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At least 37 records · Page 2

Prolongation structures of nonlinear evolution equations. II

The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.

Estabrook, F. B.↗

Asymptotic behavior of vector recurrences with applications

An investigation is conducted of the behavior of a vector recurrence relation under very weak assumptions. The obtained results are used in an analysis of the iterations for nonlinear equations and a study concerning the composition of such iterations. The results can be employed in studies of one-point iterations involving the use of memory elements. Iterations for solving nonlinear equations on parallel computers can be investigated.

Feldstein, A.↗

The method of lines in three dimensional fracture mechanics

A review of recent developments in the calculation of design parameters for fracture mechanics by the method of lines (MOL) is presented. Three dimensional elastic and elasto-plastic formulations are examined and results from previous and current research activities are reported. The application of MOL to the appropriate partial differential equations of equilibrium leads to coupled sets of simultaneous ordinary differential equations. Solutions of these equations are obtained by the Peano-Baker and by the recurrance relations methods. The advantages and limitations of both solution methods from the computational standpoint are summarized.

Gyekenyesi, J.↗

The method of lines in three-dimensional fracture mechanics

A review is presented of recent developments in the calculation of design parameters for fracture mechanics by the method of lines (MOL). Three-dimensional elastic and elasto-plastic formulations are examined and results are reported from previous and current research activities. The application of MOL to the appropriate partial differential equations of equilibrium leads to coupled sets of simultaneous ordinary differential equations. Solutions of these equations are obtained by the Peano-Baker and by the recurrence relations methods. The advantages and limitations of both solution methods from the computational standpoint are summarized.

Gyekenyesi, J.↗

An O(N squared) method for computing the eigensystem of N by N symmetric tridiagonal matrices by the divide and conquer approach

An efficient method is proposed to solve the eigenproblem of N by N Symmetric Tridiagonal (ST) matrices. Unlike the standard eigensolvers which necessitate O(N cubed) operations to compute the eigenvectors of such ST matrices, the proposed method computes both the eigenvalues and eigenvectors with only O(N squared) operations. The method is based on serial implementation of the recently introduced Divide and Conquer (DC) algorithm. It exploits the fact that by O(N squared) of DC operations, one can compute the eigenvalues of N by N ST matrix and a finite number of pairs of successive rows of its eigenvector matrix. The rest of the eigenvectors--all of them or one at a time--are computed by linear three-term recurrence relations. Numerical examples are presented which demonstrate the superiority of the proposed method by saving an order of magnitude in execution time at the expense of sacrificing a few orders of accuracy.

Gill, Doron↗

Block-Krylov component synthesis method for structural model reduction

A new analytical method is presented for generating component shape vectors, or Ritz vectors, for use in component synthesis. Based on the concept of a block-Krylov subspace, easily derived recurrence relations generate blocks of Ritz vectors for each component. The subspace spanned by the Ritz vectors is called a block-Krylov subspace. The synthesis uses the new Ritz vectors rather than component normal modes to reduce the order of large, finite-element component models. An advantage of the Ritz vectors is that they involve significantly less computation than component normal modes. Both 'free-interface' and 'fixed-interface' component models are derived. They yield block-Krylov formulations paralleling the concepts of free-interface and fixed-interface component modal synthesis. Additionally, block-Krylov reduced-order component models are shown to have special disturbability/observability properties. Consequently, the method is attractive in active structural control applications, such as large space structures. The new fixed-interface methodology is demonstrated by a numerical example. The accuracy is found to be comparable to that of fixed-interface component modal synthesis.

Craig, Roy R., Jr.↗

Verification of a Viscous Computational Aeroacoustics Code Using External Verification Analysis

The External Verification Analysis approach to code verification is extended to solve the three-dimensional Navier-Stokes equations with constant properties, and is used to verify a high-order computational aeroacoustics (CAA) code. After a brief review of the relevant literature, the details of the EVA approach are presented and compared to the similar Method of Manufactured Solutions (MMS). Pseudocode representations of EVA's algorithms are included, along with the recurrence relations needed to construct the EVA solution. The code verification results show that EVA was able to convincingly verify a high-order, viscous CAA code without the addition of MMS-style source terms, or any other modifications to the code.

Computational↗

Verification of a Viscous Computational Aeroacoustics Code using External Verification Analysis

The External Verification Analysis approach to code verification is extended to solve the three-dimensional Navier-Stokes equations with constant properties, and is used to verify a high-order computational aeroacoustics (CAA) code. After a brief review of the relevant literature, the details of the EVA approach are presented and compared to the similar Method of Manufactured Solutions (MMS). Pseudocode representations of EVA's algorithms are included, along with the recurrence relations needed to construct the EVA solution. The code verification results show that EVA was able to convincingly verify a high-order, viscous CAA code without the addition of MMS-style source terms, or any other modifications to the code.

