Equations, 43-62. doi:10.1007/978-3-642-15337-2_3Bachmayr, M., Cohen, A., & Migliorati, G. (2016). Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients. ESAIM: Mathematical Modelling and Numerical Analysis, 51(1), 321-339. doi:10.1051/m2an/2016045Ernst, O. G., Sprungk, B., & Tamellini, L. (2018). Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs). SIAM Journal on Numerical Analysis, 56(2), 877-905. doi:10.1137/17m1123079Sheng, D., & Axelsson, K. (1995). Uncoupling of coupled flows in soil—a finite element method. International Journal for Numerical and Analytical Methods in Geomechanics, 19(8), 537-553. doi:10.1002/nag.1610190804Mitchell, J. K. (1991). Conduction phenomena: from theory to geotechnical practice. Géotechnique, 41(3), 299-340. doi:10.1680/geot.1991.41.3.299Das, P. K. (1991). Optical Signal Processing. doi:10.1007/978-3-642-74962-9Ashkenazy, Y. (2017). Energy transfer of surface wind-induced currents to the deep ocean via resonance with the Coriolis force. Journal of Marine Systems, 167, 93-104. doi:10.1016/j.jmarsys.2016.11.019Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500-544. doi:10.1113/jphysiol.1952.sp004764Galiano, G. (2012). On a cross-diffusion population model deduced from mutation and splitting of a single species. Computers & Mathematics with Applications, 64(6), 1927-1936. doi:10.1016/j.camwa.2012.03.045Casabán, M. C., Company, R., & Jódar, L. (2019). Numerical solutions of random mean square Fisher‐KPP models with advection. Mathematical Methods in the Applied Sciences, 43(14), 8015-8031. doi:10.1002/mma.5942Casabán, M. C., Company, R., & Jódar, L. (2019). Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness. Mathematics, 7(9), 853. doi:10.3390/math7090853Shampine, L. F. (2008). Vectorized adaptive quadrature in MATLAB. Journal of Computational and Applied Mathematics, 211(2), 131-140. doi:10.1016/j.cam.2006.11.021Iserles, A. (2004). On the numerical quadrature of highly-oscillating integrals I: Fourier transforms. IMA Journal of Numerical Analysis, 24(3), 365-391. doi:10.1093/imanum/24.3.365Ma, J., & Liu, H. (2018). On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels. Symmetry, 10(7), 239. doi:10.3390/sym10070239Jódar, L., & Goberna, D. (1996). Exact and analytic numerical solution of coupled diffusion problems in a semi-infinite medium. Computers & Mathematics with Applications, 31(9), 17-24. doi:10.1016/0898-1221(96)00038-7Jódar, L., & Goberna, D. (1998). A matrix D’Alembert formula for coupled wave initial value problems. Computers & Mathematics with Applications, 35(9), 1-15. doi:10.1016/s0898-1221(98)00052-2Ostrowski, A. M. (1959). A QUANTITATIVE FORMULATION OF SYLVESTER’S LAW OF INERTIA. Proceedings of the National Academy of Sciences, 45(5), 740-744. doi:10.1073/pnas.45.5.740Ashkenazy, Y., Gildor, H., & Bel, G. (2015). The effect of stochastic wind on the infinite depth Ekman layer model. EPL (Europhysics Letters), 111(3), 39001. doi:10.1209/0295-5075/111/3900

Object knowledge modulates colour appearance

We investigated the memory colour effect for colour diagnostic artificial objects. Since knowledge about these objects and their colours has been learned in everyday life, these stimuli allow the investigation of the influence of acquired object knowledge on colour appearance. These investigations are relevant for questions about how object and colour information in high-level vision interact as well as for research about the influence of learning and experience on perception in general. In order to identify suitable artificial objects, we developed a reaction time paradigm that measures (subjective) colour diagnosticity. In the main experiment, participants adjusted sixteen such objects to their typical colour as well as to grey. If the achromatic object appears in its typical colour, then participants should adjust it to the opponent colour in order to subjectively perceive it as grey. We found that knowledge about the typical colour influences the colour appearance of artificial objects. This effect was particularly strong along the daylight axis

Computation of the real structured singular value via pole migration

peer-reviewedThe paper introduces a new computationally efficient algorithm to determine a lower bound on the real structured singular value . The algorithm is based on a pole migration approach where an optimization solver is used to compute a lower bound on real independent of a frequency sweep. A distinguishing feature of this algorithm from other frequency independent one-shot tests is that multiple localized optima (if they exist) are identified and returned from the search. This is achieved by using a number of alternative methods to generate different initial conditions from which the optimization solver can initiate its search from. The pole migration algorithm presented has also been extended to determine lower bounds for complex parametric uncertainties as well as full complex blocks. However, the results presented are for strictly real and repeated parametric uncertainty problems as this class of problem is the focus of this paper and are in general the most difficult to solve. Copyright (c) 2014 John Wiley & Sons, Ltd.ACCEPTEDpeer-reviewe

Defects and boundary layers in non-Euclidean plates

We investigate the behavior of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. In particular we show that are only two types of global minimizers -- deformations that remain flat and saddle shaped deformations with isolated regions of stretching near the edge of the annulus. We also show that there exist local minimizers with a periodic profile that have additional boundary layers near their lines of inflection. These additional boundary layers are a new phenomenon in thin elastic sheets and are necessary to regularize jump discontinuities in the azimuthal curvature across lines of inflection. We rigorously derive scaling laws for the width of these boundary layers as a function of the thickness of the sheet

Graphical user interfaces in an engineering educational environment

Graphical user interfaces (GUIs) are being increasingly used in the classroom to provide users of computer simulations with a friendly and visual approach to specifying all input parameters and increased configuration flexibility. In this study, the authors first describe a number of software and language options that are available to build GUIs. Subsequently, a comprehensive comparative assessment of possible alternatives is undertaken in the light of a benchmark educational program used in a course on computational fluid dynamics (CFD) at the University of Michigan. For the GUIs presented, their educational value with respect to flexible data entry and post-processing of results has been demonstrated. In addition, the authors offer recommendations for pros and cons of available options in terms of platform independence, ease of programming, facilitation of interaction with students, and flexibility. © 2005 Wiley Periodicals, Inc. Comput Appl Eng Educ 13: 48–59, 2005; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20029Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/35190/1/20029_ftp.pd

Revisiting Brownian motion as a description of animal movement: a comparison to experimental movement data

1) Characterization of patterns of animal movement is a major challenge in ecology with applications to conservation, biological invasions and pest monitoring. Brownian random walks, and diffusive flux as their mean field counterpart, provide one framework in which to consider this problem. However, it remains subject to debate and controversy. This study presents a test of the diffusion framework using movement data obtained from controlled experiments. 2) Walking beetles (Tenebrio molitor) were released in an open circular arena with a central hole and the number of individuals falling from the arena edges was monitored over time. These boundary counts were compared, using curve fitting, to the predictions of a diffusion model. The diffusion model is solved precisely, without using numerical simulations. 3) We find that the shape of the curves derived from the diffusion model is a close match to those found experimentally. Furthermore, in general, estimates of the total population obtained from the relevant solution of the diffusion equation are in excellent agreement with the experimental population. Estimates of the dispersal rate of individuals depend on how accurately the initial release distribution is incorporated into the model. 4) We therefore show that diffusive flux is a very good approximation to the movement of a population of Tenebrio molitor beetles. As such, we suggest that it is an adequate theoretical/modelling framework for ecological studies that account for insect movement, although it can be context specific. An immediate practical application of this can be found in the interpretation of trap counts, in particular for the purpose of pest monitoring