Search

Multiple Sclerosis (MS) is an incurable neuroinflammatory disease of the central nervous system that affects more than 2.2 million people globally. Although evidence shows the benefits of physical activity and exercise, participation in exercise in people with Multiple Sclerosis (pwMS) has been poor. A synthesis of qualitative research is required to better understand the factors associated with physical activity and exercise participation in pwMS. To synthesise findings from qualitative studies exploring factors associated with physical activity and exercise participation in people with MS. Qualitative systematic review using the Inductive Thematic Synthesis approach. CINAHL, Embase, MEDLINE, PsycINFO, and Scopus databases were systematically searched with further searches of reference lists and OpenGrey. Qualitative studies or mixed-method studies with relevant qualitative content that explored the factors related to physical activity and exercise participation in people with MS. Thematic Synthesis and Critical Appraisal Skills Programme (CASP) qualitative studies checklist. Thirty-nine studies met the inclusion criteria. Three analytical themes were generated from 11 descriptive themes outlining the factors associated with physical activity and exercise participation in people with MS. Physical activity and exercise participation in people with MS is influenced by internal and external factors. PwMS adopt a range of strategies to sustain physical activity and exercise participation. Healthcare professionals could play a role in the physical activity and exercise participation of pwMS. PROSPERO 2020:CRD42020214002. [ABSTRACT FROM AUTHOR]

Traditional numerical discretization-based solvers of partial differential equations (PDEs) are fundamentally agnostic to domains, boundary conditions and coefficients. In contrast, machine learnt solvers have a limited generalizability across these elements of boundary value problems. This is strongly true in the case of surrogate models that are typically trained on direct numerical simulations of PDEs applied to one specific boundary value problem. In a departure from this direct approach, the label-free machine learning of solvers is centered on a loss function that does not use computed field solutions as labels. Instead, the PDE and boundary conditions are directly incorporated in residual form to express the loss function during training. However, their generalization across boundary conditions is limited and they remain strongly domain-dependent. Here, we present a framework that generalizes across domains, boundary conditions and coefficients while simultaneously learning the PDE in weak form. Our work explores the ability of convolutional neural network (CNN)-based encoder–decoder architectures to learn to solve a PDE in greater generality than its restriction to a particular boundary value problem. In this first Communication, we take the canonical path through elliptic PDEs and focus on steady-state diffusion, linear and nonlinear elasticity. Importantly, the learning happens independently of any labeled field data from either experiments or direct numerical solutions. We develop probabilistic CNNs in the Bayesian setting using variational inference. Extensive results for these problem classes demonstrate the framework's ability to learn PDE solvers that generalize across hundreds of thousands of domains, boundary conditions and coefficients, including extrapolation beyond the learning regime. Once trained, the machine learning solvers are orders of magnitude faster than discretization-based solvers. They therefore have relevance to high-throughput solutions of PDEs on varied domains, boundary conditions and coefficients, such as for inverse modeling, optimization, design and decision-making. We place our work in the context of other recent machine learning solvers of PDEs including continuous operator learning frameworks, as well as make comparisons of performance where possible. Finally, we note extensions to transfer learning, active learning and reinforcement learning. [ABSTRACT FROM AUTHOR]

Abstract Machine learning has been effective at detecting patterns and predicting the response of systems that behave free of natural laws. Examples include learning crowd dynamics, recommender systems and autonomous mobility. There also have been applications to the search for new materials that draw upon big-data classification problems. However, when it comes to physical systems governed by conservation laws, the role of machine learning has been more limited. Here, we present our recent work in exploring the role of machine learning methods in discovering, or aiding, the search for physics. Specifically, we focus on using machine learning algorithms to represent high-dimensional free energy surfaces with the goal of identifying precipitate morphologies in alloy systems. Traditionally, this problem has been approached by combining phase field models, which impose first-order dynamics, with elasticity, to traverse a free energy landscape in search of minima. Equilibrium precipitate morphologies occur at these minima. Here, we exploit the machine learning methods to represent high-dimensional data, combined with surrogate optimization, sensitivity analysis and multifidelity modeling as an alternate framework to explore phenomena controlled by energy extremization. This combination of data-driven methods offers an alternative to the imposition of first-order dynamics via phase field methods, and represents one aspect of applying machine learning to materials physics. Highlights • Machine learning and data generation by DNS are combined to find equilibrium states. • The algorithm out-performs phase field dynamics in compute time and FLOP-count. • Our workflow leverages heterogeneous computing platforms combining CPUs and GPUs. [ABSTRACT FROM AUTHOR]

