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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.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows

We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the wave propagation is represented graphically in terms of a flow map based on the liquid and gas flow rates and the prediction carries over to the nonlinear regime with only a small deviation.

42 ENGINEERING↗
DOE OSTI2016

Quantum and classical contributions to linear magnetoresistance in topological insulator thin films

Three dimensional topological insulators possess backscattering immune relativistic Dirac fermions on their surface due to nontrivial topology of the bulk band structure. Both metallic and bulk insulating topological insulators exhibit weak-antilocalization in the low magnetic field and linear like magnetoresistance in higher fields. We explore the linear magnetoresistance in bulk insulating topological insulator Bi{sub 2-x}Sb{sub x}Te{sub 3-y}Se{sub y} thin films grown by pulsed laser deposition technique. Thin films of Bi{sub 2-x}Sb{sub x}Te{sub 3-y}Se{sub y} were found to be insulating in nature, which conclusively establishes the origin of linear magnetoresistance from surface Dirac states. The films were thoroughly characterized for their crystallinity and composition and then subjected to transport measurements. We present a careful analysis taking into considerations all the existing models of linear magnetoresistance. We comprehend that the competition between classical and quantum contributions to magnetoresistance results in linear magnetoresistance in high fields. We observe that the cross-over field decreases with increasing temperature and the physical argument for this behavior is explained.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Augmenting subspace optimization methods with linear bandits

In this work, we consider the framework of methods for unconstrained minimization that are, in each iteration, restricted to a model that is only a valid approximation to the objective function on some affine subspace containing an incumbent point. These methods are of practical interest in computational settings where derivative information is either expensive or impossible to obtain. Recent attention has been paid in the literature to employing randomized matrix sketching for generating the affine subspaces within this framework. We consider a relatively straightforward, deterministic augmentation of such a generic subspace optimization method. In particular, we consider a sequential optimization framework where actions consist of one-dimensional linear subspaces and rewards consist of (approximations to) the magnitudes of directional derivatives computed in the direction of the action subspace. Reward maximization in this context is consistent with maximizing lower bounds on descent guaranteed by first-order Taylor models. This sequential optimization problem can be analysed through the lens of dynamic regret. We modify an existing linear upper confidence bound (UCB) bandit method and prove sublinear dynamic regret in the subspace optimization setting. We demonstrate the efficacy of employing this linear UCB method in a setting where forward-mode algorithmic differentiation can provide directional derivatives in arbitrary directions and in a derivative-free setting. For the derivative-free setting, we propose SS-POUNDers, an extension of the derivative-free optimization method POUNDers that employs the linear UCB mechanism to identify promising subspaces. Our numerical experiments suggest a preference, in either computational setting, for employing a linear UCB mechanism within a subspace optimization method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Non-linear power spectra in the synchronous gauge

We study the non-linear corrections to the matter and velocity power spectra in the synchronous gauge (SG). For the leading correction to the non-linear power spectra, we consider the perturbations up to third order in a zero-pressure fluid in a flat cosmological background. Although the equations in the SG happen to coincide with those in the comoving gauge (CG) to linear order, they differ from second order. In particular, the second order hydrodynamic equations in the SG are apparently in the Lagrangian form, whereas those in the CG are in the Eulerian form. The non-linear power spectra naively presented in the original SG show rather pathological behavior quite different from the result of the Newtonian theory even on sub-horizon scales. We show that the pathology in the nonlinear power spectra is due to the absence of the convective terms in, thus the Lagrangian nature of, the SG. We show that there are many different ways of introducing the corrective convective terms in the SG equations. However, the convective terms (Eulerian modification) can be introduced only through gauge transformations to other gauges which should be the same as the CG to the second order. In our previous works we have shown that the density and velocity perturbation equations in the CG exactly coincide with the Newtonian equations to the second order, and the pure general relativistic correction terms starting to appear from the third order are substantially suppressed compared with the relativistic/Newtonian terms in the power spectra. As a result, we conclude that the SG per se is an inappropriate coordinate choice in handling the non-linear matter and velocity power spectra of the large-scale structure where observations meet with theories.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Fitting and forecasting coupled dark energy in the non-linear regime

We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β{sup 2}, with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Fourier imaging of non-linear structure formation

We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important, and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Quasi-linear toroidal simulations of resonant magnetic perturbations in eight ITER H-mode scenarios

