Search NASA⌕ Search

SEARCH · Search NASA

Results for “FLUID AMPLIFIER”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

NASA Tech Briefs, November 2012

The topics include: Visual System for Browsing, Analysis, and Retrieval of Data (ViSBARD); Time-Domain Terahertz Computed Axial Tomography NDE System; Adaptive Sampling of Time Series During Remote Exploration; A Tracking Sun Photometer Without Moving Parts; Surface Temperature Data Analysis; Modular, Autonomous Command and Data Handling Software with Built-In Simulation and Test; In-Situ Wire Damage Detection System; Amplifier Module for 260-GHz Band Using Quartz Waveguide Transitions; Wideband Agile Digital Microwave Radiometer; Buckyball Nucleation of HiPco Tubes; FACT, Mega-ROSA, SOLAROSA; An Integrated, Layered-Spinel Composite Cathode for Energy Storage Applications; Engineered Multifunctional Surfaces for Fluid Handling; Polyolefin-Based Aerogels; Adjusting Permittivity by Blending Varying Ratios of SWNTs; Gravity-Assist Mechanical Simulator for Outreach; Concept for Hydrogen-Impregnated Nanofiber/Photovoltaic Cargo Stowage System; DROP: Durable Reconnaissance and Observation Platform; Developing Physiologic Models for Emergency Medical Procedures Under Microgravity; Spectroscopic Chemical Analysis Methods and Apparatus; Low Average Sidelobe Slot Array Antennas for Radiometer Applications; Motion-Corrected 3D Sonic Anemometer for Tethersondes and Other Moving Platforms; Water Treatment Systems for Long Spaceflights; Microchip Non-Aqueous Capillary Electrophoresis (MicronNACE) Method to Analyze Long-Chain Primary Amines; Low-Cost Phased Array Antenna for Sounding Rockets, Missiles, and Expendable Launch Vehicles; Mars Science Laboratory Engineering Cameras; Seismic Imager Space Telescope; Estimating Sea Surface Salinity and Wind Using Combined Passive and Active L-Band Microwave Observations; A Posteriori Study of a DNS Database Describing Super critical Binary-Species Mixing; Scalable SCPPM Decoder; QuakeSim 2.0; HURON (HUman and Robotic Optimization Network) Multi-Agent Temporal Activity Planner/Scheduler; MPST Software: MoonKommand

Source record↗
NASA NTRS2003

Autotrophic Ecosystems on the Early Earth

Ophiolite sequences, sections of lower oceanic crust and upper mantle that have been thrust onto continental craton, are located in northern and central California and provide easily accessible areas that serve as good analogs for similar, more extensive areas of the early Earth. We have begun investigating and characterizing these sites in order to understand better the processes that may be responsible for the water chemistry, mineralogy and biology of similar environments on the early Earth. The geophysical and geochemical processes in these terranes provide niches for unique communities of extremeophiles and likely provide a good analog to the location that first gave rise to life on Earth. The ophiolites found in northern and central California include the Trinity, Josephine, Coast Range and Point Sal, all of which are approximately 160 million years old. Fluids from serpentinizing springs are generally alkaline with high pH and H2 contents, indicating that the mafic rock compositions control the fluid composition through water-rock reactions during relatively low-grade hydrothermal processes. There are significant amounts of primary mineralogy remaining in the rocks, meaning that substantial alteration processes are still occurring in these terranes. The general reaction for serpentinization of olivine is given by one of the authors. olivine + H2O = serpentine + brucite + magnetite + H2. We have analyzed the mineralogical composition of several rock samples collected from the Coast Range Ophiolite near Clear Lake, CA by electron microprobe. The remnant primary mineralogy is fairly urnform in composition, with an olivine composition of Fo(sub 90), and with pyroxene compositions of En(sub 90) for orthopyroxene and En(sub 49)Wo(sub 48)Fs(sub 03) for the clinopyroxene. Other primary phases observed include chromites and other spinels. Examination of petrographic thin sections reveals that serpentinization reactions have occurred in these locations. The serpentine resulting from aqueous alteration of olivine resides in veins that are see to cross cut the primary mineral grains. There are several generations of alteration products, comprised mostly of serpentines that are magnesium rich, with magnetite, brucite and carbonates observed as accessory minerals. The formation of carbonates can be taken to indicate the presence of CO2 in the altering fluids. We collected samples from a spring in the Coast Range Ophiolite in order to determine whether the geochemical environment serves as a habitat for chemotrophic microorganisms. DNA was extracted from the sediment samples and the 16s rRNA gene was PCR amplified using universal Archaeal primers. Denaturing gradient gel electrophoresis (DGGE) was used to determine the community of Archaea thriving in these samples. Our results indicate that there were 8 different genera of Archaea from a single sample. A sequence was obtained from one of these eight. The sequence is of an organism similar to Halorubrum tibetense, and alkalophilic Archaeon. This result suggests that these environments are likely hosts for communities of organisms that are adapted for the unique chemistry provided by the alkaline spring.

