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NASA NTRS1993

On the global dynamics of adaptive systems - A study of an elementary example

The inherent nonlinear character of adaptive systems poses serious theoretical problems for the analysis of their dynamics. On the other hand, the importance of their dynamic behavior is directly related to the practical interest in predicting such undesirable phenomena as nonlinear oscillations, abrupt transients, intermittence or a high sensitivity with respect to initial conditions. A geometrical/qualitative description of the phase portrait of a discrete-time adaptive system with unmodeled disturbances is given. For this, the motions in the phase space are referred to normally hyperbolic (structurally stable) locally invariant sets. The study is complemented with a local stability analysis of the equilibrium point and periodic solutions. The critical character of adaptive systems under rather usual working conditions is discussed. Special emphasis is put on the causes leading to intermittence. A geometric interpretation of the effects of some commonly used palliatives to this problem is given. The 'dead-zone' approach is studied in more detail. The predicted dynamics are compared with simulation results.

Espana, Martin D.↗

NASA NTRS2017

Filter Tuning Using the Chi-Squared Statistic

The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) performs orbit determination (OD) for the Aqua and Aura satellites. Both satellites are located in low Earth orbit (LEO), and are part of what is considered the A-Train satellite constellation. Both spacecraft are currently in the science phase of their respective missions. The FDF has recently been tasked with delivering definitive covariance for each satellite.The main source of orbit determination used for these missions is the Orbit Determination Toolkit developed by Analytical Graphics Inc. (AGI). This software uses an Extended Kalman Filter (EKF) to estimate the states of both spacecraft. The filter incorporates force modelling, ground station and space network measurements to determine spacecraft states. It also generates a covariance at each measurement. This covariance can be useful for evaluating the overall performance of the tracking data measurements and the filter itself. An accurate covariance is also useful for covariance propagation which is utilized in collision avoidance operations. It is also valuable when attempting to determine if the current orbital solution will meet mission requirements in the future.This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The Chi-square statistic is calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance.For the EKF to correctly calculate the covariance, error models associated with tracking data measurements must be accurately tuned. Over estimating or under estimating these error values can have detrimental effects on the overall filter performance. The filter incorporates ground station measurements, which can be tuned based on the accuracy of the individual ground stations. It also includes measurements from the NASA space network (SN), which can be affected by the assumed accuracy of the TDRS satellite state at the time of the measurement.The force modelling in the EKF is also an important factor that affects the propagation accuracy and covariance sizing. The dominant force in the LEO orbit regime is the drag force caused by atmospheric drag. Accurate accounting of the drag force is especially important for the accuracy of the propagated state. The implementation of a box and wing model to improve drag estimation accuracy, and its overall effect on the covariance state is explored.The process of tuning the EKF for Aqua and Aura support is described, including examination of the measurement errors of available observation types (Doppler and range), and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-square statistic, calculated based of the ODTK EKF solutions, are assessed versus accepted norms for the orbit regime.

Covariance Analysis↗

NASA NTRSDate not supplied

Coupling a Computational Fluid Dynamics Model to a Spacecraft Thermal System Model for the DraMS Instrument Thermal Analysis

The Dragonfly Mass Spectrometer (DraMS) is an instrument on the Dragonfly mission, which will spend 7 years in deep space cruise before landing and operating on the surface of Titan. Vacuum thermal analyses are required for deep space cruise, and convection analyses are required for the Titan surface operations. Model exchanges across multiple thermal teams are needed for all phases of the mission. For DraMS, Thermal Desktop® (TD) has been the main thermal analytical tool of choice due to its capability in modeling complex thermal systems with relatively low computational power and for its availability across thermal teams. However, TD does not have computational fluid dynamics (CFD) capability and struggles to accurately capture complex convective behavior. DraMS has fans operating in tandem and gas flow behaviors are not easily predicted due to its complex flow paths. CFD software, such as Fluent, can model and predict such complex flow behaviors, but CFD models are computationally expensive, and its workflow processes are not tailored towards simulating large and complex systems. Therefore, a coupled modeling approach was chosen for DraMS: A TD model was used for simulating all the conductive, radiative, and source terms, while a Fluent CFD model was added on, as needed, to the TD model to provide the convective boundary conditions using the System Coupling software. The coupling software allows the TD and Fluent models to communicate data and arrive at a co-solved and co-converged solution. Furthermore, Thermal Iso-value Exchange (TIE) method was developed to facilitate and improve the TD-Fluent data exchange process. This paper will discuss the analytical studies that were done to verify the accuracy and usability of the coupled approach and the challenges associated, which lead to the development of the TIE approach. DraMS thermal design and co-solved analysis results will also be discussed.

