Principal Fiber Research Articles

Radiofrequency Enhancer to Recover Signal Dropouts in 7 Tesla Diffusion MRI.

Diffusion magnetic resonance imaging (dMRI) allows for a non-invasive visualization and quantitative assessment of white matter architecture in the brain by characterizing restrictions on the random motion of water molecules. Ultra-high field MRI scanners, such as those operating at 7 Tesla (7T) or higher, can boost the signal-to-noise ratio (SNR) to improve dMRI compared with what is attainable at conventional field strengths such as 3T or 1.5T. However, wavelength effects at 7T cause reduced transmit magnetic field efficiency in the human brain, mainly in the posterior fossa, manifesting as signal dropouts in this region. Recently, we reported a simple approach of using a wireless radiofrequency (RF) surface array to improve transmit efficiency and signal sensitivity at 7T. In this study, we demonstrate the feasibility and effectiveness of the RF enhancer in improving in vivo dMRI at 7T. The electromagnetic simulation results demonstrated a 2.1-fold increase in transmit efficiency with the use of the RF enhancer. The experimental results similarly showed a 1.9-fold improvement in transmit efficiency and a 1.4-fold increase in normalized SNR. These improvements effectively mitigated signal dropouts in regions with inherently lower SNR, such as the cerebellum, resulting in a better depiction of principal fiber orientations and an enhanced visualization of extended tracts.

A geometric formulation of Schaefer’s theory of Cosserat solids

The Cosserat solid is a theoretical model of a continuum whose elementary constituents are notional rigid bodies, having both positional and orientational degrees of freedom. In this article, we present a differential geometric formulation of the mechanics of a Cosserat solid, motivated by Schaefer’s “motor field” theory. The solid is modeled as a special principal fiber bundle (a Cartan space) and its configurations are related by bundle maps. We show that the classical Lagrangian strain measure of a Cosserat solid is the difference of two Cartan connections on the bundle. The infinitesimal strain is derived by a rigorous linearization and is revealed to be the Lie derivative of a Cartan connection along the vector field representing the infinitesimal deformation. Incompatibilities in a Cosserat solid are characterised by a non-flat Cartan connection whose curvature is recognized as the density of topological defects. Stresses are defined as vector bundle-valued differential forms that are work-dual to strains and balance laws in the limit of vanishing inertia are obtained via a d’Alembert principle. Constitutive equations, with an emphasis on recent applications to active oriented solids, are briefly discussed.

Transitive Centralizer and Fibered Partially Hyperbolic Systems

Abstract We prove several rigidity results about the centralizer of a smooth diffeomorphism, concentrating on two families of examples: diffeomorphisms with transitive centralizer, and perturbations of isometric extensions of Anosov diffeomorphisms of nilmanifolds. We classify all smooth diffeomorphisms with transitive centralizer: they are exactly the maps that preserve a principal fiber bundle structure, acting minimally on the fibers and trivially on the base. We also show that for any smooth, accessible isometric extension $f_{0}\colon M\to M$ of an Anosov diffeomorphism of a nilmanifold, subject to a spectral bunching condition, any $f\in \textrm{Diff}^{\infty }(M)$ sufficiently $C^{1}$-close to $f_{0}$ has centralizer a Lie group. If the dimension of this Lie group equals the dimension of the fiber, then $f$ is a principal fiber bundle morphism covering an Anosov diffeomorphism. Using the results of this paper, we classify the centralizer of any partially hyperbolic diffeomorphism of a $3$-dimensional, nontoral nilmanifold: either the centralizer is virtually trivial, or the diffeomorphism is an isometric extension of an Anosov diffeomorphism, and the centralizer is virtually ${{\mathbb{Z}}}\times{{\mathbb{T}}}$.

Control of temperature dependent viscosity for manufacturing of Bi-doped active fiber

Bi-activated photonic materials are promising for various applications in high-capacity telecommunication, tunable laser, and advanced bioimaging and sensing. Although various Bi-doped material candidates have been explored, manufacturing of Bi heavily doped fiber with excellent optical activity remains a long-standing challenge. Herein, a novel viscosity evolutional behavior mediated strategy for manufacturing of Bi-doped active fiber with high dopant solubility is proposed. The intrinsic relation among the evolution of Bi, reaction temperature and viscosity of the glass system is established. Importantly, the effective avenue to prevent the undesired deactivation of Bi during fiber drawing by tuning the temperature dependent viscosity evolution is built. By applying the strategy, for the first time we demonstrate the success in fabrication of heavily doped Bi active fiber. Furthermore, the principal fiber amplifier device is constructed and broadband optical signal amplification is realized. Our findings indicate the effectiveness of the proposed temperature dependent viscosity mediated strategy for developing novel photonic active fiber, and they also demonstrate the great potential for application in the next-generation high-capacity telecommunication system.