Abstract Both linear and quasi-linear aspects of the plasma response to the resonant magnetic perturbation (RMP) field are numerically investigated for various H-mode scenarios in ITER, covering the pre-fusion power operation and the fusion power operation phases. Linear response computations for eight ITER scenarios, with varying plasma current and toroidal magnetic field, reveal that the best coil current phasing for controlling the type-I edge localized modes (ELMs) scales roughly linearly with the edge safety factor. The coil phasing is defined as the relative toroidal phase of the coil currents between different rows, for a given toroidal harmonic. Quasi-linear initial value simulation, which is the focus of the present study, shows that application of the n = 3 ( n is the toroidal mode number) RMP field has a minimum side effect on the plasma core momentum confinement but potentially a large effect on the global particle transport. Generally, the RMP field with the best (worst) coil phasing for ELM control produces the strongest (weakest) effect on the plasma edge flow and the overall density. This robustly holds for all eight ITER scenarios. Consequently, in order to minimize the RMP induced side effects while achieving ELM control (suppression) in ITER, a compromise is necessary in choosing the coil current configuration.

Physics↗
DOE OSTI2022

Concept of circular-linear energy recovery accelerator to probe the energy frontier

Energy-frontier accelerators provide powerful tools performing high precision measurements confirming the fundamentals of the physics and broadening new research horizons. Such machines are either driven by circular or linear accelerators. The circular machines, having the centre-of-mass (CM) energy values reaching 200 GeV (for leptons) and above, experience beam energy loss and quality dilution, for example, due to synchrotron radiation, limiting the overall CM energy achievable and requiring a constant energy top-up to compensate the loss and the beam quality dilution. Linear colliders overcome these limitations, while the finite capabilities of generating high average current beams limits the luminosity. This is partially compensated by the quality of the colliding beams. In this work, we suggest a novel design of circular-linear accelerator based on the merging of the “non-emitting”, low-energy storage rings and energy recovery linear accelerators. We suggest using the recently considered dual-axis asymmetric cavities to enable the operation of such a system, and in particular the energy recovery from spent, high-intensity beams. The machine considered, under the scope of the SNOWMASS-2021 initiative, can be potentially used to reach ultimate energy frontiers in high-energy physics as well as to drive next generation light sources. The merging of circular and linear systems, and applications of dual axes cavities, should allow the maintaining of high beam quality, high luminosity, and high energy efficiency, while offering a flexible energy management and opening clear opportunity for reducing the running cost. We note that the numbers shown in the paper are for illustration purpose and can be improved further.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Exploiting non-linear scales in galaxy–galaxy lensing and galaxy clustering: A forecast for the dark energy survey

ABSTRACT The combination of galaxy–galaxy lensing (GGL) and galaxy clustering is a powerful probe of low-redshift matter clustering, especially if it is extended to the non-linear regime. To this end, we use an N-body and halo occupation distribution (HOD) emulator method to model the redMaGiC sample of colour-selected passive galaxies in the Dark Energy Survey (DES), adding parameters that describe central galaxy incompleteness, galaxy assembly bias, and a scale-independent multiplicative lensing bias Alens. We use this emulator to forecast cosmological constraints attainable from the GGL surface density profile ΔΣ(rp) and the projected galaxy correlation function wp, gg(rp) in the final (Year 6) DES data set over scales $r_p=0.3\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$. For a $3{{\ \rm per\ cent}}$ prior on Alens we forecast precisions of $1.9{{\ \rm per\ cent}}$, $2.0{{\ \rm per\ cent}}$, and $1.9{{\ \rm per\ cent}}$ on Ωm, σ8, and $S_8 \equiv \sigma _8\Omega _m^{0.5}$, marginalized over all halo occupation distribution (HOD) parameters as well as Alens. Adding scales $r_p=0.3\!-\!3.0\, h^{-1} \, \mathrm{Mpc}$ improves the S8 precision by a factor of ∼1.6 relative to a large scale ($3.0\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$) analysis, equivalent to increasing the survey area by a factor of ∼2.6. Sharpening the Alens prior to $1{{\ \rm per\ cent}}$ further improves the S8 precision to $1.1{{\ \rm per\ cent}}$, and it amplifies the gain from including non-linear scales. Our emulator achieves per cent-level accuracy similar to the projected DES statistical uncertainties, demonstrating the feasibility of a fully non-linear analysis. Obtaining precise parameter constraints from multiple galaxy types and from measurements that span linear and non-linear clustering offers many opportunities for internal cross-checks, which can diagnose systematics and demonstrate the robustness of cosmological results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Signatures of Light Massive Relics on non-linear structure formation

