Search NASA⌕ Search

SEARCH · Search NASA

Results for “Complex functions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Reference Avionics Architecture for Lunar Surface Systems

Developing and delivering infrastructure capable of supporting long-term manned operations to the lunar surface has been a primary objective of the Constellation Program in the Exploration Systems Mission Directorate. Several concepts have been developed related to development and deployment lunar exploration vehicles and assets that provide critical functionality such as transportation, habitation, and communication, to name a few. Together, these systems perform complex safety-critical functions, largely dependent on avionics for control and behavior of system functions. These functions are implemented using interchangeable, modular avionics designed for lunar transit and lunar surface deployment. Systems are optimized towards reuse and commonality of form and interface and can be configured via software or component integration for special purpose applications. There are two core concepts in the reference avionics architecture described in this report. The first concept uses distributed, smart systems to manage complexity, simplify integration, and facilitate commonality. The second core concept is to employ extensive commonality between elements and subsystems. These two concepts are used in the context of developing reference designs for many lunar surface exploration vehicles and elements. These concepts are repeated constantly as architectural patterns in a conceptual architectural framework. This report describes the use of these architectural patterns in a reference avionics architecture for Lunar surface systems elements.

Somervill, Kevin M.↗

A system of three-dimensional complex variables

Some results of a new theory of multidimensional complex variables are reported, including analytic functions of a three-dimensional (3-D) complex variable. Three-dimensional complex numbers are defined, including vector properties and rules of multiplication. The necessary conditions for a function of a 3-D variable to be analytic are given and shown to be analogous to the 2-D Cauchy-Riemann equations. A simple example also demonstrates the analogy between the newly defined 3-D complex velocity and 3-D complex potential and the corresponding ordinary complex velocity and complex potential in two dimensions.

Martin, E. Dale↗

A system architecture for a planetary rover

Each planetary mission requires a complex space vehicle which integrates several functions to accomplish the mission and science objectives. A Mars Rover is one of these vehicles, and extends the normal spacecraft functionality with two additional functions: surface mobility and sample acquisition. All functions are assembled into a hierarchical and structured format to understand the complexities of interactions between functions during different mission times. It can graphically show data flow between functions, and most importantly, the necessary control flow to avoid unambiguous results. Diagrams are presented organizing the functions into a structured, block format where each block represents a major function at the system level. As such, there are six blocks representing telecomm, power, thermal, science, mobility and sampling under a supervisory block called Data Management/Executive. Each block is a simple collection of state machines arranged into a hierarchical order very close to the NASREM model for Telerobotics. Each layer within a block represents a level of control for a set of state machines that do the three primary interface functions: command, telemetry, and fault protection. This latter function is expanded to include automatic reactions to the environment as well as internal faults. Lastly, diagrams are presented that trace the system operations involved in moving from site to site after site selection. The diagrams clearly illustrate both the data and control flows. They also illustrate inter-block data transfers and a hierarchical approach to fault protection. This systems architecture can be used to determine functional requirements, interface specifications and be used as a mechanism for grouping subsystems (i.e., collecting groups of machines, or blocks consistent with good and testable implementations).

Smith, D. B.↗

Theory of post-block 2 VLBI observable extraction

The algorithms used in the post-Block II fringe-fitting software called 'Fit' are described. The steps needed to derive the very long baseline interferometry (VLBI) charged-particle corrected group delay, phase delay rate, and phase delay (the latter without resolving cycle ambiguities) are presented beginning with the set of complex fringe phasors as a function of observation frequency and time. The set of complex phasors is obtained from the JPL/CIT Block II correlator. The output of Fit is the set of charged-particle corrected observables (along with ancillary information) in a form amenable to the software program 'Modest.'

Lowe, Stephen T.↗

A Case Study on the Application of a Structured Experimental Method for Optimal Parameter Design of a Complex Control System

This report documents a case study on the application of Reliability Engineering techniques to achieve an optimal balance between performance and robustness by tuning the functional parameters of a complex non-linear control system. For complex systems with intricate and non-linear patterns of interaction between system components, analytical derivation of a mathematical model of system performance and robustness in terms of functional parameters may not be feasible or cost-effective. The demonstrated approach is simple, structured, effective, repeatable, and cost and time efficient. This general approach is suitable for a wide range of systems.