Schulte, M.↗
NASA NTRS1992

Connector Mechanism Has Smaller Stroke

System for connecting electrical and/or fluid lines includes mechanism reducing length of stroke necessary to make or break connections. Feature enables connection and disconnection in confined space, and compensates for misalignment between connectors. Connector in active member moves upward at twice the speed of downward stroke of passive member. Stroke amplified within connector system. Applications include connections between modular electronic units, coupled vehicles, and hydraulic systems.

Milam, M. Bruce↗
NASA NTRS1993

Control of jet noise

This reports describes experiments conducted at the High-Speed Jet Facility at the University of Southern California on supersonic jets. The goal of the study was to develop methods for controlling the noise emitted from supersonic jets by passive and/or active means. Work by Seiner et al (1991) indicates that eddy Mach wave radiation is the dominant noise source in a heated high speed jet. Eddy Mach radiation is caused by turbulent eddies traveling at supersonic speed in the shear layer of the jet. The convection velocity of the eddies decays with increasing distance from the nozzle exit due to the mixing of the jet stream with the ambient fluid. Once the convection speed reaches subsonic velocities, eddy Mach wave radiation ceases. To control noise, a rapid decay of the convection velocity is desired. This may be accomplished by enhanced mixing in the jet. In this study, small aspect ratio rectangular jet nozzles were tested. A flapping mode was noticed in the jets. By amplifying screech components of the jets and destabilizing the jet columns with a collar device, the flapping mode was excited. The result was a rapid decay of the jet velocity. A reduction in eddy Mach radiation in rectangular supersonic jets may be achieved with this device.

Schreck, Stefan↗
NASA NTRS1972

Study of fluid mechanical helium argon ion laser

An approach to an argon ion laser based on gasdynamic techniques is presented. Improvement in efficiency and power output are achieved by eliminating high heat rejection problems and plasma confinement of the seal-off conventional lasers. The process of producing population inversion between the same energy levels, as in the conventional argon ion laser, has been divided into two phases by separating each other from the processes of ionization and subsequent excitation. Line drawings and graphs are included to amplify the theoretical presentation.

Source record↗
NASA NTRS2010

A Framework for Integrated Component and System Analyses of Instabilities

Instabilities associated with fluid handling and operation in liquid rocket propulsion systems and test facilities usually manifest themselves as structural vibrations or some form of structural damage. While the source of the instability is directly related to the performance of a component such as a turbopump, valve or a flow control element, the associated pressure fluctuations as they propagate through the system have the potential to amplify and resonate with natural modes of the structural elements and components of the system. In this paper, the authors have developed an innovative multi-level approach that involves analysis at the component and systems level. The primary source of the unsteadiness is modeled with a high-fidelity hybrid RANS/LES based CFD methodology that has been previously used to study instabilities in feed systems. This high fidelity approach is used to quantify the instability and understand the physics associated with the instability. System response to the driving instability is determined through a transfer matrix approach wherein the incoming and outgoing pressure and velocity fluctuations are related through a transfer (or transmission) matrix. The coefficients of the transfer matrix for each component (i.e. valve, pipe, orifice etc.) are individually derived from the flow physics associated with the component. A demonstration case representing a test loop/test facility comprised of a network of elements is constructed with the transfer matrix approach and the amplification of modes analyzed as the instability propagates through the test loop.

