Fast integral equation methods for the Laplace-Beltrami equation on the sphere

Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mapped to a multiply-connected region in the complex plane via a stereographic projection. After discretizing the integral equation, the resulting dense linear system is solved iteratively using the fast multipole method for the 2D Coulomb potential in order to calculate the matrix-vector products. This numerical scheme requires only O(N) operations, where $N$ is the number of nodes in the discretization of the boundary. The performance of the method is demonstrated on several examples

Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: a numerical study

The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make the fluid flow highly singular. In more analytical terms, the cause of this phenomenon has been attributed to the presence of a continuous spectrum in some nonlocal zeroth-order pseudo-differential operators. In this work, we analyze the generation of these attractors from a numerical analysis perspective. First, we propose a high-order pseudo-spectral method to solve the evolution problem (whose long-term behaviour is known to be not square-integrable). Then, we use similar tools to discretize the corresponding eigenvalue problem. Since the eigenvalues are embedded in a continuous spectrum, we compute them using viscous approximations. Finally, we explore the effect that the embedded eigenmodes have on the long-term evolution of the system.Comment: 23 pages, 16 figures, MATLAB codes available at http://www.github.com/javieralmonacid/zeroth-order-operator

Cooperativity of catalytic and lectin-like domain of Trypanosoma congolense trans-sialidase modulates its catalytic activity

Trans-sialidases (TS) represent a multi-gene family of unusual enzymes, which catalyse the transfer of terminal sialic acids (Sia) from sialoglycoconjugates to terminal galactose or N-acetylgalactosamine residues of oligosaccharides without the requirement of CMP-Neu5Ac, the activated Sia used by typical sialyltransferases. Enzymes comprise a N-terminal catalytic domain (CD) followed by a lectin-like domain (LD). Most work on trypanosomal TS has been done on enzymatic activities focusing on the CD of TS from Trypanosoma cruzi (causing Chagas disease in Latin America), subspecies of Trypanosoma brucei, (causing human sleeping sickness in Africa) and Trypanosoma congolense (causing African Animal Trypanosomosis in livestock). Previously, we demonstrated that T. congolense TS (TconTS)-LD binds to several carbohydrates, such as 1,4-β-mannotriose. In this study we investigated the influence of TconTS3-LD on Sia transfer efficiency of TconTS1a-CD by swapping domains. in silico analysis on structure models of TconTS enzymes revealed the potential of domain swaps between TconTS1a and TconTS3 without structural disruptions of the enzymes overall topologies. Recombinant domain swapped TconTS1a/TS3 showed clear Sia transfer activity, when using fetuin and lactose as Sia donor and acceptor substrates, respectively. While Sia transfer activity remained unchanged from the level of TconTS1a, hydrolytic release of free Neu5Ac as a side product was suppressed resulting in increased transfer efficiency. Presence of 1,4-β-mannotriose during TS reactions modulates enzyme activities enhancing transfer efficiency possibly due to occupation of the binding site in TconTS1a-LD. Interestingly this effect was in the same range as that observed when swapping TconTS1a-CD and TconTS3-LD. In summary, this study demonstrate the proof-of-principle for swapping CDs and LDs of TconTS and that TconTS3-LD influences enzymatic activity of TconTS1a-CD providing evidence that LDs play pivotal roles in modulating activities and biological functions of TconTS and possibly other TS

A Modelling Approach for Exploring Muscle Dynamics during Cyclic Contractions

Hill-type muscle models are widely used within the field of biomechanics to predict and understand muscle behaviour, and are often essential where muscle forces cannot be directly measured. However, these models have limited accuracy, particularly during cyclic contractions at the submaximal levels of activation that typically occur during locomotion. To address this issue, recent studies have incorporated effects into Hill-type models that are oftentimes neglected, such as size-dependent, history-dependent, and activation-dependent effects. However, the contribution of these effects on muscle performance has yet to be evaluated under common contractile conditions that reflect the range of activations, strains, and strain rates that occur in vivo. The purpose of this study was to develop a modelling framework to evaluate modifications to Hill-type muscle models when they contract in cyclic loops that are typical of locomotor muscle function. Here we present a modelling framework composed of a damped harmonic oscillator in series with a Hill-type muscle actuator that consists of a contractile element and parallel elastic element. The intrinsic force-length and force-velocity properties are described using Bézier curves where we present a system to relate physiological parameters to the control points for these curves. The muscle-oscillator system can be geometrically scaled while preserving dynamic and kinematic similarity to investigate the muscle size effects while controlling for the dynamics of the harmonic oscillator. The model is driven by time-varying muscle activations that cause the muscle to cyclically contract and drive the dynamics of the harmonic oscillator. Thus, this framework provides a platform to test current and future Hill-type model formulations and explore factors affecting muscle performance in muscles of different sizes under a range of cyclic contractile conditions

