The Thirty Gigahertz Instrument Receiver for the QUIJOTE Experiment: Preliminary Polarization Measurements and Systematic-Error Analysis.

PubMed

Casas, Francisco J; Ortiz, David; Villa, Enrique; Cano, Juan L; Cagigas, Jaime; Pérez, Ana R; Aja, Beatriz; Terán, J Vicente; de la Fuente, Luisa; Artal, Eduardo; Hoyland, Roger; Génova-Santos, Ricardo

2015-08-05

This paper presents preliminary polarization measurements and systematic-error characterization of the Thirty Gigahertz Instrument receiver developed for the QUIJOTE experiment. The instrument has been designed to measure the polarization of Cosmic Microwave Background radiation from the sky, obtaining the Q, U, and I Stokes parameters of the incoming signal simultaneously. Two kinds of linearly polarized input signals have been used as excitations in the polarimeter measurement tests in the laboratory; these show consistent results in terms of the Stokes parameters obtained. A measurement-based systematic-error characterization technique has been used in order to determine the possible sources of instrumental errors and to assist in the polarimeter calibration process.

Strong variable linear polarization in the cool active star II Peg

NASA Astrophysics Data System (ADS)

Rosén, Lisa; Kochukhov, Oleg; Wade, Gregg A.

2014-08-01

Magnetic fields of cool active stars are currently studied polarimetrically using only circular polarization observations. This provides limited information about the magnetic field geometry since circular polarization is only sensitive to the line-of-sight component of the magnetic field. Reconstructions of the magnetic field topology will therefore not be completely trustworthy when only circular polarization is used. On the other hand, linear polarization is sensitive to the transverse component of the magnetic field. By including linear polarization in the reconstruction the quality of the reconstructed magnetic map is dramatically improved. For that reason, we wanted to identify cool stars for which linear polarization could be detected at a level sufficient for magnetic imaging. Four active RS CVn binaries, II Peg, HR 1099, IM Peg, and σ Gem were observed with the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope. Mean polarization profiles in all four Stokes parameters were derived using the multi-line technique of least-squares deconvolution (LSD). Not only was linear polarization successfully detected in all four stars in at least one observation, but also, II Peg showed an extraordinarily strong linear polarization signature throughout all observations. This qualifies II Peg as the first promising target for magnetic Doppler imaging in all four Stokes parameters and, at the same time, suggests that other such targets can possibly be identified.

Magnetic Doppler imaging of α2 Canum Venaticorum in all four Stokes parameters. Unveiling the hidden complexity of stellar magnetic fields

NASA Astrophysics Data System (ADS)

Kochukhov, O.; Wade, G. A.

2010-04-01

Context. Strong organized magnetic fields have been studied in the upper main sequence chemically peculiar stars for more than half a century. However, only recently have observational methods and numerical techniques become sufficiently mature to allow us to record and interpret high-resolution four Stokes parameter spectra, leading to the first assumption-free magnetic field models of these stars. Aims: Here we present a detailed magnetic Doppler imaging analysis of the spectropolarimetric observations of the prototypical magnetic Ap star α2 CVn. This is the second star for which the magnetic field topology and horizontal chemical abundance inhomogeneities have been inferred directly from phase-resolved observations of line profiles in all four Stokes parameters, free from the traditional assumption of a low-order multipolar field geometry. Methods: We interpret the rotational modulation of the circular and linear polarization profiles of the strong Fe II and Cr II lines in the spectra of α2 CVn recorded with the MuSiCoS spectropolarimeter. The surface abundance distributions of the two chemical elements and a full vector map of the stellar magnetic field are reconstructed in a self-consistent inversion using our state-of-the-art magnetic Doppler imaging code Invers10. Results: We succeeded in reproducing most of the details of the available spectropolarimetric observations of α2 CVn with a magnetic map which combines a global dipolar-like field topology with localized spots of higher field intensity. We demonstrate that these small-scale magnetic structures are inevitably required to fit the linear polarization spectra; however, their presence cannot be inferred from the Stokes I and V observations alone. We also found high-contrast surface distributions of Fe and Cr, with both elements showing abundance minima in the region of weaker and topologically simpler magnetic field. Conclusions: Our magnetic Doppler imaging analysis of α2 CVn and previous results for 53 Cam support the view that the upper main sequence stars can harbour fairly complex surface magnetic fields which resemble oblique dipoles only at the largest spatial scales. Spectra in all four Stokes parameters are absolutely essential to unveil and meaningfully characterize this field complexity in Ap stars. We therefore suggest that understanding magnetism of stars in other parts of the H-R diagram is similarly incomplete without investigation of their linear polarization spectra. Based on data obtained using the Télescope Bernard Lyot at Observatoire du Pic du Midi.

The Thirty Gigahertz Instrument Receiver for the QUIJOTE Experiment: Preliminary Polarization Measurements and Systematic-Error Analysis

PubMed Central

Casas, Francisco J.; Ortiz, David; Villa, Enrique; Cano, Juan L.; Cagigas, Jaime; Pérez, Ana R.; Aja, Beatriz; Terán, J. Vicente; de la Fuente, Luisa; Artal, Eduardo; Hoyland, Roger; Génova-Santos, Ricardo

2015-01-01

This paper presents preliminary polarization measurements and systematic-error characterization of the Thirty Gigahertz Instrument receiver developed for the QUIJOTE experiment. The instrument has been designed to measure the polarization of Cosmic Microwave Background radiation from the sky, obtaining the Q, U, and I Stokes parameters of the incoming signal simultaneously. Two kinds of linearly polarized input signals have been used as excitations in the polarimeter measurement tests in the laboratory; these show consistent results in terms of the Stokes parameters obtained. A measurement-based systematic-error characterization technique has been used in order to determine the possible sources of instrumental errors and to assist in the polarimeter calibration process. PMID:26251906

Relativistic viscoelastic fluid mechanics.

PubMed

Fukuma, Masafumi; Sakatani, Yuho

2011-08-01

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

Relativistic viscoelastic fluid mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fukuma, Masafumi; Sakatani, Yuho

2011-08-15

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for themore » propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.« less

An Undergraduate Experiment to Measure the Reflectances of a Dielectric Surface

ERIC Educational Resources Information Center

Driver, H. S. T.

1978-01-01

Describes an experiment for the measurement of the reflectances of dielectric surface. The experiment is analyzed in terms of the Stokes parameters and the Mueller calculus, and Malus law is derived. The experiment also provides an introduction to the properties of real linear polarizers. (Author/GA)

Total elimination of sampling errors in polarization imagery obtained with integrated microgrid polarimeters.

PubMed

Tyo, J Scott; LaCasse, Charles F; Ratliff, Bradley M

2009-10-15

Microgrid polarimeters operate by integrating a focal plane array with an array of micropolarizers. The Stokes parameters are estimated by comparing polarization measurements from pixels in a neighborhood around the point of interest. The main drawback is that the measurements used to estimate the Stokes vector are made at different locations, leading to a false polarization signature owing to instantaneous field-of-view (IFOV) errors. We demonstrate for the first time, to our knowledge, that spatially band limited polarization images can be ideally reconstructed with no IFOV error by using a linear system framework.

Synchronous-digitization for Video Rate Polarization Modulated Beam Scanning Second Harmonic Generation Microscopy.

PubMed

Sullivan, Shane Z; DeWalt, Emma L; Schmitt, Paul D; Muir, Ryan M; Simpson, Garth J

2015-03-09

Fast beam-scanning non-linear optical microscopy, coupled with fast (8 MHz) polarization modulation and analytical modeling have enabled simultaneous nonlinear optical Stokes ellipsometry (NOSE) and linear Stokes ellipsometry imaging at video rate (15 Hz). NOSE enables recovery of the complex-valued Jones tensor that describes the polarization-dependent observables, in contrast to polarimetry, in which the polarization stated of the exciting beam is recorded. Each data acquisition consists of 30 images (10 for each detector, with three detectors operating in parallel), each of which corresponds to polarization-dependent results. Processing of this image set by linear fitting contracts down each set of 10 images to a set of 5 parameters for each detector in second harmonic generation (SHG) and three parameters for the transmittance of the fundamental laser beam. Using these parameters, it is possible to recover the Jones tensor elements of the sample at video rate. Video rate imaging is enabled by performing synchronous digitization (SD), in which a PCIe digital oscilloscope card is synchronized to the laser (the laser is the master clock.) Fast polarization modulation was achieved by modulating an electro-optic modulator synchronously with the laser and digitizer, with a simple sine-wave at 1/10th the period of the laser, producing a repeating pattern of 10 polarization states. This approach was validated using Z-cut quartz, and NOSE microscopy was performed for micro-crystals of naproxen.

Synchronous-digitization for video rate polarization modulated beam scanning second harmonic generation microscopy

NASA Astrophysics Data System (ADS)

Sullivan, Shane Z.; DeWalt, Emma L.; Schmitt, Paul D.; Muir, Ryan D.; Simpson, Garth J.

2015-03-01

Fast beam-scanning non-linear optical microscopy, coupled with fast (8 MHz) polarization modulation and analytical modeling have enabled simultaneous nonlinear optical Stokes ellipsometry (NOSE) and linear Stokes ellipsometry imaging at video rate (15 Hz). NOSE enables recovery of the complex-valued Jones tensor that describes the polarization-dependent observables, in contrast to polarimetry, in which the polarization stated of the exciting beam is recorded. Each data acquisition consists of 30 images (10 for each detector, with three detectors operating in parallel), each of which corresponds to polarization-dependent results. Processing of this image set by linear fitting contracts down each set of 10 images to a set of 5 parameters for each detector in second harmonic generation (SHG) and three parameters for the transmittance of the fundamental laser beam. Using these parameters, it is possible to recover the Jones tensor elements of the sample at video rate. Video rate imaging is enabled by performing synchronous digitization (SD), in which a PCIe digital oscilloscope card is synchronized to the laser (the laser is the master clock.) Fast polarization modulation was achieved by modulating an electro-optic modulator synchronously with the laser and digitizer, with a simple sine-wave at 1/10th the period of the laser, producing a repeating pattern of 10 polarization states. This approach was validated using Z-cut quartz, and NOSE microscopy was performed for micro-crystals of naproxen.

A technique for measuring vertically and horizontally polarized microwave brightness temperatures using electronic polarization-basis rotation

NASA Technical Reports Server (NTRS)

Gasiewski, Albin J.

1992-01-01

This technique for electronically rotating the polarization basis of an orthogonal-linear polarization radiometer is based on the measurement of the first three feedhorn Stokes parameters, along with the subsequent transformation of this measured Stokes vector into a rotated coordinate frame. The technique requires an accurate measurement of the cross-correlation between the two orthogonal feedhorn modes, for which an innovative polarized calibration load was developed. The experimental portion of this investigation consisted of a proof of concept demonstration of the technique of electronic polarization basis rotation (EPBR) using a ground based 90-GHz dual orthogonal-linear polarization radiometer. Practical calibration algorithms for ground-, aircraft-, and space-based instruments were identified and tested. The theoretical effort consisted of radiative transfer modeling using the planar-stratified numerical model described in Gasiewski and Staelin (1990).

Construction of reduced order models for the non-linear Navier-Stokes equations using the proper orthogonal fecomposition (POD)/Galerkin method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fike, Jeffrey A.

2013-08-01

The construction of stable reduced order models using Galerkin projection for the Euler or Navier-Stokes equations requires a suitable choice for the inner product. The standard L2 inner product is expected to produce unstable ROMs. For the non-linear Navier-Stokes equations this means the use of an energy inner product. In this report, Galerkin projection for the non-linear Navier-Stokes equations using the L2 inner product is implemented as a first step toward constructing stable ROMs for this set of physics.

Assessment of tissue polarimetric properties using Stokes polarimetric imaging with circularly polarized illumination.

PubMed

Qi, Ji; He, Honghui; Lin, Jianyu; Dong, Yang; Chen, Dongsheng; Ma, Hui; Elson, Daniel S

2018-04-01

Tissue-depolarization and linear-retardance are the main polarization characteristics of interest for bulk tissue characterization, and are normally interpreted from Mueller polarimetry. Stokes polarimetry can be conducted using simpler instrumentation and in a shorter time. Here, we use Stokes polarimetric imaging with circularly polarized illumination to assess the circular-depolarization and linear-retardance properties of tissue. Results obtained were compared with Mueller polarimetry in transmission and reflection geometry, respectively. It is found that circular-depolarization obtained from these 2 methods is very similar in both geometries, and that linear-retardance is highly quantitatively similar for transmission geometry and qualitatively similar for reflection geometry. The majority of tissue circular-depolarization and linear-retardance image information (represented by local image contrast features) obtained from Mueller polarimetry is well preserved from Stokes polarimetry in both geometries. These findings can be referred to for further understanding tissue Stokes polarimetric data, and for further application of Stokes polarimetry under the circumstances where short acquisition time or low optical system complexity is a priority, such as polarimetric endoscopy and microscopy. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Boundary Layers for the Navier-Stokes Equations Linearized Around a Stationary Euler Flow

NASA Astrophysics Data System (ADS)

Gie, Gung-Min; Kelliher, James P.; Mazzucato, Anna L.