Ahuja, Vineet↗
NASA NTRS2003

Use of an Ultrasonic/Sonic Driller/Corer to Obtain Sample Powder for CHEMIN, a Combined XRD/XRF Instrument

A miniature CHEMIN XRD/XRF (X-Ray Diffraction/X-Ray Fluourescence) instrument is currently being developed for definitive mineralogic analysis of soils and rocks on Mars. One of the technical issues that must be addressed in order to enable XRD analysis on an extraterrestrial body is how best to obtain a representative sample powder for analysis. For XRD powder diffraction analyses, it is beneficial to have a fine-grained sample to reduce preferred orientation effects and to provide a statistically significant number of crystallites to the X-ray beam. Although a 2-dimensional detector as used in the CHEMIN instrument will produce good results with poorly prepared powders, the quality of the data will improve if the sample is fine-grained and randomly oriented. An Ultrasonic/Sonic Driller/Corer (USDC) currently being developed at JPL is an effective mechanism of sampling rock to produce cores and powdered cuttings. It requires low axial load (< 5N) and thus offers significant advantages for operation from lightweight platforms and in low gravity environments. The USDC is lightweight (<0.5kg), and can be driven at low power (<5W) using duty cycling. It consists of an actuator with a piezoelectric stack, ultrasonic horn, free-mass, and drill bit. The stack is driven with a 20 kHz AC voltage at resonance. The strain generated by the piezoelectric is amplified by the horn by a factor of up to 10 times the displacement amplitude. The tip impacts the free-mass and drives it into the drill bit in a hammering action. The free-mass rebounds to interact with the horn tip leading to a cyclic rebound at frequencies in the range of 60-1000 Hz. It does not require lubricants, drilling fluid or bit sharpening and it has the potential to operate at high and low temperatures using a suitable choice of piezoelectric material. To assess whether the powder from an ultrasonic drill would be adequate for analyses by an XRD/XRF spectrometer such as CHEMIN, powders obtained from the JPL ultrasonic drill were analyzed and the results were compared to carefully prepared powders obtained using a laboratory bench scale Retsch mill.

Chipera, S. J.↗
NASA NTRS2000

Study of High Lift Configurations

This project focus on the implementation of the Warren-Hassan transition / turbulence model (Journal of Aircraft, Vol. 35, No. 5) into the NASA code CFL3D and its testing for multi-element airfoils in landing configuration at different angles of attack. The Warren-Hassan transition model solves an evolution equation for a kinetic energy characteristic of non-turbulent fluctuations. This is combined with an empirical estimate of the frequency of the most amplified first-mode disturbance to yield an expression for an eddy viscosity characteristic of non-turbulent fluctuations. This is combined with the k - zeta model for fully turbulent flow to yield a unified approach capable of predicting both transition onset and extent. Blending of the non-turbulent and turbulent components of the model is accomplished by an intermittency function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4).

Edward, Jack R.↗
NASA NTRS1988

The delineation and interpretation of the earth's gravity field

A series of fluid dynamical experiments in variable viscosity fluid have been made and are in progress to study: (1) the onset of small scale convection relative to lithosphere growth rate; (2) the influence of paired fracture zones in modulating the horizontal scale of small scale convection; (3) the influence of the mantle vertical viscosity structure on determing the mode of small scale convection; and (4) the 3-D and temporal evolution of flows beneath a high viscosity lid. These experiments extend and amplify the present experimental work that has produced small scale convection beneath a downward-moving solidification front. Rapid growth of a high viscosity lid stifles the early onset of convection such that convection only begins once the lithosphere is older than a certain minimum age. The interplay of this convection with both the structure of the lithosphere and mantle provide a fertile field of investigation into the origin of geoid, gravity, and topographic anomalies in the central Pacific. These highly correlated fields of intermediate wavelength (approximately 200 to 2000 km), but not the larger wavelengths. It is the ultimate, dynamic origin of this class of anomalies that is sought in this investigation.

