Bundle Model Research Articles

Manifold Learning via the Principle Bundle Approach

In this paper, we propose a novel principal bundle model and apply it to the image denoising problem. This model is based on the fact that the patch manifold admits canonical groups actions such as rotation. We introduce an image denoising algorithm, called the diffusive vector non-local Euclidean median (dvNLEM), by combining the traditional nonlocal Euclidean median (NLEM), the rotational structure in the patch space, and the diffusion distance. A theoretical analysis of dvNLEM, as well as the traditional nonlocal Euclidean median (NLEM), is provided to explain why these algorithms work. In particular, we show how accurate we could obtain the true neighbors associated with the rotationally invariant distance (RID) and Euclidean distance in the patch space when noise exists, and how we could apply the diffusion geometry to stabilize the selected metric. The dvNLEM is applied to an image database of 1,361 images and a comparison with the NLEM is provided. Different image quality assessments based on the error-sensitivity or the human visual system are applied to evaluate the performance.

A Simplified Physical Model Construction Method and Gas-Water Micro Scale Flow Simulation in Tight Sandstone Gas Reservoirs

Accuracy defects exist when modeling fluid transport by the classical capillary bundle model for tight porous media. In this study, a three-dimensional simplified physical model construction method was developed for tight sandstone gas reservoirs based on the geological origin, sedimentary compaction and clay mineral-cementation. The idea was to reduce the porosity of the tangent spheres physical model considering the synergistic effect of the above two factors and achieve a simplified model with the same flow ability as the actual tight core. Regarding the wall surface of the simplified physical model as the boundary and using the Lattice Boltzmann (LB) method, the relative permeability curves of gas and water in the simplified model were fitted with experimental results and a synergistic coefficient could be obtained, which we propose for characterizing the synergistic effect of sedimentary compaction and clay mineral-cementation. The simplified physical model and the results simulated by the LB method are verified with the experimental results under indoor experimental conditions, and the two are consistent. Finally, we have carried out a simulation of gas flooding water under conditions of high temperature and high pressure which are consistent with the actual tight sandstone gas reservoir. The simulation results show that both gas and water have relatively stronger seepage ability compared with the results of laboratory experiments. Moreover, the interfacial tension between gas and water is lower, and the swept volume is larger during placement. In addition, the binding ability of the rock surface to the water film adhered to it becomes reduced. The method proposed in this study could indicate high frequency change of pores and throats and used to reflect the seepage resistance caused by frequent collisions with the wall in microscopic numerical simulations of tight sandstone gas reservoirs.

Morphology and dynamics in SOC universality classes

Among the main issues about SOC models are the identification of universality classes and the relation with real systems. In this work we address the relationship between a sandpile and the slow advancement of a crack in a disordered medium. By means of extensive analyses in 1d, 2d and mean field, we show a strict and quantitative correspondence between the dynamics of a two-state Manna model and of a recently introduced Fiber Bundle model effectually describing the propagation of the crack front in a heterogeneous medium. We also demonstrate the ability of the Manna model itself to describe quantitatively the crack dynamical scaling, when supplied of the suited long range redistribution rule. On the other hand the Manna model looks hardly capable to yield the right crack front morphology. Specifically, no width saturation is observed, while the roughness displays at best a logarithmic scaling. These findings pose questions about definition and limits of universality classes in non equilibrium systems, and point out a lack of understanding of the interplay between dynamics and morphology in real and model systems.

Characterization of shale matrix pore structure via experiment and model

Shale gas reservoirs develop multi-scale pores ranging in size from nanometer to micrometer, the characteristics of gas transport involve the multi-scale pore space which divided into organic and inorganic matrix pores. This paper reveals the shale pore structure with large amounts of organic mesoporous based on the techniques of focused ion beam scanning electron microscopes (FIB-SEM), high-pressure mercury intrusion (MICP), and low-pressure adsorption (LPA), which also shows the size and distribution of these pores. Then the research characterizes effective pore scale via circular tube bundle model with due regard for gas adsorption layer thickness on the walls of organic pores and water film thickness on the walls of inorganic pores, and the investigation of shale pore geometry is significant for designing and developing shale gas reservoirs. This work shows that the widely existing shale mesoporous volume with diameter of 2~50 nm accounts for 81% based on experimental testing, then it reduces to about 76% via effective diameter model calculation.