Computational↗

Analytic Expressions for Derivatives from Series Solutions to the Three Body Problem

This paper presents a notation system to facilitate to solution of differential equations via Taylor series expansions and applies it to solve the circular restricted three body problem. Unlike previous Taylor series methods in the astrodynamics literature, computer algebra solvers are not used. Instead the notation system allows one to solve a system of differential equations analytically “by hand” without resorting to computer algebra software. This method produces recurrence relations explicitly in terms of a sequence of derivatives of the state with respect to time for the coefficients of Taylor Series solutions that can be evaluated numerically or manipulated further to investigate properties of the solution. For example, additional derivatives with respect to other parameters may also be found, including those that describe the dependence of the solution on initial conditions.

Strange, Nathan↗

Recurrent active regions related to metric radio continuum emissions and the interplanetary magnetic sector structure

Active heliographic longitudes at the sun are investigated by using the observational data for long-lived metric continuum noise sources. It is shown that, for the period from 1963 to 1969, the number of such longitudes was four in general and these longitudes were very stable for this radio activity since 1963. A discussion is given on the relationship between those longitudes and the sector structure of the interplanetary magnetic field.

Sakurai, K.↗

Temperature-plant pigment-optical relations in a recurrent offshore mesoscale eddy near Point Conception, California

The temperature-plant pigment-optical structure of a mesoscale anticyclonic eddy consistently found in shipboard surveys and satellite-sensed data several hundred kilometers southwest of Point Conception, CA, is described on three different time scales (100-day mesoscale, annual, and several-year). The satellite coastal zone color scanner (CZCS) ocean color imagery detected the near-surface chlorophyll structure of the eddy, but in situ optical and plant pigment data suggest that such imagery does not provide a good estimate of the integrated chlorophyll field of the eddy. The temperature and plant pigment boundaries of the eddy, as determined from two-dimensional gradients of advanced very high resolution radiometer (AVHRR) and CZCS imagery, do not coincide spatially. This and in situ temperature, plant pigment, and optical structure provide additional evidence that some eddy systems in the California Current are not isolated vortex systems but rather continuously entrain waters of nonlocal origin laterally into their upper layers. Within the California Current a ratio of AVHRR/CZCS data is useful for separating inshore from oceanic water masses and following their surface entrainment by offshore vortices. The historical 28-year California Cooperative Oceanic Fisheries Investigations data for the Point Conception region of the California Current and remotely sensed data over this region show that the Point Conception eddy is a recurrent feature in the offshore California Current. Moreover, the available data provide evidence that a large number of warm-core mesoscale eddies occur simultaneously in a transition zone between coastal and oceanic regimes, that these features recur at preferred locations within the transition zone, and that this family of eddies should impose a significant offshore boundary condition on the flow of the California Current.

Simpson, James J.↗

Relation of large-scale coronal X-ray structure and cosmic rays. I - Sources of solar wind streams as defined by X-ray emission and H-alpha absorption features

The large-scale structure of the corona and the interplanetary medium during Carrington rotations 1601-1607 is discussed relative to recurrent high-speed solar wind streams and their coronal sources. Only streams A, C, D, and F recur on more than one rotation. Streams A and D are associated with coronal holes, while C and F originate in the high corona (20-50 solar radii) over faint X-ray emissions. The association of the streams with holes is confirmed by earlier findings that there are no large equatorial holes without an associated high-speed stream and that the area of the equatorial region of coronal holes is highly correlated with the maximum velocity observed in the associated stream near 1 AU.

Krieger, A. S.↗

Dynamics of column stability with partial end restraints

The dynamic behavior of columns with partial end restraints and loads consisting of a dead load and a pulsating load are investigated. The differential equation is solved using a lumped impulse recurrence formula relative to time coupled with a finite difference discretization along the member length. A computer program is written from which the first critical frequencies are found as a function of end stiffness. The case of a pinned ended column compares very well with the exact solution. Also, the natural frequency and buckling load formulas are derived for equal and unequal end restraints.

