Exploiting timescale separation in micro and nano flows

In this paper we describe how timescale separation in micro/nano flows can be exploited for computational acceleration. A modified version of the seamless heterogenous multiscale method (SHMM) is proposed: a multi-step SHMM. This maintains the main advantages of SHMM (e.g., re-initialisation of micro data is not required; temporal gearing (computational speed-up) is easily controlled; and it is applicable to full and intermediate degrees of timescale separation) while improving on accuracy and greatly reducing the number of macroscopic computations and micro/macro coupling instances required. The improved accuracy of the multi-step SHMM is demonstrated for two canonical one-dimensional transient flows (oscillatory Poiseuille and oscillatory Couette flow) and for rarefied-gas oscillatory Poiseuille flow

Time-step coupling for hybrid simulations of multiscale flows

A new method is presented for the exploitation of time-scale separation in hybrid continuum-molecular models of multiscale flows. Our method is a generalisation of existing approaches, and is evaluated in terms of computational efficiency and physical/numerical error. Comparison with existing schemes demonstrates comparable, or much improved, physical accuracy, at comparable, or far greater, efficiency (in terms of the number of time-step operations required to cover the same physical time). A leapfrog coupling is proposed between the ‘macro’ and ‘micro’ components of the hybrid model and demonstrates potential for improved numerical accuracy over a standard simultaneous approach. A general algorithm for a coupled time step is presented. Three test cases are considered where the degree of time-scale separation naturally varies during the course of the simulation. First, the step response of a second-order system composed of two linearly-coupled ODEs. Second, a micro-jet actuator combining a kinetic treatment in a small flow region where rarefaction is important with a simple ODE enforcing mass conservation in a much larger spatial region. Finally, the transient start-up flow of a journal bearing with a cylindrical rarefied gas layer. Our new time-stepping method consistently demonstrates as good as or better performance than existing schemes. This superior overall performance is due to an adaptability inherent in the method, which allows the most-desirable aspects of existing schemes to be applied only in the appropriate conditions

Electron capture dissociation mass spectrometry of phosphopeptides: Arginine and phosphoserine

AbstractWe have previously shown that the presence of phosphorylation can inhibit detection of electron capture dissociation (ECD) fragments of doubly charged peptide ions. The presence of non-covalent interactions, in the form of salt-bridges or ionic hydrogen bonds, prevents the separation of fragments following backbone cleavage. Here, we show the electron capture dissociation mass spectrometry of a suite of model peptides designed to investigate the relationship between phosphoserine and arginine position, namely AApSAnRAmKA (n=0–6, m=6–0), the presence of lysine residues (AApSAAKAARAKA) and AAApSARAAAAKAAAK, and the presence of proline A(A/P)ApSARAAA(A/P)KAAAK. The latter are analogous to the peptides studied previously. The results show that the presence of phosphoserine and basic amino acid residues alone does not inhibit ECD fragmentation, even when the number of basic amino acid residues is greater than the precursor charge state. Neither did the presence of proline in the peptide sequence suppress ECD backbone cleavage. Nevertheless, the presence and relative position of the phosphorylated residue do alter the observed backbone fragmentation abundance. In addition, the presence of phosphorylation appears to inhibit cleavage within the arginine side-chain regardless of the relative position of the arginine residue. The results suggest that ECD fragmentation behaviour is dependent on the three-dimensional structure of a peptide rather than its sequence

A simple and effective 1D-element discrete-based method for computational bone remodeling

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Computer Methods in Biomechanics and Biomedical Engineering on 2022, available online at: http://www.tandfonline.com/10.1080/10255842.2021.1943370.In-silico models applied to bone remodeling are widely used to investigate bone mechanics, bone diseases, bone-implant interactions, and also the effect of treatments of bone pathologies. This paper proposes a new methodology to solve the bone remodeling problem using one-dimensional (1D) elements to discretize trabecular structures more efficiently for 2D and 3D domains. An Euler integration scheme is coupled with the momentum equations to obtain the evolution of material density at each step. For the simulations, the equations were solved by using the finite element method, and two benchmark tests were solved varying mesh parameters. Proximal femur and calcaneus bone were selected as study cases given the vast research available on the topology of these bones, and compared with the anatomical features of trabecular bone reported in the literature. The presented methodology has proven to be efficient in optimizing topologies of lattice structures; It can predict the trend of formation patterns of the main trabecular groups from two different cancellous bones (femur and calcaneus) using domains set up by discrete elements as a starting point. Preliminary results confirm that the proposed approach is suitable and useful in bone remodeling problems leading to a considerable computational cost reduction. Characteristics similar to those encountered in topological optimization (TO) algorithms were identified in the benchmark tests as well, showing the viability of the proposed approach in other applications such as bio-inspired design.Peer ReviewedPostprint (author's final draft

Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes

We present a computational study of the solution of the Falkner-Skan equation (a third-order boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences schemes. There are a number of previously reported solution approaches that adopt a reduced-order system of equations, and numerical methods such as: shooting, Taylor series, Runge-Kutta and other semi-analytic methods. Interestingly, though, methods that solve the original non-reduced third-order equation directly are absent from the literature. Two high-order schemes are presented using both explicit (third-order) and implicit compact-difference (fourth-order) formulations on a semi-infinite domain; to our knowledge this is the first time that high-order finite difference schemes are presented to find numerical solutions to the non-reduced-order Falkner-Skan equation directly. This approach maintains the simplicity of Taylor-series coefficient matching methods, avoiding complicated numerical algorithms, and in turn presents valuable information about the numerical behaviour of the equation. The accuracy and effectiveness of this approach is established by comparison with published data for accelerating, constant and decelerating flows; excellent agreement is observed. In general, the numerical behaviour of formulations that seek an optimum physical domain size (for a given computational grid) is discussed. Based on new insight into such methods, an alternative optimisation procedure is proposed that should increase the range of initial seed points for which convergence can be achieved

