Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally-resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. For unbounded suspensions and suspensions sedimented against a single no-slip boundary, we rely on existing analytical expressions for the Rotne-Prager tensor combined with a fast multipole method or a direct summation on a Graphical Processing Unit to obtain an simple yet efficient and scalable implementation. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently-developed rigid-body immersed boundary method to suspensions of freely-moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid body equations converges in a bounded number of iterations regardless of the system size. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201

A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number

This contribution provides a general framework to use Lagrange multipliers for the simulation of low Reynolds number fiber dynamics based on Bead Models (BM). This formalism provides an efficient method to account for kinematic constraints. We illustrate, with several examples, to which extent the proposed formulation offers a flexible and versatile framework for the quantitative modeling of flexible fibers deformation and rotation in shear flow, the dynamics of actuated filaments and the propulsion of active swimmers. Furthermore, a new contact model called Gears Model is proposed and successfully tested. It avoids the use of numerical artifices such as repulsive forces between adjacent beads, a source of numerical difficulties in the temporal integration of previous Bead Models.Comment: 41 pages, 15 figure

Articular human joint modelling

Copyright @ Cambridge University Press 2009.The work reported in this paper encapsulates the theories and algorithms developed to drive the core analysis modules of the software which has been developed to model a musculoskeletal structure of anatomic joints. Due to local bone surface and contact geometry based joint kinematics, newly developed algorithms make the proposed modeller different from currently available modellers. There are many modellers that are capable of modelling gross human body motion. Nevertheless, none of the available modellers offer complete elements of joint modelling. It appears that joint modelling is an extension of their core analysis capability, which, in every case, appears to be musculoskeletal motion dynamics. It is felt that an analysis framework that is focused on human joints would have significant benefit and potential to be used in many orthopaedic applications. The local mobility of joints has a significant influence in human motion analysis, in understanding of joint loading, tissue behaviour and contact forces. However, in order to develop a bone surface based joint modeller, there are a number of major problems, from tissue idealizations to surface geometry discretization and non-linear motion analysis. This paper presents the following: (a) The physical deformation of biological tissues as linear or non-linear viscoelastic deformation, based on spring-dashpot elements. (b) The linear dynamic multibody modelling, where the linear formulation is established for small motions and is particularly useful for calculating the equilibrium position of the joint. This model can also be used for finding small motion behaviour or loading under static conditions. It also has the potential of quantifying the joint laxity. (c) The non-linear dynamic multibody modelling, where a non-matrix and algorithmic formulation is presented. The approach allows handling complex material and geometrical nonlinearity easily. (d) Shortest path algorithms for calculating soft tissue line of action geometries. The developed algorithms are based on calculating minimum ‘surface mass’ and ‘surface covariance’. An improved version of the ‘surface covariance’ algorithm is described as ‘residual covariance’. The resulting path is used to establish the direction of forces and moments acting on joints. This information is needed for linear or non-linear treatment of the joint motion. (e) The final contribution of the paper is the treatment of the collision. In the virtual world, the difficulty in analysing bodies in motion arises due to body interpenetrations. The collision algorithm proposed in the paper involves finding the shortest projected ray from one body to the other. The projection of the body is determined by the resultant forces acting on it due to soft tissue connections under tension. This enables the calculation of collision condition of non-convex objects accurately. After the initial collision detection, the analysis involves attaching special springs (stiffness only normal to the surfaces) at the ‘potentially colliding points’ and motion of bodies is recalculated. The collision algorithm incorporates the rotation as well as translation. The algorithm continues until the joint equilibrium is achieved. Finally, the results obtained based on the software are compared with experimental results obtained using cadaveric joints

Approaches and possible improvements in the area of multibody dynamics modeling

A wide ranging look is taken at issues involved in the dynamic modeling of complex, multibodied orbiting space systems. Capabilities and limitations of two major codes (DISCOS, TREETOPS) are assessed and possible extensions to the CONTOPS software are outlined. In addition, recommendations are made concerning the direction future development should take in order to achieve higher fidelity, more computationally efficient multibody software solutions

Learning and Simulation Algorithms for Constraint Physical Systems

This thesis explores two computational approaches to learn and simulate complex physical systems exhibiting constraint characteristics. The target applications encompass both solids and fluids. On the solid side, we proposed a new family of data-driven simulators to predict the behaviors of an unknown physical system by learning its underpinning constraints. We devised a neural projection operator facilitated by an embedded recursive neural network to interactively enforce the learned underpinning constraints and to predict its various physical behaviors. Our method can automatically uncover a broad range of constraints from observation point data, such as length, angle, bending, collision, boundary effects, and their combinations, in the context of a diverse set of physical systems including rigid bodies, ropes, articulated bodies, and multi-object collisions. On the fluid side, we proposed a gauge numerical simulator to model fluid phenomena using Clebsch wave functions. Our method combines the expressive power of Clebsch wave functions to represent coherent vortical structures and the generality of gauge methods to accommodate a broad array of fluid phenomena. We devised a transformed wave function as the system’s gauge variable to improve a fluid simulator’s vorticity generation and preservation ability. We showcase our method by simulating various types of incompressible flow phenomena, including complex vortex filament dynamics, fluids with different obstacles, and surface-tension flow

Mapping flagellated swimmers to surface-slip driven swimmers.

Flagellated microswimmers are ubiquitous in natural habitats. Understanding the hydrodynamic behavior of these cells is of paramount interest, owing to their applications in bio-medical engineering and disease spreading. Since the last two decades, computational efforts have been continuously improved to accurately capture the complex hydrodynamic behavior of these model systems. However, modeling the dynamics of such swimmers with fine details is computationally expensive due to the large number of unknowns and the small time-steps required to solve the equations. In this work we propose a method to map fully resolved flagellated microswimmers to coarse, active slip driven swimmers which can be simulated at a reduced computational cost. Using the new method, the slip driven swimmers move with the same velocity, to machine precision, as the flagellated swimmers and generate a similar flow field with a controlled accuracy. The method is validated for swimming patterns near a no-slip boundary, interactions between swimmers and scattering with large obstacles