In this communication, we propose a model to study the non-equilibrium process by which actin stress fibers develop force in contractile cells. The emphasis here is on the non-equilibrium thermodynamics, which is necessary to address the mechanics as well as the chemistry of dynamic cell contractility. In this setting, we are able to develop a framework that relates (a) the dynamics of force generation within the cell and (b) the cell's response to external stimuli to the chemical processes occurring within the cell, as well as to the mechanics of linkage between the stress fibers, focal adhesions and extracellular matrix. [ABSTRACT FROM AUTHOR]

Abstract: This work is based upon a coupled, lattice-based continuum formulation that was previously applied to problems involving strong coupling between mechanics and mass transport; e.g. diffusional creep and electromigration [K. Garikipati, L.C. Bassman, M.D. Deal, A lattice-based micromechanical continuum formulation for stress-driven mass transport in polycrystalline solids, J. Mech. Phys. Solids 49(6) (2001) 1209–1237; K. Garikipati, L.C. Bassman, Atomically-based field formulations for coupled problems of composition and mechanics, in: L.P. Kubin, J.L. Bassani, K. Cho, H. Gao, R.L.B. Selinger (Eds.), MRS symposium proceedings, Multiscale Modeling of Materials—2000, vol. 653, Materials Research Society, Warrendale, 2001, pp. Z9.6.1–Z9.6.6]. Here we discuss an enhancement of this formulation to account for migrating grain boundaries. The level set method is used to model grain-boundary migration in an Eulerian framework where a grain boundary is represented as the zero level set of an evolving higher-dimensional function. This approach can easily be generalized to model other problems involving migrating interfaces; e.g. void evolution and free-surface morphology evolution. The level-set equation is recast in a remarkably simple form which obviates the need for spatial stabilization techniques. This simplified level-set formulation makes use of velocity extension and field re-initialization techniques. In addition, a least-squares smoothing technique is used to compute the local curvature of a grain boundary directly from the level-set field without resorting to higher-order interpolation. A notable feature is that the coupling between mass transport, mechanics and grain-boundary migration is fully accounted for. The complexities associated with this coupling are highlighted and the operator-split algorithm used to solve the coupled equations is described. [Copyright &y& Elsevier]

The numerical solution of strain gradient-dependent continuum problems has been dogged by continuity demands on the basis functions. For most commonly accepted models, solutions using the finite element method demand C1 continuity of the shape functions. Here, recent developments in discontinuous Galerkin methods are explored and exploited for the solution of a prototype non-linear strain gradient-dependent continuum model. A formulation is developed that allows the rigorous solution of a strain gradient damage model using standard C0 shape functions. The formulation is tested in one dimension for the simplest possible finite element formulation: continuous piecewise linear displacement and constant (on elements) internal variable. Numerical results are shown to compare excellently with a benchmark solution. The results are remarkable given the simplicity of the proposed formulation. [Copyright &y& Elsevier]

Focuses on electrostastiscally actuated polysilicon beams fabricated in the multiuser microelectromechanical systems process. Emphasis on the behavior when the beam is in contact with an underlying silicon nitride dielectric layer; Two-dimensional electromechanical simulations; Pull-in voltage and capacitance voltage measurements.

Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamically evolving microstructures. The ability to rapidly compute the macroscopic behavior based on these detailed microstructures is of paramount importance for accelerating material discovery and design. Here, our focus is on the macroscopic, nonlinear elastic response of materials harboring microstructure. Because of the diversity of microstructural patterns that can form, there is interest in taking a purely computational approach to predicting their macroscopic response. However, the evaluation of macroscopic, nonlinear elastic properties purely based on direct numerical simulations (DNS) is computationally very expensive, and hence impractical for material design when a large number of microstructures need to be tested. A further complexity of a hierarchical nature arises if the elastic free energy and its variation with strain is a small-scale fluctuation on the dominant trajectory of the total free energy driven by microstructural dynamics. To address these challenges, we present a data-driven approach, which combines advanced neural network (NN) models with DNS to predict the homogenized, macroscopic, mechanical free energy and stress fields arising in a family of multi-component crystalline solids that develop microstructure. The microstructures are numerically generated by solving a coupled, mechanochemical spinodal decomposition problem governed by nonlinear strain gradient elasticity and the Cahn–Hilliard phase field equation. The hierarchical structure of the free energy's evolution induces a multi-resolution character to the machine learning paradigm: We construct knowledge-based neural networks (KBNNs) with either pre-trained fully connected deep neural networks (DNNs), or pre-trained convolutional neural networks (CNNs) that describe the dominant characteristic of the data to fully represent the hierarchically evolving free energy. We demonstrate multi-resolution learning of the materials physics; specifically of the nonlinear elastic response for both fixed and evolving microstructures. • Hybrid neural network model based on pre-trained model (knowledge) is constructed. • Knowledge-based neural networks resolve homogenized free energy and stresses. • Knowledge-based neural networks also capture multi-resolution information in data. • Multiple features are pre-selected to characterize microstructures in DNNs. • We show that CNNs outperform DNNs in representing microstructures. [ABSTRACT FROM AUTHOR]

