Interrogation of spline surfaces with application to isogeometric design and analysis of lattice-skin structures

A novel surface interrogation technique is proposed to compute the intersection of curves with spline surfaces in isogeometric analysis. The intersection points are determined in one-shot without resorting to a Newton-Raphson iteration or successive refinement. Surface-curve intersection is required in a wide range of applications, including contact, immersed boundary methods and lattice-skin structures, and requires usually the solution of a system of nonlinear equations. It is assumed that the surface is given in form of a spline, such as a NURBS, T-spline or Catmull-Clark subdivision surface, and is convertible into a collection of B\'ezier patches. First, a hierarchical bounding volume tree is used to efficiently identify the B\'ezier patches with a convex-hull intersecting the convex-hull of a given curve segment. For ease of implementation convex-hulls are approximated with k-dops (discrete orientation polytopes). Subsequently, the intersections of the identified B\'ezier patches with the curve segment are determined with a matrix-based implicit representation leading to the computation of a sequence of small singular value decompositions (SVDs). As an application of the developed interrogation technique the isogeometric design and analysis of lattice-skin structures is investigated. The skin is a spline surface that is usually created in a computer-aided design (CAD) system and the periodic lattice to be fitted consists of unit cells, each containing a small number of struts. The lattice-skin structure is generated by projecting selected lattice nodes onto the surface after determining the intersection of unit cell edges with the surface. For mechanical analysis, the skin is modelled as a Kirchhoff-Love thin-shell and the lattice as a pin-jointed truss. The two types of structures are coupled with a standard Lagrange multiplier approach

Transgenic Overexpression of LARGE Induces alpha-Dystroglycan Hyperglycosylation in Skeletal and Cardiac Muscle

Background: LARGE is one of seven putative or demonstrated glycosyltransferase enzymes defective in a common group of muscular dystrophies with reduced glycosylation of alpha-dystroglycan. Overexpression of LARGE induces hyperglycosylation of alpha-dystroglycan in both wild type and in cells from dystroglycanopathy patients, irrespective of their primary gene defect, restoring functional glycosylation. Viral delivery of LARGE to skeletal muscle in animal models of dystroglycanopathy has identical effects in vivo, suggesting that the restoration of functional glycosylation could have therapeutic applications in these disorders. Pharmacological strategies to upregulate Large expression are also being explored.Methodology/Principal Findings: In order to asses the safety and efficacy of long term LARGE over-expression in vivo, we have generated four mouse lines expressing a human LARGE transgene. On observation, LARGE transgenic mice were indistinguishable from the wild type littermates. Tissue analysis from young mice of all four lines showed a variable pattern of transgene expression: highest in skeletal and cardiac muscles, and lower in brain, kidney and liver. Transgene expression in striated muscles correlated with alpha-dystroglycan hyperglycosylation, as determined by immunoreactivity to antibody IIH6 and increased laminin binding on an overlay assay. Other components of the dystroglycan complex and extracellular matrix ligands were normally expressed, and general muscle histology was indistinguishable from wild type controls. Further detailed muscle physiological analysis demonstrated a loss of force in response to eccentric exercise in the older, but not in the younger mice, suggesting this deficit developed over time. However this remained a subclinical feature as no pathology was observed in older mice in any muscles including the diaphragm, which is sensitive to mechanical load-induced damage.Conclusions/Significance: This work shows that potential therapies in the dystroglycanopathies based on LARGE upregulation and alpha-dystroglycan hyperglycosylation in muscle should be safe

Fully probabilistic deep models for forward and inverse problems in parametric PDEs

