Reduction In Degrees Of Freedom Research Articles

A biomechanical perspective on spinal mechanisms of coordinated muscular action: an architecture principle.

A principle of organization of spinal circuitry which emerges from the studies reviewed here is that the structure of the distributed network of pathways in the spinal cord contains a detailed representation of the corresponding three dimensional architecture of the musculoskeletal system. The pertinent architectural features for a given muscle include (1) the number and identity of spanned joints, and (2) the line of action at a joint with respect to the torque directions of other muscles and to the gravity vector. In accordance with established ideas, muscles with common primary actions (synergists) at the ankle are linked by excitatory, length-dependent pathways. Those muscles which have opposite actions are linked by reciprocal inhibition, although muscles which are not principally involved in postural control are not connected in this way. Among antigravity and stabilizing muscles, force-dependent, inhibitory pathways link (1) muscles crossing different joints, and (2) members of different synergistic groups which exert torques in different directions. Therefore, each muscle has a unique set of actions in terms of joints spanned and line of action, and each muscle receives a unique combination of reflex inputs. The cross-joint coordination resulting from actions of force-dependent pathways becomes stronger at higher forces with a consequent reduction in degrees of freedom of the musculoskeletal system. Length-dependent pathways link muscles which share some, but not all, mechanical actions at a joint and may have different patterns of activation during locomotion. Length-dependent pathways appear to coordinate muscle responses to postural disturbances and enhance joint stiffness.

Accuracy and convergence of the p‐ and hp‐type finite element methods for the Navier‐Stokes equation

AbstractHigher‐order p and hp finite element algorithms for modeling the flow of New‐tonian fluids have been developed. Numerical computations in three test geometries were carried out to compare the performance of these methods to that of conventional h‐type finite elements. Computations demonstrated that for solutions which are analytic everywhere in the domain of interest, p extensions exhibit an exponential rate of convergence as opposed to the characteristic linear convergence of h‐type finite element procedures. Moreover, for solutions which are analytic everywhere in the domain except at a set of points, hp extensions with geometric mesh refinement based on effective error indicators (individually, the error in the energy norm, local and global deviations from mass and momentum conservation) also give rise to an exponential convergence rate. This rapid convergence of p and hp finite element formulations enables the achievement of the solution of linear Stokes problems with an order of magnitude reduction in degrees of freedom. In nonlinear problems, these computational savings are appreciated by a factor approximately equal to the number of iterations required to obtain converged solutions.

Design and analysis of recursive periodically time-varying digital filters with highly quantized coefficients

A design for recursive filters with coefficients epsilon (1, 0, -1) that can change at each filter update is introduced. This flexibility of allowing the multipliers to be functions of time can be used to offset the reduction in degrees of freedom when such quantization is used. This result will be especially useful in filtering applications in which a controllable or adaptive filter is required and high-speed multipliers are not available. A general transition-matrix state-variable formulation similar to Floquet theory for differential equations is developed that can be used to design IIR (infinite-impulse response) filters characterized by a periodically time-varying feedback matrix. By defining a time-varying similarity transformation and introducing circulant feedback matrices, a significant simplification of the highly quantized time-varying state recursion equation is realized. This leads to the enumeration of the filter transfer function and to a simple eigenvalue structure that facilitates the design of filters with desired pole locations. These analytical results are verified in simulations of lowpass and bandpass filter designs. >

Digital Image Processing in Flow Visualization

Flow visualization results from the interaction between light and matter. Classical methods such as shadowgraphy, schlieren photography, and interferometry visualize variation in the index of refraction induced by changes in density, pressure, or temperature. Nonuniformities of these physical observables modify the phase of optical waves, rendered visible by free-space propagation (shadowgraphy), optical processing in the back focal plane of a lens (schlieren photography), or interference with a ref­ erence wave (interferometry). The classical methods visualize variations of the index of refraction or spatial derivatives thereof integrated along the light path through the fluid. Three-dimensional space is projected onto a plane with the corresponding reduction in degrees of freedom. Except for axial symmetric or two-dimensional flows, spatial structures cannot be recovered from a single image. Interior detail may be visualized by illuminating the flow with a sheet of light and imaging scattered radiation from variations in particle density or physical observables. Mie scattering is widely used because particles scatter more efficiently than molecules. Rayleighand Raman-scattering cross sections are small, necessitating intense laser sources for flow visu­ alization. Excellent reviews of classical flow-visualization methods have been pub­ lished, for example, by Merzkirch (1974) and Lauterborn & Vogel (1984) and a beautiful and inspiring collection of pictures by Van Dyke (1982).