Heat transfer↗

NASA NTRS2015

Use of Generalized Fluid System Simulation Program (GFSSP) for Teaching and Performing Senior Design Projects at the Educational Institutions

This paper describes the experience of the authors in using the Generalized Fluid System Simulation Program (GFSSP) in teaching Design of Thermal Systems class at University of Alabama in Huntsville. GFSSP is a finite volume based thermo-fluid system network analysis code, developed at NASA/Marshall Space Flight Center, and is extensively used in NASA, Department of Defense, and aerospace industries for propulsion system design, analysis, and performance evaluation. The educational version of GFSSP is freely available to all US higher education institutions. The main purpose of the paper is to illustrate the utilization of this user-friendly code for the thermal systems design and fluid engineering courses and to encourage the instructors to utilize the code for the class assignments as well as senior design projects. The need for a generalized computer program for thermofluid analysis in a flow network has been felt for a long time in aerospace industries. Designers of thermofluid systems often need to know pressures, temperatures, flow rates, concentrations, and heat transfer rates at different parts of a flow circuit for steady state or transient conditions. Such applications occur in propulsion systems for tank pressurization, internal flow analysis of rocket engine turbopumps, chilldown of cryogenic tanks and transfer lines, and many other applications of gas-liquid systems involving fluid transients and conjugate heat and mass transfer. Computer resource requirements to perform time-dependent, three-dimensional Navier-Stokes computational fluid dynamic (CFD) analysis of such systems are prohibitive and therefore are not practical. Available commercial codes are generally suitable for steady state, single-phase incompressible flow. Because of the proprietary nature of such codes, it is not possible to extend their capability to satisfy the above-mentioned needs. Therefore, the Generalized Fluid System Simulation Program (GFSSP1) has been developed at NASA Marshall Space Flight Center (MSFC) as a general fluid flow system solver capable of handling phase changes, compressibility, mixture thermodynamics and transient operations. It also includes the capability to model external body forces such as gravity and centrifugal effects in a complex flow network. The objectives of GFSSP development are: a) to develop a robust and efficient numerical algorithm to solve a system of equations describing a flow network containing phase changes, mixing, and rotation; and b) to implement the algorithm in a structured, easy-to-use computer program. The analysis of thermofluid dynamics in a complex network requires resolution of the system into fluid nodes and branches, and solid nodes and conductors as shown in Figure 1. Figure 1 shows a schematic and GFSSP flow circuit of a counter-flow heat exchanger. Hot nitrogen gas is flowing through a pipe, colder nitrogen is flowing counter to the hot stream in the annulus pipe and heat transfer occurs through metal tubes. The problem considered is to calculate flowrates and temperature distributions in both streams. GFSSP has a unique data structure, as shown in Figure 2, that allows constructing all possible arrangements of a flow network with no limit on the number of elements. The elements of a flow network are boundary nodes where pressure and temperature are specified, internal nodes where pressure and temperature are calculated, and branches where flowrates are calculated. For conjugate heat transfer problems, there are three additional elements: solid node, ambient node, and conductor. The solid and fluid nodes are connected with solid-fluid conductors. GFSSP solves the conservation equations of mass and energy, and equation of state in internal nodes to calculate pressure, temperature and resident mass. The momentum conservation equation is solved in branches to calculate flowrate. It also solves for energy conservation equations to calculate temperatures of solid nodes. The equations are coupled and nonlinear; therefore, they are solved by an iterative numerical scheme. GFSSP employs a unique numerical scheme known as simultaneous adjustment with successive substitution (SASS), which is a combination of Newton-Raphson and successive substitution methods. The mass and momentum conservation equations and the equation of state are solved by the Newton-Raphson method while the conservation of energy and species are solved by the successive substitution method. GFSSP is linked with two thermodynamic property programs, GASP2 and WASP3 and GASPAK4, that provide thermodynamic and thermophysical properties of selected fluids. Both programs cover a range of pressure and temperature that allows fluid properties to be evaluated for liquid, liquid-vapor (saturation), and vapor region. GASP and WASP provide properties of 12 fluids. GASPAK includes a library of 36 fluids. GFSSP has three major parts. The first part is the graphical user interface (GUI), visual thermofluid analyzer of systems and components (VTASC). VTASC allows users to create a flow circuit by a 'point and click' paradigm. It creates the GFSSP input file after the completion of the model building process. GFSSP's GUI provides the users a platform to build and run their models. It also allows post-processing of results. The network flow circuit is first built using three basic elements: boundary node, internal node, and branch.

