Quasicontinuum representations of atomic-scale mechanics: From proteins to dislocations

Computation is one of the centerpieces of both the physical and biological sciences. A key thrust in computational science is the explicit mechanistic simulation of the spatiotemporal evolution of materials ranging from macromolecules to intermetallic alloys. However, our ability to simulate such systems is in the end always limited in both the spatial extent of the systems that are considered, as well as the duration of the time that can be simulated. As a result, a variety of efforts have been put forth that aim to finesse these challenges in both space and time through new techniques in which constraint is exploited to reduce the overall computational burden. The aim of this review is to describe in general terms some of the key ideas that have been set forth in both the materials and biological setting and to speculate on future developments along these lines. We begin by developing general ideas on the exploitation of constraint as a systematic tool for degree of freedom thinning. These ideas are then applied to case studies ranging from the plastic deformation of solids to the interactions of proteins and DNA

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

Development and Characterization of Velocity Workspaces for the Human Knee.

The knee joint is the most complex joint in the human body. A complete understanding of the physical behavior of the joint is essential for the prevention of injury and efficient treatment of infirmities of the knee. A kinematic model of the human knee including bone surfaces and four major ligaments was studied using techniques pioneered in robotic workspace analysis. The objective of this work was to develop and test methods for determining displacement and velocity workspaces for the model and investigate these workspaces. Data were collected from several sources using magnetic resonance imaging (MRI) and computed tomography (CT). Geometric data, including surface representations and ligament lengths and insertions, were extracted from the images to construct the kinematic model. Fixed orientation displacement workspaces for the tibia relative to the femur were computed using ANSI C programs and visualized using commercial personal computer graphics packages. Interpreting the constraints at a point on the fixed orientation displacement workspace, a corresponding velocity workspace was computed based on extended screw theory, implemented using MATLAB(TM), and visually interpreted by depicting basis elements. With the available data and immediate application of the displacement workspace analysis to clinical settings, fixed orientation displacement workspaces were found to hold the most promise. Significant findings of the velocity workspace analysis include the characterization of the velocity workspaces depending on the interaction of the underlying two-systems of the constraint set, an indication of the contributions from passive constraints to force closure of the joint, computational means to find potentially harmful motions within the model, and realistic motions predicted from solely geometric constraints. Geometric algebra was also investigated as an alternative method of representing the underlying mathematics of the computations with promising results. Recommendations for improving and continuing the research may be divided into three areas: the evolution of the knee model to allow a representation for cartilage and the menisci to be used in the workspace analysis, the integration of kinematic data with the workspace analysis, and the development of in vivo data collection methods to foster validation of the techniques outlined in this dissertation

Direct numerical simulations and experimental investigation of dielectrophoresis

This dissertation deals with the numerical and experimental studies of the phenomenon of dielectrophoresis, i.e., the motion of neutral particles in nonuniform electric fields. Dielectrophoresis is the translatory motion of neutral particles suspended in a dielectric medium when they are subjected to an external nonuniform electric field. The translatory motion occurs because a force called the dielectrophoretic force, which depends on the spatial variation of the electric field, acts on the particles. As the generation of force involves no moving parts and the particles can be moved without touching them, dielectrophoresis can be used in many applications, including manipulation and separation of biological particles, manipulation of nanoparticles, etc. In the present study, the numerical simulations of the fluid-particle system are performed using a direct numerical simulation scheme based on the distributed Lagrange multiplier method. In this scheme, the fluid flow equations are solved both inside and outside the particle boundaries and flow inside the particle boundary is forced to be a rigid body motion by using the distributed Lagrange multiplier. The electrostatic force acting on the particles is computed using the point dipole method. The scheme is used to study the behavior of particles in the suspension under the influence of a nonuniform electric field. The numerical scheme is used to study the influence of a dimensionless parameter, which is the ratio of electrostatic particle-particle interactions and dielectrophoretic force, in the dynamics of particle structure formation and the eventual particle collection. When this parameter is of order one or greater, which corresponds to the regime where particle-particle interactions are comparable in magnitude to the dielectrophoretic force, simulations reveal that the particles form interparticle chains and the chains then move to the electrode edges in the case of positive dielectrophoresis. When this parameter is of order ten the particles collect in the form of chains extending from one electrode to the opposite one clogging the entire domain. On the other hand, when this parameter is less than order one, particles move to the electrode edges individually and agglomerate at the edges of the electrodes. The results of numerical simulations are verified experimentally using a suspension of viable yeast cells subjected to dielectrophoresis using microelectrodes. The experiments show that at frequencies much smaller than the crossover frequency where the value of the above parameter is greater than order one, the yeast particles form chains and then move and collect at the electrode edges. Where as, at frequencies closer to the crossover frequency where the value of the parameter is less than order one, particles move individually without forming chains and agglomerate at the electrode edges. The numerical simulation scheme is also used to study the dielectrophoresis of nanoparticles. Simulations show that in a uniform electric field the Brownian force is dominant and results in the random scattering of the particles. In the case of nonuniform electric field, it is possible to overcome the Brownian force and collect the particles at pre-determined locations, even though the trajectories of the particles are influenced by Brownian motion. Finally, the method of images is used to improve the electric field solution when the particles are close to the domain walls. Simulations performed for uniform electric fields with the method of images shows that when the distance between the particle and domain boundary is of the order of particle diameter the influence of the particles on the electric field boundary conditions is significant

Multi-loop position analysis via iterated linear programming

Robotics: Science and Systems Conference (RSS), 2006, Filadelfia (EE.UU.)This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology, and complete, in the sense that all possible solutions get accurately bounded, irrespectively of whether the analyzed linkage is rigid or mobile. The problem is tackled by formulating a system of linear, parabolic, and hyperbolic equations, which is here solved by a new strategy exploiting its structure. The method is conceptually simple, geometric in nature, and easy to implement, yet it provides solutions at the desired accuracy in short computation times.This work was supported by the project 'Planificador de trayectorias para sistemas robotizados de arquitectura arbitraria' (J-00930).Peer Reviewe