Torres-Pomales, Wilfredo↗

Application of signal analysis to cavitation

The diagnostic facilities of the cross power spectrum and the coherence function have been employed to enhance the identification of not only the inception of cavitation, but also its level. Two piezoelectric pressure transducers placed in the downstream chamber of a model spool valve undergoing various levels of cavitation allowed for the use of both functions - the phase angle of the complex cross spectrum and the dimensionless coherence function - to sense clearly the difference between noise levels associated with a noncavitating jet from those once cavitation inception is attained. The cavitation noise within the chamber exhibited quite a regular character in terms of the phase difference between instruments for limited cavitation. Varying cavitation levels clearly illustrated the effect of bubble size on the attendant frequency range for which there was an extremely high coherence or nearly perfect causality.

Martin, C. S.↗

Gene Fusion: A Genome Wide Survey

As a well known fact, organisms form larger and complex multimodular (composite or chimeric) and mostly multi-functional proteins through gene fusion of two or more individual genes which have independent evolution histories and functions. We call each of these components a module. The existence of multimodular proteins may improves the efficiency in gene regulation and in cellular functions, and thus may give the host organism advantages in adaptation to environments. Analysis of all gene fusions in present-day organisms should allow us to examine the patterns of gene fusion in context with cellular functions, to trace back the evolution processes from the ancient smaller and uni-functional proteins to the present-day larger and complex multi-functional proteins, and to estimate the minimal number of ancestor proteins that existed in the last common ancestor for all life on earth. Although many multimodular proteins have been experimentally known, identification of gene fusion events systematically at genome scale had not been possible until recently when large number of completed genome sequences have been becoming available. In addition, technical difficulties for such analysis also exist due to the complexity of this biological and evolutionary process. We report from this study a new strategy to computationally identify multimodular proteins using completed genome sequences and the results surveyed from 22 organisms with the data from over 40 organisms to be presented during the meeting. Additional information is contained in the original extended abstract.

Liang, Ping↗

A Newton algorithm for complex curve fitting

The problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type which converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions.

Spanos, J. T.↗

Reduction of Subjective and Objective System Complexity

Occam's razor is often used in science to define the minimum criteria to establish a physical or philosophical idea or relationship. Albert Einstein is attributed the saying "everything should be made as simple as possible, but not simpler". These heuristic ideas are based on a belief that there is a minimum state or set of states for a given system or phenomena. In looking at system complexity, these heuristics point us to an idea that complexity can be reduced to a minimum. How then, do we approach a reduction in complexity? Complexity has been described as a subjective concept and an objective measure of a system. Subjective complexity is based on human cognitive comprehension of the functions and inter relationships of a system. Subjective complexity is defined by the ability to fully comprehend the system. Simplifying complexity, in a subjective sense, is thus gaining a deeper understanding of the system. As Apple's Jonathon Ive has stated," It's not just minimalism or the absence of clutter. It involves digging through the depth of complexity. To be truly simple, you have to go really deep". Simplicity is not the absence of complexity but a deeper understanding of complexity. Subjective complexity, based on this human comprehension, cannot then be discerned from the sociological concept of ignorance. The inability to comprehend a system can be either a lack of knowledge, an inability to understand the intricacies of a system, or both. Reduction in this sense is based purely on a cognitive ability to understand the system and no system then may be truly complex. From this view, education and experience seem to be the keys to reduction or eliminating complexity. Objective complexity, is the measure of the systems functions and interrelationships which exist independent of human comprehension. Jonathon Ive's statement does not say that complexity is removed, only that the complexity is understood. From this standpoint, reduction of complexity can be approached in finding the optimal or 'best balance' of the system functions and interrelationships. This is achievable following von Bertalanffy's approach of describing systems as a set of equations representing both the system functions and the system interrelationships. Reduction is found based on an objective function defining the system output given variations in the system inputs and the system operating environment. By minimizing the objective function with respect to these inputs and environments, a reduced system can be found. Thus, a reduction of the system complexity is feasible.

