Exponential integration algorithms applied to viscoplasticity

Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps

From differential to difference equations for first order ODEs

When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE

Asymptotic integration algorithms for first-order ODEs with application to viscoplasticity

When constructing an algorithm for the numerical integration of a differential equation, one must first convert the known ordinary differential equation (ODE), which is defined at a point, into an ordinary difference equation (O(delta)E), which is defined over an interval. Asymptotic, generalized, midpoint, and trapezoidal, O(delta)E algorithms are derived for a nonlinear first order ODE written in the form of a linear ODE. The asymptotic forward (typically underdamped) and backward (typically overdamped) integrators bound these midpoint and trapezoidal integrators, which tend to cancel out unwanted numerical damping by averaging, in some sense, the forward and backward integrations. Viscoplasticity presents itself as a system of nonlinear, coupled first-ordered ODE's that are mathematically stiff, and therefore, difficult to numerically integrate. They are an excellent application for the asymptotic integrators. Considering a general viscoplastic structure, it is demonstrated that one can either integrate the viscoplastic stresses or their associated eigenstrains

Thermoviscoplastic analysis of fibrous periodic composites using triangular subvolumes

The nonlinear viscoplastic behavior of fibrous periodic composites is analyzed by discretizing the unit cell into triangular subvolumes. A set of these subvolumes can be configured by the analyst to construct a representation for the unit cell of a periodic composite. In each step of the loading history, the total strain increment at any point is governed by an integral equation which applies to the entire composite. A Fourier series approximation allows the incremental stresses and strains to be determined within a unit cell of the periodic lattice. The nonlinearity arising from the viscoplastic behavior of the constituent materials comprising the composite is treated as fictitious body force in the governing integral equation. Specific numerical examples showing the stress distributions in the unit cell of a fibrous tungsten/copper metal matrix composite under viscoplastic loading conditions are given. The stress distribution resulting in the unit cell when the composite material is subjected to an overall transverse stress loading history perpendicular to the fibers is found to be highly heterogeneous, and typical homogenization techniques based on treating the stress and strain distributions within the constituent phases as homogeneous result in large errors under inelastic loading conditions

Viscoplastic Model Development with an Eye Toward Characterization

A viscoplastic theory is developed that reduces analytically to creep theory under steady-state conditions. A viscoplastic model is constructed within this theoretical framework by defining material functions that have close ties to the physics of inelasticity. As a consequence, this model is easily characterized-only steady-state creep data, monotonic stress-strain curves, and saturated stress-strain hysteresis loops are required

Nonlinear Asymptotic Integration Algorithms for One-dimensional Autonomous Dissipative First-order Odes

Nonlinear asymptotic integrators are applied to one-dimensional, nonlinear, autonomous, dissipative, ordinary differential equations. These integrators, including a one-step explicit, a one-step implicit, and a one- and two-step midpoint algorithm, are designed to follow the asymptotic behavior of a system approaching a steady state. The methods require that the differential equation be written in a particular asymptotic form. This is always possible for a one-dimensional equation with a globally asymptotic steady state. In this case, conditions are obtained to guarantee that the implicit algorithms are well defined. Further conditions are determined for the implicit methods to be contractive. These methods are all first order accurate, while under certain conditions the midpoint algorithms may also become second order accurate. The stability of each method is investigated and an estimate of the local error is provided

Variation in salamander tail regeneration is associated with genetic factors that determine tail morphology