Majumdar, A. K.↗

NASA NTRSDate not supplied

Coupling a Computational Fluid Dynamics (CFD) Model to a Spacecraft Thermal System Model for the DraMS Instrument Thermal Analysis

The Dragonfly Mass Spectrometer (DraMS) is an instrument on the Dragonfly mission, which will spend 7 years in deep space cruise before landing and operating on the surface of Titan. Vacuum thermal analyses are required for deep space cruise, and convection analyses are required for the Titan surface operations. Model exchanges across multiple thermal teams are needed for all phases of the mission. For DraMS, Thermal Desktop (TD) has been the main thermal analytical tool of choice due to its capability in modeling complex thermal systems with relatively low computational power and for its availability across thermal teams. However, TD does not have computational fluid dynamics (CFD) capability and struggles to accurately capture complex convective behavior. DraMS has fans operating in tandem and gas flow behaviors are not easily predicted due to its complex flow paths. CFD software, such as Fluent, can model and predict such complex flow behaviors, but CFD models are computationally expensive, and its workflow processes are not tailored towards simulating large and complex systems. Therefore, a coupled modeling approach was chosen for DraMS: A TD model was used for simulating all the conductive, radiative, and source terms, while a Fluent CFD model was added on, as needed, to the TD model to provide the convective boundary conditions using the System Coupling software. The coupling software allows the TD and Fluent models to communicate data and arrive at a co-solved and co-converged solution. Furthermore, Thermal Iso-value Exchange (TIE) method was developed to facilitate and improve the TD-Fluent data exchange process. This paper will discuss the analytical studies that were done to verify the accuracy and usability of the coupled approach and the challenges associated, which lead to the development of the TIE approach. DraMS thermal design and co-solved analysis results will also be discussed.

heat transfer↗

NASA NTRS1972

New considerations for pogo prevention on space shuttle

Recommendations for improving the methodology of pogo suppression for the space shuttle include: Consideration of inter-pump location for accumulator or active device, inclusion of tank outflow effects in dynamic structural analysis, the use of simplified transfer functions in systems studies, three phase dynamic testing program for turbopump with development of dynamic flowmeters, and the use of a linearized mathematical model for engine physics studies.

Rubin, S.↗

NASA NTRS1981

The nonlinear wave equation for higher harmonics in free-electron lasers

The nonlinear wave equation and self-consistent pendulum equation are generalized to describe free-electron laser operation in higher harmonics; this can significantly extend their tunable range to shorter wavelengths. The dynamics of the laser field's amplitude and phase are explored for a wide range of parameters using families of normalized gain curves applicable to both the fundamental and harmonics. The electron phase-space displays the fundamental physics driving the wave, and this picture is used to distinguish between the effects of high gain and Coulomb forces.

Colson, W. B.↗

NASA NTRS1985

Dynamic Thermophysical Measurements in Space

The objective is to develop techniques for the dynamic measurement of selected thermophysical properties (e.g., heat of fusion, heat capacity, electrical resistivity) of solids and liquids at temperatures above 2000 K in a near zero-gravity environment. The first phase involves establishing the stability (geometrical) limits of specimens when rapidly heated to temperatures beyond their melting point. A test equipment package was designed and constructed for this purpose, consisting of removable specimen cartridge cells, a battery-bank power supply, a high-speed framing camera, a single-wavelength pyrometer, and electronic switching and control equipment. The operation of the equipment package was tested in the laboratory in preparation for near zero-gravity experiments to be performed during a KC-135 flight in September, 1984.