2018-03-01

We study the viscous boundary layer that forms at small viscosity near a rigid wall for the solution to the Navier-Stokes equations linearized around a smooth and stationary Euler flow (LNSE for short) in a smooth bounded domain Ω \\subset R^3 under no-slip boundary conditions. LNSE is supplemented with smooth initial data and smooth external forcing, assumed ill-prepared, that is, not compatible with the no-slip boundary condition. We construct an approximate solution to LNSE on the time interval [0, T], 0

The Primordial Inflation Polarization Explorer (PIPER)

NASA Technical Reports Server (NTRS)

Chuss, David T.

2010-01-01

The Primordial Inflation Polarization Explorer (PIPER) is a ba1loon-borne instrument designed to search for the faint signature of inflation in the polarized component of the cosmic microwave background (CMB). PIPER will measure the CMB polarization at 4 frequencies (l per flight) using a pair of cryogenic telescopes, one for measuring each of Stokes Q and U in the instrument frame. Each telescope receives both linear orthogonal polarizations in two 32 by 40 element planar arrays that utilize Transition-Edge Sensors (TES). The first element in each telescope is a variable-delay polarization modulator (VPM) that fully modulates the Stokes parameter to which the telescope is sensitive.

Magnetic Doppler imaging of 53 Camelopardalis in all four Stokes parameters

NASA Astrophysics Data System (ADS)

Kochukhov, O.; Bagnulo, S.; Wade, G. A.; Sangalli, L.; Piskunov, N.; Landstreet, J. D.; Petit, P.; Sigut, T. A. A.

2004-02-01

We present the first investigation of the structure of the stellar surface magnetic field using line profiles in all four Stokes parameters. We extract the information about the magnetic field geometry and abundance distributions of the chemically peculiar star 53 Cam by modelling time-series of high-resolution spectropolarimetric observations with the help of a new magnetic Doppler imaging code. This combination of the unique four Stokes parameter data and state-of-the-art magnetic imaging technique makes it possible to infer the stellar magnetic field topology directly from the rotational variability of the Stokes spectra. In the magnetic imaging of 53 Cam we discard the traditional multipolar assumptions about the structure of magnetic fields in Ap stars and explore the stellar magnetic topology without introducing any global a priori constraints on the field structure. The complex magnetic model of 53 Cam derived with our magnetic Doppler imaging method achieves a good fit to the observed intensity, circular and linear polarization profiles of strong magnetically sensitive Fe II spectral lines. Such an agreement between observations and model predictions was not possible with any earlier multipolar magnetic models, based on modelling Stokes I spectra and fitting surface averaged magnetic observables (e.g., longitudinal field, magnetic field modulus, etc.). Furthermore, we demonstrate that even the direct inversion of the four Stokes parameters of 53 Cam assuming a low-order multipolar magnetic geometry is incapable of achieving an adequate fit to our spectropolarimetric observations. Thus, as a main result of our investigation, we discover that the magnetic field topology of 53 Cam is considerably more complex than any low-order multipolar expansion, raising a general question about the validity of the multipolar assumption in the studies of magnetic field structures of Ap stars. In addition to the analysis of the magnetic field of 53 Cam, we reconstruct surface abundance distributions of Si, Ca, Ti, Fe and Nd. These abundance maps confirm results of the previous studies of 53 Cam, in particular dramatic antiphase variation of Ca and Ti abundances. Based on observations obtained with the Bernard Lyot telescope of the Pic du Midi Observatory and Isaac Newton Telescope of the La Palma Observatory.

Generalized Knudsen Number for Unsteady Fluid Flow.

PubMed

Kara, V; Yakhot, V; Ekinci, K L

2017-02-17

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Generalized Knudsen Number for Unsteady Fluid Flow

NASA Astrophysics Data System (ADS)

Kara, V.; Yakhot, V.; Ekinci, K. L.

2017-02-01

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Gravitational Stokes parameters. [for electromagnetic and gravitational radiation in relativity

NASA Technical Reports Server (NTRS)

Anile, A. M.; Breuer, R. A.

1974-01-01

The electromagnetic and gravitational Stokes parameters are defined in the general theory of relativity. The general-relativistic equation of radiative transfer for polarized radiation is then derived in terms of the Stokes parameters for both high-frequency electromagnetic and gravitational waves. The concept of Stokes parameters is generalized for the most general class of metric theories of gravity, where six (instead of two) independent states of polarization are present.

Spectral quantum fluctuations in a stimulated Raman generator: a description in terms of temporally coherent modes.

PubMed

Walmsley, I A

1992-03-15

The probability density of the single-shot mean Stokes frequency from a linear Raman generator is calculated. It is shown that the fluctuations in the Stokes pulse energy spectrum that arise from the quantum initiation of the Stokes light are reduced in the transient regime of amplification. Also, it appears that saturation of the Raman gain does not reduce the phase fluctuations of the Stokes light below those present in the unsaturated gain (linear) regime.

Dynamic characteristics of a multi-wavelength Brillouin-Raman fiber laser assisted by multiple four-wave mixing processes in a ring cavity

NASA Astrophysics Data System (ADS)

Shirazi, M. R.; Mohamed Taib, J.; De La Rue, R. M.; Harun, S. W.; Ahmad, H.

2015-03-01

Dynamic characteristics of a multi-wavelength Brillouin-Raman fiber laser (MBRFL) assisted by four-wave mixing have been investigated through the development of Stokes and anti-Stokes lines under different combinations of Brillouin and Raman pump power levels and different Raman pumping schemes in a ring cavity. For a Stokes line of order higher than three, the threshold power was less than the saturation power of its last-order Stokes line. By increasing the Brillouin pump power, the nth order anti-Stokes and the (n+4)th order Stokes power levels were unexpectedly increased almost the same before the Stokes line threshold power. It was also found out that the SBS threshold reduction (SBSTR) depended linearly on the gain factor for the 1st and 2nd Stokes lines, as the first set. This relation for the 3rd and 4th Stokes lines as the second set, however, was almost linear with the same slope before SBSTR -6 dB, then, it approached to the linear relation in the first set when the gain factor was increased to 50 dB. Therefore, the threshold power levels of Stokes lines for a given Raman gain can be readily estimated only by knowing the threshold power levels in which there is no Raman amplification.

Mid-infrared Raman amplification and wavelength conversion in dispersion engineered silicon-on-sapphire waveguides

NASA Astrophysics Data System (ADS)

Wang, Zhaolu; Liu, Hongjun; Huang, Nan; Sun, Qibing; Li, Xuefeng

2014-01-01

Raman amplification based on stimulated Stokes Raman scattering (SSRS) and wavelength conversion based on coherent anti-Stokes Raman scattering (CARS) are theoretically investigated in silicon-on-sapphire (SOS) waveguides in the mid-infrared (IR) region. When the linear phase mismatch Δk is close to zero, the Stokes gain and conversion efficiency drop down quickly due to the effect of parametric gain suppression when the Stokes-pump input ratio is sufficiently large. The Stokes gain increases with the increase of Δk, whereas efficient wavelength conversion needs appropriate Δk under different pump intensities. The conversion efficiency at exact linear phase matching (Δk = 0) is smaller than that at optimal linear phase mismatch by a factor of about 28 dB when the pump intensity is 2 GW cm-2.

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Stokes parameters of phase-locked partially coherent flat-topped array laser beams propagating through turbulent atmosphere

NASA Astrophysics Data System (ADS)

Golmohammady, Sh; Ghafary, B.

2016-06-01

In this study, generalized Stokes parameters of a phase-locked partially coherent flat-topped array beam based on the extended Huygens-Fresnel principle and the unified theory of coherence and polarization have been reported. Analytical formulas for 2  ×  2 cross-spectral density matrix elements, and consequently Stokes parameters of a phase-locked partially coherent flat-topped array beam propagating through the turbulent atmosphere have been formulated. Effects of many physical attributes such as wavelength, turbulence strength, flatness order and other source parameters on the Stokes parameters, and therefore spectral degree of polarization upon propagation have been studied thoroughly. The behaviour of the spectral degree of coherence of a delineated beam for different source conditions has been investigated. It can be shown that four generalized Stokes parameters increase by raising the flatness order at the same propagation distance. Increasing the number of beams leads to a decrease in the Stokes parameters to zero slowly. The results are of utmost importance for optical communications.

On HMI's Mod-L Sequence: Test and Evaluation

NASA Astrophysics Data System (ADS)

Liu, Yang; Baldner, Charles; Bogart, R. S.; Bush, R.; Couvidat, S.; Duvall, Thomas L.; Hoeksema, Jon Todd; Norton, Aimee Ann; Scherrer, Philip H.; Schou, Jesper

2016-05-01

HMI Mod-L sequence can produce full Stokes parameters at a cadence of 90 seconds by combining filtergrams from both cameras, the front camera and the side camera. Within the 90-second, the front camera takes two sets of Left and Right Circular Polarizations (LCP and RCP) at 6 wavelengths; the side camera takes one set of Linear Polarizations (I+/-Q and I+/-U) at 6 wavelengths. By combining two cameras, one can obtain full Stokes parameters of [I,Q,U,V] at 6 wavelengths in 90 seconds. In norminal Mod-C sequence that HMI currently uses, the front camera takes LCP and RCP at a cadence of 45 seconds, while the side camera takes observation of the full Stokes at a cadence of 135 seconds. Mod-L should be better than Mod-C for providing vector magnetic field data because (1) Mod-L increases cadence of full Stokes observation, which leads to higher temporal resolution of vector magnetic field measurement; (2) decreases noise in vector magnetic field data because it uses more filtergrams to produce [I,Q,U,V]. There are two potential issues in Mod-L that need to be addressed: (1) scaling intensity of the two cameras’ filtergrams; and (2) if current polarization calibration model, which is built for each camera separately, works for the combined data from both cameras. This presentation will address these questions, and further place a discussion here.

Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

NASA Astrophysics Data System (ADS)

Tsuchida, Satoshi; Kuratsuji, Hiroshi

2018-05-01

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

Linear modeling of turbulent skin-friction reduction due to spanwise wall motion

NASA Astrophysics Data System (ADS)

Duque-Daza, Carlos; Baig, Mirza; Lockerby, Duncan; Chernyshenko, Sergei; Davies, Christopher; University of Warwick Team; Imperial College Team; Cardiff University Team

2012-11-01

We present a study on the effect of streamwise-travelling waves of spanwise wall velocity on the growth of near-wall turbulent streaks using a linearized formulation of the Navier-Stokes equations. The changes in streak amplification due to the travelling waves induced by the wall velocity are compared to published results of direct numerical simulation (DNS) predictions of the turbulent skin-friction reduction over a range of parameters; a clear correlation between these two sets of results is observed. Additional linearized simulations but at a much higher Reynolds numbers, more relevant to aerospace applications, produce results that show no marked differences to those obtained at low Reynolds number. It is also observed that a close correlation exists between DNS data of drag reduction and a very simple characteristic of the ``generalized'' Stokes layer generated by the streamwise-travelling waves. Carlos.Duque-Daza@warwick.ac.uk - School of Engineering, University of Warwick, Coventry CV4 7AL, UK caduqued@unal.edu.co - Department of Mechanical and Mechatronics Engineering, Universidad Nacional de Colombia.

Three-dimensional facial recognition using passive long-wavelength infrared polarimetric imaging.

PubMed

Yuffa, Alex J; Gurton, Kristan P; Videen, Gorden

2014-12-20

We use a polarimetric camera to record the Stokes parameters and the degree of linear polarization of long-wavelength infrared radiation emitted by human faces. These Stokes images are combined with Fresnel relations to extract the surface normal at each pixel. Integrating over these surface normals yields a three-dimensional facial image. One major difficulty of this technique is that the normal vectors determined from the polarizations are not unique. We overcome this problem by introducing an additional boundary condition on the subject. The major sources of error in producing inversions are noise in the images caused by scattering of the background signal and the ambiguity in determining the surface normals from the Fresnel coefficients.

