Characterisation of hidden objects in electrical impedance tomography using adaptive boundary elements

Electromagnetic inverse problems involve determining the location and identifying the shape and parameters of hidden conducting objects. Low-frequency, low-conductivity applications, range from geophysical applications, such as electric resistivity imaging (ERI), including groundwater detection or minerals and oil identification, to medical imaging problems using electrical impedance tomography (EIT). EIT consists of finding the conductivity contrast between an anomaly and a healthy tissue from voltage measurements around the patient body. For EIT, the perturbed electrical potential field (which is related to the voltage measurements) can be described by an asymptotic expansion as the size of an isolated inclusion goes to 0, which the leading order term separating into the gradient of a free-space Green's function, the gradient of the background potential field at the position of the object and the polarization tensor. In this work, we present an adaptive boundary element mesh algorithm to compute the polarization tensor accurately using BEM++. Moreover, the relationship of the computational discretisation of the object is investigated through a series of numerical experiments

Predicting multibody assembly of proteins

textThis thesis addresses the multi-body assembly (MBA) problem in the context of protein assemblies. [...] In this thesis, we chose the protein assembly domain because accurate and reliable computational modeling, simulation and prediction of such assemblies would clearly accelerate discoveries in understanding of the complexities of metabolic pathways, identifying the molecular basis for normal health and diseases, and in the designing of new drugs and other therapeutics. [...] [We developed] F²Dock (Fast Fourier Docking) which includes a multi-term function which includes both a statistical thermodynamic approximation of molecular free energy as well as several of knowledge-based terms. Parameters of the scoring model were learned based on a large set of positive/negative examples, and when tested on 176 protein complexes of various types, showed excellent accuracy in ranking correct configurations higher (F² Dock ranks the correcti solution as the top ranked one in 22/176 cases, which is better than other unsupervised prediction software on the same benchmark). Most of the protein-protein interaction scoring terms can be expressed as integrals over the occupied volume, boundary, or a set of discrete points (atom locations), of distance dependent decaying kernels. We developed a dynamic adaptive grid (DAG) data structure which computes smooth surface and volumetric representations of a protein complex in O(m log m) time, where m is the number of atoms assuming that the smallest feature size h is [theta](r[subscript max]) where r[subscript max] is the radius of the largest atom; updates in O(log m) time; and uses O(m)memory. We also developed the dynamic packing grids (DPG) data structure which supports quasi-constant time updates (O(log w)) and spherical neighborhood queries (O(log log w)), where w is the word-size in the RAM. DPG and DAG together results in O(k) time approximation of scoring terms where k << m is the size of the contact region between proteins. [...] [W]e consider the symmetric spherical shell assembly case, where multiple copies of identical proteins tile the surface of a sphere. Though this is a restricted subclass of MBA, it is an important one since it would accelerate development of drugs and antibodies to prevent viruses from forming capsids, which have such spherical symmetry in nature. We proved that it is possible to characterize the space of possible symmetric spherical layouts using a small number of representative local arrangements (called tiles), and their global configurations (tiling). We further show that the tilings, and the mapping of proteins to tilings on arbitrary sized shells is parameterized by 3 discrete parameters and 6 continuous degrees of freedom; and the 3 discrete DOF can be restricted to a constant number of cases if the size of the shell is known (in terms of the number of protein n). We also consider the case where a coarse model of the whole complex of proteins are available. We show that even when such coarse models do not show atomic positions, they can be sufficient to identify a general location for each protein and its neighbors, and thereby restricts the configurational space. We developed an iterative refinement search protocol that leverages such multi-resolution structural data to predict accurate high resolution model of protein complexes, and successfully applied the protocol to model gp120, a protein on the spike of HIV and currently the most feasible target for anti-HIV drug design.Computer Science

Boundary integral equations in Kinetic Plasma Theory

In this thesis, we use boundary integral equations (BIE) as a powerful tool to gain new insights into the dynamics of plasmas. On the theoretical side, our work provides new results regarding the oscillation of bounded plasmas. With the analytical computation of the frequencies for a general ellipsoid we contribute a new benchmark for numerical methods. Our results are validated by an extensive numerical study of several three-dimensional problems, including a particle accelerator with complex geometry and mixed boundary conditions. The use of Boundary Element Methods (BEM) reduces the dimension of the problem from three to two, thus drastically reducing the number of unknowns. By employing hierarchical methods for the computation of the occurring nonlocal sums and integral operators, our method scales linearly with the number of particles and the number of surface triangles, where the error decays exponentially in the expansion parameter. Furthermore, our method allows the pointwise evaluation of the electric field without loss of convergence order. As we are able to compute the occurring boundary integrals analytically, we can precisely predict the electric field near the boundary. This property makes our method exceptionally well suited for the numerical simulation of plasma sheaths near irregular boundaries or of plasma-surface interaction such as etching of semiconductors.In der vorliegenden Arbeit nutzen wir Randintegralgleichungen als ein mächtiges Werkzeug, um neue Einsichten in die Dynamik von Plasmen zu gewinnen. Auf theoretischer Seite entwickelt diese Arbeit neue Resultate bezüglich der Oszillation beschränkter Plasmen. Durch die ana- lytische Berechnung der Frequenzen im Fall eines allgemeinen Ellipsoids stellen wir ein neues Testbeispiel für numerische Methoden bereit. Unsere Resultate werden durch umfangreiche numerische Untersuchen dreidimensionaler Beispiele validiert, etwa einen Partikelbeschleuniger mit komplexer Geometrie und gemischten Randwerten. Mithilfe der Randelementmethode reduziert sich die Dimension des Problems von drei auf zwei, womit sich die Anzahl der Un- bekannten drastisch reduziert. Dank der Nutzung hierarchischer Methoden zur Berechnung der auftauchenden nichtlokalen Summen und Integraloperatoren skaliert unsere Methode linear mit der Anzahl der Partikel und der Anzahl der Oberflächendreiecken, wobei der Fehler exponen- tiell im Entwicklungsparameter abfällt. Des Weiteren erlaubt unsere Methode die Berechnung des elektrischen Felds ohne Verringerung der Konvergenzordnung. Da wir die auftretenden Randintegrale analytisch berechnen können, können wir präzise Aussagen über das elektrische Feld nahe des Rands treffen. Dank dieser Eigenschaft ist unsere Methode außergewöhnlich gut geeignet, um Plasmaränder nahe irregulärer Ränder oder Plasma-Oberflächen-Interaktionen, etwa das Ätzen von Halbleitern, zu simulieren