A maximum-entropy length-orientation closure for short-fiber reinforced composites

We describe an algorithm for generating fiber-filled volume elements for use in computational homogenization schemes which accounts for a coupling of the fiber-length and the fiber-orientation. For prescribed fiber-length distribution and fiber-orientation tensor of second order, a maximum-entropy estimate is used to produce a fiber-length-orientation distribution which mimics real injection molded specimens, where longer fibers show a stronger alignment than shorter fibers. We derive the length-orientation closure from scratch, discuss its integration into the sequential addition and migration algorithm for generating fiber-filled microstructures for industrial volume fractions and investigate the resulting effective elastic properties. We demonstrate that accounting for the length-orientation coupling permits to match the measured Young’s moduli in principal fiber direction and transverse to it more accurately than for closure approximations ignoring the length-orientation coupling.

A Principal Bundle Framework for Generalised Notions of Formation and Rigidity

In this work, the notions of formation and rigidity (first developed for formation control in Euclidean spaces) are recast in a general framework of principal fiber bundles and a control law is derived for second order systems for driving the system to a given formation. The Euclidean inter-agent distance measurements and congruence transformations are generalised as output maps and Lie group actions respectively, to capture more generic scenarios.

Variational Estimation for Mechanical Systems on Lie Groups based on Geometric Mechanics

Geometric mechanics analyzes mechanical systems in the framework of variational mechanics, while accounting for the geometry of the configuration space. From the late 1970s, developments in this area produced several schemes for geometric control of mechanical systems in continuous time and discrete time. In the mid to late 2000s, geometric mechanics was first applied to state estimation of mechanical systems, particularly systems evolving on Lie groups as configuration manifolds, like rigid body systems. Much of the existing work on geometric mechanics-based estimation has been in continuous time, using deterministic, semi-stochastic and stochastic approaches. While the body of existing literature on discrete-time estimation schemes on Lie groups is not as extensive, the literature on this topic is contemporaneous with continuous-time schemes. This work describes some recent and ongoing research on geometric mechanics-based estimation schemes in continuous and discrete time from the mid-2010s, which were developed using the Lagrange-d’Alembert principle applied to rigid body systems. This approach gives (deterministic) observer designs with strong stability and robustness properties. This work concludes with potential extensions of this approach to mechanical systems with principal fiber bundles as configuration manifolds.

Chern–Simons field theory on the general affine group, 3d-gravity and the extension of Cartan connections

The purpose of this article is to study the correspondence between 3d-gravity and the Chern–Simons field theory from the perspective of geometric mechanics, specifically in the case where the structure group is the general affine group. To accomplish this, the paper discusses a variational problem of the Chern–Simons type on a principal fiber bundle with this group as its structure group. The connection to the usual Chern–Simons theory is established by utilizing a generalization, in the context of Cartan connections, of the notion of extension and reduction of connections.

Geometric phases of nonlinear elastic [formula omitted]-rotors via Cartan’s moving frames

We study the geometric phases of nonlinear elastic N-rotors with continuous rotational symmetry. In the Hamiltonian framework, the geometric structure of the phase space is a principal fiber bundle, i.e., a base, or shape manifold B, and fibers F along the symmetry direction attached to it. The symplectic structure of the Hamiltonian dynamics determines the connection and curvature forms of the shape manifold. Using Cartan’s structural equations with zero torsion we find an intrinsic (pseudo) Riemannian metric for the shape manifold. Without lose of generality, we show that one has the freedom to define the rotation sign of the total angular momentum A of the elastic rotors as either positive or negative, e.g., counterclockwise or clockwise, respectively, or viceversa. This endows the base manifold B with two distinct metrics both compatible with the geometric phase. In particular, the metric is pseudo-Riemannian if A<0, and the shape manifold is a 2D Robertson-Walker spacetime with positive curvature. For A>0, the shape manifold is the hyperbolic plane H2 with negative curvature. We then generalize our results to free elastic N-rotors. We show that the associated shape manifold B is reducible to the product manifold of N−1 hyperbolic planes H2 (A>0), or 2D Robertson-Walker spacetimes (A<0) depending on the convection used to define the rotation sign of the total angular momentum. We then consider elastic N-rotors subject to time-dependent self-equilibrated moments. The N-dimensional shape manifold of the extended autonomous system has a structure similar to that of the (N−1)-dimensional shape manifold of free elastic rotors. The Riemannian structure of the shape manifold provides an intrinsic measure of the closeness of one shape to another in terms of curvature, or induced geometric phase.