Marsh, Bruce D.↗
NASA NTRS2014

The Link Between Shocks, Turbulence, and Magnetic Reconnection in Collisionless Plasmas

Global hybrid (electron fluid, kinetic ions) and fully kinetic simulations of the magnetosphere have been used to show surprising interconnection between shocks, turbulence and magnetic reconnection. In particular collisionless shocks with their reflected ions that can get upstream before retransmission can generate previously unforeseen phenomena in the post shocked flows: (i) formation of reconnecting current sheets and magnetic islands with sizes up to tens of ion inertial length. (ii) Generation of large scale low frequency electromagnetic waves that are compressed and amplified as they cross the shock. These 'wavefronts' maintain their integrity for tens of ion cyclotron times but eventually disrupt and dissipate their energy. (iii) Rippling of the shock front, which can in turn lead to formation of fast collimated jets extending to hundreds of ion inertial lengths downstream of the shock. The jets, which have high dynamical pressure, 'stir' the downstream region, creating large scale disturbances such as vortices, sunward flows, and can trigger flux ropes along the magnetopause. This phenomenology closes the loop between shocks, turbulence and magnetic reconnection in ways previously unrealized. These interconnections appear generic for the collisionless plasmas typical of space, and are expected even at planar shocks, although they will also occur at curved shocks as occur at planets or around ejecta.

MAGNETOSPHERE↗
NASA NTRS2006

Nonenzymatic catalytic signal amplification for nucleic acid hybridization assays

Devices, methods, and kits for amplifying the signal from hybridization reactions between nucleic acid probes and their cognate targets are presented. The devices provide partially-duplexed, immobilized probe complexes, spatially separate from and separately addressable from immobilized docking strands. Cognate target acts catalytically to transfer probe from the site of probe complex immobilization to the site of immobilized docking strand, generating a detectable signal. The methods and kits of the present invention may be used to identify the presence of cognate target in a fluid sample.

Fan, Wenhong↗
NASA NTRS2013

FRET-Aptamer Assays for Bone Marker Assessment, C-Telopeptide, Creatinine, and Vitamin D

Astronauts lose 1.0 to 1.5% of their bone mass per month on long-duration spaceflights. NASA wishes to monitor the bone loss onboard spacecraft to develop nutritional and exercise countermeasures, and make adjustments during long space missions. On Earth, the same technology could be used to monitor osteoporosis and its therapy. Aptamers bind to targets against which they are developed, much like antibodies. However, aptamers do not require animal hosts or cell culture and are therefore easier, faster, and less expensive to produce. In addition, aptamers sometimes exhibit greater affinity and specificity vs. comparable antibodies. In this work, fluorescent dyes and quenchers were added to the aptamers to enable pushbutton, one-step, bind-and-detect fluorescence resonance energy transfer (FRET) assays or tests that can be freeze-dried, rehydrated with body fluids, and used to quantitate bone loss of vitamin D levels with a handheld fluorometer in the spacecraft environment. This work generated specific, rapid, one-step FRET assays for the bone loss marker C-telopeptide (CTx) when extracted from urine, creatinine from urine, and vitamin D congeners in diluted serum. The assays were quantified in nanograms/mL using a handheld fluorometer connected to a laptop computer to convert the raw fluorescence values into concentrations of each analyte according to linear standard curves. DNA aptamers were selected and amplified for several rounds against a 26- amino acid form of CTx, creatinine, and vitamin D. The commonalities between loop structures were studied, and several common loop structures were converted into aptamer beacons with a fluorophore and quencher on each end. In theory, when the aptamer beacon binds its cognate target (CTx bone peptide, creatinine, or vitamin D), it is forced open and no longer quenched, so it gives off fluorescent light (when excited) in proportion to the amount of target present in a sample. This proportional increase in fluorescence is called a "lights on" FRET response. The vitamin D aptamer beacon gives a "lights off" or inversely proportional fluorescence response to the amount of vitamin D present in diluted serum. These FRET-aptamer assays are rapid (<30 minutes), sensitive (low ng/mL detection limits), and quite easy to carry out (add sample, mix, and detect in the handheld reader). Benefits include the speed of the assays as well as the small amount of space taken up by the handheld reader and cuvette assays. The aptamer DNA sequences represent novel additional features of the existing (patent-pending) FRET-aptamer assay platform.