Accurately predicting errors incurred in a cross-section model for two-step reactor analysis enables the development of optimal case matrices and more efficient cross-section models. In a companion paper, we developed a systematic methodology for the partial derivatives cross-section model through rigorous analytic error analysis. In this paper, we verify our methodology against the conventional "brute force" numerical approach using a typical pressurized water reactor (PWR) lattice. By successfully reproducing known results, we gain confidence in our methodology's application to advanced reactor environments, where optimal case matrices are generally not known. Our error methodology relies on accurately estimating bounds on the derivatives of the cross-section functions, a task we achieve through an order of convergence study. We use these derivative bounds in derived error expressions to obtain pointwise and setwise cross-section error bounds and verify these results with reference solutions of various two-group cross sections. We then propagate the cross-section error bounds to reactivity error using first-order perturbation theory and analyze their combined effect. Application of this approach to our test problem corroborates our prior qualitative findings with quantitative evidence and reveals the relative magnitudes of interpolation and model form error sources across diverse PWR cross-section functionalizations. Our results suggest systematic pathways for improving case matrix construction to minimize the overall error. These findings also confirm what is well known to the light water reactor design community, which is that interpolation error of cross sections for standard interpolation procedures and case matrix structures is on the order of 10 pcm or less. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multi-lattice problems, and investigating historical effects within the macroscopic depletion model. [ABSTRACT FROM AUTHOR]

Accurate assessment of uncertainties in cross-section data is crucial for reliable nuclear reactor simulations and safety analyses. In this study, we focus on the interpolation procedure of the partial derivatives (PD) cross-section model used to evaluate nodal parameters from pregenerated multigroup libraries. Our primary objective is to develop a systematic methodology that enables prediction of the incurred errors in the cross-section model, leading to the development of optimal case matrices, more efficient cross-section models, and informed case matrix construction for reactor types lacking substantial data and experience. We make progress toward this objective through a rigorous analytic error analysis enabled by the derivation of error expressions and bounds for the PD model based on the discovery that the method is a form of Lagrange interpolation. Our investigations reveal distinct outcomes depending on the chosen cross-section functionalizations, achieved by identifying the sources of error. These error sources are found to include interpolation error, which is always present, and model form error, which is a property of the supplied case matrix. We show that simply increasing grid refinement through the addition of branches may not always lead to decreased cross-section errors, particularly in cases where the model form error predominantly contributes to the total error. We present numerical results and verification in a companion paper, showing these different error characteristics for various cross-section functionalizations. Although applied to current light water reactor environments, our methodology offers a means for advanced reactor analysts to develop case matrices with quantified error levels, advancing the goal of a general methodology for robust two-step reactor analysis. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multilattice problems, and investigating historical effects within the macroscopic depletion model. [ABSTRACT FROM AUTHOR]

We introduce a class of unconditionally energy-stable, high-order-accurate schemes for gradient flows in a very general setting. The new schemes are a high-order analogue of the minimizing-movements approach for generating a time discrete approximation to a gradient flow by solving a sequence of optimization problems. In particular, each step entails minimizing the associated energy of the gradient flow plus a movement limiter term that is, in the classical context of steepest descent with respect to an inner product, simply quadratic. A variety of existing unconditionally stable numerical methods can be recognized as (typically just first-order-accurate-in-time) minimizing-movement schemes for their associated evolution equations, already requiring the optimization of the energy plus a quadratic term at every time step. Therefore, our approach gives a painless way to extend these to high-order-accurate-in-time schemes while maintaining their unconditional stability. In this sense, it can be viewed as a variational analogue of Richardson extrapolation. [ABSTRACT FROM AUTHOR]