An indirect method of imaging the Stokes parameters of a submicron particle with sub-diffraction scattering

NASA Astrophysics Data System (ADS)

Ullah, Kaleem; Garcia-Camara, Braulio; Habib, Muhammad; Yadav, N. P.; Liu, Xuefeng

2018-07-01

In this work, we report an indirect way to image the Stokes parameters of a sample under test (SUT) with sub-diffraction scattering information. We apply our previously reported technique called parametric indirect microscopic imaging (PIMI) based on a fitting and filtration process to measure the Stokes parameters of a submicron particle. A comparison with a classical Stokes measurement is also shown. By modulating the incident field in a precise way, fitting and filtration process at each pixel of the detector in PIMI make us enable to resolve and sense the scattering information of SUT and map them in terms of the Stokes parameters. We believe that our finding can be very useful in fields like singular optics, optical nanoantenna, biomedicine and much more. The spatial signature of the Stokes parameters given by our method has been confirmed with finite difference time domain (FDTD) method.

The Zeeman effect or linear birefringence? VLA polarimetric spectral line observations of H2O masers

NASA Astrophysics Data System (ADS)

Zhao, Jun-Hui; Goss, W. M.; Diamond, P.

We present line profiles of the four Stokes parameters of H2O masers at 22 GHz observed with the VLA in full polarimetric spectral line mode. With careful calibration, the instrumental effects such as linear leakage and the difference of antenna gain between RCP and LCP, can be minimized. Our measurements show a few percent linear polarization. Weak circular polarization was detected at a level of 0.1 percent of the peak intensity. A large uncertainty in the measurements of weak circular polarization is caused by telescope pointing errors. The observed polarization of H2O masers can be interpreted as either the Zeeman effect or linear birefringence.

Advantages of measuring the Q Stokes parameter in addition to the total radiance I in the detection of absorbing aerosols

NASA Astrophysics Data System (ADS)

Stamnes, Snorre; Fan, Yongzhen; Chen, Nan; Li, Wei; Tanikawa, Tomonori; Lin, Zhenyi; Liu, Xu; Burton, Sharon; Omar, Ali; Stamnes, Jakob J.; Cairns, Brian; Stamnes, Knut

2018-05-01

A simple but novel study was conducted to investigate whether an imager-type spectroradiometer instrument like MODIS, currently flying on board the Aqua and Terra satellites, or MERIS, which flew on board Envisat, could detect absorbing aerosols if they could measure the Q Stokes parameter in addition to the total radiance I, that is if they could also measure the linear polarization of the light. Accurate radiative transfer calculations were used to train a fast neural network forward model, which together with a simple statistical optimal estimation scheme was used to retrieve three aerosol parameters: aerosol optical depth at 869 nm, optical depth fraction of fine mode (absorbing) aerosols at 869 nm, and aerosol vertical location. The aerosols were assumed to be bimodal, each with a lognormal size distribution, located either between 0 and 2 km or between 2 and 4 km in the Earth's atmosphere. From simulated data with 3% random Gaussian measurement noise added for each Stokes parameter, it was found that by itself the total radiance I at the nine MODIS VIS channels was generally insufficient to accurately retrieve all three aerosol parameters (˜ 15% to 37% successful), but that together with the Q Stokes component it was possible to retrieve values of aerosol optical depth at 869 nm to ± 0.03, single-scattering albedo at 869 nm to ± 0.04, and vertical location in ˜ 65% of the cases. This proof-of-concept retrieval algorithm uses neural networks to overcome the computational burdens of using vector radiative transfer to accurately simulate top-of-atmosphere (TOA) total and polarized radiances, enabling optimal estimation techniques to exploit information from multiple channels. Therefore such an algorithm could, in concept, be readily implemented for operational retrieval of aerosol and ocean products from moderate or hyperspectral spectroradiometers.

An Analytical Calibration Approach for the Polarimetric Airborne C Band Radiometer

NASA Technical Reports Server (NTRS)

Pham, Hanh; Kim, Edward J.

2004-01-01

Passive microwave remote sensing is sensitive to the quantity and distribution of water in soil and vegetation. During summer 2000, the Microwave Geophysics Group a t the University of Michigan conducted the seventh Radiobrighness Energy Balance Experiment (REBEX-7) over a corn canopy in Michigan. Long time series of brightness temperatures, soil moisture and micrometeorology on the plot were taken. This paper addresses the calibration of the NASA GSFC polarimetric airborne C band microwave radiometer (ACMR) that participated in REBEX-7. These passive polarimeters are typically calibrated using an end-to-end approach based upon a standard artificial target or a well-known geophysical target. Analyzing the major internal functional subsystems offers a different perspective. The primary goal of this approach is to provide a transfer function that not only describes the system in its entire5 but also accounts for the contributions of each subsystem toward the final modified Stokes parameters. This approach does not assume that the radiometric system is linear as it does not take polarization isolation for granted, and it also serves as a realistic instrument simulator, a useful tool for future designs. The ACMR architecture can be partitioned into functional subsystems. The characteristics of each subsystem was extensively measured and the estimated parameters were imported into the overall dosed form system model. Inversion of the model yields a calibration for the modeled Stokes parameters with uncertainties of 0.2 K for the V and H polarizations and 2.4 K for the 3rd and 4th parameters. Application to the full Stokes parameters over a senescent cornfield is presented.

Polarization of the Sunyaev-Zel'dovich effect: relativistic imprint of thermal and non-thermal plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emritte, Mohammad Shehzad; Colafrancesco, Sergio; Marchegiani, Paolo, E-mail: Sergio.Colafrancesco@wits.ac.za, E-mail: emrittes@yahoo.com, E-mail: Paolo.Marchegiani@wits.ac.za

2016-07-01

Inverse Compton (IC) scattering of the anisotropic CMB fluctuations off cosmic electron plasmas generates a polarization of the associated Sunyaev-Zel'dovich (SZ) effect. The polarized SZ effect has important applications in cosmology and in astrophysics of galaxy clusters. However, this signal has been studied so far mostly in the non-relativistic regime which is valid only in the very low electron temperature limit for a thermal electron population and, as such, has limited astrophysical applications. Partial attempts to extend this calculation to the IC scattering of a thermal electron plasma in the relativistic regime have been done but these cannot be appliedmore » to a more general or mildly relativistic electron distribution. In this paper we derive a general form of the SZ effect polarization that is valid in the full relativistic approach for both thermal and non-thermal electron plasmas, as well as for a generic combination of various electron population which can be co-spatially distributed in the environments of galaxy clusters or radiogalaxy lobes. We derive the spectral shape of the Stokes parameters induced by the IC scattering of every CMB multipole for both thermal and non-thermal electron populations, focussing in particular on the CMB quadrupole and octupole that provide the largest detectable signals in cosmic structures (like galaxy clusters). We found that the CMB quadrupole induced Stoke parameter Q is always positive with a maximum amplitude at a frequency ≈ 216 GHz which increases non-linearly with increasing cluster temperature. On the contrary, the CMB octupole induced Q spectrum shows a cross-over frequency which depends on the cluster electron temperature in a linear way, while it shows a non-linear dependence on the minimum momentum p {sub 1} of a non-thermal power-law spectrum as well as a linear dependence on the power-law spectral index of the non-thermal electron population. We discuss some of the possibilities to disentangle the quadrupole-induced Q spectrum from the octupole-induced one which will allow to measure these important cosmological quantities through the SZ effect polarization at different cluster locations in the universe. We finally apply our model to the Bullet cluster and derive the visibility windows of the total, quandrupole-induced and octupole-induced Stoke parameter Q in the frequency ranges accessible to SKA, ALMA, MILLIMETRON and CORE++ experiments.« less

Methods and means of Stokes-polarimetry microscopy of optically anisotropic biological layers

NASA Astrophysics Data System (ADS)

Ushenko, A. G.; Dubolazov, A. V.; Ushenko, V. A.; Ushenko, Yu. A.; Sakhnovskiy, M. Yu.; Sidor, M.; Prydiy, O. G.; Olar, O. I.; Lakusta, I. I.

2016-12-01

The results of optical modeling of biological tissues polycrystalline multilayer networks have been presented. Algorithms of reconstruction of parameter distributions were determined that describe the linear and circular birefringence. For the separation of the manifestations of these mechanisms we propose a method of space-frequency filtering. Criteria for differentiation of benign and malignant tissues of the women reproductive sphere were found.

Above threshold spectral dependence of linewidth enhancement factor, optical duration and linear chirp of quantum dot lasers.

PubMed

Kim, Jimyung; Delfyett, Peter J

2009-12-07

The spectral dependence of the linewidth enhancement factor above threshold is experimentally observed from a quantum dot Fabry-Pérot semiconductor laser. The linewidth enhancement factor is found to be reduced when the quantum dot laser operates approximately 10 nm offset to either side of the gain peak. It becomes significantly reduced on the anti-Stokes side as compared to the Stokes side. It is also found that the temporal duration of the optical pulses generated from quantum dot mode-locked lasers is shorter when the laser operates away from the gain peak. In addition, less linear chirp is impressed on the pulse train generated from the anti-Stokes side whereas the pulses generated from the gain peak and Stokes side possess a large linear chirp. These experimental results imply that enhanced performance characteristics of quantum dot lasers can be achieved by operating on the anti-Stokes side, approximately 10 nm away from the gain peak.

Stokes-polarimetry imaging of tissue

NASA Astrophysics Data System (ADS)

Wu, Paul J.

A novel Stokes-polarimetry imaging system and technique was developed to quantify fully the polarization properties of light remitted from tissue. The uniqueness of the system and technique is established in the incident polarization. Here, the diffuse illumination is varied and controlled with the intention to improve the visibility of tissue structures. Since light retains some polarization even after multiple-scattering events, the polarization of remitted light depends upon the interactions within the material. Differentiation between tissue structures is accomplished by two-dimensional mapping of the imaged area using metrics such as the degree of linear polarization, degree of circular polarization, ellipticity, and Stokes parameters. While Stokes-polarimetry imaging can be applied to a variety of tissues and conditions, this thesis focuses on tissue types associated with the disease endometriosis. The current standard in diagnosing endometriosis is visual laparoscopy with tissue biopsy. The documented correlation between laparoscopy inspection and histological confirmation of suspected lesions was at best 67%. Endometrial lesions vary greatly in their appearance and depth of infiltration. Although laparoscopy permits tissue to be assessed by color and texture, to advance beyond the state-of-the-art, a new imaging modality involving polarized light was investigated; in particular, Stokes-polarimetry imaging was used to determine the polarization signature of light that interacted with tissue. Basic science studies were conducted on rat tails embedded within turbid gelatin. The purpose of these experiments was to determine how identification of sub-surface structures could be improved. Experimental results indicate image contrast among various structures such as tendon, soft tissue and intervertebral discs. Stokes-polarimetry imaging experiments were performed on various tissues associated with endometriosis to obtain a baseline characterization for each tissue type. Structures such as birefringent collagen, smooth-muscle fiber-bundles, and nerve bundles were visualized that were otherwise not observable with unpolarized light imaging. Finally, a study of cutaneous scars indicated the feasibility of using Stokes-polarimetry imaging in the detection of atypical tissue. A relationship between incident linear polarization angle and skin anatomy was determined so as to obtain maximum contrast between scar tissue and normal skin.

Generalized Knudsen Number for Oscillatory Flows Generated by MEMS and NEMS Resonators

NASA Astrophysics Data System (ADS)

Ekinci, Kamil; Kara, Vural; Yakhot, Victor

2017-11-01

We have explored the scaling behavior of oscillatory flows that are generated by the oscillations of MEMS and NEMS resonators in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect; or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimensions and the frequencies of the MEMS and NEMS resonators, we experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the linear dimension and the frequency of each resonator. This proposed Knudsen number for oscillatory flows is rooted in a fundamental symmetry principle, namely Galilean invariance. We acknowledge support from US NSF through Grant No. CBET-1604075.

Multigrid and Krylov Subspace Methods for the Discrete Stokes Equations

NASA Technical Reports Server (NTRS)

Elman, Howard C.

1996-01-01

Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizations, a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the discretization. In this paper, we compare the performance of four such methods: variants of the Uzawa, preconditioned conjugate gradient, preconditioned conjugate residual, and multigrid methods, for solving several two-dimensional model problems. The results indicate that where it is applicable, multigrid with smoothing based on incomplete factorization is more efficient than the other methods, but typically by no more than a factor of two. The conjugate residual method has the advantage of being both independent of iteration parameters and widely applicable.

The Fundamental Solution of the Linearized Navier Stokes Equations for Spinning Bodies in Three Spatial Dimensions Time Dependent Case

NASA Astrophysics Data System (ADS)

Thomann, Enrique A.; Guenther, Ronald B.