Uncertainty in Damage Assessment and Remaining Life Prediction of Engineering Materials Used In Petrochemical Industry

In this paper creep damage assessment of about 11 years’ service exposed HP-40 grade of steel used in hydrogen reformer of a petrochemical industry has been carried out in terms of a discontinuous Markov process. Experimentally determined conventional creep data under identical testing condition were used in the present investigation. Scatter and damage accumulation due to creep deformation were evaluated through microstructural assessment using light optical microscope and scanning electron microscope. Quantification of creep damage was made from replicated creep data in terms of two damage parameters A and A*. Statistical analysis of void area fraction has been carried out extensively for the both top and bottom portions of the reformer tube at 870 o C in the stress range of 52-68 MPa. In addition, the proposed probabilistic model has been compared with the Kachanav’s Continuum Damage Mechanics (CDM) model. Both the approaches displayed quantitative experimental support. A residual life of > 10 years is estimated at 870 degree C / operating stress. For 55 years’ service exposed Catalytic Cold Cracking (CCU) reactor vessel and Feed Processing Unit (FPU) distillation column materials of a petrochemical industry remnant life assessment studies were estimated by incorporating the uncertainty involved in calculation of LMP (Larson Miller Parameter) values and from extrapolation of stress vs. LMP plot. Variability of normalized creep damage for reactor and column materials is well approximated with the aid of Weibull distribution. As expected, it is observed that the distributions shift towards the higher range of damage with increase in service exposure time

The Energy of Muscle Contraction. III. Kinetic Energy During Cyclic Contractions

During muscle contraction, chemical energy is converted to mechanical energy when ATP is hydrolysed during cross-bridge cycling. This mechanical energy is then distributed and stored in the tissue as the muscle deforms or is used to perform external work. We previously showed how energy is distributed through contracting muscle during fixed-end contractions; however, it is not clear how the distribution of tissue energy is altered by the kinetic energy of muscle mass during dynamic contractions. In this study we conducted simulations of a 3D continuum muscle model that accounts for tissue mass, as well as force-velocity effects, in which the muscle underwent sinusoidal work-loop contractions coupled with bursts of excitation. We found that increasing muscle size, and therefore mass, increased the kinetic energy per unit volume of the muscle. In addition to greater relative kinetic energy per cycle, relatively more energy was also stored in the aponeurosis, and less was stored in the base material, which represented the intra and extracellular tissue components apart from the myofibrils. These energy changes in larger muscles due to greater mass were associated lower mass-specific mechanical work output per cycle, and this reduction in mass-specific work was greatest for smaller initial pennation angles. When we compared the effects of mass on the model tissue behaviour to that of in situ muscle with added mass during comparable work-loop trials, we found that greater mass led to lower maximum and higher minimum acceleration in the longitudinal (x) direction near the middle of the muscle compared to at the non-fixed end, which indicates that greater mass contributes to tissue non-uniformity in whole muscle. These comparable results for the simulated and in situ muscle also show that this modelling framework behaves in ways that are consistent with experimental muscle. Overall, the results of this study highlight that muscle mass is an important determinant of whole muscle behaviour

The Contributions of Extracellular Matrix and Sarcomere Properties to Passive Muscle Stiffness in Cerebral Palsy

Cerebral palsy results from an upper motor neuron lesion and significantly affects skeletal muscle stiffness. The increased stiffness that occurs is partly a result of changes in the microstructural components of muscle. In particular, alterations in extracellular matrix, sarcomere length, fibre diameter, and fat content have been reported; however, experimental studies have shown wide variability in the degree of alteration. Many studies have reported changes in the extracellular matrix, while others have reported no differences. A consistent finding is increased sarcomere length in cerebral palsy affected muscle. Often many components are altered simultaneously, making it difficult to determine the individual effects on muscle stiffness. In this study, we use a three dimensional modelling approach to isolate individual effects of microstructural alterations typically occurring due to cerebral palsy on whole muscle behaviour; in particular, the effects of extracellular matrix volume fraction, stiffness, and sarcomere length. Causation between the changes to the microstructure and the overall muscle response is difficult to determine experimentally, since components of muscle cannot be manipulated individually; however, utilising a modelling approach allows greater control over each factor. We find that extracellular matrix volume fraction has the largest effect on whole muscle stiffness and mitigates effects from sarcomere length