Comprehensive parametric analyses on the mechanical performance of 3D printed continuous carbon fibre reinforced plastic

This study presents a novel in-house modelling method called “Fibre Path Generator” and comprehensive parametric analyses on the mechanical performance of carbon fibre reinforced plastic (CFRP) with the fibre path along the principal stress direction, using both finite element (FE) simulations and experiments. The reliability of the developed CFRP model is validated through the fabrication of open-hole tensile test specimens using a co-extrusion composite 3D-printer, which demonstrated a highly compatible maximum tensile load with an error less than 3%. A comparative analysis is conducted to assess the mechanical performance of the CFRP specimen with principal stress fibre placement, which result shows that the maximum tensile load achieved is 172.84% higher than a CFRP model with uniaxial fibre placement. Furthermore, comprehensive parametric studies are carried out, varying the carbon fibre location and width-to-depth (w/D) ratio of the open-hole specimen, in order to evaluate the mechanical performance under the tensile loading. This study results provide useful insights to engineers when enhancing the mechanical performance of CFRP composite structures with effective continuous fibre placement.

Algorithm for fast evaluation of in-plane fiber orientation in reinforced plastics using light microscopy images

Methods for evaluating the orientation of carbon fibers in reinforced plastics vary in complexity and are application specific. Here, we report an algorithm that quickly evaluates in-plane fiber orientation based on determining the correlation coefficient of adjacent regions in microscopy images. The result is not the fiber orientation of individual fibers, but the principal fiber orientation of small image areas. This method is applicable to large areas due to its low computation time and captures varying fiber orientations, making it suitable for the study of injection molded samples with complex geometries. A great advantage is that no information about the fibers or the matrix, or their combination, is needed prior to the analysis. This approach is also suitable for samples with surface defects. Demonstrations of this technique are given for Polyamide 6 and Polypropylene with 30 weight % carbon fibers of different fiber lengths.

Emerging electric or magnetic parts of Weyl tensor

In this paper, we study the PNDP-manifold, which has shown to be effective in applications, particularly in the field of general relativity, by introducing a new topological approach to the emergent electric or magnetic parts associated to the Weyl tensor. The working hypothesis in this study is that the electric or magnetic parts of the Weyl tensor are the dimensions of the PNDP-manifold and the interaction that emerges as “virtual” point-like manifolds and as a manifold with positive/ negative dimensions results in the generation of the purely electric or purely magnetic parts of the Weyl tensor. The PNDP metric for the electric or magnetic parts of the Weyl tensor is also derived. The generalized Lorentz transformations on the PNDP manifold are introduced. These can give rise to novel forms of gauge theories if we consider local Lorentz transformations. Also we briefly show that principal fiber bundles with PNDP manifolds as base manifolds can be constructed.

Morpho-mechanical mapping of human dura mater microstructure

The human dura mater is known to impact vastly traumatic brain injury mechanopathology. In spite of this involvement, dura mater is typically neglected in computational and physical human head models. The lack of location-dependent microstructural and related mechanical data of dura mater may be considered a rationale behind this simplification. The anisotropic nature of dura mater under various loading conditions so far remains unelucidated. Furthermore, principal collagen fiber orientation is yet to be quantified for a morpho-mechanically-informed material model on the dura mater. This study aims to assess how location-dependent mechanical anisotropy is linked to principal collagen fiber orientation. Uniaxial extension tests were performed in a heated tissue bath for 60 samples from six individuals and correlated to the three-dimensional collagen structure in four individuals using second-harmonic generation (SHG) imaging. Failure stress and stretch at failure, elastic modulus, and a microstructurally motivated material model were integrated to examine local differences in dura mater morpho-mechanics. The quantitative observation of collagen fiber orientation and dispersion confirmed that collagen is highly aligned in the human dura mater and that both fiber orientation and dispersion differ depending on the location investigated. This observation provides a possible explanation for the previously observed isotropic mechanical behavior, as the main collagen fiber direction is not oriented along the anterior-posterior or medial-lateral direction at most of the mapped locations. Additionally, these site-dependent structural properties have implications for the mechanical load response and therefore potentially for the regional functions dura mater has to fulfill. The here chosen non-symmetrical fiber dispersion material model fits the data well and provides a comprehensive parameter base for further studies and future finite element models. Statement of significanceThe human dura mater greatly affects traumatic brain injury mechanisms, but it is often ignored in computational and physical head models. This is because there is a lack of detailed microstructural and mechanical data specific to the dura mater. Its anisotropic nature and collagen fiber orientation have not been fully understood, hindering the development of an accurate material model. Hence, this study combines morphological data on collagen fiber orientation and dispersion at multiple locations of human cranial dura mater, and links microstructure to location-specific load-displacement behavior. It provides microstructurally informed mechanical information towards realistic head models for predicting location-dependent tissue behavior and failure for assessing brain injury and graft material development.