2006-02-01

Explicit formulae for the fundamental solution of the linearized time dependent Navier Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L p (R 3), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.

Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

2018-05-01

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

Parameter investigation with line-implicit lower-upper symmetric Gauss-Seidel on 3D stretched grids

NASA Astrophysics Data System (ADS)

Otero, Evelyn; Eliasson, Peter

2015-03-01

An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier-Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.

A comparison of Stokes parameters for sky and a soybean canopy

NASA Technical Reports Server (NTRS)

Schutt, John B.; Holben, Brent N.; Mcmurtrey, James E., III

1991-01-01

An evaluation of the polarization signatures obtained from the four Stokes parameters is reported for the atmosphere and a soybean canopy. The polarimeter design and operation are set forth, and the Stokes parameters' relationships are discussed. The canopy polarization was different from the sky at azimuths of 90 and 270 degrees, demonstrating a response that reflecting the sky polarization signatures across a plane parallel to the polarization axis and passing through a phase angle of about 90 degrees would produce. Classical behavior in terms of electromagnetic theory was found in the fourth Stokes parameter of the canopy which was obtained in the principal plane. Only the third Stokes parameter is demonstrated to be unambiguously affected in a comparison of sky polarization signatures and aerosol optical densities. The similarity between the sky at azimuth 180 degrees and the soybean canopy data at the principal plane is interesting considering the disparity of the subjects.

Development of real-time rotating waveplate Stokes polarimeter using multi-order retardation for ITER poloidal polarimeter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Imazawa, R., E-mail: imazawa.ryota@jaea.go.jp; Kawano, Y.; Ono, T.

The rotating waveplate Stokes polarimeter was developed for ITER (International Thermonuclear Experimental Reactor) poloidal polarimeter. The generalized model of the rotating waveplate Stokes polarimeter and the algorithm suitable for real-time field-programmable gate array (FPGA) processing were proposed. Since the generalized model takes into account each component associated with the rotation of the waveplate, the Stokes parameters can be accurately measured even in unideal condition such as non-uniformity of the waveplate retardation. Experiments using a He-Ne laser showed that the maximum error and the precision of the Stokes parameter were 3.5% and 1.2%, respectively. The rotation speed of waveplate was 20 000more » rpm and time resolution of measuring the Stokes parameter was 3.3 ms. Software emulation showed that the real-time measurement of the Stokes parameter with time resolution of less than 10 ms is possible by using several FPGA boards. Evaluation of measurement capability using a far-infrared laser which ITER poloidal polarimeter will use concluded that measurement error will be reduced by a factor of nine.« less

Development of real-time rotating waveplate Stokes polarimeter using multi-order retardation for ITER poloidal polarimeter.

PubMed

Imazawa, R; Kawano, Y; Ono, T; Itami, K

2016-01-01

The rotating waveplate Stokes polarimeter was developed for ITER (International Thermonuclear Experimental Reactor) poloidal polarimeter. The generalized model of the rotating waveplate Stokes polarimeter and the algorithm suitable for real-time field-programmable gate array (FPGA) processing were proposed. Since the generalized model takes into account each component associated with the rotation of the waveplate, the Stokes parameters can be accurately measured even in unideal condition such as non-uniformity of the waveplate retardation. Experiments using a He-Ne laser showed that the maximum error and the precision of the Stokes parameter were 3.5% and 1.2%, respectively. The rotation speed of waveplate was 20 000 rpm and time resolution of measuring the Stokes parameter was 3.3 ms. Software emulation showed that the real-time measurement of the Stokes parameter with time resolution of less than 10 ms is possible by using several FPGA boards. Evaluation of measurement capability using a far-infrared laser which ITER poloidal polarimeter will use concluded that measurement error will be reduced by a factor of nine.

Structuring Stokes correlation functions using vector-vortex beam

NASA Astrophysics Data System (ADS)

Kumar, Vijay; Anwar, Ali; Singh, R. P.

2018-01-01

Higher order statistical correlations of the optical vector speckle field, formed due to scattering of a vector-vortex beam, are explored. Here, we report on the experimental construction of the Stokes parameters covariance matrix, consisting of all possible spatial Stokes parameters correlation functions. We also propose and experimentally realize a new Stokes correlation functions called Stokes field auto correlation functions. It is observed that the Stokes correlation functions of the vector-vortex beam will be reflected in the respective Stokes correlation functions of the corresponding vector speckle field. The major advantage of proposing Stokes correlation functions is that the Stokes correlation function can be easily tuned by manipulating the polarization of vector-vortex beam used to generate vector speckle field and to get the phase information directly from the intensity measurements. Moreover, this approach leads to a complete experimental Stokes characterization of a broad range of random fields.

The polarization of continuum radiation in sunspots. I - Rayleigh and Thomson scattering

NASA Technical Reports Server (NTRS)

Finn, G. D.; Jefferies, J. T.

1974-01-01

Expressions are derived for the Stokes parameters of light scattered by a layer of free electrons and hydrogen atoms in a sunspot. A physically reasonable sunspot model was found so that the direction of the calculated linear polarization agrees reasonably with observations. The magnitude of the calculated values of the linear polarization agrees generally with values observed in the continuum at 5830 A. Circular polarization in the continuum also accompanies electron scattering in spot regions; however for commonly accepted values of the longitudinal magnetic field, the predicted circular polarization is much smaller than observed.

Simulation of the influence of aerosol particles on Stokes parameters of polarized skylight

NASA Astrophysics Data System (ADS)

Li, L.; Li, Z. Q.; Wendisch, M.

2014-03-01

Microphysical properties and chemical compositions of aerosol particles determine polarized radiance distribution in the atmosphere. In this paper, the influences of different aerosol properties (particle size, shape, real and imaginary parts of refractive index) on Stokes parameters of polarized skylight in the solar principal and almucantar planes are studied by using vector radiative transfer simulations. The results show high sensitivity of the normalized Stokes parameters due to fine particle size, shape and real part of refractive index of aerosols. It is possible to utilize the strength variations at the peak positions of the normalized Stokes parameters in the principal and almucantar planes to identify aerosol types.

Spectrographic Polarimeter and Method of Recording State of Polarity

NASA Technical Reports Server (NTRS)

Sparks, William B. (Inventor)

2015-01-01

A single-shot real-time spectropolarimeter for use in astronomy and other sciences that captures and encodes some or all of the Stokes polarization parameters simultaneously using only static, robust optical components with no moving parts is described. The polarization information is encoded onto the spectrograph at each wavelength along the spatial dimension of the 2D output data array. The varying embodiments of the concept include both a two-Stokes implementation (in which any two of the three Stokes polarization parameters are measured) and a full Stokes implementation (in which all three of the Stokes polarization parameters are measured), each of which is provided in either single beam or dual beam forms.

Unsteady translational motion of a slip sphere in a viscous fluid using the fractional Navier-Stokes equation

NASA Astrophysics Data System (ADS)

Ashmawy, E. A.

2017-03-01

In this paper, we investigate the translational motion of a slip sphere with time-dependent velocity in an incompressible viscous fluid. The modified Navier-Stokes equation with fractional order time derivative is used. The linear slip boundary condition is applied on the spherical boundary. The integral Laplace transform technique is employed to solve the problem. The solution in the physical domain is obtained analytically by inverting the Laplace transform using the complex inversion formula together with contour integration. An exact formula for the drag force exerted by the fluid on the spherical object is deduced. This formula is applied to some flows, namely damping oscillation, sine oscillation and sudden motion. The numerical results showed that the order of the fractional derivative contributes considerably to the drag force. The increase in this parameter resulted in an increase in the drag force. In addition, the values of the drag force increased with the increase in the slip parameter.

Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy.

PubMed

Mu, Tingkui; Pacheco, Shaun; Chen, Zeyu; Zhang, Chunmin; Liang, Rongguang

2017-02-13

In this paper, the design and experimental demonstration of a snapshot linear-Stokes imaging spectropolarimeter (SLSIS) is presented. The SLSIS, which is based on division-of-focal-plane polarimetry with four parallel linear polarization channels and integral field spectroscopy with numerous slit dispersive paths, has no moving parts and provides video-rate Stokes-vector hyperspectral datacubes. It does not need any scanning in the spectral, spatial or polarization dimension and offers significant advantages of rapid reconstruction without heavy computation during post-processing. The principle and the experimental setup of the SLSIS are described in detail. The image registration, Stokes spectral reconstruction and calibration procedures are included, and the system is validated using measurements of tungsten light and a static scene. The SLSIS's snapshot ability to resolve polarization spectral signatures is demonstrated using measurements of a dynamic scene.

Snapshot linear-Stokes imaging spectropolarimeter using division-of-focal-plane polarimetry and integral field spectroscopy

PubMed Central

Mu, Tingkui; Pacheco, Shaun; Chen, Zeyu; Zhang, Chunmin; Liang, Rongguang

2017-01-01

In this paper, the design and experimental demonstration of a snapshot linear-Stokes imaging spectropolarimeter (SLSIS) is presented. The SLSIS, which is based on division-of-focal-plane polarimetry with four parallel linear polarization channels and integral field spectroscopy with numerous slit dispersive paths, has no moving parts and provides video-rate Stokes-vector hyperspectral datacubes. It does not need any scanning in the spectral, spatial or polarization dimension and offers significant advantages of rapid reconstruction without heavy computation during post-processing. The principle and the experimental setup of the SLSIS are described in detail. The image registration, Stokes spectral reconstruction and calibration procedures are included, and the system is validated using measurements of tungsten light and a static scene. The SLSIS’s snapshot ability to resolve polarization spectral signatures is demonstrated using measurements of a dynamic scene. PMID:28191819

A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

PubMed

Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

2010-02-01

Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

On entanglement of light and Stokes parameters

NASA Astrophysics Data System (ADS)

Żukowski, Marek; Laskowski, Wiesław; Wieśniak, Marcin

2016-08-01

We present a new approach to Stokes parameters, which enables one to see better non-classical properties of bright quantum light, and of undefined overall photon numbers. The crucial difference is as follows. The standard quantum optical Stokes parameters are averages of differences of intensities of light registered at the two exits of polarization analyzers, and one gets their normalized version by dividing them by the average total intensity. The new ones are averages of the registered normalized Stokes parameters, for the duration of the experiment. That is, we redefine each Stokes observable as the difference of photon number operators at the two exits of a polarizing beam splitter multiplied by the inverse of their sum. The vacuum eigenvalue of the operator is defined a zero. We show that with such an approach one can obtain more sensitive entanglement indicators based on polarization measurements.

Incompressible limit of the degenerate quantum compressible Navier-Stokes equations with general initial data

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam; Li, Fucai

2018-03-01

In this paper we study the incompressible limit of the degenerate quantum compressible Navier-Stokes equations in a periodic domain T3 and the whole space R3 with general initial data. In the periodic case, by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity, we prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations converge to the strong solution of the incompressible Navier-Stokes equations. Our results improve considerably the ones obtained by Yang, Ju and Yang [25] where only the well-prepared initial data case is considered. While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given.

The Prediction of Scattered Broadband Shock-Associated Noise

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2015-01-01

A mathematical model is developed for the prediction of scattered broadband shock-associated noise. Model arguments are dependent on the vector Green's function of the linearized Euler equations, steady Reynolds-averaged Navier-Stokes solutions, and the two-point cross-correlation of the equivalent source. The equivalent source is dependent on steady Reynolds-averaged Navier-Stokes solutions of the jet flow, that capture the nozzle geometry and airframe surface. Contours of the time-averaged streamwise velocity component and turbulent kinetic energy are examined with varying airframe position relative to the nozzle exit. Propagation effects are incorporated by approximating the vector Green's function of the linearized Euler equations. This approximation involves the use of ray theory and an assumption that broadband shock-associated noise is relatively unaffected by the refraction of the jet shear layer. A non-dimensional parameter is proposed that quantifies the changes of the broadband shock-associated noise source with varying jet operating condition and airframe position. Scattered broadband shock-associated noise possesses a second set of broadband lobes that are due to the effect of scattering. Presented predictions demonstrate relatively good agreement compared to a wide variety of measurements.

