Modeling of Spatial Uncertainties in the Magnetic Reluctivity

In this paper a computationally efficient approach is suggested for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines, such as a single phase transformer (a benchmark example that is considered in this paper). The approach is based on the Karhunen-Lo\`{e}ve expansion. The stochastic model is further used to study the statistics of the self inductance of the primary coil as a quantity of interest.Comment: submitted to COMPE

Fast Numerical Methods for Non-local Operators

[no abstract available

Multi-scale mechanics of collagen extracellular matrix

Extracellular matrix (ECM) provides the principal avenue for mechanochemical communication between tissue and cells. ECM not only plays an important role in providing structural and biomechanical support, but also in regulating a series of cellular behaviors. However, the underlying mechanisms by which the ECM mechanics influence cell and tissue function remain to be elucidated, since this process span size scales from tissue to molecular level. Furthermore, ECM has a hierarchical 3D structure and the load distribution is highly dependent on the architecture and mechanical properties. In this thesis, the multiscale mechanics of collagen ECM was studied using both experimental and modeling approaches. Rheological and biaxial tensile testing were performed to study the macroscopic mechanical properties. A theoretical framework was developed to determine the continuous relaxation spectrum. Investigating the spectrum in terms of number of peaks, peak intensity and time constants sheds light on the main intrinsic properties of viscoelastic materials. Material parameters from continuous relaxation spectrum were used in finite element models to simulate the dynamic rheological measurements of collagen matrix. The microscopic mechanical properties were measured using Optical Magnetic Twisting Cytometry (OMTC). Ferromagnetic beads embedded in the matrix were used as mechanical probes. Our study on the macro- and micro-scopic mechanical properties of collage matrix suggested several interesting differences originated from the scales of measurements. In macroscopic measurements, the storage and shear modulus increase with collagen concentration. At microscopic scale, the apparent storage and loss modulus are less sensitive to changes in collagen concentration. However, the loss modulus is more affected by the local interstitial fluid environment, leading to an increase in viscosity, especially at higher frequencies. A novel experimental approach was established to study the multi-scale ECM mechanics that allows the measurements of local ECM mechanical properties with controlled tissue-level mechanical loading by integrating the OMTC and biaxial tensile tester. Multiphoton imaging reveals structural changes in the collagen network that involve gradual straightening and collagen fiber recruitment with tissue level mechanical loading. Our study shows there is a complex interplay among structural heterogeneity, collagen fiber orientation, and fiber engagement in determining the ECM local mechanical properties

Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices

abstract: Mechanical interactions between cells and their microenvironment dictate cell phenotype and behavior, calling for cell mechanics measurements in three-dimensional (3D) extracellular matrices (ECM). Here we describe a novel technique for quantitative mechanical characterization of soft, heterogeneous samples in 3D. The technique is based on the integration of atomic force microscopy (AFM) based deep indentation, confocal fluorescence microscopy, finite element (FE) simulations and analytical modeling. With this method, the force response of a cell embedded in 3D ECM can be decoupled from that of its surroundings, enabling quantitative determination of the elastic properties of both the cell and the matrix. We applied the technique to the quantification of the elastic properties of metastatic breast adenocarcinoma cells invading into collagen hydrogels. We found that actively invading and fully embedded cells are significantly stiffer than cells remaining on top of the collagen, a clear example of phenotypical change in response to the 3D environment. Treatment with Rho-associated protein kinase (ROCK) inhibitor significantly reduces this stiffening, indicating that actomyosin contractility plays a major role in the initial steps of metastatic invasion.The final version of this article, as published in Scientific Reports, can be viewed online at: https://www.nature.com/articles/srep1968

Fourier Transforms

The 21st century ushered in a new era of technology that has been reshaping everyday life, simplifying outdated processes, and even giving rise to entirely new business sectors. Today, contemporary users of products and services expect more and more personalized products and services that can meet their unique needs. In that sense, it is necessary to further develop existing methods, adapt them to new applications, or even discover new methods. This book provides a thorough review of some methods that have an increasing impact on humanity today and that can solve different types of problems even in specific industries. Upgrading with Fourier Transformation gives a different meaning to these methods that support the development of new technologies and have a good projected acceleration in the future

Viscoelasticity and Spectral Analysis with Tikhonov Regularization

The focus of this independent study is an in-depth study of viscoelasticity and the mechanisms to obtaining a viscoelastic spectrum from stress data. The independent study begins with a study of simple models such as the Maxwell, Kelvin, and Zener models. It then proceeds to biphasic models associated with Biot theory, as expounded upon by Mow and co-workers. The paper culminates with a study of spectral methods and Tikhonov regularization for the spectral analysis of material behavior, including noise sensitivity and signal-noise information

A potential-flow BEM for large-displacement FSI

This work concerns the interaction of light membrane structures enclosing incompressible fluids. Large displacements and collapsed boundaries (initially slender subdomains) are characteristic of this class of problems. A finite-element/boundary-element (FE/BE) coupled discretization is discussed in this work which addresses these challenges. Most common linear fluid models have a boundary-integral representation, restricting the problem to the boundary and making them amenable to a boundary element method (BEM) discretization. A marked advantage of this representation with respect to the conventional partial-differential-equation-based view of finite-element methods for fluids is the bypassing of volumetric meshing. The FE/BE approach is therefore an enabling method for fluid-structure interaction (FSI) problems involving membranes, and the present work serves as a proof of concept for this approach. Numerical experiments show the capabilities of the proposed scheme

Contract stresses in hip replacements.

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