Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures

The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body

Efficient Localization of Discontinuities in Complex Computational Simulations

Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, the error and convergence rate of many approximation methods deteriorate substantially. This paper details a method for efficiently localizing discontinuities in the input parameter domain, so that the model output can be approximated as a piecewise smooth function. The approach comprises an initialization phase, which uses polynomial annihilation to assign function values to different regions and thus seed an automated labeling procedure, followed by a refinement phase that adaptively updates a kernel support vector machine representation of the separating surface via active learning. The overall approach avoids structured grids and exploits any available simplicity in the geometry of the separating surface, thus reducing the number of model evaluations required to localize the discontinuity. The method is illustrated on examples of up to eleven dimensions, including algebraic models and ODE/PDE systems, and demonstrates improved scaling and efficiency over other discontinuity localization approaches

Stellar Double Coronagraph: a multistage coronagraphic platform at Palomar observatory

We present a new instrument, the "Stellar Double Coronagraph" (SDC), a flexible coronagraphic platform. Designed for Palomar Observatory's 200" Hale telescope, its two focal and pupil planes allow for a number of different observing configurations, including multiple vortex coronagraphs in series for improved contrast at small angles. We describe the motivation, design, observing modes, wavefront control approaches, data reduction pipeline, and early science results. We also discuss future directions for the instrument.Comment: 25 pages, 12 figures. Correspondence welcome. The published work is open access and differs trivially from the version posted here. The published version may be found at http://iopscience.iop.org/article/10.1088/1538-3873/128/965/075003/met

The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries

We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase-field approximations of sharp domains. Leveraging the properties of the phase-field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase-field solutions of the Allen-Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase-field in the diffuse boundary region and a uniform mesh for the representation of the physics-based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty-type methods. In the context of imaging based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human vertebral body

Data-driven Soft Sensors in the Process Industry

In the last two decades Soft Sensors established themselves as a valuable alternative to the traditional means for the acquisition of critical process variables, process monitoring and other tasks which are related to process control. This paper discusses characteristics of the process industry data which are critical for the development of data-driven Soft Sensors. These characteristics are common to a large number of process industry fields, like the chemical industry, bioprocess industry, steel industry, etc. The focus of this work is put on the data-driven Soft Sensors because of their growing popularity, already demonstrated usefulness and huge, though yet not completely realised, potential. A comprehensive selection of case studies covering the three most important Soft Sensor application fields, a general introduction to the most popular Soft Sensor modelling techniques as well as a discussion of some open issues in the Soft Sensor development and maintenance and their possible solutions are the main contributions of this work

Vibration-based adaptive novelty detection method for monitoring faults in a kinematic chain

Postprint (published version

Computational physics of the mind

In the XIX century and earlier such physicists as Newton, Mayer, Hooke, Helmholtz and Mach were actively engaged in the research on psychophysics, trying to relate psychological sensations to intensities of physical stimuli. Computational physics allows to simulate complex neural processes giving a chance to answer not only the original psychophysical questions but also to create models of mind. In this paper several approaches relevant to modeling of mind are outlined. Since direct modeling of the brain functions is rather limited due to the complexity of such models a number of approximations is introduced. The path from the brain, or computational neurosciences, to the mind, or cognitive sciences, is sketched, with emphasis on higher cognitive functions such as memory and consciousness. No fundamental problems in understanding of the mind seem to arise. From computational point of view realistic models require massively parallel architectures

Adaptive Filters for 2-D and 3-D Digital Images Processing

Práce se zabývá adaptivními filtry pro vizualizaci obrazů s vysokým rozlišením. V teoretické části je popsán princip činnosti konfokálního mikroskopu a matematicky korektně zaveden pojem digitální obraz. Pro zpracování obrazů je volen jak frekvenční přístup (s využitím 2-D a 3-D diskrétní Fourierovy transformace a frekvenčních filtrů), tak přístup pomocí digitální geometrie (s využitím adaptivní ekvalizace histogramu s adaptivním okolím). Dále jsou popsány potřebné úpravy pro práci s neideálními obrazy obsahujícími aditivní a impulzní šum. Závěr práce se věnuje prostorové rekonstrukci objektů na základě jejich optických řezů. Veškeré postupy a algoritmy jsou i prakticky zpracovány v softwaru, který byl vyvinut v rámci této práce.The thesis is concerned with filters for visualization of high dynamic range images. In the theoretical part, the principle of confocal microscopy is described and the term digital image is defined in a mathematically correct way. Both frequency approach (using 2-D and 3-D discrete Fourier transform and frequency filters) and digital geometry approach (using adaptive histogram equalization with adaptive neighbourhood) are chosen for the processing of images. Necessary adjustments when working with non-ideal images containing additive and impulse noise are described as well. The last part of the thesis is interested in 3-D reconstruction from optical cuts of an object. All the procedures and algorithms are also implemented in the software developed as a part of this thesis.