Understanding the dimensional and mechanical properties of coastal Langmuir Circulations

NASA Astrophysics Data System (ADS)

Shrestha, Kalyan; Kuehl, Joseph; Anderson, William

2017-11-01

Non-linear interaction of surface waves and wind-driven shear instability in the upper ocean mixed layer form counter-rotating vortical structures called Langmuir Circulations. This oceanic microscale turbulence is one of the key contributors of mixing and vertical transport in the upper ocean mixed layer. Langmuir turbulence in the open (deep) ocean has already been the topic of a large research effort. However, coastal Langmuir cells are distinctly different from Langmuir cells in open-ocean regions, where additional bottom-boundary layer shear alters the kinematic properties of Langmuir cells. For this study, we have conducted a wide-ranging numerical study (solving the grid-filtered Craik-Leibovich equations) of coastal Langmuir turbulence, assessing which parameters affect Langmuir cells and defining the parametric hierarchy. The Stokes profile (aggregate velocity due to orbital wave motion) is functionally dependent on Stokes drift velocity and wavenumber of the surface waves. We explain that these parameters, which correspond to the environmental forcing variables, control the horizontal and vertical length scales of Langmuir cell respectively. This result is important in understanding the transport and dispersion of materials in the upper mixed layer of coastal ocean. We argue that wind stress is a parameter governing the strength of Langmuir cells.

Bayesian parameter estimation of a k-ε model for accurate jet-in-crossflow simulations

DOE PAGES

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan; ...

2016-05-31

Reynolds-averaged Navier–Stokes models are not very accurate for high-Reynolds-number compressible jet-in-crossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-averaged Navier–Stokes model. In this study, the hypothesis is pursued that Reynolds-averaged Navier–Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow.

Complete Stokes polarimetry of magneto-optical Faraday effect in a terbium gallium garnet crystal at cryogenic temperatures.

PubMed

Majeed, Hassaan; Shaheen, Amrozia; Anwar, Muhammad Sabieh

2013-10-21

We report the complete determination of the polarization changes caused in linearly polarized incident light due to propagation in a magneto-optically active terbium gallium garnet (TGG) single crystal, at temperatures ranging from 6.3 to 300 K. A 28-fold increase in the Verdet constant of the TGG crystal is seen as its temperature decreases to 6.3 K. In contrast with polarimetry of light emerging from a Faraday material at room temperature, polarimetry at cryogenic temperatures cannot be carried out using the conventional fixed polarizer-analyzer technique because the assumption that ellipticity is negligible becomes increasingly invalid as temperature is lowered. It is shown that complete determination of light polarization in such a case requires the determination of its Stokes parameters, otherwise inaccurate measurements will result with negative implications for practical devices.

Exact Solutions for Stokes' Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach

NASA Astrophysics Data System (ADS)

Aziz, Taha; Aziz, A.; Khalique, C. M.

2016-07-01

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

Uncertainties of atmospheric polarimetric measurements with sun-sky radiometers induced by errors of relative orientations of polarizers

NASA Astrophysics Data System (ADS)

Li, Li; Li, Zhengqiang; Li, Kaitao; Sun, Bin; Wu, Yanke; Xu, Hua; Xie, Yisong; Goloub, Philippe; Wendisch, Manfred

2018-04-01

In this study errors of the relative orientations of polarizers in the Cimel polarized sun-sky radiometers are measured and introduced into the Mueller matrix of the instrument. The linearly polarized light with different polarization directions from 0° to 180° (or 360°) is generated by using a rotating linear polarizer in front of an integrating sphere. Through measuring the referential linearly polarized light, the errors of relative orientations of polarizers are determined. The efficiencies of the polarizers are obtained simultaneously. By taking the error of relative orientation into consideration in the Mueller matrix, the accuracies of the calculated Stokes parameters, the degree of linear polarization, and the angle of polarization are remarkably improved. The method may also apply to other polarization instruments of similar types.

Including fluid shear viscosity in a structural acoustic finite element model using a scalar fluid representation

PubMed Central

Cheng, Lei; Li, Yizeng; Grosh, Karl

2013-01-01

An approximate boundary condition is developed in this paper to model fluid shear viscosity at boundaries of coupled fluid-structure system. The effect of shear viscosity is approximated by a correction term to the inviscid boundary condition, written in terms of second order in-plane derivatives of pressure. Both thin and thick viscous boundary layer approximations are formulated; the latter subsumes the former. These approximations are used to develop a variational formation, upon which a viscous finite element method (FEM) model is based, requiring only minor modifications to the boundary integral contributions of an existing inviscid FEM model. Since this FEM formulation has only one degree of freedom for pressure, it holds a great computational advantage over the conventional viscous FEM formulation which requires discretization of the full set of linearized Navier-Stokes equations. The results from thick viscous boundary layer approximation are found to be in good agreement with the prediction from a Navier-Stokes model. When applicable, thin viscous boundary layer approximation also gives accurate results with computational simplicity compared to the thick boundary layer formulation. Direct comparison of simulation results using the boundary layer approximations and a full, linearized Navier-Stokes model are made and used to evaluate the accuracy of the approximate technique. Guidelines are given for the parameter ranges over which the accurate application of the thick and thin boundary approximations can be used for a fluid-structure interaction problem. PMID:23729844

Including fluid shear viscosity in a structural acoustic finite element model using a scalar fluid representation.

PubMed

Cheng, Lei; Li, Yizeng; Grosh, Karl

2013-08-15

An approximate boundary condition is developed in this paper to model fluid shear viscosity at boundaries of coupled fluid-structure system. The effect of shear viscosity is approximated by a correction term to the inviscid boundary condition, written in terms of second order in-plane derivatives of pressure. Both thin and thick viscous boundary layer approximations are formulated; the latter subsumes the former. These approximations are used to develop a variational formation, upon which a viscous finite element method (FEM) model is based, requiring only minor modifications to the boundary integral contributions of an existing inviscid FEM model. Since this FEM formulation has only one degree of freedom for pressure, it holds a great computational advantage over the conventional viscous FEM formulation which requires discretization of the full set of linearized Navier-Stokes equations. The results from thick viscous boundary layer approximation are found to be in good agreement with the prediction from a Navier-Stokes model. When applicable, thin viscous boundary layer approximation also gives accurate results with computational simplicity compared to the thick boundary layer formulation. Direct comparison of simulation results using the boundary layer approximations and a full, linearized Navier-Stokes model are made and used to evaluate the accuracy of the approximate technique. Guidelines are given for the parameter ranges over which the accurate application of the thick and thin boundary approximations can be used for a fluid-structure interaction problem.

A nonperturbative approximation for the moderate Reynolds number Navier–Stokes equations

PubMed Central

Roper, Marcus; Brenner, Michael P.

2009-01-01

The nonlinearity of the Navier–Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier–Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes. PMID:19211800

A nonperturbative approximation for the moderate Reynolds number Navier-Stokes equations.

PubMed

Roper, Marcus; Brenner, Michael P

2009-03-03

The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.

An infrared polarimetric study of sunspots

NASA Astrophysics Data System (ADS)

Hewagama, Tilak

A polarimetric study of the extremely Zeeman sensitive 12.32 microns neutral magnesium (Mg I) emission line from sunspots is discussed. A single blocked impurity band (BIB) detector in a cryogenic grating postdisperser was used to limit the McMath Fourier transform spectrometer (FTS) bandpass and obtain high signal/noise spectra at 0.005 cm-1 spectral resolution with 4.5 sec spatial resolution. A polarization analyzer preceded the FTS and consisted of an anti-reflection coated CdS 1/4 waveplate and a thin film Ge linear polarizer. A second 1/4 waveplate was mounted at 45 deg to the linear polarizer to eliminate dependence on the polarization properties of the FTS optics and postdisperser grating. The instrument polarization introduced by the McMath telescope is shown to be negligible for the purpose of 12 microns polarimetry, and theoretical arguments are presented to show that the 12 microns observations are not corrupted by magneto-optical effects. Stokes I,Q,U, and V profiles were generated by subtracting successive interferograms. The time resolution of a set of Stokes parameters was 12 minutes. Within the sunspot the Zeeman triplet was fully resolved. Since the line is optically thin, it was possible to derive vector fields by non-linear least squares fits of the Seares formulae to the observed Stokes profiles. The observations of a visually symmetric sunspot (23-28 Oct. 1989) show that the 12 microns emission is completely polarized. This implies that the sunspot magnetic field at the 12 microns altitude is not filamentary in the sense of containing field-free regions nor is there cancellation of field, over any spatial scale, in the beam area. The sunspot field strength varied from 2050 G in the umbra to 650 G at the outer penumbral edge, and the magnetic structure extended well beyond the photometric edge of the sunspot. Vector magnetograms obtained for the same spot by the Haleakala Stokes polarimeter, operating at 6302.5 A, show an umbral field strength which is larger by 400 G. On this basis the altitude of formation for the Mg I line is estimated to be approximately 600 km above tau approximately 1 for the 6302.5 A line.

Ortho-Babinet polarization-interrogating filter: an interferometric approach to polarization measurement.

PubMed

Van Delden, Jay S

2003-07-15

A novel, interferometric, polarization-interrogating filter assembly and method for the simultaneous measurement of all four Stokes parameters across a partially polarized irradiance image in a no-moving-parts, instantaneous, highly sensitive manner is described. In the reported embodiment of the filter, two spatially varying linear retarders and a linear polarizer comprise an ortho-Babinet, polarization-interrogating (OBPI) filter. The OBPI filter uniquely encodes the incident ensemble of electromagnetic wave fronts comprising a partially polarized irradiance image in a controlled, deterministic, spatially varying manner to map the complete state of polarization across the image to local variations in a superposed interference pattern. Experimental interferograms are reported along with a numerical simulation of the method.

Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.

PubMed

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

The probability density function (PDF) of Lagrangian Turbulence

NASA Astrophysics Data System (ADS)

Birnir, B.

2012-12-01

The statistical theory of Lagrangian turbulence is derived from the stochastic Navier-Stokes equation. Assuming that the noise in fully-developed turbulence is a generic noise determined by the general theorems in probability, the central limit theorem and the large deviation principle, we are able to formulate and solve the Kolmogorov-Hopf equation for the invariant measure of the stochastic Navier-Stokes equations. The intermittency corrections to the scaling exponents of the structure functions require a multiplicative (multipling the fluid velocity) noise in the stochastic Navier-Stokes equation. We let this multiplicative noise, in the equation, consists of a simple (Poisson) jump process and then show how the Feynmann-Kac formula produces the log-Poissonian processes, found by She and Leveque, Waymire and Dubrulle. These log-Poissonian processes give the intermittency corrections that agree with modern direct Navier-Stokes simulations (DNS) and experiments. The probability density function (PDF) plays a key role when direct Navier-Stokes simulations or experimental results are compared to theory. The statistical theory of turbulence is determined, including the scaling of the structure functions of turbulence, by the invariant measure of the Navier-Stokes equation and the PDFs for the various statistics (one-point, two-point, N-point) can be obtained by taking the trace of the corresponding invariant measures. Hopf derived in 1952 a functional equation for the characteristic function (Fourier transform) of the invariant measure. In distinction to the nonlinear Navier-Stokes equation, this is a linear functional differential equation. The PDFs obtained from the invariant measures for the velocity differences (two-point statistics) are shown to be the four parameter generalized hyperbolic distributions, found by Barndorff-Nilsen. These PDF have heavy tails and a convex peak at the origin. A suitable projection of the Kolmogorov-Hopf equations is the differential equation determining the generalized hyperbolic distributions. Then we compare these PDFs with DNS results and experimental data.

Experimental Observation of Near-Field Deterioration Induced by Stimulated Rotational Raman Scattering in Long Air Paths

NASA Astrophysics Data System (ADS)

Wang, Jing; Zhang, Xiao-Min; Han, Wei; Li, Fu-Quan; Zhou, Li-Dan; Feng, Bin; Xiang, Yong

2011-08-01

We report the experimental investigation of a stimulated rotational Raman scattering effect in long air paths on SG-III TIL, with a 1053 nm, 20-cm-diameter, linearly polarized, 3 ns flat-topped laser pulse. An intense speckle pattern of near field with thickly dotted hot spots is observed at the end of propagation with an intensity-length product above 17TW/cm. The Stokes developing from the scattering of the laser beam by quantum fluctuations is characterized by a combination of high spatial frequency components. The observed speckle pattern with small-diameter hot spots results from the combination of the nonlinear Raman amplification and the linear diffraction propagation effect of the Stokes with a noise pattern arising from the spontaneous Raman scattering. A new promising suppression concept based on the special characteristic of the Stokes, called active and selective filtering of Stokes, is proposed.

Calculations of High-Temperature Jet Flow Using Hybrid Reynolds-Average Navier-Stokes Formulations

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Elmiligui, Alaa; Giriamaji, Sharath S.

