2,039 research outputs found
Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging
Locally adaptive differential frames (gauge frames) are a well-known
effective tool in image analysis, used in differential invariants and
PDE-flows. However, at complex structures such as crossings or junctions, these
frames are not well-defined. Therefore, we generalize the notion of gauge
frames on images to gauge frames on data representations defined on the extended space of positions and
orientations, which we relate to data on the roto-translation group ,
. This allows to define multiple frames per position, one per
orientation. We compute these frames via exponential curve fits in the extended
data representations in . These curve fits minimize first or second
order variational problems which are solved by spectral decomposition of,
respectively, a structure tensor or Hessian of data on . We include
these gauge frames in differential invariants and crossing preserving PDE-flows
acting on extended data representation and we show their advantage compared
to the standard left-invariant frame on . Applications include
crossing-preserving filtering and improved segmentations of the vascular tree
in retinal images, and new 3D extensions of coherence-enhancing diffusion via
invertible orientation scores
Data-inspired advances in geometric measure theory: generalized surface and shape metrics
Modern geometric measure theory, developed largely to solve the Plateau
problem, has generated a great deal of technical machinery which is
unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g.,
flat norm distance and decomposition in generalized surface space) hold
interest from a theoretical perspective but computational infeasibility
prevented practical use. Others, like nonasymptotic densities as shape
signatures, have been developed independently for data analysis (e.g., the
integral area invariant).
The flat norm measures distance between currents (generalized surfaces) by
decomposing them in a way that is robust to noise. The simplicial deformation
theorem shows currents can be approximated on a simplicial complex,
generalizing the classical cubical deformation theorem and proving sharper
bounds than Sullivan's convex cellular deformation theorem.
Computationally, the discretized flat norm can be expressed as a linear
programming problem and solved in polynomial time. Furthermore, the solution is
guaranteed to be integral for integral input if the complex satisfies a simple
topological condition (absence of relative torsion). This discretized
integrality result yields a similar statement for the continuous case: the flat
norm decomposition of an integral 1-current in the plane can be taken to be
integral, something previously unknown for 1-currents which are not boundaries
of 2-currents.
Nonasymptotic densities (integral area invariants) taken along the boundary
of a shape are often enough to reconstruct the shape. This result is easy when
the densities are known for arbitrarily small radii but that is not generally
possible in practice. When only a single radius is used, variations on
reconstruction results (modulo translation and rotation) of polygons and (a
dense set of) smooth curves are presented.Comment: 123 pages, dissertation, includes chapters based on arXiv:1105.5104
and arXiv:1308.245
Coarse-grained simulations of RNA and DNA duplexes
Although RNAs play many cellular functions little is known about the dynamics
and thermodynamics of these molecules. In principle, all-atom molecular
dynamics simulations can investigate these issues, but with current computer
facilities, these simulations have been limited to small RNAs and to short
times.
HiRe-RNA, a recently proposed high-resolution coarse-grained for RNA that
captures many geometric details such as base pairing and stacking, is able to
fold RNA molecules to near-native structures in a short computational time. So
far it had been applied to simple hairpins, and here we present its application
to duplexes of a couple dozen nucleotides and show how with our model and with
Replica Exchange Molecular Dynamics (REMD) we can easily predict the correct
double helix from a completely random configuration and study the dissociation
curve. To show the versatility of our model, we present an application to a
double stranded DNA molecule as well.