We present an energy basin finding algorithm for identifying the states in absorbing Markov chains used for accelerating kinetic Monte Carlo (KMC) simulations out of trapping energy basins. The algorithm saves groups of states corresponding to basic energy basins in which there is (i) a minimum energy saddle point and (ii) in moving away from the minimum the saddle point energies do not decrease between successive moves. When necessary, these groups are merged to help the system escape basins of basins. Energy basins are identified either as the system visits states, or by exploring surrounding states before the system visits them. We review exact and approximate methods for accelerating KMC simulations out of trapping energy basins and implement them within our algorithm. Its flexibility to store varying numbers of states, and ability to merge sets of saved states as the program runs, allows it to efficiently escape complicated trapping energy basins. Through simulations of vacancy-As cluster dissolution in Si, we demonstrate our algorithm can be several orders of magnitude faster than standard KMC simulations. [ABSTRACT FROM AUTHOR]

Cellular heterogeneity is a ubiquitous aspect of biology and a major obstacle to successful cancer treatment. Several techniques have emerged to quantify heterogeneity in live cells along axes including cellular migration, morphology, growth, and signaling. Crucially, these studies reveal that cellular heterogeneity is not a result of randomness or a failure in cellular control systems, but instead is a predictable aspect of multicellular systems. We hypothesize that individual cells in complex tissues can behave as reward-maximizing agents and that differences in reward perception can explain heterogeneity. In this perspective, we introduce inverse reinforcement learning as a novel approach for analyzing cellular heterogeneity. We briefly detail experimental approaches for measuring cellular heterogeneity over time and how these experiments can generate datasets consisting of cellular states and actions. Next, we show how inverse reinforcement learning can be applied to these datasets to infer how individual cells choose different actions based on heterogeneous states. Finally, we introduce potential applications of inverse reinforcement learning to three cell biology problems. Overall, we expect inverse reinforcement learning to reveal why cells behave heterogeneously and enable identification of novel treatments based on this new understanding. [ABSTRACT FROM AUTHOR]

We present careful numerical convergence studies, using parameterized curves to reach very high resolutions in two dimensions, of a level set method for multiphase curvature motion known as the Voronoi implicit interface method. Our tests demonstrate that in the unequal, additive surface tension case, the Voronoi implicit interface method does not converge to the desired limit. We then present a variant that maintains the spirit of the original algorithm and appears to fix the nonconvergence. As a bonus, the new variant extends the Voronoi implicit interface method to unequal mobilities. [ABSTRACT FROM AUTHOR]

New criteria for energy stability of multi-step, multi-stage, and mixed schemes are introduced in the context of evolution equations that arise as gradient flow with respect to a metric. These criteria are used to exhibit second and third order consistent, energy stable schemes, which are then demonstrated on several partial differential equations that arise as gradient flow with respect to the 2-Wasserstein metric. • Energy stability conditions for multi-step, multi-stage, and mixed schemes for gradient flow in arbitrary metric spaces. • New criteria are proposed based on embedding of finite graphs into Euclidean spaces. • Second order energy stable and third order energy bounded schemes are exhibited. [ABSTRACT FROM AUTHOR]

Coronary Artery Disease (CAD) is one of the most common forms of heart disease, caused by a buildup of atherosclerotic plaque in the coronary arteries. When this buildup is extensive, it can result in obstructions in the lumen of the blood vessels (known as stenosis) that lead to insufficient delivery of essential molecules like oxygen to the heart. Fractional Flow Reserve (FFR), defined as the ratio of pressures distal and proximal to the stenosis, is the physiologic gold standard for assessing the severity of CAD in the cardiac catheterization laboratory and relies upon the placement of an invasive coronary wire. Despite its strong diagnostic value, invasive FFR assessment is underutilized due to its cost, time-consuming nature, technique-dependent variability, and the small potential of increased risk to the patient. In this study, an attention-based multi-fidelity machine learning model (AttMulFid) is proposed for efficient and accurate virtual FFR (vFFR) assessment, including uncertainty quantification, without the use of an invasive coronary wire. Within AttMulFid, an autoencoder is used to select geometric features from the coronary arteries, with additional attention to the stenosis region. A convolutional neural network (feature fusion U-Net) combines multi-fidelity data, geometric features, and boundary conditions to produce accurate estimates of vFFR. We present results that demonstrate the good performance of AttMulFid against CFD FFR data, as well as in vivo, invasive FFR assessment from patients. Our results also show that the selected geometric features learned by the autoencoder can accurately represent the entire geometry, with greater attention on key features such as stenosis. AttMulFid thus presents itself as a feasible approach for non-invasive, rapid, and accurate vFFR assessment. [ABSTRACT FROM AUTHOR]