We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation leverages conventional PDE discretization techniques, deep neural networks, probabilistic modelling, and variational inference to assemble a fully probabilistic coherent framework. In the posited probabilistic model, both the forward and inverse maps are approximated as Gaussian distributions with a mean and covariance parameterized by deep neural networks. The PDE residual is assumed to be an observed random vector of value zero, hence we model it as a random vector with a zero mean and a user-prescribed covariance. The model is trained by maximizing the probability, that is the evidence or marginal likelihood, of observing a residual of zero by maximizing the evidence lower bound (ELBO). Consequently, the proposed methodology does not require any independent PDE solves and is physics-informed at training time, allowing the real-time solution of PDE forward and inverse problems after training. The proposed framework can be easily extended to seamlessly integrate observed data to solve inverse problems and to build generative models. We demonstrate the efficiency and robustness of our method on finite element discretized parametric PDE problems such as linear and nonlinear Poisson problems, elastic shells with complex 3D geometries, and time-dependent nonlinear and inhomogeneous PDEs using a physics-informed neural network (PINN) discretization. We achieve up to three orders of magnitude speed-up after training compared to traditional finite element method (FEM), while outputting coherent uncertainty estimates

Isogeometric analysis using manifold-based smooth basis functions

We present an isogeometric analysis technique that builds on manifold-based smooth basis functions for geometric modelling and analysis. Manifold-based surface construction techniques are well known in geometric modelling and a number of variants exist. Common to all is the concept of constructing a smooth surface by blending together overlapping patches (or, charts), as in differential geometry description of manifolds. Each patch on the surface has a corresponding planar patch with a smooth one-to-one mapping onto the surface. In our implementation, manifold techniques are combined with conformal parametrisations and the partition-of-unity method for deriving smooth basis functions on unstructured quadrilateral meshes. Each vertex and its adjacent elements on the surface control mesh have a corresponding planar patch of elements. The star-shaped planar patch with congruent wedge-shaped elements is smoothly parameterised with copies of a conformally mapped unit square. The conformal maps can be easily inverted in order to compute the transition functions between the different planar patches that have an overlap on the surface. On the collection of star-shaped planar patches the partition of unity method is used for approximation. The smooth partition of unity, or blending functions, are assembled from tensor-product b-spline segments defined on a unit square. On each patch a polynomial with a prescribed degree is used as a local approximant. To obtain a mesh-based approximation scheme, the coefficients of the local approximants are expressed in dependence of vertex coefficients. This yields a basis function for each vertex of the mesh which is smooth and non-zero over a vertex and its adjacent elements. Our numerical simulations indicate the optimal convergence of the resulting approximation scheme for Poisson problems and near optimal convergence for thin-plate and thin-shell problems

Subdivision surfaces with isogeometric analysis adapted refinement weights

Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are becoming available in a number of geometric modelling systems for engineering design. The subdivision refinement rules are usually adapted from knot insertion rules for splines. The quadrilateral Catmull-Clark scheme considered in this work is equivalent to cubic B-splines away from extraordinary, or irregular, vertices with other than four adjacent elements. Around extraordinary vertices the surface consists of a nested sequence of smooth spline patches which join $C^1$ continuously at the point itself. As known from geometric design literature, the subdivision weights can be optimised so that the surface quality is improved by minimising short-wavelength surface oscillations around extraordinary vertices. We use the related techniques to determine weights that minimise finite element discretisation errors as measured in the thin-shell energy norm. The optimisation problem is formulated over a characteristic domain and the errors in approximating cup- and saddle-like quadratic shapes obtained from eigenanalysis of the subdivision matrix are minimised. In finite element analysis the optimised subdivision weights for either cup- or saddle-like shapes are chosen depending on the shape of the solution field around an extraordinary vertex. As our computations confirm, the optimised subdivision weights yield a reduction of $50\%$ and more in discretisation errors in the energy and $L_2$ norms. Although, as to be expected, the convergence rates are the same as for the classical Catmull-Clark weights, the convergence constants are improved.Partial support through Trimble Inc and Cambridge Trust is gratefully acknowledged

Pentacene-Gate Dielectric Interface Modification with Silicon Nanoparticles for OTFTs