Gregory, Peyton B.↗

Quantitative EEG Monitoring of Vigilance: Effects of Sleep Deprivation, Circadian Phase and Sympathetic Activation

Shuttle astronauts typically sleep only 6 to 6.5 hours per day while in orbit. This sleep loss is related to recurrent sleep cycle shifting--due to mission-dependent orbital mechanics and mission duration requirements-- and associated circadian displacement of sleep, the operational demands of space flight, noise and space motion sickness. Such sleep schedules are known to produce poor subjective sleep quality, daytime sleepiness, reduced attention, negative mood, slower reaction times, and impaired daytime alertness. Countermeasures to allow crew members to obtain an adequate amount of sleep and maintain adequate levels of neurobehavioral performance are being developed and investigated. However, it is necessary to develop methods that allow effective and attainable in-flight monitoring of vigilance to evaluate the effectiveness of these countermeasures and to detect and predict online critical decrements in alertness/performance. There is growing evidence to indicate that sleep loss and associated decrements in neurobehavioral function are reflected in the spectral composition of the electroencephalogram (EEG) during wakefulness as well as in the incidence of slow eye movements recorded by the electro-oculogram (EOG). Further-more, our preliminary data indicated that these changes in the EEG during wakefulness are more pronounced when subjects are in a supine posture, which mimics some of the physiologic effects of microgravity. Therefore, we evaluate the following hypotheses: (1) that during a 40-hour period of wakefulness (i.e., one night of total sleep deprivation) neurobehavioral function deteriorates, the incidence of slow eye-movements and EEG power density in the theta frequencies increases especially in frontal areas of the brain; (2) that the sleep deprivation induced deterioration of neurobehavioral function and changes in the incidence of slow eye movements and the spectral composition of the EEG are more pronounced when subjects are in a supine position; and (3) that based on assessment of slow-eye movements and quantitative on-line topographical analyses of EEG during wakefulness an EEG and or EOG parameter can be derived/constructed which accurately predicts changes in neurobehavioral function.

Dijk, Derk-Jan↗

On neural networks in identification and control of dynamic systems

This paper presents a discussion of the applicability of neural networks in the identification and control of dynamic systems. Emphasis is placed on the understanding of how the neural networks handle linear systems and how the new approach is related to conventional system identification and control methods. Extensions of the approach to nonlinear systems are then made. The paper explains the fundamental concepts of neural networks in their simplest terms. Among the topics discussed are feed forward and recurrent networks in relation to the standard state-space and observer models, linear and nonlinear auto-regressive models, linear, predictors, one-step ahead control, and model reference adaptive control for linear and nonlinear systems. Numerical examples are presented to illustrate the application of these important concepts.

Phan, Minh↗

Relationships between solar activity and climate change

Recurrent droughts are related to the double sunspot cycle. It is suggested that high solar activity generally increases meridional circulations and blocking patterns at high and intermediate latitudes, especially in winter. This effect is related to the sudden formation of cirrus clouds during strong geomagnetic activity that originates in the solar corpuscular emission.

Roberts, W. O.↗

Recurrence in truncated Boussinesq models for nonlinear waves in shallow water

The rapid spatial recurrence of weakly nonlinear and weakly dispersive progressive shallow-water waves is examined using a numerical integration technique on the discretized and truncated form of the Boussinesq equations. This study primarily examines recurrence in wave fields with Ursell number O(1) and characterizes the sensitivity of recurrence to initial spectral shape and number of allowed frequency modes. It is shown that the rapid spatial recurrence is not an inherent property of the considered Boussinesq systems for evolution distances of 10-50 wavelengths. The main result of the study is that highly truncated Boussinesq models of resonant shallow-water ocean surface gravity waves predict rapid multiple recurrence cycles, but that this is an artifact dependent on the number of allowed modes. For initial conditions consisting of essentially all energy concentrated in a single mode, damping of the recurrence cycles increases as the number of low-power background modes increases. When more than 32 modes are allowed, the recurrence behavior is relatively insensitive to the number of allowed modes.

Elgar, Steve↗

The earth's magnetosphere under continued forcing - Substorm activity during the passage of an interplanetary magnetic cloud

Magnetic field and energetic particle observations from six spacecraft in the near-earth magnetotail are described and combined with ground magnetograms to document for the first time the magnetospheric substorm activity during a 30-hour long transit of an interplanetary cloud at 1 AU. During an earlier 11-hr interval when B(z) was continuously positive, the magnetosphere was quiescent, while in a later 18-hr interval when B(z) was uninterruptedly negative a large magnetic storm was set off. In the latter interval the substorm onsets recurred on average every 50 min. Their average recurrence frequency remained relatively undiminished even when the magnetic cloud B(z) and other measures of the interplanetary energy input decreased considerably. These results concur with current models of magnetospheric substorms based on deterministic nonlinear dynamics. The substorm onset occurred when the cloud's magnetic field had a persistent northward component but was predominantly westward pointing.

Farrugia, C. J.↗