2008-01-01

Two multiscale-type turbulence models are implemented in the PAB3D solver. The models are based on modifying the Reynolds-averaged Navier Stokes equations. The first scheme is a hybrid Reynolds-averaged- Navier Stokes/large-eddy-simulation model using the two-equation k(epsilon) model with a Reynolds-averaged-Navier Stokes/large-eddy-simulation transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier Stokes model in which the unresolved kinetic energy parameter f(sub k) is allowed to vary as a function of grid spacing and the turbulence length scale. This parameter is estimated based on a novel two-stage procedure to efficiently estimate the level of scale resolution possible for a given flow on a given grid for partially averaged Navier Stokes. It has been found that the prescribed scale resolution can play a major role in obtaining accurate flow solutions. The parameter f(sub k) varies between zero and one and is equal to one in the viscous sublayer and when the Reynolds-averaged Navier Stokes turbulent viscosity becomes smaller than the large-eddy-simulation viscosity. The formulation, usage methodology, and validation examples are presented to demonstrate the enhancement of PAB3D's time-accurate turbulence modeling capabilities. The accurate simulations of flow and turbulent quantities will provide a valuable tool for accurate jet noise predictions. Solutions from these models are compared with Reynolds-averaged Navier Stokes results and experimental data for high-temperature jet flows. The current results show promise for the capability of hybrid Reynolds-averaged Navier Stokes and large eddy simulation and partially averaged Navier Stokes in simulating such flow phenomena.

Fully Polarimetric Passive W-band Millimeter Wave Imager for Wide Area Search

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tedeschi, Jonathan R.; Bernacki, Bruce E.; Sheen, David M.

2013-09-27

We describe the design and phenomenology imaging results of a fully polarimetric W-band millimeter wave (MMW) radiometer developed by Pacific Northwest National Laboratory for wide-area search. Operating from 92 - 94 GHz, the W-band radiometer employs a Dicke switching heterodyne design isolating the horizontal and vertical mm-wave components with 40 dB of polarization isolation. Design results are presented for both infinite conjugate off-axis parabolic and finite conjugate off-axis elliptical fore-optics using optical ray tracing and diffraction calculations. The received linear polarizations are down-converted to a microwave frequency band and recombined in a phase-shifting network to produce all six orthogonal polarizationmore » states of light simultaneously, which are used to calculate the Stokes parameters for display and analysis. The resulting system performance produces a heterodyne receiver noise equivalent delta temperature (NEDT) of less than 150m Kelvin. The radiometer provides novel imaging capability by producing all four of the Stokes parameters of light, which are used to create imagery based on the polarization states associated with unique scattering geometries and their interaction with the down welling MMW energy. The polarization states can be exploited in such a way that man-made objects can be located and highlighted in a cluttered scene using methods such as image comparison, color encoding of Stokes parameters, multivariate image analysis, and image fusion with visible and infrared imagery. We also present initial results using a differential imaging approach used to highlight polarization features and reduce common-mode noise. Persistent monitoring of a scene using the polarimetric passive mm-wave technique shows great promise for anomaly detection caused by human activity.« less

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

PubMed Central

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. PMID:24235888

Third Stokes parameter emission from a periodic water surface

NASA Technical Reports Server (NTRS)

Johnson, J. T.; Kong, J. A.; Shin, R. T.; Staelin, D. H.; Oneill, K.; Lohanick, A.

1991-01-01

An experiment in which the third Stokes parameter thermal emission from a periodic water surface was measured is documented. This parameter is shown to be related to the direction of periodicity of the periodic surface and to approach brightnesses of up to 30 K at X band for the surface used in the experiment. The surface actually analyzed was a 'two-layer' periodic surface; the theory of thermal emission from such a surface is derived and the theoretical results are found to be in good agreement with the experimental measurements. These results further the idea of using the third Stokes parameter emission as an indicator of wind direction over the ocean.

Fibrous filter efficiency and pressure drop in the viscous-inertial transition flow regime.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanchez, Andres L.; Brockmann, John E.; Dellinger, Jennifer Gwynne

2011-10-01

Fibrous filter pressure drop and aerosol collection efficiency were measured at low air pressures (0.2 to 0.8 atm) and high face velocities (5 to 20 meters per second) to give fiber Reynolds numbers in the viscous-inertial transition flow regime (1 to 16). In this regime, contemporary filtration theory based on Kuwabara's viscous flow through an ensemble of fibers under-predicts single fiber impaction by several orders of magnitude. Streamline curvature increases substantially as inertial forces become dominant. Dimensionless pressure drop measurements followed the viscous-inertial theory of Robinson and Franklin rather than Darcy's linear pressure-velocity relationship (1972). Sodium chloride and iron nano-agglomeratemore » test aerosols were used to evaluate the effects of particle density and shape factor. Total filter efficiency collapsed when plotted against the particle Stokes and fiber Reynolds numbers. Efficiencies were then fitted with an impactor type equation where the cutpoint Stokes number and a steepness parameter described data well in the sharply increasing portion of the curve (20% to 80% efficiency). The cutpoint Stokes number was a linearly decreasing function of fiber Reynolds number. Single fiber efficiencies were calculated from total filter efficiencies and compared to contemporary viscous flow impaction theory (Stechkina et al. 1969), and numerical simulations from the literature. Existing theories under-predicted measured single fiber efficiencies although the assumption of uniform flow conditions for each successive layer of fibers is questionable; the common exponential relationship between single fiber efficiency and total filter efficiency may not be appropriate in this regime.« less

Polarimetric image reconstruction algorithms

NASA Astrophysics Data System (ADS)

Valenzuela, John R.

In the field of imaging polarimetry Stokes parameters are sought and must be inferred from noisy and blurred intensity measurements. Using a penalized-likelihood estimation framework we investigate reconstruction quality when estimating intensity images and then transforming to Stokes parameters (traditional estimator), and when estimating Stokes parameters directly (Stokes estimator). We define our cost function for reconstruction by a weighted least squares data fit term and a regularization penalty. It is shown that under quadratic regularization, the traditional and Stokes estimators can be made equal by appropriate choice of regularization parameters. It is empirically shown that, when using edge preserving regularization, estimating the Stokes parameters directly leads to lower RMS error in reconstruction. Also, the addition of a cross channel regularization term further lowers the RMS error for both methods especially in the case of low SNR. The technique of phase diversity has been used in traditional incoherent imaging systems to jointly estimate an object and optical system aberrations. We extend the technique of phase diversity to polarimetric imaging systems. Specifically, we describe penalized-likelihood methods for jointly estimating Stokes images and optical system aberrations from measurements that contain phase diversity. Jointly estimating Stokes images and optical system aberrations involves a large parameter space. A closed-form expression for the estimate of the Stokes images in terms of the aberration parameters is derived and used in a formulation that reduces the dimensionality of the search space to the number of aberration parameters only. We compare the performance of the joint estimator under both quadratic and edge-preserving regularization. The joint estimator with edge-preserving regularization yields higher fidelity polarization estimates than with quadratic regularization. Under quadratic regularization, using the reduced-parameter search strategy, accurate aberration estimates can be obtained without recourse to regularization "tuning". Phase-diverse wavefront sensing is emerging as a viable candidate wavefront sensor for adaptive-optics systems. In a quadratically penalized weighted least squares estimation framework a closed form expression for the object being imaged in terms of the aberrations in the system is available. This expression offers a dramatic reduction of the dimensionality of the estimation problem and thus is of great interest for practical applications. We have derived an expression for an approximate joint covariance matrix for object and aberrations in the phase diversity context. Our expression for the approximate joint covariance is compared with the "known-object" Cramer-Rao lower bound that is typically used for system parameter optimization. Estimates of the optimal amount of defocus in a phase-diverse wavefront sensor derived from the joint-covariance matrix, the known-object Cramer-Rao bound, and Monte Carlo simulations are compared for an extended scene and a point object. It is found that our variance approximation, that incorporates the uncertainty of the object, leads to an improvement in predicting the optimal amount of defocus to use in a phase-diverse wavefront sensor.

Passive millimeter wave differential interference contrast polarimetry

DOEpatents

Bernacki, Bruce E; Kelly, James F; Sheen, David M; Tedeschi, Jonathan R; Hall, Thomas E; Hatchell, Brian K; Valdez, Patrick; McMakin, Douglas L

2014-04-29

Differential polarization imaging systems include an axicon configured to provide a displacement of ray bundles associated with different image patches. The displaced ray bundles are directed to antenna horns and orthomode transducers so as to provide outputs correspond to orthogonal linear states of polarization (SOPs). The outputs are directed to a differential radiometer so that Stokes parameter differences between image patches can be obtained. The ray bundle displacements can be selected to correspond to a mechanical spacing of antenna horns. In some examples, ray bundle displacement corresponds to a displacement less than the diffraction limit.

Dynamic heterogeneity in crossover spin facilitated model of supercooled liquid and fractional Stokes-Einstein relation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Seo-Woo; Kim, Soree; Jung, YounJoon, E-mail: yjjung@snu.ac.kr

Kinetically constrained models have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many experiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong liquid-like behavior and the fragile liquid-like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einsteinmore » relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the Frederickson-Andersen model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.« less

Computed and Experimental Flutter/LCO Onset for the Boeing Truss-Braced Wing Wind-Tunnel Model

NASA Technical Reports Server (NTRS)

Bartels, Robert E.; Scott, Robert C.; Funk, Christie J.; Allen, Timothy J.; Sexton, Bradley W.

2014-01-01

This paper presents high fidelity Navier-Stokes simulations of the Boeing Subsonic Ultra Green Aircraft Research truss-braced wing wind-tunnel model and compares the results to linear MSC. Nastran flutter analysis and preliminary data from a recent wind-tunnel test of that model at the NASA Langley Research Center Transonic Dynamics Tunnel. The simulated conditions under consideration are zero angle of attack, so that structural nonlinearity can be neglected. It is found that, for Mach number greater than 0.78, the linear flutter analysis predicts flutter onset dynamic pressure below the wind-tunnel test and that predicted by the Navier-Stokes analysis. Furthermore, the wind-tunnel test revealed that the majority of the high structural dynamics cases were wing limit cycle oscillation (LCO) rather than flutter. Most Navier-Stokes simulated cases were also LCO rather than hard flutter. There is dip in the wind-tunnel test flutter/LCO onset in the Mach 0.76-0.80 range. Conditions tested above that Mach number exhibited no aeroelastic instability at the dynamic pressures reached in the tunnel. The linear flutter analyses do not show a flutter/LCO dip. The Navier-Stokes simulations also do not reveal a dip; however, the flutter/LCO onset is at a significantly higher dynamic pressure at Mach 0.90 than at lower Mach numbers. The Navier-Stokes simulations indicate a mild LCO onset at Mach 0.82, then a more rapidly growing instability at Mach 0.86 and 0.90. Finally, the modeling issues and their solution related to the use of a beam and pod finite element model to generate the Navier-Stokes structure mode shapes are discussed.

A proposed standard method for polarimetric calibration and calibration verification

NASA Astrophysics Data System (ADS)

Persons, Christopher M.; Jones, Michael W.; Farlow, Craig A.; Morell, L. Denise; Gulley, Michael G.; Spradley, Kevin D.

2007-09-01

Accurate calibration of polarimetric sensors is critical to reducing and analyzing phenomenology data, producing uniform polarimetric imagery for deployable sensors, and ensuring predictable performance of polarimetric algorithms. It is desirable to develop a standard calibration method, including verification reporting, in order to increase credibility with customers and foster communication and understanding within the polarimetric community. This paper seeks to facilitate discussions within the community on arriving at such standards. Both the calibration and verification methods presented here are performed easily with common polarimetric equipment, and are applicable to visible and infrared systems with either partial Stokes or full Stokes sensitivity. The calibration procedure has been used on infrared and visible polarimetric imagers over a six year period, and resulting imagery has been presented previously at conferences and workshops. The proposed calibration method involves the familiar calculation of the polarimetric data reduction matrix by measuring the polarimeter's response to a set of input Stokes vectors. With this method, however, linear combinations of Stokes vectors are used to generate highly accurate input states. This allows the direct measurement of all system effects, in contrast with fitting modeled calibration parameters to measured data. This direct measurement of the data reduction matrix allows higher order effects that are difficult to model to be discovered and corrected for in calibration. This paper begins with a detailed tutorial on the proposed calibration and verification reporting methods. Example results are then presented for a LWIR rotating half-wave retarder polarimeter.

Methods and means of Fourier-Stokes polarimetry and the spatial frequency filtering of phase anisotropy manifestations

NASA Astrophysics Data System (ADS)

Novakovskaya, O. Yu.; Ushenko, A. G.; Dubolazov, A. V.; Ushenko, V. A.; Ushenko, Yu. A.; Sakhnovskiy, M. Yu.; Soltys, I. V.; Zhytaryuk, V. H.; Olar, O. V.; Sidor, M.; Gorsky, M. P.