Stability in a fiber bundle model: Existence of strong links and the effect of disorder.

The present paper deals with a fiber bundle model which consists of a fraction α of infinitely strong fibers. The inclusion of such an unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical value α_{c}. The present work has a twofold purpose: (i) a study of failure abruptness, mainly the brittle to quasibrittle transition point with varying α and (ii) variation of α_{c} as we change the strength of disorder introduced in the model. The brittle to quasibrittle transition is confirmed from the failure abruptness. On the other hand, the α_{c} is obtained from the knowledge of failure abruptness as well as the statistics of avalanches. It is observed that the brittle to quasibrittle transition point scales to lower values, suggesting more quasi-brittle-like continuous failure when α is increased. At the same time, the bundle becomes stronger as there are larger numbers of strong links to support the external stress. High α in a highly disordered bundle leads to an ideal situation where the bundle strength, as well as the predictability in failure process is very high. Also, the critical fraction α_{c}, required to make the model deviate from the conventional results, increases with decreasing strength of disorder. The analytical expression for α_{c} shows good agreement with the numerical results. Finally, the findings in the paper are compared with previous results and real-life applications of composite materials.

SO(32) heterotic line bundle models

We search for the three-generation standard-like and/or Pati-Salam models from the SO(32) heterotic string theory on smooth, quotient complete intersection Calabi-Yau threefolds with multiple line bundles, each with structure group U(1). These models are S- and T-dual to intersecting D-brane models in type IIA string theory. We find that the stable line bundles and Wilson lines lead to the standard model gauge group with an extra U(1)B−L via a Pati-Salam-like symmetry and the obtained spectrum consists of three chiral generations of quarks and leptons, and vector-like particles. Green-Schwarz anomalous U(1) symmetries control not only the Yukawa couplings of the quarks and leptons but also the higher-dimensional operators causing the proton decay.

Framework for cascade size calculations on random networks.

We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary degree distribution, degree-degree correlations, and, in case of threshold models, for arbitrary threshold distribution. With our approach, we shift the perspective from the known branching process approximations to the iterative update of suitable probability distributions. Such distributions are key to capture cascade dynamics that involve possibly continuous quantities and that depend on the cascade history, e.g., if load is accumulated over time. As a proof of concept, we provide two examples: (a) Constant load models that cover many of the analytically tractable casacade models, and, as a highlight, (b) a fiber bundle model that was not tractable by branching process approximations before. Our derivations cover the whole cascade dynamics, not only their steady state. This allows us to include interventions in time or further model complexity in the analysis.

Differential cocycles and Dixmier–Douady bundles

This paper exhibits equivalences of 2-stacks between certain models of $\mathbb{S}^1$-gerbes and differential 3-cocycles. We focus primarily on the model of Dixmier-Douady bundles, and provide an equivalence between the 2-stack of Dixmier-Douady bundles and the 2-stack of differential 3-cocycles of height 1, where the 'height' is related to the presence of connective structure. Differential 3-cocycles of height 2 (resp. height 3) are shown to be equivalent to $\mathbb{S}^1$-bundle gerbes with connection (resp. with connection and curving). These equivalences extend to the equivariant setting of $\mathbb{S}^1$-gerbes over Lie groupoids.

The influence of tube wall on fluid flow, permeability and streaming potential in porous transducer for liquid circular angular accelerometers

The effects of the tube wall on the fluid flow, permeability and streaming potential are reported for a porous transducer for use in a liquid circular angular accelerometer. Fluid flow and pressure near the surface of the transducer are modeled and validated numerically. We show that the differential pressure across the transducer is not affected by the tube wall. A capillary bundle model is employed to represent the transducer to obtain the radial porosity, permeability and streaming potential distributions due to wall effects. A simulated spherical packing is generated from measured particle parameters to specify the model by calculating the radial porosity distribution. The theoretical permeability and streaming potential coupling coefficient are located within one standard deviation from the mean of measurements. Due to the radial distribution of streaming potential, the electrode can be configured into a large streaming potential region to measure the signal more efficiently. Three electrode configurations are described based on these results, which can be applied to increase the signal of the sensor.