Cezairliyan, A.↗

NASA NTRS1987

Solar dynamic organic Rankine cycle heat rejection system simulation

The use of a rotary fluid management device (RFMD) and shear flow condenser for two-phase fluid management in microgravity organic Rankine cycle (ORC) applications is examined. A prototype of the proposed Space Station ORC heat rejection system was constructed to evaluate the performance of the inventory control method. The design and operation of the RFMD, shear flow condenser, and inventory control fluid accumulator are described. A schematic diagram of the ORC, RFMD, and condenser, and a functional diagram of the heat rejection system for the ORC are presented.

Havens, V. N.↗

NASA NTRS2000

Adaptive Management of Computing and Network Resources for Spacecraft Systems

It is likely that NASA's future spacecraft systems will consist of distributed processes which will handle dynamically varying workloads in response to perceived scientific events, the spacecraft environment, spacecraft anomalies and user commands. Since all situations and possible uses of sensors cannot be anticipated during pre-deployment phases, an approach for dynamically adapting the allocation of distributed computational and communication resources is needed. To address this, we are evolving the DeSiDeRaTa adaptive resource management approach to enable reconfigurable ground and space information systems. The DeSiDeRaTa approach embodies a set of middleware mechanisms for adapting resource allocations, and a framework for reasoning about the real-time performance of distributed application systems. The framework and middleware will be extended to accommodate (1) the dynamic aspects of intra-constellation network topologies, and (2) the complete real-time path from the instrument to the user. We are developing a ground-based testbed that will enable NASA to perform early evaluation of adaptive resource management techniques without the expense of first deploying them in space. The benefits of the proposed effort are numerous, including the ability to use sensors in new ways not anticipated at design time; the production of information technology that ties the sensor web together; the accommodation of greater numbers of missions with fewer resources; and the opportunity to leverage the DeSiDeRaTa project's expertise, infrastructure and models for adaptive resource management for distributed real-time systems.

Pfarr, Barbara↗

NASA NTRS2007

NASA Tech Briefs, June 2007

Topics covered include: High-Accuracy, High-Dynamic-Range Phase-Measurement System; Simple, Compact, Safe Impact Tester; Multi-Antenna Radar Systems for Doppler Rain Measurements; 600-GHz Electronically Tunable Vector Measurement System; Modular Architecture for the Measurement of Space Radiation; VLSI Design of a Turbo Decoder; Architecture of an Autonomous Radio Receiver; Improved On-Chip Measurement of Delay in an FPGA or ASIC; Resource Selection and Ranking; Accident/Mishap Investigation System; Simplified Identification of mRNA or DNA in Whole Cells; Printed Multi-Turn Loop Antennas for RF Biotelemetry; Making Ternary Quantum Dots From Single-Source Precursors; Improved Single-Source Precursors for Solar-Cell Absorbers; Spray CVD for Making Solar-Cell Absorber Layers; Glass/BNNT Composite for Sealing Solid Oxide Fuel Cells; A Method of Assembling Compact Coherent Fiber-Optic Bundles; Manufacturing Diamond Under Very High Pressure; Ring-Resonator/Sol-Gel Interferometric Immunosensor; Compact Fuel-Cell System Would Consume Neat Methanol; Algorithm Would Enable Robots to Solve Problems Creatively; Hypothetical Scenario Generator for Fault-Tolerant Diagnosis; Smart Data Node in the Sky; Pseudo-Waypoint Guidance for Proximity Spacecraft Maneuvers; Update on Controlling Herds of Cooperative Robots; and Simulation and Testing of Maneuvering of a Planetary Rover.

Source record↗

NASA NTRS2014

An Integrated Reliability and Physics-Based Risk Modeling Approach for Assessing Human Spaceflight Systems

This paper presents an integrated reliability and physics-based risk modeling approach for assessing human spaceflight systems. The approach is demonstrated using an example, end-to-end risk assessment of a generic-crewed space transportation system during a reference mission to the International Space Station. The behavior of the system is modeled using analysis techniques from multiple disciplines in order to properly capture the dynamic time- and state- dependent consequences of failures encountered in different mission phases. We discuss how to combine traditional reliability analyses with Monte Carlo simulation methods and physics-based engineering models to produce loss-of- mission and loss-of-crew risk estimates supporting risk-based decision-making and requirement verification. This approach facilitates risk-informed design by providing more realistic representation of system failures and interactions; identifying key risk-driving sensitivities, dependencies, and assumptions; and tracking multiple figures of merit within a single, responsive assessment framework that can readily incorporate evolving design information throughout system development.