Chemotaxis, regulated by oscillatory signals, drives critical processes in cancer metastasis. Crucial chemoattractant molecules in breast cancer, CXCL12 and EGF, drive the activation of ERK and Akt. Regulated by feedback and crosstalk mechanisms, oscillatory signals in ERK and Akt control resultant changes in cell morphology and chemotaxis. While commonly studied at the population scale, metastasis arises from small numbers of cells that successfully disseminate, underscoring the need to analyze processes that cancer cells use to connect oscillatory signaling to chemotaxis at single-cell resolution. Furthermore, little is known about how to successfully target fast-migrating cells to block metastasis. We investigated to what extent oscillatory networks in single cells associate with heterogeneous chemotactic responses and how targeted inhibitors block signaling processes in chemotaxis. We integrated live, single-cell imaging with time-dependent data processing to discover oscillatory signal processes defining heterogeneous chemotactic responses. We identified that short ERK and Akt waves, regulated by MEK-ERK and p38-MAPK signaling pathways, determine the heterogeneous random migration of cancer cells. By comparison, long ERK waves and the morphological changes regulated by MEK-ERK signaling, determine heterogeneous directed motion. This study indicates that treatments against chemotaxis in consider must interrupt oscillatory signaling. [ABSTRACT FROM AUTHOR]

Contemporary material characterization techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterization problem. As material models and descriptions differ, so too must the approaches for identifying parameters and their corresponding mechanisms. The widely used Ogden material model can be comprised of a chosen number of terms of the same mathematical form, which presents challenges of parsimonious representation, interpretability and stability. Robust techniques for system identification of any material model are important to assess and improve experimental design, in addition to their centrality to forward computations. Using fully three-dimensional displacement fields acquired in silicone elastomers with our recently developed magnetic resonance cartography (MR-u) technique on the order of greater than 20 000 points per sample , we leverage partial differential equation-constrained optimization as the basis of variational system identification of our material parameters. We incorporate the statistical F-test to maintain parsimony of representation. Using a new, local deformation decomposition locally into mixtures of biaxial and uniaxial tensile states, we evaluate experiments based on an analytical sensitivity metric and discuss the implications for experimental design. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'. [ABSTRACT FROM AUTHOR]

Abstract: Predictions of crack propagation is a valuable resource for ensuring structural integrity and damage tolerance of aerospace structures. Towards that end, a variational multiscale approach to predict mixed mode in-plane cohesive crack propagation is presented here. To demonstrate applicability and to provide validation of the finite element based predictive methodology, a comparative study of the numerical results with the corresponding experimental observations of crack propagation in laminated fiber reinforced composite panels is presented. [Copyright &y& Elsevier]

Abstract: Fracture experiments were carried out on continuous fiber polymer matrix laminated composite panels to investigate cohesive, through-the-thickness crack propagation. The experiments were designed to examine curved cracks, resulting from either eccentric loading or non-symmetric specimen geometry with respect to the starter crack. The constitutive description of the observed complex diffused damage zone, which from a continuum viewpoint may be considered a macroscopic crack, involves complex/evolving traction–separation relations and mode-mixity conditions. This paper presents some relevant experimental investigations and their numerical modeling using the variational multiscale cohesive method developed by Rudraraju et al. which is an effective framework for simulating cohesive crack evolution and thereby predicting the residual strength of cracked composite panels. [Copyright &y& Elsevier]

Abstract: A series of experimental results on the in-plane fracture of a fiber reinforced laminated composite panel is analyzed using the variational multiscale cohesive method (VMCM). The VMCM results demonstrate the influence of specimen geometry and load distribution on the propagation of large scale bridging cracks in the fiber reinforced panel. Experimentally observed variation in fracture resistance is substantiated numerically by comparing the experimental and VMCM load–displacement responses of geometrically scaled single edge-notch three point bend (SETB) specimens. The results elucidate the size dependence of the traction-separation relationship for this class of materials even in moderately large specimens, contrary to the conventional understanding of it being a material property. The existence of a “free bridging zone” (different from the conventional “full bridging zone”) is recognized, and its influence on the evolving fracture resistance is discussed. The numerical simulations and ensuing bridging zone evolution analysis demonstrates the versatility of VMCM in objectively simulating progressive crack propagation, compared against conventional numerical schemes like traditional cohesive zone modeling, which require a priori knowledge of the crack path. [Copyright &y& Elsevier]