The avalanche process of the fiber bundle model with defect in local loading sharing

The fiber bundle model with defect is an extended model based on the classical fiber bundle model to describe the impact of the defect size and the defect density on the failure process in actual materials with defect. In order to explore the dynamic properties of the breakdown of materials with defect in short-range correlation, the model in local load sharing condition is numerically studied in detail in both uniform and Weibull threshold distribution cases. The simulation results show that both the defect size and the defect density have diverse impacts on the macroscopic mechanical properties and the statistical nature. From macroscopic view, the model parameters mainly impact the macroscopic fracture stage of the stretch process, while the initial tensile stage of the constitutive curves are almost not affected by the defect size and defect density. In the microscopic scale, the avalanche size distributions have no universality and are significantly influenced by the defect size and defect density.

Heterotic line bundle models on elliptically fibered Calabi-Yau three-folds

We analyze heterotic line bundle models on elliptically fibered Calabi-Yau three-folds over weak Fano bases. In order to facilitate Wilson line breaking to the standard model group, we focus on elliptically fibered three-folds with a second section and a freely-acting involution. Specifically, we consider toric weak Fano surfaces as base manifolds and identify six such manifolds with the required properties. The requisite mathematical tools for the construction of line bundle models on these spaces, including the calculation of line bundle cohomology, are developed. A computer scan leads to more than 400 line bundle models with the right number of families and an SU(5) GUT group which could descend to standard-like models after taking the ℤ2 quotient. A common and surprising feature of these models is the presence of a large number of vector-like states.

Impact of different chestnut coppice managements on root reinforcement and shallow landslide susceptibility

Abstract The abandonment of chestnut coppice management since the end of WWII has caused a general overaging of coppice stands leading to their inability to meet stand and soil stability standards. In view of the important role played by roots against the triggering of shallow landslides, we investigated root systems and their contribution to slope stability in chestnut coppices. In particular, we looked at possible different root regrowth dynamics and their effects on root reinforcement as function of different sylvicultural treatments. To this purpose we selected young (managed and unmanaged) and an old unmanaged coppice stands in two sites (Gerra and Bedano) in the southern Swiss Alps. We collected data on root distribution and root tensile force in the field and then applied the RBMw (Root Bundle Model Weibull) to estimate the degree of root reinforcement provided by the different silvicultural options. Results highlight the chestnut tree’s ability to renew the root system each time a stool is subject to a coppicing again. This implies there are important differences in terms of root regeneration, distribution and contribution to soil stability between young and overaged coppices. No significant differences in terms of root distribution and related soil reinforcement could be detected as a function of the different management options in young trees. Whenever possible, long-term silvicultural strategies in areas prone to shallow landslides should aim to convert pure chestnut coppices into mixed high forest stands.

Statistical size effect of flexural members in steel structures

This paper presents the results of theoretical and experimental investigations on the statistical size effect (SSE) of flexural members in steel. The chain of bundle model is developed, which is based on a stochastic material model by Weibull and lognormal distribution. Furthermore, this model is embedded into the finite element method (FEM) software for the analysis of a complicated structure with a stress gradient. In order to determine the stochastic material model parameters, uniaxial tensile tests were carried out based on specimens using the same steel with different sizes. By comparing the experimental and simulation results, the material parameters could be analyzed based on the relationship between the specimen sizes and strength. Moreover, the 3-point and 4-point bending tests were performed and simulated with the developed model. The experimental and simulation results demonstrate that the SSE also exists in the flexural member, and the equivalent yield stress is closely related to the stress distribution and volume of the structure component.

Fiber Bundle Model Under Heterogeneous Loading

The present work deals with the behavior of fiber bundle model under heterogeneous loading condition. The model is explored both in the mean-field limit as well as with local stress concentration. In the mean field limit, the failure abruptness decreases with increasing order k of heterogeneous loading. In this limit, a brittle to quasi-brittle transition is observed at a particular strength of disorder which changes with k. On the other hand, the model is hardly affected by such heterogeneity in the limit where local stress concentration plays a crucial role. The continuous limit of the heterogeneous loading is also studied and discussed in this paper. Some of the important results related to fiber bundle model are reviewed and their responses to our new scheme of heterogeneous loading are studied in details. Our findings are universal with respect to the nature of the threshold distribution adopted to assign strength to an individual fiber.

Electro-mechanical response of a 3D nerve bundle model to mechanical loads leading to axonal injury.