ABSTRACT Cosmologies with Light Massive Relics (LiMRs) as a subdominant component of the dark sector are well-motivated from a particle physics perspective, and can also have implications for the σ8 tension between early and late time probes of clustering. The effects of LiMRs on the cosmic microwave background (CMB) and structure formation on large (linear) scales have been investigated extensively. In this paper, we initiate a systematic study of the effects of LiMRs on smaller, non-linear scales using cosmological N-body simulations; focusing on quantities relevant for photometric galaxy surveys. For most of our study, we use a particular model of non-thermal LiMRs but the methods developed generalizing to a large class of LiMR models – we explicitly demonstrate this by considering the Dodelson–Widrow velocity distribution. We find that, in general, the effects of LiMR on small scales are distinct from those of a ΛCDM universe, even when the value of σ8 is matched between the models. We show that weak lensing measurements around massive clusters, between ∼0.1 h−1Mpc and ∼10 h−1Mpc, should have sufficient signal-to-noise in future surveys to distinguish between ΛCDM and LiMR models that are tuned to fit both CMB data and linear scale clustering data at late times. Furthermore, we find that different LiMR cosmologies indistinguishable by conventional linear probes can be distinguished by non-linear probes if their velocity distributions are sufficiently different. LiMR models can, therefore, be best tested by jointly analyzing the CMB and late-time structure formation on both large and small scales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Emulating galaxy clustering and galaxy–galaxy lensing into the deeply non-linear regime: methodology, information, and forecasts

The combination of galaxy–galaxy lensing (GGL) with galaxy clustering is one of the most promising routes to determining the amplitude of matter clustering at low redshifts. Here, we show that extending clustering+GGL analyses from the linear regime down to |${\sim } 0.5 \, h^{-1}$| Mpc scales increases their constraining power considerably, even after marginalizing over a flexible model of non-linear galaxy bias. Using a grid of cosmological N -body simulations, we construct a Taylor-expansion emulator that predicts the galaxy autocorrelation ξ gg ( r ) and galaxy-matter cross-correlation ξ gm ( r ) as a function of σ 8 , Ω m , and halo occupation distribution (HOD) parameters, which are allowed to vary with large-scale environment to represent possible effects of galaxy assembly bias. We present forecasts for a fiducial case that corresponds to BOSS LOWZ galaxy clustering and SDSS-depth weak lensing (effective source density ~0.3 arcmin -2 ). Using tangential shear and projected correlation function measurements over |$0.5 \le r_\mathrm{ p} \le 30 \, h^{-1}$| Mpc yields a 2 per cent constraint on the parameter combination |$\sigma _8\Omega _\mathrm{ m}^{0.6}$| , a factor of two better than a constraint that excludes non-linear scales ( |$r_\mathrm{ p} \gt 2 \, h^{-1}$| Mpc, |$4 \, h^{-1}$| Mpc for γ t , |$w$| p ). Much of this improvement comes from the non-linear clustering information, which breaks degeneracies among HOD parameters. Increasing the effective source density to 3 arcmin -2 sharpens the constraint on |$\sigma _8\Omega _\mathrm{ m}^{0.6}$| by a further factor of two. With robust modelling into the non-linear regime, low-redshift measurements of matter clustering at the 1-per cent level with clustering+GGL alone are well within reach of current data sets such as those provided by the Dark Energy Survey.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Linearization of an Electron Beam’s Longitudinal Phase Space Using a Hollow-Channel Plasma

The removal of undesired beam nonlinear energy chirp (time-energy correlation) or linearization of the beam longitudinal phase space (LPS) is crucial for high-brightness linac-based scientific applications, such as x-ray free-electron lasers. In this paper, we propose that a low-density hollow channel plasma can be used as a near-ideal passive linearizer to significantly linearize the beam LPS and, at the same time, preserve the beam emittance. Physically, the passage of the beam through the hollow plasma channel excites a strong quasicosinoidal longitudinal wakefield that acts to mitigate the beam nonlinear energy chirp by superimposing a reverse chirp on the beam. The theoretical analyses and large-scale three-dimensional start-to-end simulations confirm that the beam longitudinal phase space can be almost completely linearized without noticeable beam emittance growth. In conclusion, application of such a near-ideal linearizer may significantly improve the performance of numerous accelerator-based applications.

