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The critical behavior of two-dimensional vesicles in the deflated regime is studied analytically using a mapping onto a gauge model, scaling arguments, and exact inequalities. In agreement with the results of earlier studies the critical behavior is governed by a branched-polymer fixed point. The shape of the critical line in the gauge model is deduced in the weak and in the infinitely deflated regime.
There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.
A method of identification of coherent structures in a random turbulent flow is outlined with emphasis on the structure best correlated with a random energy-integrable field and application of the proper orthogonal decomposition to the shear flow of the wall region. The wall region of a pipe flow with almost pure glycerine is investigated experimentally, dynamic equations are obtained, and an energy-transfer model is employed. Numerical solutions are obtained, implications for the flow in the wall region are discussed with focus placed on the sets of solutions exhibiting intermittency. The most significant finding of the study is considered to be the suggestion of the etiology of the bursting phenomenon; presuming that abrupt transitions from one fixed point to the other can be identified with a burst, these bursts appear to be produced autonomously by the wall region, but be triggered by pressure signals from the outer layer.
The errors introduced into GPS measurements of a geodetic network by means of adopting different sets of stations in central and southern California as fixed points (termed fiducial stations) were investigated. Solutions for a crustal deformation network spanning distances up to 350 km were computed with a variety of fiducial networks, using fiducial coordinates determined from VLBI. Results showed that three receivers collocated with VLBI sites provide a stable reference system at a few millimeter level in the horizontal components and at 10 mm in the vertical components, indicating that local survey errors between VLBI and GPS markers at fiducial sites do not severely affect the estimates of interstation vectors.
Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low Reynolds number fully developed turbulence are compared. Several flows are noted: fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, only fully chaotic is classified as turbulent. Besides the sustained flows, a flow which decays as it becomes turbulent is examined. For the finest grid, 128(exp 3) points, the spatial resolution appears to be quite good. As a final note, the variation of the velocity derivatives skewness of a Navier-Stokes flow as the Reynolds number goes to zero is calculated numerically. The value of the skewness is shown to become small at low Reynolds numbers, in agreement with intuitive arguments that nonlinear terms should be negligible.
The two-Riccati-equation method solution to a standard H(infinity) control problem can be used to characterize all possible stabilizing optimal or suboptimal H(infinity) controllers if the optimal or suboptimal H(infinity) norm is available in the literature. An iterative algorithm for computing the optimal H(infinity) norm is proposed. The algorithm employs fixed-point, double secant and bisection to guarantee a super linear convergence.
The interdisciplinary optimization of engineering systems is discussed from the standpoint of the computational alternatives available to the designer. The analysis of such systems typically requires the solution of coupled systems of nonlinear algebraic equations. The solution procedure is necessarily iterative in nature. It is shown that the system can be solved by fixed point iteration, by Newton's method, or by a combination of the two. However, the need for sensitivity analysis may affect the choice of analysis solution method. Similarly, the optimization of the system can be formulated in several ways that are discussed in the paper. It is shown that the effect of the topology of the interaction between disciplines is a key factor in the choice of analysis, sensitivity and optimization methods. Several examples are presented to illustrate the discussion.
Formal neuronal networks (FNN), which are comprised of threshold gates, make use of the unit step function. It is regarded as a degenerated distribution function (DDF) and will be referred to here as a non-fuzzy threshold operator (nFTO). Special networks of this kind generating long cycles of states are modified by introduction of fuzzy threshold operators (FTO), i.e., non-degenerated distribution functions (nDDF). The cyclic behavior of the new nets is compared with the original ones. The interconnection matrix and threshold values are not modified. It is concluded that the original long cycles change the fixed points and short cycles, and as the computer simulations demonstrate, the aperiodic motion that is associated with chaotic behavior appears. The emergence of the above changes depend on the steepness of the threshold operators.
It has been possible to measure glacier recession on the basis of Landsat data, in conjunction with comparisons of the magnitude of recession of a glacier margin with in situ measurements at fixed points along the same margin. Attention is presently given to the cases of Vatnajokull ice cap, in Iceland, and the Pasterze Glacier, in Austria, on the basis of satellite data from 1973-1987 and 1984-1990, respectively. Indications of a trend toward negative mass balance are noted. Nevertheless, while most of the world's small glaciers have been receding, some are advancing either due to local climate or the tidewater glacier cycle.
With the assistance and cooperation of the National Advisory Committee for Aeronautics the Bureau of Standards has been engaged for the past year in an investigation of turbulence in wind tunnels, especially in so far as turbulence affects the results of measurements in different wind tunnels. Two methods of making such studies are described in this report together with the results of the use in the 54-inch wind tunnel of the Bureau of Standards. The first method consists in measuring the drag of circular cylinders; the second in measuring the static pressure at some fixed point. Both methods show that the flow is not entirely free from irregularities.
A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.
The optimum decoding of component codes in block coded modulation (BCM) schemes requires the use of the log-likelihood ratio (LLR) as the signal metric. An approximation to the LLR for the least reliable bit (LRB) in an 8-PSK modulation based on planar equations with fixed point arithmetic is developed that is both accurate and easily realizable for practical BCM schemes. Through an error power analysis and an example simulation it is shown that the approximation results in 0.06 dB in degradation over the exact expression at an E(sub s)/N(sub o) of 10 dB. It is also shown that the approximation can be realized in combinatorial logic using roughly 7300 transistors. This compares favorably to a look up table approach in typical systems.