2016-12-01

The theoretical background of azimuthally stable method of Jones-matrix mapping of histological sections of biopsy of myocardium tissue on the basis of spatial frequency selection of the mechanisms of linear and circular birefringence is presented. The diagnostic application of a new correlation parameter - complex degree of mutual anisotropy - is analytically substantiated. The method of measuring coordinate distributions of complex degree of mutual anisotropy with further spatial filtration of their high- and low-frequency components is developed. The interconnections of such distributions with parameters of linear and circular birefringence of myocardium tissue histological sections are found. The comparative results of measuring the coordinate distributions of complex degree of mutual anisotropy formed by fibrillar networks of myosin fibrils of myocardium tissue of different necrotic states - dead due to coronary heart disease and acute coronary insufficiency are shown. The values and ranges of change of the statistical (moments of the 1st - 4th order) parameters of complex degree of mutual anisotropy coordinate distributions are studied. The objective criteria of differentiation of cause of death are determined.

Nonlinear travelling waves in rotating Hagen–Poiseuille flow

NASA Astrophysics Data System (ADS)

Pier, Benoît; Govindarajan, Rama

2018-03-01

The dynamics of viscous flow through a rotating pipe is considered. Small-amplitude stability characteristics are obtained by linearizing the Navier–Stokes equations around the base flow and solving the resulting eigenvalue problems. For linearly unstable configurations, the dynamics leads to fully developed finite-amplitude perturbations that are computed by direct numerical simulations of the complete Navier–Stokes equations. By systematically investigating all linearly unstable combinations of streamwise wave number k and azimuthal mode number m, for streamwise Reynolds numbers {{Re}}z ≤slant 500 and rotational Reynolds numbers {{Re}}{{Ω }} ≤slant 500, the complete range of nonlinear travelling waves is obtained and the associated flow fields are characterized.

Formulating viscous hydrodynamics for large velocity gradients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pratt, Scott

2008-02-15

Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity gradients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, which treat the spatial components of the stress-energy tensor {tau}{sub ij} as dynamical objects, introduce new parameters, such as the relaxation times describing nonequilibrium behavior of the elements {tau}{sub ij}. By considering linear response theory and entropy constraints, we show how the additional parameters are related to fluctuations of {tau}{sub ij}. Furthermore, the Israel-Stewart parameters are analyzed for their ability to provide stable and physical solutions for sound waves.more » Finally, it is shown how these parameters, which are naturally described by correlation functions in real time, might be constrained by lattice calculations, which are based on path-integral formulations in imaginary time.« less

Effect of solvent hydrogen bonding on the photophysical properties of intramolecular charge transfer probe trans-ethyl p-(dimethylamino) cinamate and its derivative

NASA Astrophysics Data System (ADS)

Singh, T. Sanjoy; Moyon, N. S.; Mitra, Sivaprasad

2009-08-01

Intramolecular charge transfer (ICT) behavior of trans-ethyl p-(dimethylamino) cinamate (EDAC) and 4-(dimethylamino) cinnamic acid (DMACA) were studied by steady state absorption and emission, picosecond time-resolved fluorescence experiments in various pure and mixed solvent systems. The large fluorescence spectral shift in more polar solvents indicates an efficient charge transfer from the donor site to the acceptor moiety in the excited state compared to the ground state. The energy for 0,0 transition ( ν0,0) for EDAC shows very good linear correlation with static solvent dielectric property; however, fluorescence emission maximum, stokes shift and fluorescence quantum yield show significant deviation from linearity in polar protic solvents, indicating a large contribution of solvent hydrogen bonding on the excited state relaxation mechanism. A quantitative estimation of contribution from different solvatochromic parameters was made using linear free energy relationship based on Kamlet-Taft equation.

Solving the aerodynamics of fungal flight: How air viscosity slows spore motion

PubMed Central

Fischer, Mark W. F.; Stolze-Rybczynski, Jessica L.; Davis, Diana J.; Cui, Yunluan; Money, Nicholas P.

2010-01-01

Viscous drag causes the rapid deceleration of fungal spores after high-speed launches and limits discharge distance. Stokes' law posits a linear relationship between drag force and velocity. It provides an excellent fit to experimental measurements of the terminal velocity of free-falling spores and other instances of low Reynolds number motion (Re<1). More complex, non-linear drag models have been devised for movements characterized by higher Re, but their effectiveness for modeling the launch of fast-moving fungal spores has not been tested. In this paper, we use data on spore discharge processes obtained from ultra-high-speed video recordings to evaluate the effects of air viscosity predicted by Stokes' law and a commonly used non-linear drag model. We find that discharge distances predicted from launch speeds by Stokes' model provide a much better match to measured distances than estimates from the more complex drag model. Stokes' model works better over a wide range projectile sizes, launch speeds, and discharge distances, from microscopic mushroom ballistospores discharged at <1 m/s over a distance of <0.1 mm (Re<1.0), to macroscopic sporangia of Pilobolus that are launched at >10 m/s and travel as far as 2.5 m (Re>100). PMID:21036338

Linear Polarization, Circular Polarization, and Depolarization of Gamma-ray Bursts: A Simple Case of Jitter Radiation

NASA Astrophysics Data System (ADS)

Mao, Jirong; Wang, Jiancheng

2017-04-01

Linear and circular polarizations of gamma-ray bursts (GRBs) have been detected recently. We adopt a simplified model to investigate GRB polarization characteristics in this paper. A compressed two-dimensional turbulent slab containing stochastic magnetic fields is considered, and jitter radiation can produce the linear polarization under this special magnetic field topology. Turbulent Faraday rotation measure (RM) of this slab makes strong wavelength-dependent depolarization. The jitter photons can also scatter with those magnetic clumps inside the turbulent slab, and a nonzero variance of the Stokes parameter V can be generated. Furthermore, the linearly and circularly polarized photons in the optical and radio bands may suffer heavy absorptions from the slab. Thus we consider the polarized jitter radiation transfer processes. Finally, we compare our model results with the optical detections of GRB 091018, GRB 121024A, and GRB 131030A. We suggest simultaneous observations of GRB multi-wavelength polarization in the future.

The Stability Region for Feedback Control of the Wake Behind Twin Oscillating Cylinders

NASA Astrophysics Data System (ADS)

Borggaard, Jeff; Gugercin, Serkan; Zietsman, Lizette

2016-11-01

Linear feedback control has the ability to stabilize vortex shedding behind twin cylinders where cylinder rotation is the actuation mechanism. Complete elimination of the wake is only possible for certain Reynolds numbers and cylinder spacing. This is related to the presence of asymmetric unstable modes in the linearized system. We investigate this region of parameter space using a number of closed-loop simulations that bound this region. We then consider the practical issue of designing feedback controls based on limited state measurements by building a nonlinear compensator using linear robust control theory with and incorporating the nonlinear terms in the compensator (e.g., using the extended Kalman filter). Interpolatory model reduction methods are applied to the large discretized, linearized Navier-Stokes system and used for computing the control laws and compensators. Preliminary closed-loop simulations of a three-dimensional version of this problem will also be presented. Supported in part by the National Science Foundation.

Linear Polarization, Circular Polarization, and Depolarization of Gamma-ray Bursts: A Simple Case of Jitter Radiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mao, Jirong; Wang, Jiancheng, E-mail: jirongmao@mail.ynao.ac.cn

Linear and circular polarizations of gamma-ray bursts (GRBs) have been detected recently. We adopt a simplified model to investigate GRB polarization characteristics in this paper. A compressed two-dimensional turbulent slab containing stochastic magnetic fields is considered, and jitter radiation can produce the linear polarization under this special magnetic field topology. Turbulent Faraday rotation measure (RM) of this slab makes strong wavelength-dependent depolarization. The jitter photons can also scatter with those magnetic clumps inside the turbulent slab, and a nonzero variance of the Stokes parameter V can be generated. Furthermore, the linearly and circularly polarized photons in the optical and radiomore » bands may suffer heavy absorptions from the slab. Thus we consider the polarized jitter radiation transfer processes. Finally, we compare our model results with the optical detections of GRB 091018, GRB 121024A, and GRB 131030A. We suggest simultaneous observations of GRB multi-wavelength polarization in the future.« less

Polarization Rotation and the Third Stokes Parameter: The Effects of Spacecraft Attitude and Faraday Rotation

NASA Technical Reports Server (NTRS)

Meissner, Thomas; Wentz, Frank J.

2006-01-01

The third Stokes parameter of ocean surface brightness temperatures measured by the WindSat instrument is sensitive to the rotation angle between the polarization vectors at the ocean surface and the instrument. This rotation angle depends on the spacecraft attitude (roll, pitch, yaw) as well as the Faraday rotation of the electromagnetic radiation passing through the Earth's ionosphere. Analyzing the WindSat antenna temperatures, we find biases in the third Stokes parameter as function of the along-scan position of up to 1.5 K in all feedhorns. This points to a misspecification of the reported spacecraft attitude. A single attitude correction of -0.16deg roll and 0.18deg pitch for the whole instrument eliminates all the biases. We also study the effect of Faraday rotation at 10.7 GHz on the accuracy of the third Stokes parameter and the sea surface wind direction retrieval and demonstrate how this error can be corrected using values from the International Reference Ionosphere for the total electron content when computing Faraday rotation.

Thermal radiation from optically driven Kerr (χ{sup (3)}) photonic cavities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khandekar, Chinmay; Rodriguez, Alejandro W.; Lin, Zin

2015-04-13

We describe thermal radiation from nonlinear (χ{sup (3)}) photonic cavities coupled to external channels and subject to incident monochromatic light. Our work extends related work on nonlinear mechanical oscillators to the problem of thermal radiation, demonstrating that bistability can enhance thermal radiation by orders of magnitude and result in strong lineshape alternations, including “super-narrow spectral peaks” occurring at the onset of kinetic phase transitions. We show that when the cavities are designed to exhibit perfect linear emissivity (rate matching), such thermally activated transitions can be exploited to dramatically tune the output power and radiative properties of the cavity, leading tomore » a kind of Kerr-mediated thermo-optic effect. Finally, we demonstrate that in certain parameter regimes, the output radiation exhibits Stokes and anti-Stokes side peaks whose relative magnitudes can be altered by tuning the internal temperature of the cavity relative to its surroundings, a consequence of strong correlations and interference between the emitted and reflected radiation.« less

Global Mass Flux Solutions from GRACE: A Comparison of Parameter Estimation Strategies - Mass Concentrations Versus Stokes Coefficients

NASA Technical Reports Server (NTRS)

Rowlands, D. D.; Luthcke, S. B.; McCarthy J. J.; Klosko, S. M.; Chinn, D. S.; Lemoine, F. G.; Boy, J.-P.; Sabaka, T. J.

2010-01-01

The differences between mass concentration (mas con) parameters and standard Stokes coefficient parameters in the recovery of gravity infonnation from gravity recovery and climate experiment (GRACE) intersatellite K-band range rate data are investigated. First, mascons are decomposed into their Stokes coefficient representations to gauge the range of solutions available using each of the two types of parameters. Next, a direct comparison is made between two time series of unconstrained gravity solutions, one based on a set of global equal area mascon parameters (equivalent to 4deg x 4deg at the equator), and the other based on standard Stokes coefficients with each time series using the same fundamental processing of the GRACE tracking data. It is shown that in unconstrained solutions, the type of gravity parameter being estimated does not qualitatively affect the estimated gravity field. It is also shown that many of the differences in mass flux derivations from GRACE gravity solutions arise from the type of smoothing being used and that the type of smoothing that can be embedded in mas con solutions has distinct advantages over postsolution smoothing. Finally, a 1 year time series based on global 2deg equal area mascons estimated every 10 days is presented.

Stark problem in terms of the Stokes multipliers for the triconfluent Heun equation

NASA Astrophysics Data System (ADS)

Osherov, V. I.; Ushakov, V. G.

2013-11-01

The solution of the Stark problem is obtained in terms of the Stokes multipliers for the triconfluent Heun equation (the quartic oscillator equation). The Stokes multipliers are found in an analytical form at positive energies. For negative energies, the Stokes parameters are calculated in frames of a consistent asymptotic approach. The scattering phase, positions, and widths of the Stark resonances are determined as solutions of an implicit equation.