Traumatic brain injuries and damage are major causes of death and disability. We propose a 3D fully coupled electro-mechanical model of a nerve bundle to investigate the electrophysiological impairments due to trauma at the cellular level. The coupling is based on a thermal analogy of the neural electrical activity by using the finite element software Abaqus CAE 6.13-3. The model includes a real-time coupling, modulated threshold for spiking activation, and independent alteration of the electrical properties for each 3-layer fibre within a nerve bundle as a function of strain. Results of the coupled electro-mechanical model are validated with previously published experimental results of damaged axons. Here, the cases of compression and tension are simulated to induce (mild, moderate, and severe) damage at the nerve membrane of a nerve bundle, made of 4 fibres. Changes in strain, stress distribution, and neural activity are investigated for myelinated and unmyelinated nerve fibres, by considering the cases of an intact and of a traumatised nerve membrane. A fully coupled electro-mechanical modelling approach is established to provide insights into crucial aspects of neural activity at the cellular level due to traumatic brain injury. One of the key findings is the 3D distribution of residual stresses and strains at the membrane of each fibre due to mechanically induced electrophysiological impairments, and its impact on signal transmission.

Interaction of antivirals with a heptameric bundle model of the p7 protein of hepatitis C virus.

A series of ligands are known experimentally to affect the infectivity cycle of the hepatitis C virus. The target protein for the ligands is proposed to be p7, a 63 amino acid polytopic channel-forming protein, with possibly two transmembrane domains. Protein p7 is found to assemble into functional oligomers of various sizes, depending on the genotype (GT). Nine ligands are docked to various sites of a computationally derived heptameric bundle of p7 of GT1a. The energy of interaction, here binding energy, is calculated using three different docking programs (Autodock, MOE, LeadIT). Three protein regions are defined to which the ligands are placed, the loop region and the site with the termini as well as the mid-region which is supposed to track poses inside the putative pore. A common feature is that the loop sites and poses either within the pore or at the intermonomer space of the bundle are preferred for all ligands with proposed binding energies smaller than -10kJ/mol. BIT225, benzamine, amantadine, and NN-DNJ show good overall scoring.

Abstract A22: Stromal cell signature in luminal breast cancer associated with response to neoadjuvant chemotherapy

Abstract Background: In locally advanced breast cancer, neoadjuvant chemotherapy may reduce tumor dimension and allow breast-conserving surgeries. However, it is not yet possible to predict which patients will benefit from neoadjuvant chemotherapy, as some patients may not experience tumor reduction, especially in luminal tumor samples. Tumor behavior reflects an intense crosstalk between malignant and stromal cells; however, little importance has been placed on the influence of the stromal cell in tumor response to chemotherapy. Objective: Our aim was to evaluate whether a stromal cell transcriptional signature might be associated with response to neoadjuvant anthracycline and taxane, in locally advanced luminal breast cancer, using a direct approach of stromal cell selection. Methodology: Twenty-nine patients diagnosed with locally advanced luminal breast cancer received neoadjuvant chemotherapy (doxorubicin and cyclophosphamide followed by paclitaxel). Breast cancer slices were submitted to laser-capture microdissection (LCM) to select stromal cells. Total RNA from stromal enriched cells were isolated using Arcturus PicoPure RNA isolation (Life technologies) according to the manufacturer's protocol. Linearly amplified two-round RiboAmp HSPlus2-round and Low Input Quick Amp (Agilent Technologies) protocols were adapted to optimize the amplification for the small numbers of cells produced by LCM. The labelled cRNAs were hybridized onto the Sure Print G3 (8×60K, Agilent Technologies). After having washed the slides, the arrays were scanned with the Agilent Bundle Model B Microarray Scanner System (Agilent Technologies). Scanned image files were visually inspected for artifacts, and the fluorescence intensities were extracted and preprocessed with Agilent Feature Extraction software (v10.7.1) and to normalize the results geneSpring GX12.1 software (Agilent Technologies) was used. Expression levels were compared using MultiExperiment Viewer (MeV) software, applying significance analysis of microarrays (SAM). Gene set enrichment analysis (GSEA) was used to identify whether predefined gene sets might associate with gene expression differences between phenotypes (http://software.broadinstitute.org/gsea/index.jsp). This methodology makes it possible to detect situations where all genes, in a predefined set, change in a small but coordinated way. Results: In estrogen receptor (ER) positive tumors, GSEA (FDR < 0.1) indicated that tumor down-staging was correlated with one KEGG gene set: antigen processing antigen presentation (comprehending CD74, CD8A, CD8B, and 9 molecules of HLA complex, among others) and with four Gene Ontology (GO) gene sets (biologic process), including one related with immune response: regulation of T cell activation (comprehending genes such as ZAP70, LCK, CD24, CD47, CD3E, among others). Gene sets associated with tumor non-down-staging (GSEA FDR < 0.25) were KEGG gene set: extracellular cell matrix (ECM) receptor interaction (including 5 types of integrins, 6 collagens, 4 laminins, fibronectin 1, and trombospondin 1), as well as seven GO gene sets (biologic process): cell adhesion; cell recognition; embryonic development; (cellular component): cortical cytoskeleton; cell projection part; cell surface; cytosolic part. Conclusion: A stromal signature associated with immune response in locally advanced luminal breast cancer may be associated with tumor down-staging following neoadjuvant chemotherapy. Financial Support: FAPESP 09/100088-7. Citation Format: Maria Lucia H. Katayama, Rene A da Costa Vieira, Rosimeire A. Roela, Victor P. Andrade, Luiz Guilherme C. A. de Lima, Giselly Encinas, Ligia M. Kerr, Simone Maistro, M. Mitzi Brentani, Maria A. A. Koike Folgueira. Stromal cell signature in luminal breast cancer associated with response to neoadjuvant chemotherapy [abstract]. In: Proceedings of the AACR International Conference held in cooperation with the Latin American Cooperative Oncology Group (LACOG) on Translational Cancer Medicine; May 4-6, 2017; São Paulo, Brazil. Philadelphia (PA): AACR; Clin Cancer Res 2018;24(1_Suppl):Abstract nr A22.