Risk assessment↗

NASA NTRS2020

Test-Analysis Modal Correlation of Rocket Engine Structures in Liquid Hydrogen - Phase II

Many structures in a launch vehicle operate in liquid hydrogen, from the hydrogen fuel tanks through the ducts and valves and into the turbopumps. Calculating the structural dynamic response of these structures is critical for successful qualification, but accurate knowledge of the natural frequencies is based entirely on numerical or analytical predictions since testing in operating conditions is problematic. A comprehensive test/analysis program has therefore been performed at NASA/MSFC to enable accurate prediction of the modal characteristics of the Space Launch System’s (SLS) RS-25 Low Pressure Fuel Turbopump Inducer including the effects of fluid-added mass, mechanical property change at cryogenic temperatures, operation within tight tip clearances, acoustic/structure interaction, and hydroelasticity. The process also has to account for complicated cyclic symmetry mode shapes which can be easily mistuned in test, and geometric, boundary condition, and material modifications between the sub-scale inducer used as a test article and the actual flight component. The first phase of the program, documented previously, focused on testing of a cantilever beam in a number of fluids and temperatures to isolate the effects of fluid-added mass and temperature, while the second phase reported here documents the additional issues associated with the more realistic inducer test article. Preliminary structural dynamic analysis of the flight hardware including variability for the above parameters indicated potential severe resonances, requiring implementation of undesired programmatic constraints, so the improved predictive capability may allow removal of these constraints.

Brown, Andrew M.↗

NASA NTRS1992

Adaptive low-bandwidth tracking of Galileo and Pioneer 10 carriers

In the Deep Space Network, tracking of residual carrier phase typically occurs with a fixed-bandwidth phase-locked loop using a bandwidth sufficiently wide to prevent loss of lock under worst-case conditions of signal dynamics, received signal phase noise, and receiver phase noise. Much of the time, however, such a high bandwidth is not required and may inflict unnecessarily heavy penalties on loop signal-to-noise ratios. This article describes a technique for improving tracking performance by permitting initial tracking at narrow bandwidths and gradually widening the loop as needed. The cost is a requirement for signal buffering, which is relatively inexpensive for low data rate applications. Results based on off-line processing of recorded carrier data from Galileo and Pioneer 10 are presented, and show potential 10-16 dB gains in loop SNR over worst-case fixed-bandwidth tracking.

Watola, D. A.↗

NASA NTRS2007

Cryogenic Pressure Control Modeling for Ellipsoidal Space Tanks

A computational fluid dynamics (CFD) model is developed to simulate pressure control of an ellipsoidal-shaped liquid hydrogen tank under external heating in normal gravity. Pressure control is provided by an axial jet thermodynamic vent system (TVS) centered within the vessel that injects cooler liquid into the tank, mixing the contents and reducing tank pressure. The two-phase cryogenic tank model considers liquid hydrogen in its own vapor with liquid density varying with temperature only and a fully compressible ullage. The axisymmetric model is developed using a custom version of the commercially available FLOW-31) software. Quantitative model validation is ,provided by engineering checkout tests performed at Marshall Space Flight Center in 1999 in support of the Solar Thermal Upper Stage_ Technology Demonstrator (STUSTD) program. The engineering checkout tests provide cryogenic tank self-pressurization test data at various heat leaks and tank fill levels. The predicted self-pressurization rates, ullage and liquid temperatures at discrete locations within the STUSTD tank are in good agreement with test data. The work presented here advances current CFD modeling capabilities for cryogenic pressure control and helps develop a low cost CFD-based design process for space hardware.