Abstract: A discontinuous Galerkin finite element method has been developed to treat the high-order spatial derivatives appearing in the Cahn–Hilliard equation. The Cahn–Hilliard equation is a fourth-order nonlinear parabolic partial differential equation, originally proposed to model phase segregation of binary alloys. The developed discontinuous Galerkin approach avoids the need for mixed finite element methods, coupled equations or interpolation functions with a high degree of continuity that have been employed in the literature to treat the fourth-order spatial derivatives. The variational formulation of the discontinuous Galerkin method, its implementation and numerical examples are presented. In this communication, it is also shown under what conditions the method is stable, and an error estimate in an energy-type norm is presented. The method is evaluated by comparison with a standard finite element treatment in which the Cahn–Hilliard equation is decomposed into two coupled partial differential equations. [Copyright &y& Elsevier]

Abstract: A discontinuous Galerkin method has been developed for strain gradient-dependent damage. The strength of this method lies in the fact that it allows the use of C 0 interpolation functions for continuum theories involving higher-order derivatives, while in a conventional framework at least C 1 interpolations are required. The discontinuous Galerkin formulation thereby offers significant potential for engineering computations with strain gradient-dependent models. When using basis functions with a low degree of continuity, jump conditions arise at element edges which are incorporated in the weak form. In addition to the formulation itself, a detailed study of the convergence properties of the method for various element types is presented and an error analysis is undertaken. Numerical results of some one- and two-dimensional problems are presented and discussed. [Copyright &y& Elsevier]

We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possibly with respect to an inner product that depends on the solution, and we establish their energy stability. This class includes as a special case high order, unconditionally stable schemes obtained via convexity splitting. The new schemes are demonstrated on a variety of gradient flows, including partial differential equations that are gradient flow with respect to the Wasserstein (mass transport) distance. • High-order, energy stable, semi-implicit schemes for general gradient flows. • The schemes cost as much as multiple calls per time step to a first-order scheme. • Schemes for gradient flows with varying inner products, such as Wasserstein. • Numerical examples of the new schemes on a variety of gradient flows. [ABSTRACT FROM AUTHOR]

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelitymodelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff-Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a 'phase diagram' for its symmetric and broken-symmetry states. [ABSTRACT FROM AUTHOR]

Tissue folds are structural motifs critical to organ function. In the intestine, bending of a flat epithelium into a periodic pattern of folds gives rise to villi, finger-like protrusions that enable nutrient absorption. However, the molecular and mechanical processes driving villus morphogenesis remain unclear. Here, we identify an active mechanical mechanism that simultaneously patterns and folds the intestinal epithelium to initiate villus formation. At the cellular level, we find that PDGFRA+ subepithelial mesenchymal cells generate myosin II-dependent forces sufficient to produce patterned curvature in neighboring tissue interfaces. This symmetry-breaking process requires altered cell and extracellular matrix interactions that are enabled by matrix metalloproteinase-mediated tissue fluidization. Computational models, together with in vitro and in vivo experiments, revealed that these cellular features manifest at the tissue level as differences in interfacial tensions that promote mesenchymal aggregation and interface bending through a process analogous to the active dewetting of a thin liquid film. [Display omitted] • Mesenchymal aggregates generate forces that fold the mammalian intestinal epithelium • Active and fluid-like properties of aggregates program tissue geometry and pattern • Matrix metalloproteinases fluidize the subepithelial mesenchyme to initiate aggregation • Mesenchymal patterning conceptually resembles water dewetting from a hydrophobic surface Subepithelial mesenchyme behaves like a dewetting fluid to pattern and fold the intestinal epithelium, initiating the formation of villi. [ABSTRACT FROM AUTHOR]

• Second order two-phase mean curvature motion threshold dynamics algorithm in any dimension. • Unconditionally stable second order two-phase mean curvature motion threshold dynamics algorithm in two dimensions. • Rigorous consistency calculations for both of the aforementioned methods. The threshold dynamics algorithm of Merriman, Bence, and Osher is only first order accurate in the two-phase setting. Its accuracy degrades further to half order in the multi-phase setting, a shortcoming it has in common with other related, more recent algorithms such as the equal surface tension version of the Voronoi implicit interface method. As a first, rigorous step in addressing this shortcoming, we present two different second order accurate versions of two-phase threshold dynamics. Unlike in previous efforts in this direction, we present careful consistency calculations for both of our algorithms. The first algorithm is consistent with its limit (motion by mean curvature) up to second order in any space dimension. The second achieves second order accuracy only in dimension two, but comes with a rigorous stability guarantee (unconditional energy stability) in any dimension – a first for high order schemes of its type. [ABSTRACT FROM AUTHOR]