Bruno, John G.↗
NASA NTRS2006

Neuro-Prosthetic Implants With Adjustable Electrode Arrays

Brushlike arrays of electrodes packaged with application-specific integrated circuits (ASICs) are undergoing development for use as electronic implants especially as neuro-prosthetic devices that might be implanted in brains to detect weak electrical signals generated by neurons. These implants partly resemble the ones reported in Integrated Electrode Arrays for Neuro-Prosthetic Implants (NPO-21198), NASA Tech Briefs, Vol. 27, No. 2 (February 2003), page 48. The basic idea underlying both the present and previously reported implants is that the electrodes would pick up signals from neurons and the ASICs would amplify and otherwise preprocess the signals for monitoring by external equipment. The figure presents a simplified and partly schematic view of an implant according to the present concept. Whereas the electrodes in an implant according to the previously reported concept would be microscopic wires, the electrodes according to the present concept are in the form of microscopic needles. An even more important difference would be that, unlike the previously reported concept, the present concept calls for the inclusion of microelectromechanical actuators for adjusting the depth of penetration of the electrodes into brain tissue. The prototype implant now under construction includes an array of 100 electrodes and corresponding array of electrode contact pads formed on opposite faces of a plate fabricated by techniques that are established in the art of microelectromechanical systems (MEMS). A mixed-signal ASIC under construction at the time of reporting the information for this article will include 100 analog amplifier channels (one amplifier per electrode). On one face of the mixed-signal ASIC there will be a solder-bump/micro-pad array that will have the same pitch as that of the electrode array, and that will be used to make the electrical and mechanical connections between the electrode array and the ASIC. Once the electrode array and the ASIC are soldered together, the remaining empty space between them will be filled with a biocompatible epoxy, the remaining exposed portions of the ASIC will be covered with micromachined plates for protection against corrosive bodily fluids, and then the ASIC and its covering micromachined plates will be coated with parylene

Whitacre, Jay↗
NASA NTRS2000

Unsteady Phenomena During Operation of the SSME Fuel Flowmeter

This report describes a part of the analysis carried in support of the SSME (Space Shuttle Main Engine) Fuel Flowmeter redesign, addressing an intensely researched phenomenon known as "shifting" of the flowmeter constant value. It consists of a sudden change in the flowmeter indication, which occurs simultaneously with the onset of an oscillatory variation of the rotor speed. The change in the flowmeter indications does not correspond to a real change in the volumetric flow through the device. Several causes have been investigated in detail, in the past, without conclusive evidence towards a cause of this phenomenon. The present analysis addresses the flow physics through the flowmeter by assembling results from 3-D CFD (computational fluid dynamics) calculations, airfoil C(sub D)/C(sub L) performance curves and mass moment of inertia characteristics of the rotor into a synergistic calculation which simulates the unsteady regime of the flowmeter operation. The results show that the 4-bladed rotor interacts with the periodic flow pattern created behind the flow straightener upstream in a manner that generates a steady, periodic fluctuation in the rotor's speed. The amplitude of this fluctuation is significantly smaller than the 0.5% of mean speed threshold which constitutes a flight operational limit. When manufacturing errors occur, however, the fluctuations are amplified and can generate a significant apparent change in the flowmeter indication. Two types of possible fabrication errors-which can occur even for parts fabricated within the accepted tolerances for the blade airfoil-are presented, together with their effect on the flowmeter operation.

Marcu, Bogdan↗
NASA NTRS2004

Collaborative Aerospace Research and Fellowship Program at NASA Glenn Research Center