Lopez, Alfredo↗

NASA NTRS2009

Probabilistic Risk Assessment for Decision Making During Spacecraft Operations

Decisions made during the operational phase of a space mission often have significant and immediate consequences. Without the explicit consideration of the risks involved and their representation in a solid model, it is very likely that these risks are not considered systematically in trade studies. Wrong decisions during the operational phase of a space mission can lead to immediate system failure whereas correct decisions can help recover the system even from faulty conditions. A problem of special interest is the determination of the system fault protection strategies upon the occurrence of faults within the system. Decisions regarding the fault protection strategy also heavily rely on a correct understanding of the state of the system and an integrated risk model that represents the various possible scenarios and their respective likelihoods. Probabilistic Risk Assessment (PRA) modeling is applicable to the full lifecycle of a space mission project, from concept development to preliminary design, detailed design, development and operations. The benefits and utilities of the model, however, depend on the phase of the mission for which it is used. This is because of the difference in the key strategic decisions that support each mission phase. The focus of this paper is on describing the particular methods used for PRA modeling during the operational phase of a spacecraft by gleaning insight from recently conducted case studies on two operational Mars orbiters. During operations, the key decisions relate to the commands sent to the spacecraft for any kind of diagnostics, anomaly resolution, trajectory changes, or planning. Often, faults and failures occur in the parts of the spacecraft but are contained or mitigated before they can cause serious damage. The failure behavior of the system during operations provides valuable data for updating and adjusting the related PRA models that are built primarily based on historical failure data. The PRA models, in turn, provide insight into the effect of various faults or failures on the risk and failure drivers of the system and the likelihood of possible end case scenarios, thereby facilitating the decision making process during operations. This paper describes the process of adjusting PRA models based on observed spacecraft data, on one hand, and utilizing the models for insight into the future system behavior on the other hand. While PRA models are typically used as a decision aid during the design phase of a space mission, we advocate adjusting them based on the observed behavior of the spacecraft and utilizing them for decision support during the operations phase.

dynamic fault trees↗

NASA NTRSDate not supplied

Two-Phase Flow in Filters and Orifices: In preparation for Measurements on ISS Packed Bed Reactor Experiment-Water Recovery Series (PBRE-WRS)

Understanding the hydrodynamics of adiabatic two-phase flows in packed bed reactors offers numerous benefits. It enables the optimization of chemical reactions rates and products, crucial for pharmaceuticals and energy production industries. Additionally, this understanding aids in designing more efficient and compact reactors, reducing space and resource requirements. Insights gained from studying such flows in microgravity contribute to advancements of space technologies and the enhancement of our capabilities for undertaking future long duration safe, and sustainable space exploration missions. The Packed Bed Reactor Experiment-Water Recovery Series (PBRE-WRS) is a flight experiment planned for operation on the Microgravity Science Glove box (MSG) facility of the International Space Station (ISS). The objective of the experiment is to validate hydrodynamic models at a range of gas and liquid flow rates. The microgravity environment allows for measurement and observation of aspects of fluid dynamics that are unique when compared to observations made in full or partial gravity environments. The experiment consists of testing two-phase flow hydrodynamics in three different filters, four (4) orifices and one check valve test articles. The experiment utilizes the hardware of the previously flown PBRE and PBRE-2 with packed beds of different packings materials and sizes. The fluid system of the PBRE-WRS consists of a nitrogen gas delivery and water delivery subsystems. The gas delivery subsystem can accommodate two ranges of gas flow rates, just as for the water delivery system. The nitrogen gas loop is open whereas the water loop is closed. Gas is separated from the water using a gas-liquid phase separator which is located in the water delivery module. Preliminary results from ground testing show the pressure drop increasing at different rates with the liquid and gas flow rates in the Brine filter. In this work, a detailed system description is presented along with a summary of results from ground performance testing of different test sections in an end-to-end preflight testing campaign.

Packed Bed Reactor Experiment↗

NASA NTRS1992

Periodic and chaotic spatiotemporal states in a phase-conjugate resonator using a photorefractive BaTiO3 phase-conjugate mirror

The dynamics of an externally pumped phase-conjugate resonator that uses four-wave mixing in BaTi03 is investigated experimentally. The emergence of spatiotemporal instabilities as the degree of transverse confinement is varied by changing the Fresnel number is described in detail. Local intensity time series show that relaxing the transverse confinement leads the system from a stationary state to periodic, then to quasi-periodic, motions and finally to chaotic behavior. In some regions of parameter space two frequencies are identified in the power spectra of the time series, indicating a route to chaos following the Ruelle-Takens-Newhouse scheme. Wave-front topological defects are identified by interferometry. As the system's confinement is varied, the phase-defect density and the spatial correlation index are found to follow similar trends, indicating that the observed spatiotemporal dynamics may indeed be an example of defect-mediated turbulence.

Liu, Siuying R.↗