43 PARTICLE ACCELERATORS↗
DOE OSTI2019

Limited accuracy of linearized gravity

Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations. In an era of precision cosmology, we should ask: are these approximate predictions sufficiently accurate for comparison to observations, and can we draw meaningful conclusions about properties of our Universe from them? In this work we examine the accuracy of linearized gravity in the presence of collisionless matter and a cosmological constant utilizing fully general relativistic simulations. We observe the gauge dependence of corrections to linear theory, and note the amplitude of these corrections. For perturbations whose amplitudes are in line with expectations from the standard Λ cold dark matter model, we find that the full, general relativistic metric is well described by linear theory in Newtonian and harmonic gauges, while the metric in comoving-synchronous gauge is not. Furthermore, for the most extreme observed structures in our Universe, such as supervoids, our results suggest that corrections to linear gravitational theory can reach or surpass the percent level in all gauges.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

DEEP NEURAL NETWORKS FOR NON-LINEAR MODEL-BASED ULTRASOUND RECONSTRUCTION

Ultrasound reflection tomography is widely used to image large complex specimens that are only accessible from a single side, such as well systems and nuclear power plant containment walls. Typical methods for inverting the measurement rely on delay-and-sum algorithms that rapidly produce reconstructions but with significant artifacts. Recently, model-based reconstruction approaches using a linear forward model have been shown to significantly improve image quality compared to the conventional approach. Nonetheless, even these techniques result in artifacts for complex objects because of the inherent non-linearity of the ultrasound forward model.In this paper, we propose a non-iterative model-based reconstruction method for inverting measurements that are based on non-linear forward models for ultrasound imaging. Our approach involves obtaining an approximate estimate of the reconstruction using a simple linear back-projection and training a deep neural network to refine this to the actual reconstruction. As a result, we apply our method to simulated and experimental ultrasound data to demonstrate dramatic improvements in image quality compared to the delay-and-sum approach and the linear model-based reconstruction approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

TH-CD-207B-05: Measurement of CT Bow-Tie Profiles Using a Linear Array Detector

Purpose: To accurately measure CT bow-tie profiles from various manufacturers and to provide non-proprietary information for CT system modeling. Methods: A GOS-based linear detector (0.8 mm per pixel and 51.2 cm in length) with a fast data sampling speed (0.24 ms/sample) was used to measure the relative profiles of bow-tie filters from a collection of eight CT scanners by three different vendors, GE (LS Xtra, LS VCT, Discovery HD750), Siemens (Sensation 64, Edge, Flash, Force), and Philips (iBrilliance 256). The linear detector was first calibrated for its energy response within typical CT beam quality ranges and compared with an ion chamber and analytical modeling (SPECTRA and TASMIP). A geometrical calibration process was developed to determine key parameters including the distance from the focal spot to the linear detector, the angular increment of the gantry at each data sampling, the location of the central x-ray on the linear detector, and the angular response of the detector pixel. Measurements were performed under axial-scan modes for most representative bow-tie filters and kV selections from each scanner. Bow-tie profiles were determined by re-binning the measured rotational data with an angular accuracy of 0.1 degree using the calibrated geometrical parameters. Results: The linear detector demonstrated an energy response as a solid state detector, which is close to the CT imaging detector. The geometrical calibration was proven to be sufficiently accurate (< 1mm in error for distances >550 mm) and the bow-tie profiles measured from rotational mode matched closely to those from the gantry-stationary mode. Accurate profiles were determined for a total of 21 bow-tie filters and 83 filter/kV combinations from the abovementioned scanner models. Conclusion: A new improved approach of CT bow-tie measurement was proposed and accurate bow-tie profiles were provided for a broad list of CT scanner models.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Linear instability of plane Couette and Poiseuille flows

It is shown that linear instability of plane Couette flow can take place even at finite Reynolds numbers Re > Re{sub th} ≈ 139, which agrees with the experimental value of Re{sub th} ≈ 150 ± 5 [16, 17]. This new result of the linear theory of hydrodynamic stability is obtained by abandoning traditional assumption of the longitudinal periodicity of disturbances in the flow direction. It is established that previous notions about linear stability of this flow at arbitrarily large Reynolds numbers relied directly upon the assumed separation of spatial variables of the field of disturbances and their longitudinal periodicity in the linear theory. By also abandoning these assumptions for plane Poiseuille flow, a new threshold Reynolds number Re{sub th} ≈ 1035 is obtained, which agrees to within 4% with experiment—in contrast to 500% discrepancy for the previous estimate of Re{sub th} ≈ 5772 obtained in the framework of the linear theory under assumption of the “normal” shape of disturbances [2].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