Modes of failure in disordered solids.

The two principal ingredients determining the failure modes of disordered solids are the strength of heterogeneity and the length scale of the region affected in the solid following a local failure. While the latter facilitates damage nucleation, the former leads to diffused damage-the two extreme natures of the failure modes. In this study, using the random fiber bundle model as a prototype for disordered solids, we classify all failure modes that are the results of interplay between these two effects. We obtain scaling criteria for the different modes and propose a general phase diagram that provides a framework for understanding previous theoretical and experimental attempts of interpolation between these modes. As the fiber bundle model is a long-standing model for interpreting various features of stressed disordered solids, the general phase diagram can serve as a guiding principle in anticipating the responses of disordered solids in general.

A Fractal Model for Oil Transport in Tight Porous Media

Tight porous media are mainly composed of micro/nano-pores and throats, which leads to obvious microscale effect and nonlinear seepage characteristics. Based on the capillary bundle model and the fractal theory, a new nonlinear seepage equation was deduced, and a further fractal permeability model was obtained for oil transport in tight porous media by considering the effect of the boundary layer. The predictions of the model were then compared with experimental data to demonstrate that the model is valid. This model clarifies the oil transport mechanisms in tight porous media: the effective permeability is no longer a constant value and is governed by properties of tight porous media and oil. Furthermore, parameters influencing effective permeability were analyzed. The model can accurately present the seepage characteristics of the oil in tight porous media and provide a reliable basis for the development of unconventional reservoirs.

Probabilistic crack bridge model reflecting random bond properties and elastic matrix deformation

Abstract A semi-analytical probabilistic model of an isolated composite crack bridge is presented in this paper. With the assumptions of heterogeneous fibrous reinforcement embedded in an elastic matrix the model is capable of evaluating the stress and strain fields in both fibers and matrix. In order to be applicable as a representative unit in models at higher scales, the micromechanical response of the composite crack bridge is homogenized by using a probabilistic approach. Specifically, the mean response of a crack bridge is obtained as the integral of the response of a single fiber over the domain of random variables weighted by their joint probability density function. This approach has been used by the authors in a recent publication describing a single crack bridge with rigid matrix. The main extension of the present crack bridge model is the incorporation of elastic matrix deformations and of boundary conditions restricting fiber debonding at the crack bridge boundaries. The latter extension is needed to reflect the effects of interactions with neighboring cracks within a tensile specimen with multiple cracks. The model is verified against three limiting cases with known analytical solutions (fiber bundle model, crack bridge with rigid matrix, mono-filament in elastic matrix) and is shown to be in exact conformity with all of these limiting cases.