Physical demand but not dexterity is associated with motor flexibility during rapid reaching in healthy young adults

Healthy humans are able to place light and heavy objects in small and large target locations with remarkable accuracy. Here we examine how dexterity demand and physical demand affect flexibility in joint coordination and end-effector kinematics when healthy young adults perform an upper extremity reaching task. We manipulated dexterity demand by changing target size and physical demand by increasing external resistance to reaching. Uncontrolled manifold analysis was used to decompose variability in joint coordination patterns into variability stabilizing the end-effector and variability de-stabilizing the end-effector during reaching. Our results demonstrate a proportional increase in stabilizing and de-stabilizing variability without a change in the ratio of the two variability components as physical demands increase. We interpret this finding in the context of previous studies showing that sensorimotor noise increases with increasing physical demands. We propose that the larger de-stabilizing variability as a function of physical demand originated from larger sensorimotor noise in the neuromuscular system. The larger stabilizing variability with larger physical demands is a strategy employed by the neuromuscular system to counter the de-stabilizing variability so that performance stability is maintained. Our findings have practical implications for improving the effectiveness of movement therapy in a wide range of patient groups, maintaining upper extremity function in old adults, and for maximizing athletic performance

Multiscale Finite Element Methods for Nonlinear Problems and their Applications

In this paper we propose a generalization of multiscale finite element methods (Ms-FEM) to nonlinear problems. We study the convergence of the proposed method for nonlinear elliptic equations and propose an oversampling technique. Numerical examples demonstrate that the over-sampling technique greatly reduces the error. The application of MsFEM to porous media flows is considered. Finally, we describe further generalizations of MsFEM to nonlinear time-dependent equations and discuss the convergence of the method for various kinds of heterogeneities

Multiscale simulations of porous media flows in flow-based coordinate system

In this paper, we propose a multiscale technique for the simulation of porous media flows in a flow-based coordinate system. A flow-based coordinate system allows us to simplify the scale interaction and derive the upscaled equations for purely hyperbolic transport equations. We discuss the applications of the method to two-phase flows in heterogeneous porous media. For two-phase flow simulations, the use of a flow-based coordinate system requires limited global information, such as the solution of single-phase flow. Numerical results show that one can achieve accurate upscaling results using a flow-based coordinate system

Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models

We study the preconditioning of Markov chain Monte Carlo (MCMC) methods using coarse-scale models with applications to subsurface characterization. The purpose of preconditioning is to reduce the fine-scale computational cost and increase the acceptance rate in the MCMC sampling. This goal is achieved by generating Markov chains based on two-stage computations. In the first stage, a new proposal is first tested by the coarse-scale model based on multiscale finite volume methods. The full fine-scale computation will be conducted only if the proposal passes the coarse-scale screening. For more efficient simulations, an approximation of the full fine-scale computation using precomputed multiscale basis functions can also be used. Comparing with the regular MCMC method, the preconditioned MCMC method generates a modified Markov chain by incorporating the coarse-scale information of the problem. The conditions under which the modified Markov chain will converge to the correct posterior distribution are stated in the paper. The validity of these assumptions for our application and the conditions which would guarantee a high acceptance rate are also discussed. We would like to note that coarse-scale models used in the simulations need to be inexpensive but not necessarily very accurate, as our analysis and numerical simulations demonstrate. We present numerical examples for sampling permeability fields using two-point geostatistics. The Karhunen--Loève expansion is used to represent the realizations of the permeability field conditioned to the dynamic data, such as production data, as well as some static data. Our numerical examples show that the acceptance rate can be increased by more than 10 times if MCMC simulations are preconditioned using coarse-scale models

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation

Convergence of a nonconforming multiscale finite element method

The multiscale finite element method (MsFEM) [T. Y. Hou, X. H. Wu, and Z. Cai, Math. Comp., 1998, to appear; T. Y. Hou and X. H. Wu, J. Comput. Phys., 134 (1997), pp. 169-189] has been introduced to capture the large scale solutions of elliptic equations with highly oscillatory coefficients. This is accomplished by constructing the multiscale base functions from the local solutions of the elliptic operator. Our previous study reveals that the leading order error in this approach is caused by the "resonant sampling," which leads to large error when the mesh size is close to the small scale of the continuous problem. Similar difficulty also arises in numerical upscaling methods. An oversampling technique has been introduced to alleviate this difficulty [T. Y. Hou and X. H. Wu, J. Comput. Phys., 134 (1997), pp. 169-189]. A consequence of the oversampling method is that the resulting finite element method is no longer conforming. Here we give a detailed analysis of the nonconforming error. Our analysis also reveals a new cell resonance error which is caused by the mismatch between the mesh size and the wavelength of the small scale. We show that the cell resonance error is of lower order. Our numerical experiments demonstrate that the cell resonance error is generically small and is difficult to observe in practice

A dynamic data-driven application simulation framework for contaminant transport problems

AbstractWe describe, devise, and augment dynamic data-driven application simulations (DDDAS). DDDAS offers interesting computational and mathematically unsolved problems, such as, how do you analyze, compute, and predict the solution of a generalized PDE when you do not know either where or what the boundary conditions are at any given moment in the simulation in advance? A summary of DDDAS features and why this is a intellectually stimulating new field are included in the paper.We apply the DDDAS methodology to some examples from a contaminant transport problem. We demonstrate that the multiscale interpolation and backward in time error monitoring are useful to long running simulations