AbstractWe report on the properties of pentacene layers and OTFTs (Organic Thin Film Transistors) deposited on semiconductor-gate insulator interfaces covered with silicon nanoparticles (SiNPs) monolayer prepared by the Langmuir-Blodgett method compared to a reference sample (without SiNPs) prepared in an otherwise identical way. To analyse the structural quality, micro-Raman spectroscopy was employed and the correspondence between thin and bulk phase of the integral intensities peaks ratio (α) at 1154 and 1158cm-1 (α = Int1154 /Int1158) was evaluated. The AFM analysis of the pentacene layers reveals that the different surface treatment of SiO2 gate insulator (hydrophobic or hydrophilic) before SiNPs monolayer deposition has a distinct influence on the formation of different pentacene grain size and morphology. We demonstrate the higher time stability of pentacene OTFT and increasing of saturation current (∼ 2.5 ×) behavior after storage time if the semiconductor-gate insulator interface is modified using a SiNP monolayer

The effect of racemic gossypol and AT-101 on angiogenic profile of OVCAR-3 cells: a preliminary molecular framework for gossypol enantiomers

To compare the effect of racemic gossypol with its (–)/(–) enantiomer (AT-101) on expression profiles of angiogenic molecules by mRNA levels in human ovarian cancer cell line OVCAR-3. Methods: Cell viability assay (2,3-bis (2-methoxy-4-nitro-5- sulfophenyl)-5-[(phenylamino) carbonyl]-2H-tetrazolium hydroxide) was used to detect cytotoxicity of gossypol enantiomers. DNA fragmentation by an enzyme-linked immunosorbent (ELISA) assay was used to evaluate the rate of apoptosis. The mRNA expression levels of angiogenic molecules were investigated by Human Angiogenesis RT2 ProfilerTM PCR Array (SuperArray, Frederick, MD). Results: Both racemic form and AT-101 resulted in a significant cytotoxicity and induced apoptosis. This effect was observed in a dose- and time dependent manner. However, AT-101 was much more potent. In addition, the treatment of 10 μM of racemic gossypol alone and 3 μM of AT-101 alone resulted in significant down-regulation (≥ 3 fold) in mRNA levels of some pivotal angiogenic molecules in OVCAR-3, but altered gene profiles were different by the treatment of each enantiomer. Conclusion: The efficacy of two gossypol enantiomers in OVCAR-3 cells showed distinction. AT-101 was much more potent than racemic gossypol, not only by means of cell death and apoptosis, but also by modulation of angiogenic molecules released from OVCAR-3 cells. Further studies with endothelial cells should be done to verify the anti-angiogenic effect of gossypol enantiomers in cancer treatment

Cute Balloons with Thickness

Based on the fnite element method, we present a simple volume-preserved thin shell deformation algorithm to simulate the process of inflating a balloon. Diff erent from other thin shells, the material of balloons has special features: large stretch, small bend and shear, and incompressibility. Previous deformation methods often focus on typical three-dimensional models or thin plate models such as cloth model. The rest thin shell methods are complex or ignore the special features of thin shells especially balloons. We modify the triangle element to simple three-prism element, ignore bending and shearing deformation, and use volume preservation algorithm to match the incompressibility of balloons. Simple gas model is used, which interacts with shells to make the balloons inflated. Di different balloon examples have been tested in our experiments and the results are compared with those of other methods. The experiments show that our algorithm is simple and effective

Prenatal muscle development in a mouse model for the secondary dystroglycanopathies

The defective glycosylation of α-dystroglycan is associated with a group of muscular dystrophies that are collectively referred to as the secondary dystroglycanopathies. Mutations in the gene encoding fukutin-related protein (FKRP) are one of the most common causes of secondary dystroglycanopathy in the UK and are associated with a wide spectrum of disease. Whilst central nervous system involvement has a prenatal onset, no studies have addressed prenatal muscle development in any of the mouse models for this group of diseases. In view of the pivotal role of α-dystroglycan in early basement membrane formation, we sought to determine if the muscle formation was altered in a mouse model of FKRP-related dystrophy