A reconstruction algorithm allows us to obtain full atom structures from the
coarse-grained model. Through atomistic Molecular Dynamics (MD) we can compare
the dynamics starting from a representative structure of a low temperature
replica or from the experimental structure, and show how the two are
statistically identical, highlighting the validity of a coarse-grained approach
for structured RNAs and DNAs.Comment: 28 pages, 11 figure
Multiscale Modeling of Multiphase Polymers
Accurately simulating material systems in a virtual environment requires the synthesis and utilization of all relevant information regarding performance mechanisms for the material occurring over a range of length and time scales. Multiscale modeling is the basis for the Integrated Computational Materials Engineering (ICME) Paradigm and is a powerful tool for accurate material simulations. However, while ICME has experienced adoption among those in the metals community, it has not gained traction in polymer research. This thesis seeks establish a hierarchical multiscale modeling methodology for simulating polymers containing secondary phases. The investigation laid out in the chapters below uses mesoscopic Finite Element Analysis (FEA) as a foundation to build a multiscale modeling methodology for polymer material systems. At the mesoscale a Design of Experiments (DOE) parametric study utilizing FEA of polymers containing defects compared the relative impacts of a selection of parameters on damage growth and coalescence in polymers. Of the parameters considered, the applied stress state proved to be the most crucial parameter affecting damage growth and coalescence. At the macroscale, the significant influence of the applied stress state on damage growth and coalescence in polymers (upscaled from the mesoscale) motivated an expansion of the Bouvard Internal State Variable (ISV) (Bouvard et al. 2013) polymer model stress state sensitivity. Deviatoric stress invariants were utilized to modify the Bouvard ISV model to account for asymmetry in polymer mechanical performance across different stress states (tension, compression, torsion). Lastly, this work implements a hierarchical multiscale modeling methodology to examine parametric effects of heterogeneities on Polymer/Clay Nanocomposite’s (PCNs) mechanical performance under uncertainty. A Virtual Composite Structure Generator (VCSG) built three-dimensional periodic Representative Volume Elements (RVEs) coupled to the Bouvard ISV model and a Cohesive Zone Model (CZM) which featured a Traction-Separation (T-S) rule calibrated to results upscaled from Molecular Dynamics (MD) simulations. A DOE parametric examination utilized the RVEs to determine the relative effects of a selection of parameters on the mechanical performance of PCNs. DOE results determined that nanoclay particle orientation was the most influential parameter affecting PCN elastic modulus while intercalated interlamellar gallery strength had the greatest influence on PCN yield stres
On the coupling between an ideal fluid and immersed particles
In this paper we use Lagrange-Poincare reduction to understand the coupling
between a fluid and a set of Lagrangian particles that are supposed to simulate
it. In particular, we reinterpret the work of Cendra et al. by substituting
velocity interpolation from particle velocities for their principal connection.
The consequence of writing evolution equations in terms of interpolation is
two-fold. First, it gives estimates on the error incurred when interpolation is
used to derive the evolution of the system. Second, this form of the equations
of motion can inspire a family of particle and hybrid particle-spectral methods
where the error analysis is "built-in". We also discuss the influence of other
parameters attached to the particles, such as shape, orientation, or
higher-order deformations, and how they can help with conservation of momenta
in the sense of Kelvin's circulation theorem.Comment: to appear in Physica D, comments and questions welcom
EXTRACTING FLOW FEATURES USING BAG-OF-FEATURES AND SUPERVISED LEARNING TECHNIQUES
Measuring the similarity between two streamlines is fundamental to many important flow data analysis and visualization tasks such as feature detection, pattern querying and streamline clustering. This dissertation presents a novel streamline similarity measure inspired by the bag-of-features concept from computer vision. Different from other streamline similarity measures, the proposed one considers both the distribution of and the distances among features along a streamline. The proposed measure is tested in two common tasks in vector field exploration: streamline similarity query and streamline clustering. Compared with a recent streamline similarity measure, the proposed measure allows users to see the interesting features more clearly in a complicated vector field.
In addition to focusing on similar streamlines through streamline similarity query or clustering, users sometimes want to group and see similar features from different streamlines. For example, it is useful to find all the spirals contained in different streamlines and present them to users. To this end, this dissertation proposes to segment each streamline into different features. This problem has not been studied extensively in flow visualization. For instance, many flow feature extraction techniques segment streamline based on simple heuristics such as accumulative curvature or arc length, and, as a result, the segments they found usually do not directly correspond to complete flow features. This dissertation proposes a machine learning-based streamline segmentation algorithm to segment each streamline into distinct features.
It is shown that the proposed method can locate interesting features (e.g., a spiral in a streamline) more accurately than some other flow feature extraction methods. Since streamlines are space curves, the proposed method also serves as a general curve segmentation method and may be applied in other fields such as computer vision.
Besides flow visualization, a pedagogical visualization tool DTEvisual for teaching access control is also discussed in this dissertation. Domain Type Enforcement (DTE) is a powerful abstraction for teaching students about modern models of access control in operating systems. With DTEvisual, students have an environment for visualizing a DTE-based policy using graphs, visually modifying the policy, and animating the common DTE queries in real time. A user study of DTEvisual suggests that the tool is helpful for students to understand DTE
Multiscale constitutive modeling of polymer materials
Materials are inherently multi-scale in nature consisting of distinct characteristics at various length scales from atoms to bulk material. There are no widely accepted predictive multi-scale modeling techniques that span from atomic level to bulk relating the effects of the structure at the nanometer (10-9 meter) on macro-scale properties. Traditional engineering deals with treating matter as continuous with no internal structure. In contrast to engineers, physicists have dealt with matter in its discrete structure at small length scales to understand fundamental behavior of materials. Multiscale modeling is of great scientific and technical importance as it can aid in designing novel materials that will enable us to tailor properties specific to an application like multi-functional materials.