Martingales on principal fiber bundles

Let P(M,G) be a principal fiber bundle, let ω be a connection form on P(M,G), and consider a projectable connection ∇P on P(M,G). The aim of this work is to determine the ∇P -martingales in P(M,G). Our results allow establishing new characterizations of harmonic maps from Riemannian manifolds to principal fiber bundles.

Asymmetry of radiomics features in the white matter of patients with primary progressive aphasia.

Primary Progressive Aphasia (PPA) is a neurological disease characterized by linguistic deficits. Semantic (svPPA) and non-fluent/agrammatic (nfvPPA) variants are the two main clinical subtypes. We applied a novel analytical framework, based on radiomic analysis, to investigate White Matter (WM) asymmetry and to examine whether asymmetry is associated with verbal fluency performance. Analyses were performed on T1-weighted images including 56 patients with PPA (31 svPPA and 25 nfvPPA) and 53 age- and sex-matched controls. Asymmetry Index (AI) was computed for 86 radiomics features in 34 white matter regions. The relationships between AI, verbal fluency performance (semantic and phonemic) and Boston Naming Test score (BNT) were explored through Spearman correlation analysis. Relative to controls, WM asymmetry in svPPA patients involved regions adjacent to middle temporal cortex as part of the inferior longitudinal (ILF), fronto-occipital (IFOF) and superior longitudinal fasciculi. Conversely, nfvPPA patients showed an asymmetry of WM in lateral occipital regions (ILF/IFOF). A higher lateralization involving IFOF, cingulum and forceps minor was found in nfvPPA compared to svPPA patients. In nfvPPA patients, semantic fluency was positively correlated to asymmetry in ILF/IFOF tracts. Performances at BNT were associated with AI values of the middle temporal (ILF/SLF) and parahippocampal (ILF/IFOF) gyri in svPPA patients. Radiomics features depicted distinct pathways of asymmetry in svPPA and nfvPPA involving damage of principal fiber tracts associated with speech and language. Assessing asymmetry of radiomics in PPA allows achieving a deeper insight into the neuroanatomical damage and may represent a candidate severity marker for language impairments in PPA patients.

Ga-hybridization-mediated broadband optical amplification in Bi-activated photonic glass and fiber.

A Ga hybridization strategy is proposed for simultaneously enhancing the near-infrared activity and extending the bandwidth of Bi-activated photonic glass. Systematic studies on the near-infrared optical responses of Ga/Bi and Al/Bi co-doped silica glasses are performed. It is interesting to note that Ga/Bi co-doped glasses have a similar near-infrared emission center to Al/Bi co-doped glass, while the former is more effective in improving near-infrared activity. The different luminescence mechanisms of Ga/Bi and Al/Bi co-doped silica glasses are elucidated, and the corresponding microstructure-optical response relationship is discussed. In addition, the Ga/Bi co-doped silica optical fiber is successfully prepared, and the principal fiber amplifier device is fabricated. Furthermore, amplified spontaneous emission and broadband on-off gain are realized. The results suggest that Ga-hybridized Bi-activated photonic glass is a promising gain material for broadband fiber amplifiers.