Nanoinformatics

Machine learning; Big data; Atomic resolution characterization; First-principles calculations; Nanomaterials synthesi

MULTI-LENGTH SCALE MODELING OF THE HIGH-PRESSURE, LARGE-STRAIN, HIGH-STRAIN-RATE RESPONSE OF SODA-LIME GLASS

Development of new transparent armor systems is essential for the protection of the current and future US armed forces, especially in light of the recent military operations The Operation Iraqi Freedom in Iraq and The Operation Enduring Freedom in Afghanistan. These conflicts have introduced a new military theater without a well-defined battle front and new types of threats (e.g. improvised explosive devices, IEDs). Development and modeling of new transparent armor systems for use in numerous applications from vehicle windows to face shields is a current area of thrust aimed at addressing the shortcomings of existing systems in order to better protect US soldiers and align with the military\u27s goal of becoming more mobile, deployable, and sustainable. This dissertation is focused predominately on the computational modeling of transparent armor materials and structures. Glass remains the dominant constituent in many modern transparent armor systems for a number of performance and manufacturing related reasons and thus is the material of focus in the present work. The present work is concerned with the development and further enhancement of a continuum-level, physically-based, high strain-rate, large-strain, high-pressure mechanical material model for soda-lime (and borosilicate) glass. The model is being developed in attempt to capture the complex stochastic, pre-existing flaw-controlled damage nature of glass under blast and impact conditions and do so in a computationally efficient manner. Numerous finite element simulations were carried out using the computational code ABAQUS/Explicit to assess the utility of the model under physically realistic ballistic loading conditions, including multi-hit impact scenarios. Further enhancements of the glass material model are made with the inclusion of the following: (i) differentiation of the mechanical properties of the so-called air-side and tin-side of glass plates manufactured using the float glass process; and (ii) a damage tensor to produce an orthotropic macro-cracked material. In addition a multi-length scale modeling approach for glass is taken to elucidate phenomena at different length scales (e.g. glass irreversible densification, shock response, etc.) with the ultimate objective of enhancing the efficacy of the current continuum-level material model. The irreversible densification of glass under ballistic (shock) loading conditions is investigated at multiple length scales (atomistic-level and continuum-level) in order to understand its effect on the ballistic penetration resistance of glass. The findings related to the material shock response and irreversible densification of glass were subsequently included in the continuum-level glass material model equation of state to further increase its efficacy. The results from the various test scenarios and modifications to the continuum-level glass material models reveal that: (a) transient non-linear dynamics computational analyses, when utilizing the glass material model, have demonstrated to be a useful tool in understanding the multi-hit ballistic-protection performance of laminated glass/polycarbonate transparent armor systems. The loss of the ballistic-protection performance of the armor caused by a sequence of closely spaced bullet impacts has been observed and the results of these analyses are validated against their experimental counterparts; (b) while it was expected (based on quasi-static mechanical testing result) that orienting the borofloat tin-side as a three-layer laminate strike face would enhance its ballistic protection performance, experimental findings did not support this conjecture. Computational simulations of the laminate impact established the capability of the borosilicate glass material model to capture the prominent experimentally observed damage modes and the measured V50, reconfirming the experimental findings; and (c) a 2-4% (shock strength-dependent) irreversible density increase in glass is capture computationally at multiple lengths scales. Subsequent modifications of the continuum-level material model for glass to include the effect of irreversible-densification resulted in minor improvements in the ballistic-penetration resistance of glass and only for high projectile initial velocities

The role of local structure in dynamical arrest

Amorphous solids, or glasses, are distinguished from crystalline solids by their lack of long-range structural order. At the level of two-body structural correlations, glassformers show no qualitative change upon vitrifying from a supercooled liquid. Nonetheless the dynamical properties of a glass are so much slower that it appears to take on the properties of a solid. While many theories of the glass transition focus on dynamical quantities, a solid's resistance to flow is often viewed as a consequence of its structure. Here we address the viewpoint that this remains the case for a glass. Recent developments using higher-order measures show a clear emergence of structure upon dynamical arrest in a variety of glass formers and offer the tantalising hope of a structural mechanism for arrest. However a rigorous fundamental identification of such a causal link between structure and arrest remains elusive. We undertake a critical survey of this work in experiments, computer simulation and theory and discuss what might strengthen the link between structure and dynamical arrest. We move on to highlight the relationship between crystallisation and glass-forming ability made possible by this deeper understanding of the structure of the liquid state, and emphasize the potential to design materials with optimal glassforming and crystallisation ability, for applications such as phase-change memory. We then consider aspects of the phenomenology of glassy systems where structural measures have yet to make a large impact, such as polyamorphism (the existence of multiple liquid states), aging (the time-evolution of non-equilibrium materials below their glass transition) and the response of glassy materials to external fields such as shear.Comment: 70 page