Polymer nanocomposite materials have the potential to provide significant increases in mechanical properties relative to current polymers used for structural applications. The nanoscale reinforcements have the potential to increase the effective interface between the reinforcement and the matrix by orders of magnitude for a given reinforcement volume fraction as relative to traditional micro- or macro-scale reinforcements. To facilitate the development of polymer nanocomposite materials, constitutive relationships must be established that predict the bulk mechanical properties of the materials as a function of the molecular structure. A computational hierarchical multiscale modeling technique is developed to study the bulk-level constitutive behavior of polymeric materials as a function of its molecular chemistry. Various parameters and modeling techniques from computational chemistry to continuum mechanics are utilized for the current modeling method. The cause and effect relationship of the parameters are studied to establish an efficient modeling framework. The proposed methodology is applied to three different polymers and validated using experimental data available in literature
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Multiscale modelling of woven and knitted fabric membranes
Light-weight fabric membranes have gained increasing popularity over the past years due to their tailorable structural and material performances. These tailorable properties include stretch forming and deep drawing formability that exhibits excellent stretchability and drapeability properties of textiles and textile composites. Since the inception of computerised numerical control for three-dimensional textile-manufacturing machines,
technical textiles paved their way to numerous applications, certainly not limited to; aerospace, biomedical, civil engineering, defence, marine and medical industries. Digital interlooping and digital interlacing technology in additive manufacturing greatly advanced the manufacturing processes of textiles. In this work, we consider two branches of technical fabrics, namely plain-woven and weft-knitted.
Multiscale modelling is the tool of choice for homogenising periodic structures and has been used extensively to model and analyse the mechanical behaviour of woven and knitted fabrics. But there is a plethora of literature discussing the demerits of such conventional multiscale modelling. These demerits include higher computational costs,
rigid numerical models, ineffcient algorithmic computations and inability to incorporate geometric nonlinearities. We propose a data-driven nonlinear multiscale modelling technique to analyse the complex mechanical behaviour of plain-woven and weft-knitted fabrics with a neat extension to fabric material designing. We show how the integration of statistical learning techniques mitigates the weaknesses of conventional multiscale modelling. Moreover, we discuss the avenues that will open in many potential fields with regard to material modelling, structural engineering and textile industries.
In the proposed data-driven nonlinear computational homogenisation technique, we effi ciently integrate the microscale and macroscale using Gaussian Process Regression (GPR) statistical learning technique. In the microscale, representative volume elements (RVEs) are modelled using nite deformable isogeometric spatial rods and deformation is homogenised using periodic boundary conditions. This nite deformable rod is profi cient in handling large deformations, rod-to-rod contacts, arbitrary cross-section de finitions and follower loads. Respecting the principle of separation of scales, we construct response databases by applying different homogenised strain states to the RVEs and recording the respective incremental volume-averaged energy values. We use GPR
to learn a model using a 5-fold cross-validation technique by optimising the log marginal likelihood. In the macroscale, textiles are modelled as nonlinear orthotropic membranes for which the stresses and material constitutive relations are predicted by the trained GPR model. This coupling between GPR and membrane models is achieved through a
systematic and seamless nite element integration using C++ and Python environments. A neat extension to material designing is also discussed with potentials to extend the work into other related fi elds.Cambridge trust and Trinity Hall scholarshi
Simplicial Flat Norm with Scale
We study the multiscale simplicial flat norm (MSFN) problem, which computes
flat norm at various scales of sets defined as oriented subcomplexes of finite
simplicial complexes in arbitrary dimensions. We show that the multiscale
simplicial flat norm is NP-complete when homology is defined over integers. We
cast the multiscale simplicial flat norm as an instance of integer linear
optimization. Following recent results on related problems, the multiscale
simplicial flat norm integer program can be solved in polynomial time by
solving its linear programming relaxation, when the simplicial complex
satisfies a simple topological condition (absence of relative torsion). Our
most significant contribution is the simplicial deformation theorem, which
states that one may approximate a general current with a simplicial current
while bounding the expansion of its mass. We present explicit bounds on the
quality of this approximation, which indicate that the simplicial current gets
closer to the original current as we make the simplicial complex finer. The
multiscale simplicial flat norm opens up the possibilities of using flat norm
to denoise or extract scale information of large data sets in arbitrary
dimensions. On the other hand, it allows one to employ the large body of
algorithmic results on simplicial complexes to address more general problems
related to currents.Comment: To appear in the Journal of Computational Geometry. Since the last
version, the section comparing our bounds to Sullivan's has been expanded. In
particular, we show that our bounds are uniformly better in the case of
boundaries and less sensitive to simplicial irregularit
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