SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.

Analytical Parametric Model Used to Study the Influence of Electrostatic Force on Surface Coverage During Electrospinning of Polymer Fibers

Electrospinning (ES) can readily produce polymer fibers with cross-sectional dimensions ranging from tens of nanometers to tens of microns. Qualitative estimates of surface area coverage are rather intuitive. However, quantitative analytical and numerical methods for predicting surface coverage during ES have not been covered in sufficient depth to be applied in the design of novel materials, surfaces, and devices from ES fibers. This article presents a modeling approach to ES surface coverage where an analytical model is derived for use in quantitative prediction of surface coverage of ES fibers. The analytical model is used to predict the diameter of circular deposition areas of constant field strength and constant electrostatic force. Experimental results of polyvinyl alcohol fibers are reported and compared to numerical models to supplement the analytical model derived. The analytical model provides scientists and engineers a method for estimating surface area coverage. Both applied voltage and capillary-to-collection-plate separation are treated as independent variables for the analysis. The electric field produced by the ES process was modeled using COMSOL Multiphysics software to determine a correlation between the applied field strength and the size of the deposition area of the ES fibers. MATLAB scripts were utilized to combine the numerical COMSOL results with derived analytical equations. Experimental results reinforce the parametric trends produced via modeling and lend credibility to the use of modeling techniques for the qualitative prediction of surface area coverage from ES. (Copyright: 2014 American Vacuum Society.)

Corticospinal output and loss of force during motor fatigue

The objective of this study was to analyze central motor output changes in relation to contraction force during motor fatigue. The triple stimulation technique (TST, Magistris et al. in Brain 121(Pt 3):437-450, 1998) was used to quantify a central conduction index (CCI = amplitude ratio of central conduction response and peripheral nerve response, obtained simultaneously by the TST). The CCI removes effects of peripheral fatigue from the quantification. It allows a quantification of the percentage of the entire target muscle motor unit pool driven to discharge by a transcranial magnetic stimulus. Subjects (n = 23) performed repetitive maximal voluntary contractions (MVC) of abductor digiti minimi (duration 1 s, frequency 0.5 Hz) during 2 min. TST recordings were obtained every 15 s, using stimulation intensities sufficient to stimulate all cortical motor neurons (MNs) leading to the target muscle, and during voluntary contractions of 20% of the MVC to facilitate the responses. TST was also repetitively recorded during recovery. This basic exercise protocol was modified in a number of experiments to further characterize influences on CCI of motor fatigue (4 min exercise at 50% MVC; delayed fatigue recovery during local hemostasis, "stimulated exercise" by 20 Hz trains of 1 s duration at 0.5 Hz during 2 min). In addition, the cortical silent period was measured during the basic exercise protocol. Force fatigued to approximately 40% of MVC in all experiments and in all subjects. In all subjects, CCI decreased during exercise, but this decrease varied markedly between subjects. On average, CCI reductions preceded force reductions during exercise, and CCI recovery preceded force recovery. Exercising at 50% for 4 min reduced muscle force more markedly than CCI. Hemostasis induced by a cuff delayed muscle force recovery, but not CCI recovery. Stimulated exercise reduced force markedly, but CCI decreased only marginally. Summarized, force reduction and reduction of the CCI related poorly quantitatively and in time, and voluntary drive was particularly critical to reduce the CCI. The fatigue induced reduction of CCI may result from a central inhibitory phenomenon. Voluntary muscle activation is critical for the CCI reduction, suggesting a primarily supraspinal mechanism.