During the summer of 2004, a 10-week activity for university faculty entitled the NASA-OAI Collaborative Aerospace Research and Fellowship Program (CFP) was conducted at the NASA Glenn Research Center in collaboration with the Ohio Aerospace Institute (OAI). This is a companion program to the highly successful NASA Faculty Fellowship Program and its predecessor, the NASA-ASEE Summer Faculty Fellowship Program that operated for 38 years at Glenn. The objectives of CFP parallel those of its companion, viz., (1) to further the professional knowledge of qualified engineering and science faculty,(2) to stimulate an exchange of ideas between teaching participants and employees of NASA, (3) to enrich and refresh the research and teaching activities of participants institutions, and (4) to contribute to the research objectives of Glenn. However, CFP, unlike the NASA program, permits faculty to be in residence for more than two summers and does not limit participation to United States citizens. Selected fellows spend 10 weeks at Glenn working on research problems in collaboration with NASA colleagues and participating in related activities of the NASA-ASEE program. This year's program began officially on June 1, 2004 and continued through August 7, 2004. Several fellows had program dates that differed from the official dates because university schedules vary and because some of the summer research projects warranted a time extension beyond the 10 weeks for satisfactory completion of the work. The stipend paid to the fellows was $1200 per week and a relocation allowance of $1000 was paid to those living outside a 50-mile radius of the Center. In post-program surveys from this and previous years, the faculty cited numerous instances where participation in the program has led to new courses, new research projects, new laboratory experiments, and grants from NASA to continue the work initiated during the summer. Many of the fellows mentioned amplifying material, both in undergraduate and graduate courses, on the basis of the summer s experience at Glenn. A number of 2004 fellows indicated that proposals to NASA will grow out of their summer research projects. In addition, some journal articles and NASA publications will result from this past summer s activities. Fellows from past summers continue to send reprints of articles that resulted from work initiated at Glenn. This report is intended primarily to summarize the research activities comprising the 2004 CFP Program at Glenn. Particular research studies include: 1) Development of an Imaging-Based, Computational Fluid Dynamics Tool to Assess Fluid Mechanics in Experimental Models that Simulate Blood Vessels; 2) Analysis of Nanomaterials Produced from Precursors; and 3) LEO Propagation Analysis Tool.

Heyward, Ann O.↗
NASA NTRS1985

Nonlinear shock acceleration. III - Finite wave velocity, wave pressure, and entropy generation via wave damping

The nonlinear theory of shock acceleration developed in earlier papers, which treated the waves as being completely frozen into the fluid, is generalized to include wave dynamics. In the limit where damping keeps the wave amplitude small, it is found that a finite phase velocity (V sub ph) of the scattering waves through the background fluid, tempers the acceleration generated by high Mach number shocks. Asymptotic spectra proportional to 1/E sq are possible only when the ratio of wave velocity to shock velocity is less than 0.13. For a given asymptotic spectrum, the efficiency of relativistic particle production is found to be practically independent of the value of V sub ph, so that earlier results concerning its value remain valid for finite V sub ph. In the limit where there is no wave damping, it is shown that for modest Alfven Mach numbers, approximately greater than 4 and less than 6, the magnetic field is amplified by the energetic particles to the point of being in rough equipartition with them, as models of synchrotron emission frequently take the field to be. In this case, the disordering and amplification of field energy may play a major role in the shock transition.

Eichler, D.↗
NASA NTRS1994

Static and dynamic force/moment measurements in the Eidetics water tunnel

Water tunnels have been utilized in one form or another to explore fluid mechanics and aerodynamics phenomena since the days of Leonardo da Vinci. Water tunnel testing is attractive because of the relatively low cost and quick turn-around time to perform flow visualization experiments and evaluate the results. The principal limitation of a water tunnel is that the low flow speed, which provides for detailed visualization, also results in very small hydrodynamic (aerodynamic) forces on the model, which, in the past, have proven to be difficult to measure accurately. However, the advent of semi-conductor strain gage technology and devices associated with data acquisition such as low-noise amplifiers, electronic filters, and digital recording have made accurate measurements of very low strain levels feasible. The principal objective of this research effort was to develop a multi-component strain gage balance to measure forces and moments on models tested in flow visualization water tunnels. A balance was designed that allows measuring normal and side forces, and pitching, yawing and rolling moments (no axial force). The balance mounts internally in the model and is used in a manner typical of wind tunnel balances. The key differences between a water tunnel balance and a wind tunnel balance are the requirement for very high sensitivity since the loads are very low (typical normal force is 0.2 lbs), the need for water proofing the gage elements, and the small size required to fit into typical water tunnel models.

Carlos J Suarez↗
NASA NTRS1992

A new direction in hydrodynamic stability: Beyond eigenvalues

Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and looking for unstable eigenvalues of the linearized problem, but the results agree poorly in many cases with experiments. Nevertheless, it has become clear in recent years that linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis can be obtained by considering the 'pseudospectra' of the linearized problem, which reveals that small perturbations to the smooth flow in the form of streamwise vortices may be amplified by factors on the order of 10(exp 5) by a linear mechanism, even though all the eigenmodes are stable. The same principles apply also to other problems in the mathematical sciences that involve non-orthogonal eigenfunctions.

Trefethen, Lloyd N.↗