Mollusk shells are an ideal model system for understanding the morpho-elastic basis of morphological evolution of invertebrates’ exoskeletons. During the formation of the shell, the mantle tissue secretes proteins and minerals that calcify to form a new incremental layer of the exoskeleton. Most of the existing literature on the morphology of mollusks is descriptive. The mathematical understanding of the underlying coupling between pre-existing shell morphology, de novo surface deposition and morpho-elastic volume growth is at a nascent stage, primarily limited to reduced geometric representations. Here, we propose a general, three-dimensional computational framework coupling pre-existing morphology, incremental surface growth by accretion, and morpho-elastic volume growth. We exercise this framework by applying it to explain the stepwise morphogenesis of seashells during growth: new material surfaces are laid down by accretive growth on the mantle whose form is determined by its morpho-elastic growth. Calcification of the newest surfaces extends the shell as well as creates a new scaffold that constrains the next growth step. We study the effects of surface and volumetric growth rates, and of previously deposited shell geometries on the resulting modes of mantle deformation, and therefore of the developing shell’s morphology. Connections are made to a range of complex shells ornamentations. [ABSTRACT FROM AUTHOR]

• Ferroelastic toughening can solve the mechanics challenges of solid electrolytes. • Twin boundary migration can reversibly accommodate cyclic strains. • Fundamental materials principles are described to design solid electrolytes. The most promising solid electrolytes for all-solid-state Li batteries are oxide and sulfide ceramics. Current ceramic solid electrolytes are brittle and lack the toughness to withstand the mechanical stresses of repeated charge and discharge cycles. Solid electrolytes are susceptible to crack propagation due to dendrite growth from Li metal anodes and to debonding processes at the cathode/electrolyte interface due to cyclic variations in the cathode lattice parameters. In this perspective, we argue that solutions to the mechanics challenges of all-solid-state batteries can be borrowed from the aerospace industry, which successfully overcame similar hurdles in the development of thermal barrier coatings of superalloy turbine blades. Their solution was to exploit ferroelastic and transformation toughening mechanisms to develop ceramics that can withstand cyclic stresses due to large variations in temperature. This perspective describes fundamental materials design principles with which to search for solid electrolytes that are ferroelastically toughened. [ABSTRACT FROM AUTHOR]

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energy data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here, we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. Spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials. [ABSTRACT FROM AUTHOR]

Swelling of a commercial 5 Ah lithium-ion cell with a nickel/manganese/cobalt-oxide cathode is investigated as a function of the charge state and the charge/discharge rate. In combination with sensitive displacement measurements, knowledge of the electrode configuration within this prismatic cell's interior allows macroscopic deformations of the casing to be correlated to electrochemical and mechanical transformations in individual anode/separator/cathode layers. Thermal expansion and interior charge state are both found to cause significant swelling. At low rates, where thermal expansion is negligible, the electrode sandwich dilates by as much as 1.5% as the charge state swings from 0% to 100% because of lithium-ion intercalation. At high rates a comparably large residual swelling was observed at the end of discharge. Thermal expansion caused by joule heating at high discharge rate results in battery swelling. The changes in displacement with respect to capacity at low rate correlate well with the potential changes known to accompany phase transitions in the electrode materials. Although the potential response changes minimally with the C-rate, the extent of swelling varies significantly, suggesting that measurements of swelling may provide a sensitive gauge for characterizing dynamic operating states. [ABSTRACT FROM AUTHOR]

It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an in vitro tumor model, which isolates mechanical interactions between cancer tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling the same, oft-reported observation of in vivo tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that are stiffer than the tumors, but when they grow in more compliant hydrogels they remain closer to spherical in shape. Using large scale, nonlinear elasticity computations we show that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesize that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. This result may hold significance for explaining the shape progression of early solid tumors in vivo and is an important step in understanding the processes underlying solid tumor growth. [ABSTRACT FROM AUTHOR]

In this work we employ an encoder–decoder convolutional neural network to predict the failure locations of porous metal tension specimens based only on their initial porosities. The process we model is complex, with a progression from initial void nucleation, to saturation, and ultimately failure. The objective of predicting failure locations presents an extreme case of class imbalance since most of the material in the specimens does not fail. In response to this challenge, we develop and demonstrate the effectiveness of data- and loss-based regularization methods. Since there is considerable sensitivity of the failure location to the particular configuration of voids, we also use variational inference to provide uncertainties for the neural network predictions. We connect the deterministic and Bayesian convolutional neural network formulations to explain how variational inference regularizes the training and predictions. We demonstrate that the resulting predicted variances are effective in ranking the locations that are most likely to fail in any given specimen. [ABSTRACT FROM AUTHOR]