Watson, Michael D.↗

Wall-function boundary conditions in the solution of the Navier-Stokes equations for complex compressible flows

To make computer codes for two-dimensional compressible flows more robust and economical, wall functions for these flows, under adiabatic conditions, have been developed and tested. These wall functions have been applied to three two-equation models of turbulence. The tests consist of comparisons of calculated and experimental results for transonic and supersonic flow over a flat plate and for two-dimensional and axisymmetrical transonic shock-wave/boundary-layer interaction flows with and without separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that results obtained agree very well with the data for the complex compressible flows tested, provided criteria for use of the wall functions are followed. The expected savings in cost of the computations and improved robustness of the code were achieved.

Viegas, J. R.↗

Complex-coordinate calculation of (1,3)P resonances in Ps(-) using Hylleraas functions

An accurate calculation for (1,3)P autodetaching resonances in Ps(-) has been carried out using the complex-rotation method, which has the advantage of giving resonance position and width at the same time. The wave function is of the Hylleraas type with an available number of terms up to 1140. One 1P and two 3P resonances below the n = 2 threshold and two 1P and two 3P resonances below the n = 3 threshold of the positronium atom. Resonance parameters are compared with those obtained from scattering and adiabatic calculations where available.

Bhatia, A. K.↗

Ion Sources and Acceleration Mechanisms Inferred from Local Distribution Functions

This study investigates the sources of the ions up the complex and nonisotropic H(+) velocity distribution functions observed by the Geotail spacecraft on May 23, 1995, in the near-Earth magnetotail region and recently reported by Frank et al. [1996]. A distribution function observed by Geotail at -10 R(sub E) downtail is used as input for the large scale kinetic (LSK) technique to follow the trajectories of approximately 90,000 H(+) ions backward in time. Time-dependent magnetic and electric fields are taken from a global magnetohydrodynamic (MHD) simulation of the magnetosphere and its interactions with appropriate solar wind and IMF conditions. The ion population described by the Geotail distribution function was found to consist of a mixture of particles originating from three distinct sources: the ionosphere, the low latitude boundary layer (LLBL), and the high latitude plasma mantle. Ionospheric particles had direct access along field lines to Geotail, and LLBL ions convected adiabatically to the Geotail location. Plasma mantle ions, on the other hand, exhibited two distinct types of behavior. Most near-Earth mantle ions reached Geotail on adiabatic orbits, while distant mantle ions interacted with the current sheet tailward of Geotail and had mostly nonadiabatic orbits. Ions from the ionosphere, the LLBL, and the near-Earth mantle were directly responsible for the well-separated, low energy structures easily discernible in the observed and modeled distribution functions. Distant mantle ions formed the higher energy portion of the Geotail distribution. Thus, we have been successful in extracting useful information about particle sources, their relative contribution to the measured distribution and the acceleration processes that affected particle transport during this time.

Ashour-Abdalla, M.↗

Propagation and stability of wavelike solutions of finite difference equations with variable coefficients

The propagation and dissipation of wavelike solutions to finite difference equations is analyzed on the basis of an asymptotic approach in which a wave solution is expressed as a product of a complex amplitude and an oscillatory phase function whose frequency and wavenumber may also be complex. An asymptotic expansion leads to a local dispersion relation for wavenumber and frequency; the first-order terms produce an equation for the amplitude in which the local group velocity appears as the convection velocity of the amplitude. Equations for the motion of wavepackets and their interaction at boundaries are derived, and a global stability analysis is carried out.

Giles, M. B.↗

Initial flight qualification and operational maintenance of X-29A flight software

This paper is predominantly a nontechnical discussion of some significant aspects of the initial flight qualification and operational maintenance of the flight control system software for the X-29A technology demonstrator. Flight qualification and maintenance of complex, embedded flight control system software poses unique problems. The X-29A technology demonstrator aircraft has a digital flight control system which incorporates functions generally considered too complex for analog systems. Organizational responsibilities, software assurance issues, tools, and facilities are discussed.

Earls, Michael R.↗

Initial flight qualification and operational maintenance of X-29A flight software

A discussion is presented of some significant aspects of the initial flight qualification and operational maintenance of the flight control system softward for the X-29A technology demonstrator. Flight qualification and maintenance of complex, embedded flight control system software poses unique problems. The X-29A technology demonstrator aircraft has a digital flight control system which incorporates functions generally considered too complex for analog systems. Organizational responsibilities, software assurance issues, tools, and facilities are discussed.