Curvature Invariants of Equivariant Isometric Minimal Immersions into Grassmannian Manifolds

Using theories of principal fibre bundles and connections in [11], we study curvature invariants as Riemannian submanifolds for equivariant isometric minimal immersions from Riemannian or Hermitian symmetric spaces of compact type into Grassmannian manifolds. First we calculate principal curvatures of all equivariant full isometric minimal immersions from the complex projective line to complex quadrics. It is shown that they do not depend on the parameter of the moduli space. According to the preceding research, it is important for the study of curvature invariants to examine the behavior of higher order covariant derivative of the second fundamental form. It also enables us to distinguish those maps by curvature invariants in the moduli space. In addition, we calculate principal curvatures of all equivariant full holomorphic isometric embeddings between the complex projective spaces.

Stress-adapted fiber orientation along the principal stress directions for continuous fiber-reinforced material extrusion

A proven method to enhance the mechanical properties of additively manufactured plastic parts is the embedding of continuous fibers. Due to its great flexibility, continuous fiber-reinforced material extrusion allows fiber strands to be deposited along optimized paths. Nevertheless, the fibers have so far been embedded in the parts contour-based or on the basis of regular patterns. The outstanding strength and stiffness properties of the fibers in the longitudinal direction cannot be optimally utilized. Therefore, a method is proposed which allows to embed fibers along the principal stresses into the parts in a load-oriented manner. A G-code is generated from the calculated principal stress trajectories and the part geometry, which also takes into account the specific restrictions of the manufacturing technology used. A distinction is made between fiber paths and the matrix so that the average fiber volume content can be set in a defined way. To determine the mechanical properties, tensile and flexural tests are carried out on specimens consisting of carbon fiber-reinforced polyamide. In order to increase the influence of the principal stress-based fiber orientation, open-hole plates are used for the tensile tests, as this leads to variable stresses across the cross section. In addition, a digital image correlation system is used to determine the deformations during the mechanical tests. It was found that the peak load of the optimized open-hole plates was greater by a factor of 3 and the optimized flexural specimens by a factor of 1.9 than the comparison specimens with unidirectional fiber alignment.

Damage evolution in quasi-statically indented alumina based oxide/oxide ceramic matrix composites: An experimental investigation

In this study, the evolution of damage in an alumina-based oxide/oxide ceramic matrix composite is experimentally evaluated. A 12.7 mm tungsten-carbide hemispherical indentor is utilized in quasi-statically inducing damage in laminates held by corner clamps, with the back side unsupported. Multiple laminates are loaded in displacement control to “first load drop”, as well as to crosshead displacements corresponding to 30%, 50%, 75% and 100% of the respective laminate thicknesses. Upon reaching the target displacements the laminates are unloaded. The nature and extent of external and internal damage in the laminates is characterized and quantified using state-of-the-art techniques such as optical surface profilometry, X-ray Computed Tomography (CT), flash thermography and laser scanning microscopy. State of damage for the different depths of indentation closely correlates with critical transition points in the load-displacement plots, especially the first load drop, the peak load and the residual dent depth. Flash thermography results show a small region of sub-surface laminate damage at first load drop, while major cracks along the two principal fiber directions are observed for the 75% and 100% displacement cases. X-ray CT images also reveal a central, conical damage zone typical of such indentation events, with the delaminations extending beyond the cone region. The sequence of damage events identified through this study is anticipated to be useful in correctly incorporating damage mechanics in low energy impacts of ceramic matrix composites.

Geometry and Spectral Theory Applied to Credit Bubbles in Arbitrage Markets: The Geometric Arbitrage Approach to Credit Risk

We apply Geometric Arbitrage Theory (GAT) to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. The remarkable aspect of the GAT is the gauge symmetry, which can be translated to the financial context, by packaging all of the asset model information into a (stochastic) principal fiber bundle. We obtain closed-form equations involving default intensities and loss-given defaults characterizing the no-free-lunch-with-vanishing-risk condition for government and corporate bond markets while relying on the spread-term structure with default intensity and loss-given default. Moreover, we provide a sufficient condition equivalent to the Novikov condition implying the absence of arbitrage. Furthermore, the generic dynamics for an isolated credit market allowing for arbitrage possibilities (and minimizing the total quantity of potential arbitrage) are derived, and arbitrage credit bubbles for both base credit assets and credit derivatives are explicitly computed. The existence of an approximated risk-neutral measure allowing the definition of fundamental values for the assets is inferred through spectral theory. We show that instantaneous bond returns are serially uncorrelated and centered, that the expected value of credit bubbles remains constant for future times where no coupons are paid, and that the variance of the market portfolio nominals is concurrent with that of the corresponding bond deflators.