Understanding the molecular alterations that confer cancer cells with motile, metastatic properties is needed to improve patient survival. Here, we report that p38γ motogen-activated protein kinase regulates breast cancer cell motility and metastasis, in part, by controlling expression of the metastasis-associated small GTPase RhoC. This p38γ--RhoC regulatory connection wasmediated by a novelmechanismofmodulating RhoC ubiquitination. This relationship persisted across multiple cell lines and in clinical breast cancer specimens. Using a computational mechanical model based on the finite element method, we showed that p38γ-mediated cytoskeletal changes are sufficient to control cell motility. This model predicted novel dynamics of leading edge actin protrusions,whichwere experimentally verified and established to be closely related to cell shape and cytoskeletal morphology. Clinical relevance was supported by evidence that elevated expression of p38γ is associated with lower overall survival of patientswith breast cancer. Taken together, our results offer a detailed characterization of how p38γ contributes to breast cancer progression. Herein we present a new mechanics-based analysis of cell motility, and report on the discovery of a leading edge behavior in motile cells to accommodate modified cytoskeletal architecture. In summary, these findings not only identify a novel mechanism for regulating RhoC expression but also advance p38γ as a candidate therapeutic target. [ABSTRACT FROM AUTHOR]

Background: We consider a focal adhesion to be made up of molecular complexes, each consisting of a ligand, an integrin molecule, and associated plaque proteins. Free energy changes drive the binding and unbinding of these complexes and thereby controls the focal adhesion's dynamic modes of growth, treadmilling and resorption. Principal Findings: We have identified a competition among four thermodynamic driving forces for focal adhesion dynamics: (i) the work done during the addition of a single molecular complex of a certain size, (ii) the chemical free energy change associated with the addition of a molecular complex, (iii) the elastic free energy change associated with deformation of focal adhesions and the cell membrane, and (iv) the work done on a molecular conformational change. We have developed a theoretical treatment of focal adhesion dynamics as a nonlinear rate process governed by a classical kinetic model. We also express the rates as being driven by out-of-equilibrium thermodynamic driving forces, and modulated by kinetics. The mechanisms governed by the above four effects allow focal adhesions to exhibit a rich variety of behavior without the need to introduce special constitutive assumptions for their response. For the reaction-limited case growth, treadmilling and resorption are all predicted by a very simple chemo-mechanical model. Treadmilling requires symmetry breaking between the ends of the focal adhesion, and is achieved by driving force (i) above. In contrast, depending on its numerical value (ii) causes symmetric growth, resorption or is neutral, (iii) causes symmetric resorption, and (iv) causes symmetric growth. These findings hold for a range of conditions: temporally-constant force or stress, and for spatiallyuniform and non-uniform stress distribution over the FA. The symmetric growth mode dominates for temporally-constant stress, with a reduced treadmilling regime. Significance: In addition to explaining focal adhesion dynamics, this treatment can be coupled with models of cytoskeleton dynamics and contribute to the understanding of cell motility. [ABSTRACT FROM AUTHOR]

In the two-step method for nuclear reactor simulation, lattice physics calculations are performed to compute homogenized cross-sections for a variety of burnups and lattice configurations. A nodal code is then used to perform full-core analysis using the pre-calculated homogenized cross-sections. One source of uncertainty introduced in this method is that the lattice configuration or depletion conditions typically do not match a pre-calculated one from the lattice physics simulations. Therefore, some interpolation model must be used to estimate the homogenized cross-sections in the nodal code. This current study provides a methodology for sensitivity analysis to quantify the impact of state variables on the homogenized cross-sections. This methodology also allows for analyses of the historical effect that the state variables have on homogenized cross-sections. An application of this methodology on a lattice for the Westinghouse AP1000® reactor is presented where coolant density, fuel temperature, soluble boron concentration, and control rod insertion are the state variables of interest. The effects of considering the instantaneous values of the state variables, historical values of the state variables, and burnup-averaged values of the state variables are analyzed. Using these methods, it was found that a linear model that only considers the instantaneous and burnup-averaged values of state variables can fail to capture some variations in the homogenized cross-sections. [ABSTRACT FROM AUTHOR]