Earls, Michael R.↗

The Origin and Early Evolution of Membrane Proteins

Membrane proteins mediate functions that are essential to all cells. These functions include transport of ions, nutrients and waste products across cell walls, capture of energy and its transduction into the form usable in chemical reactions, transmission of environmental signals to the interior of the cell, cellular growth and cell volume regulation. In the absence of membrane proteins, ancestors of cell (protocells), would have had only very limited capabilities to communicate with their environment. Thus, it is not surprising that membrane proteins are quite common even in simplest prokaryotic cells. Considering that contemporary membrane channels are large and complex, both structurally and functionally, a question arises how their presumably much simpler ancestors could have emerged, perform functions and diversify in early protobiological evolution. Remarkably, despite their overall complexity, structural motifs in membrane proteins are quite simple, with a-helices being most common. This suggests that these proteins might have evolved from simple building blocks. To explain how these blocks could have organized into functional structures, we performed large-scale, accurate computer simulations of folding peptides at a water-membrane interface, their insertion into the membrane, self-assembly into higher-order structures and function. The results of these simulations, combined with analysis of structural and functional experimental data led to the first integrated view of the origin and early evolution of membrane proteins.

Pohorille, Andrew↗

Parameter identification for nonlinear aerodynamic systems

Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

Pearson, Allan E.↗

What’s That Supposed to Mean? Capturing Micro-Behaviors in Teams

Future long-duration space exploration (LDSE) crews will require extensive coordination, cooperation, and team functioning as they face a myriad of challenges rooted in both taskwork and teamwork (Bell et al., 2015; Landon et al., 2018). While exposed to extreme conditions, crew members must navigate living and working together in prolonged confinement. Moreover, astronaut teams are becoming increasingly diverse, introducing significant variability in team composition. This increasing diversity, alongside traditional constraints of LDSE, introduces additional challenges into effective team functioning. To date, most methods for capturing team functioning rely on self-report measures. Such measures are prone to several limitations, including but not limited to social desirability bias, halo effect, and leniency effects (Trull & Ebner-Priemer, 2013), which skew data and limit nuanced understandings of phenomena at play. Self-report measures broadly capture team functioning, lending the nature of such methods to identifying underlying “macro”-behaviors (i.e., behaviors that are long-standing and last over time). However, team functioning is far more complex than a series of macro-behaviors, rendering reliance on self-report data deficient for accurate measurement. Recent research demonstrates the potential of alternative methods for capturing team functioning, such as speech and physiological data (Chaffin et al., 2017; Murray & Oertel, 2018). Consequently, these methods are more suitable for capturing micro-behaviors: brief, often unconscious expressions that affect the extent to which an individual feels included by others around them (Paletz et al., 2013). Micro-behaviors can be further classified into microaggressions (i.e., subtle, negative exchanges; Keller & Galgay, 2010) or micro-affirmations (i.e., subtle, positive exchanges; Kyte et al. 2020), both of which influence team functioning. Due to the subtle nature of micro-behaviors, contextual factors have a significant impact when determining if it is aggressive or affirmative. Additionally, several iterations of microbehaviors can have lingering effects on team interactions. For example, the use of “mm-hmm” by a crew member can function as both a micro-affirmation and micro-aggression. Specifically, it can be indication of active listening (i.e., micro-affirmation) or as an expression of annoyance (i.e., aggression) depending on the context in which it occurs. Auditory features (e.g., tone, frequency) can help delineate between the two forms; however, the contextual factors (e.g., previous interactions between team members, crew demographics) add a layer of complexity that render auditory features alone as insufficient to capture micro-behaviors. Consequently, this paper seeks to provide a novel approach in which multi-modal data (i.e., auditory features and contextual features) are used in a random-forest model to better identify distinguishing characteristics between micro-affirmations and micro-aggressions. In turn, detected micro-behaviors are used to predict team performance, thereby demonstrating the value of capturing micro-behaviors as supplemental data to macro-behaviors.

Sydney R. Begerowski↗