Efficient time-step coupling for hybrid continuum/molecular modelling of unsteady micro-scale gas flows

In this paper we describe a numerical method for the efficient time-accurate coupling of hybrid continuum/molecular micro gas flow solvers. Hybrid approaches are commonly used when non-equilibrium effects in the flow field are spatially localized; in these regions a more accurate, but typically more expensive, solution procedure is adopted. Although this can greatly increase efficiency in steady flows, in unsteady flows the evolution of the solution as a whole is restricted by the maximum time step allowed by the molecular-based/kinetic model; numerically speaking, this is a stiff problem. In the method presented in this paper we exploit time-scale separation, when it exists, to partially decouple the temporal evolution of the two parts of the hybrid model. This affords major computational savings. The method is a modified/extended version of the seamless heterogeneous multiscale method (SHMM). Our approach allows multiple micro steps (molecular steps) before coupling with the macro (continuum) solver: we call this a multi-step SHMM. This maintains the main advantages of SHMM (computational speed-up and flexible application) while improving on accuracy and greatly reducing the number of continuum computations and instances of coupling required. The improved accuracy of the multi-step SHMM is demonstrated for two canonical one-dimensional transient flows (oscillatory Poiseuille and oscillatory Couette flow) and for rarefied-gas oscillatory Poiseuille flow

Sobre la aparición de la biomecánica y la mecanobiología computacional: experimentos computacionales y recientes hallazgos About the appearance of Biomechanics and computation mechanobiology: computation experiments and recent findings

Procesos de desarrollo de órganos y remodelado de tejidos se ven influenciados por múltiples factores que van desde el componente biológico hasta la mecánica propia del sistema, donde cada uno de estos afecta en mayor o menor medida dependiendo del tipo de ente orgánico que se estudie. Desde esta perspectiva se ha desarrollado un nuevo campo de estudio de la bioingeniería denominado mecanobiología. Esta nueva área de trabajo involucra el estudio de modelos y la realización de experimentos con el ánimo de entender los procesos complejos que se dan en la génesis y mantenimiento de órganos y tejidos. Gracias a esta disciplina se ha logrado aislar y analizar diversos efectos como lo son la genética, los factores moleculares autocrinos y paracrinos, las cargas mecánicas sobre órganos y los efectos electromagnéticos. Con este conocimiento se han construido nuevos modelos matemáticos que pueden simular, de forma aproximada, el comportamiento in vivo. En este orden de ideas, el presente trabajo recoge las principales experiencias en el campo de la mecanobiología a nivel mundial, donde se han desarrollado trabajos que predicen la formación de huesos, el remodelado óseo, la formación y mantenimiento del cartílago articular, entre otros

Modelling turbulent skin-friction control using linearized Navier–Stokes equations

Linearized Navier–Stokes equations are solved to investigate the impact on the growth of near-wall turbulent streaks that arises from streamwise-travelling waves of spanwise wall velocity. The percentage change in streak amplification due to the travelling waves, over a range of wave parameters, is compared to published direct numerical simulation (DNS) predictions of turbulent skin-friction reduction; a clear correlation between the two is observed. Linearized simulations at a much higher Reynolds number, more relevant to aerospace applications, produce results that show no marked differences to those obtained at low Reynolds number. It is also observed that there is a close correlation between DNS data of drag reduction and a very simple characteristic of the ‘generalized’ Stokes layer generated by the streamwise-travelling waves

Turing patterns on spheres with continuous growth

En este artículo se desarrollan varios ejemplos numéricos sobre ecuaciones de reacción-difusión con dominio creciente, empleando el modelo de reacción de Schnakenberg, con parámetros en el espacio de Turing. Por tanto, se realizan ensayos numéricos sobre la aparición de los patrones de Turing en superficies esféricas. Para la solución de las ecuaciones de reacción-difusión se presenta un método de solución en superficies en tres dimensiones mediante el método de los elementos finitos con el uso de la formulación lagrangiana total. Los resultados muestran que la formación de los patrones de Turing depende de la velocidad de crecimiento de la superficie, el tipo de número de onda predicho en la teoría de dominios cuadrados y su tiempo de estabilización. Estos resultados pueden esclarecer algunos fenómenos de cambio de patrón en la superficie de la piel de los animales que exhiben manchas características.We have developed several numerical examples of reaction-diffusion equations with growth surface domain. In this research we use the Schnakenberg reaction model, with parameters in the Turing space. Therefore,numerical tests are performed on the appearence of Turing patterns in spherical surfaces. For the solution of reaction diffusion equations provides a method of settling on surfaces in three dimensions using the finite element method under the total Lagrangian formulation. The results show that the formation of Turing patterns depends on the growth rate of the surface, the type of wave number predicted in the theory of square domains and their stabilization time. These results may explain some phenomena of pattern change on the surface of the skin of animals that exhibit characteristic spots