Very little is known about the factors that cause variation in regenerative potential within and between species. Here, we used a genetic approach to identify heritable genetic factors that explain variation in tail regenerative outgrowth. A hybrid ambystomatid salamander (Ambystoma mexicanum x A. andersoni) was crossed to an A. mexicanum and 217 offspring were induced to undergo metamorphosis and attain terrestrial adult morphology using thyroid hormone. Following metamorphosis, each salamander’s tail tip was amputated and allowed to regenerate, and then amputated a second time and allowed to regenerate. Also, DNA was isolated from all individuals and genotypes were determined for 187 molecular markers distributed throughout the genome. The area of tissue that regenerated after the first and second amputations was highly positively correlated across males and females. Males presented wider tails and regenerated more tail tissue during both episodes of regeneration. Approximately 66–68% of the variation in regenerative outgrowth was explained by tail width, while tail length and genetic sex did not explain a significant amount of variation. A small effect QTL was identified as having a sex-independent effect on tail regeneration, but this QTL was only identified for the first episode of regeneration. Several molecular markers significantly affected regenerative outgrowth during both episodes of regeneration, but the effect sizes were small (\u3c4%) and correlated with tail width. The results show that ambysex and minor effect QTL explain variation in adult tail morphology and importantly, tail width. In turn, tail width at the amputation plane largely determines the rate of regenerative outgrowth. Because amputations in this study were made at approximately the same position of the tail, our results resolve an outstanding question in regenerative biology: regenerative outgrowth positively co-varies as a function of tail width at the amputation site

Phantom and clinical evaluation of the effect of full Monte Carlo collimator modelling in post-SIRT yttrium-90 Bremsstrahlung SPECT imaging

Background: Post-therapy SPECT/CT imaging of Y-90 microspheres delivered to hepatic malignancies is difficult, owing to the continuous, high-energy Bremsstrahlung spectrum emitted by Y-90. This study aimed to evaluate the utility of a commercially available software package (HybridRecon, Hermes Medical Solutions AB) which incorporates full Monte Carlo collimator modelling. Analysis of image quality was performed on both phantom and clinical images in order to ultimately provide a recommendation of an optimum reconstruction for post-therapy Y-90 microsphere SPECT/CT imaging. A 3D-printed anthropomorphic liver phantom was filled with Y-90 with a sphere-to-background ratio of 4:1 and imaged on a GE Discovery 670 SPECT/CT camera. Datasets were reconstructed using ordered-subsets expectation maximization (OSEM) 1-7 iterations in order to identify the optimal OSEM reconstruction (5 iterations, 15 subsets). Quantitative analysis was subsequently carried out on phantom datasets obtained using four reconstruction algorithms: the default OSEM protocol (2 iterations, 10 subsets) and the optimised OSEM protocol, both with and without full Monte Carlo collimator modelling. The quantitative metrics contrast recovery (CR) and background variability (BV) were calculated. The four algorithms were then used to retrospectively reconstruct 10 selective internal radiation therapy (SIRT) patient datasets which were subsequently blind scored for image quality by a consultant radiologist. Results: The optimised OSEM reconstruction (5 iterations, 15 subsets with full MC collimator modelling) increased the CR by 42% (p <0.001) compared to the default OSEM protocol (2 iterations, 10 subsets). The use of full Monte Carlo collimator modelling was shown to further improve CR by 14% (30 mm sphere, CR = 90%, p <0.05). The consultant radiologist had a significant preference for the optimised OSEM over the default OSEM protocol (p <0. 001), with the optimised OSEM being the favoured reconstruction in every one of the 10 clinical cases presented. Conclusions: OSEM (5 iterations, 15 subsets) with full Monte Carlo collimator modelling is quantitatively the optimal image reconstruction for post-SIRT 90Y Bremsstrahlung SPECT/CT imaging. The use of full Monte Carlo collimator modelling for correction of image-degrading effects significantly increases contrast recovery without degrading clinical image quality.Peer reviewe

Dynamically Updated Location-Based User Groups for Context-Specific Communication

Groups on social networking and messaging platforms enable users to communicate with others in a compartmentalized and targeted manner. However, curating such groups requires manual effort and does not support scenarios in which users wish to communicate with context-specific groups that are dynamic and transient. This disclosure describes techniques that enable dynamically creation and update of user groups based on user location. A messaging backend can enable users to communicate with others in the dynamic location-based groups connected to specific locations. The techniques enable seamless formation and update of context-specific groups without manual effort