The goal of this project was the feasibility study of a particular architecture of a digital signal processing machine operating in real time which could do in a pipeline fashion the computation of the fast Fourier transform (FFT) of a time-domain sampled complex digital data stream. The particular architecture makes use of simple identical processors (called inner product processors) in a linear organization called a systolic array. Through computer simulation the new architecture to compute the FFT with systolic arrays was proved to be viable, and computed the FFT correctly and with the predicted particulars of operation. Integrated circuits to compute the operations expected of the vital node of the systolic architecture were proven feasible, and even with a 2 micron VLSI technology can execute the required operations in the required time. Actual construction of the integrated circuits was successful in one variant (fixed point) and unsuccessful in the other (floating point).
On the Moon or Mars, it is necessary to have an anchor, or a stable, fixed point able to support the forces necessary to rescue a stuck vehicle, act as a stake for a tent in a Martian gale, act as a fulcrum in the erection of general construction poles, or support tent-like regolith shields. The anchor emplacement system must be highly autonomous. It must supply the energy and stability for anchor deployment. The goal of the anchor emplacement system project is to design and build a prototype anchor and to design a conceptual anchor emplacement system. Various anchors were tested in a 1.3 cubic meter test bed containing decomposed granite. A simulated lunar soil was created by adjusting the moisture and compaction characteristics of the soil. We conducted tests on emplacement torque, amount of force the anchor could withstand before failure, anchor pull out force at various angles, and soil disturbances caused by placing the anchor. A single helix auger anchor performed best in this test bed based on energy to emplace, and the ultimate holding capacity. The anchor was optimized for ultimate holding capacity, minimum emplacement torque, and minimum soil disturbance in sandy soils yielding the following dimensions: helix diameter (4.45 cm), pitch (1.27 cm), blade thickness (0.15 cm), total length (35.56 cm), shaft diameter (0.78 cm), and a weight of 212.62 g. The experimental results showed that smaller diameter, single-helix augers held more force than larger diameter augers for a given depth. The emplacement system consists of a flywheel and a motor for power, sealed in a protective box supported by four legs. The flywheel system was chosen over a gear system based on its increased reliability in the lunar environment.
Cosmic balloons are spherical domain walls with relativistic particles trapped inside. We derive the exact mass and radius relations for a static cosmic balloon using Gauss-Codazzi equations. The cosmic balloon mass as a function of its radius, M(R), is found to have a functional form similar to that of fermion soliton stars, with a fixed point at 2GM(R)/R approximately or equal to 0.486 which corresponds to the limit of infinite central density. We derive a simple analytical approximation for the mass density of a spherically symmetric relativistic gas star. When applied to the computation of the mass and radius of a cosmic balloon, the analytical approximation yields fairly good agreement with the exact numerical solutions.
A method for active fluid flow control based on control theory is discussed. Dynamic programming and fixed point successive approximations are used to accommodate the nonlinear control problem. The long-term goal of this project is to establish an effective method applicable to complex flows such as turbulence and jets. However, in this report, the method is applied to stochastic Burgers equation as an intermediate step towards this goal. Numerical results are compared with those obtained by gradient search methods.
This report contains the results of a study performed under the sponsorship of the National Aeronautics and Space Administration (NASA) made as a grant to the Center for Space Telemetering and Telecommunication Systems at New Mexico State University. The purpose of this phase of the grant is to increase user access to the Space Network (SN) run by NASA for supplying space-to-ground communications for satellites and associated control centers. The identified need is to bring more users into the community of those accessing the SN, especially those in the small satellite class of users. The initial phase of the study concerned the potential for modifications to the standard transponder used in the SN. The results of that investigation are summarized in Section 4. As the hardware modifications were being investigated, a second option was developed, namely to consider changes to the operational mode for the small satellites. This operational concept was to use a single, fixed-pointing antenna in a spin-stabilized satellite and let the antenna pattern sweep past the Tracking and Data Relay Satellites (TDRS) in the SN. The question to be answered by this phase of the study was twofold: could enough contact time per day be made available using this simple operating mode and could the data rate be high enough to allow for sufficient data throughput to satisfy the user community using existing components. Section 2 outlines the methodology and simulation results to answer these questions. Section 3 contains a summary of an operational simulation of a simple satellite payload using these contact scenarios. The simulation is not all inclusive but shows how a payload simulation could be configured to utilize variable contact times. The answer to both of the questions desired to be answered is affirmative. By carefully choosing the correct system transmission power and antenna pattern, the system will allow support to the 50th percentile of expected systems. It is recommended that based on this initial study, further work be done to quantify the exact parameters for transmission through the space network and to optimize usage of the contact time to maximize throughput.
We report the results of extensive numerical experiments on the Kuramoto-Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly unstable modes enter the dynamics. General initial conditions are used and evolving states do not assume odd-parity. A large number of numerical experiments are employed in order to obtain quantitative characteristics of the dynamics. We report on different routes to chaos and provide numerical evidence and construction of strange attractors with self-similar characteristics. As the 'viscosity' parameter decreases the dynamics becomes increasingly more complicated and chaotic. In particular it is found that regular behavior in the form of steady state or steady state traveling waves is supported amidst the time-dependent and irregular motions. We show that multimodal steady states emerge and are supported on decreasing windows in parameter space. In addition we invoke a self-similarity property of the equation, to show that these profiles are obtainable from global fixed point attractors of the Kuramoto-Sivashinsky equation at much larger values of the viscosity.