Third order nonlinear phenomena in silica solid and hollow whispering gallery mode resonators

NASA Astrophysics Data System (ADS)

Farnesi, D.; Barucci, A.; Berneschi, S.; Cosi, F.; Righini, G. C.; Nunzi Conti, G.; Soria, Silvia

2016-03-01

We report efficient generation of nonlinear phenomena related to third order optical non-linear susceptibility χ(3) interactions in resonant silica microspheres and microbubbles in the regime of normal dispersion. The interactions here reported are: Stimulated Raman Scattering (SRS), and four wave mixing processes comprising Stimulated Anti-stokes Raman Scattering (SARS) and comb generation. Unusually strong anti-Stokes components and extraordinarily symmetric spectra have been observed. Resonant SARS and SRS corresponding to different Raman bands were also observed. The lack of correlation between stimulated anti-stokes and stokes scattering spectra indicates that the signal has to be resonant with the cavity.

Full Stokes IQUV spectropolarimetry of AGB and post-AGB stars: probing surface magnetism and atmospheric dynamics

NASA Astrophysics Data System (ADS)

Lèbre, Agnès; Aurière, Michel; Fabas, Nicolas; Gillet, Denis; Josselin, Eric; Mathias, Philippe; Petit, Pascal

2015-10-01

Full Stokes spectropolarimetric observations of a Mira star (χ Cyg) and a RV Tauri star (R Sct) are presented and analyzed comparatively. From their Stokes V data (circular polarization), we report the detection of a weak magnetic field at the surface of these cool and evolved radially pulsating stars. For both stars, we analyse this detection in the framework of their complex atmospheric dynamics, with the possibility that shock waves may imprint an efficient compressive effect on the surface magnetic field. We also report strong Stokes U and Stokes Q signatures associated to metallic lines (as a global trend), those linear polarimetric features appear to be time variable along the pulsating phase. More surprising, in the Stokes U and Stokes Q data, we also detect signatures associated to individual metallic lines (such as Sr i 460.7 nm, Na D2 588.9 nm), that are known (from the solar case) to be easily polarizable in case of a global asymmetry at the photospheric level.

Polarization pattern of vector vortex beams generated by q-plates with different topological charges.

PubMed

Cardano, Filippo; Karimi, Ebrahim; Slussarenko, Sergei; Marrucci, Lorenzo; de Lisio, Corrado; Santamato, Enrico

2012-04-01

We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge q at its center (q-plate). The polarization topological structures for different q-plates and different input polarization states have been studied experimentally by measuring the Stokes parameters point-by-point in the beam transverse plane. Furthermore, we used a tuned q=1/2-plate to generate cylindrical vector beams with radial or azimuthal polarizations, with the possibility of switching dynamically between these two cases by simply changing the linear polarization of the input beam.

Vortex breakdown simulation - A circumspect study of the steady, laminar, axisymmetric model

NASA Technical Reports Server (NTRS)

Salas, M. D.; Kuruvila, G.

1989-01-01

The incompressible axisymmetric steady Navier-Stokes equations are written using the streamfunction-vorticity formulation. The resulting equations are discretized using a second-order central-difference scheme. The discretized equations are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers (based on vortex core radius) 100-1800 and swirl parameter 0.9-1.1. The effects of inflow boundary conditions, the location of farfield and outflow boundaries, and mesh refinement are examined. Finally, the stability of the steady solutions is investigated by solving the time-dependent equations.

Spin in Compton scattering with pronounced polarization dynamics

NASA Astrophysics Data System (ADS)

Ahrens, Sven; Sun, Chang-Pu

2017-12-01

We theoretically investigate a scattering configuration in Compton scattering, in which the orientation of the electron spin is reversed and, simultaneously, the photon polarization changes from linear polarization into circular polarization. The intrinsic angular momentum of electron and photon are computed along the coincident propagation direction of the incoming and outgoing photon. We find that this intrinsic angular momentum is not conserved in the considered scattering process. We also discuss the generation of entanglement for the considered scattering setup and present an angle-dependent investigation of the corresponding differential cross section, Stokes parameters, and spin expectation.

Spectroscopic ellipsometry in vacuum ultraviolet spectral area

NASA Astrophysics Data System (ADS)

Fuchs, Detlef

An ellipsometer is developed and built, which allows the direct spectroscopic evaluation of dielectric function of solid bodies in the energy area 5 to 35 eV. A linear polarized synchrotron radiation was used as light source. The Stokes parameters and the Mueller matrices were used for the mathematical modeling, which take into account the properties of the synchrotron light and the analyzer, which depend on the wavelength. The crystals of the semiconductor bindings GaAs, GaP, InP and ZnS were examined. Ellipsometric measurements and reflection spectra show a displacement of spectral structures towards lower photon energies after the storage.

Radiometric and Polarimetric Accuracy Assessment and Calibration of the Hyper-Angular Rainbow Polarimeter (HARP) Instrument

NASA Astrophysics Data System (ADS)

McBride, B.; Martins, J. V.; Fernandez Borda, R. A.; Barbosa, H. M.

2017-12-01

The Laboratory for Aerosols, Clouds, and Optics (LACO) at the University of Maryland, Baltimore County (UMBC) present a novel, wide FOV, hyper-angular imaging polarimeter for the microphysical sampling of clouds and aerosols from aircraft and space. The instrument, the Hyper-Angular Rainbow Polarimeter (HARP), is a precursor to the multi-angle imaging polarimeter solicited by the upcoming NASA Aerosols, Clouds, and Ecosystems (ACE) mission. HARP currently operates in two forms: a spaceborne CubeSat slated for a January 2018 launch to the ISS orbit, and an identical aircraft platform that participated in the Lake Michigan Ozone Study (LMOS) and Aerosol Characterization from Polarimeter and Lidar (ACEPOL) NASA campaigns in 2017. To ensure and validate the instrument's ability to produce high quality Level 2 cloud and aerosol microphysical products, a comprehensive calibration scheme that accounts for flatfielding, radiometry, and all optical interference processes that contribute to the retrieval of Stokes parameters I, Q, and U, is applied across the entirety of HARP's 114° FOV. We present an innovative calibration algorithm that convolves incident polarization from a linear polarization state generator with intensity information observed at three distinct linear polarizations. The retrieved results are pixel-level, modified Mueller matrices that characterize the entire HARP optical assembly, without the need to characterize every individual element or perform ellipsometric studies. Here we show results from several pre- and post- LMOS campaign radiometric calibrations at NASA GSFC and polarimetric calibration using a "polarization dome" that allows for full-FOV characterization of Stokes parameters I, Q, and U. The polarization calibration is verified by passing unpolarized light through partially-polarized, tilted glass plates with well-characterized degree of linear polarization (DoLP). We apply this calibration to a stratocumulous cloud deck case observed during the LMOS campaign on June 19 2017, and assess the polarized cloudbow for cloud droplet effective radius and variance information at 0.67µm.

Synchronous fluorescence spectroscopic study of solvatochromic curcumin dye

NASA Astrophysics Data System (ADS)

Patra, Digambara; Barakat, Christelle

2011-09-01

Curcumin, the main yellow bioactive component of turmeric, has recently acquired attention by chemists due its wide range of potential biological applications as an antioxidant, an anti-inflammatory, and an anti-carcinogenic agent. This molecule fluoresces weakly and poorly soluble in water. In this detailed study of curcumin in thirteen different solvents, both the absorption and fluorescence spectra of curcumin was found to be broad, however, a narrower and simple synchronous fluorescence spectrum of curcumin was obtained at Δ λ = 10-20 nm. Lippert-Mataga plot of curcumin in different solvents illustrated two sets of linearity which is consistent with the plot of Stokes' shift vs. the ET30. When Stokes's shift in wavenumber scale was replaced by synchronous fluorescence maximum in nanometer scale, the solvent polarity dependency measured by λSFSmax vs. Lippert-Mataga plot or ET30 values offered similar trends as measured via Stokes' shift for protic and aprotic solvents for curcumin. Better linear correlation of λSFSmax vs. π* scale of solvent polarity was found compared to λabsmax or λemmax or Stokes' shift measurements. In Stokes' shift measurement both absorption/excitation as well as emission (fluorescence) spectra are required to compute the Stokes' shift in wavenumber scale, but measurement could be done in a very fast and simple way by taking a single scan of SFS avoiding calculation and obtain information about polarity of the solvent. Curcumin decay properties in all the solvents could be fitted well to a double-exponential decay function.

Coherence parameter measurements for neon and hydrogen

NASA Astrophysics Data System (ADS)

Wright, Robert; Hargreaves, Leigh; Khakoo, Murtadha; Zatsarinny, Oleg; Bartschat, Klaus; Stauffer, Al

2015-09-01

We present recent coherence parameter measurements for excitation of neon and hydrogen by 50 eV electrons. The measurements were made using a crossed electron/gas beam spectrometer, featuring a hemispherically selected electron energy analyzer for detecting scattered electrons and double-reflection VUV polarization analyzer to register fluorescence photons. Time-coincidence counting methods on the electron and photon signals were employed to determine Stokes Parameters at each scattering angle, with data measured at angles between 20 - 115 degrees. The data are compared with calculated results using the B-Spline R-Matrix (BSR) and Relativistic Distorted Wave (RDW) approaches. Measurements were made of both the linear (Plin and γ) and circular (Lperp) parameters for the lowest lying excited states in these two targets. We particularly focus on results in the Lperp parameter, which shows unusual behavior in these particular targets, including strong sign changes implying reversal of the angular momentum transfer. In the case of neon, the unusual behavior is well captured by the BSR, but not by other models.

Intrinsic coincident full-Stokes polarimeter using stacked organic photovoltaics.

PubMed

Yang, Ruonan; Sen, Pratik; O'Connor, B T; Kudenov, M W

2017-02-20

An intrinsic coincident full-Stokes polarimeter is demonstrated by using strain-aligned polymer-based organic photovoltaics (OPVs) that can preferentially absorb certain polarized states of incident light. The photovoltaic-based polarimeter is capable of measuring four Stokes parameters by cascading four semitransparent OPVs in series along the same optical axis. This in-line polarimeter concept potentially ensures high temporal and spatial resolution with higher radiometric efficiency as compared to the existing polarimeter architecture. Two wave plates were incorporated into the system to modulate the S₃ Stokes parameter so as to reduce the condition number of the measurement matrix and maximize the measured signal-to-noise ratio. Radiometric calibration was carried out to determine the measurement matrix. The polarimeter presented in this paper demonstrated an average RMS error of 0.84% for reconstructed Stokes vectors after normalized to S₀. A theoretical analysis of the minimum condition number of the four-cell OPV design showed that for individually optimized OPV cells, a condition number of 2.4 is possible.

PRIMORDIAL GRAVITATIONAL WAVES AND RESCATTERED ELECTROMAGNETIC RADIATION IN THE COSMIC MICROWAVE BACKGROUND

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Dong-Hoon; Trippe, Sascha, E-mail: ki13130@gmail.com, E-mail: trippe@astro.snu.ac.kr

Understanding the interaction of primordial gravitational waves (GWs) with the Cosmic Microwave Background (CMB) plasma is important for observational cosmology. In this article, we provide an analysis of an apparently as-yet-overlooked effect. We consider a single free electric charge and suppose that it can be agitated by primordial GWs propagating through the CMB plasma, resulting in periodic, regular motion along particular directions. Light reflected by the charge will be partially polarized, and this will imprint a characteristic pattern on the CMB. We study this effect by considering a simple model in which anisotropic incident electromagnetic (EM) radiation is rescattered bymore » a charge sitting in spacetime perturbed by GWs, and becomes polarized. As the charge is driven to move along particular directions, we calculate its dipole moment to determine the leading-order rescattered EM radiation. The Stokes parameters of the rescattered radiation exhibit a net linear polarization. We investigate how this polarization effect can be schematically represented out of the Stokes parameters. We work out the representations of gradient modes (E-modes) and curl modes (B-modes) to produce polarization maps. Although the polarization effect results from GWs, we find that its representations, the E- and B-modes, do not practically reflect the GW properties such as strain amplitude, frequency, and polarization states.« less

Solving the aerodynamics of fungal flight: how air viscosity slows spore motion.

PubMed

Fischer, Mark W F; Stolze-Rybczynski, Jessica L; Davis, Diana J; Cui, Yunluan; Money, Nicholas P

2010-01-01

Viscous drag causes the rapid deceleration of fungal spores after high-speed launches and limits discharge distance. Stokes' law posits a linear relationship between drag force and velocity. It provides an excellent fit to experimental measurements of the terminal velocity of free-falling spores and other instances of low Reynolds number motion (Re<1). More complex, non-linear drag models have been devised for movements characterized by higher Re, but their effectiveness for modeling the launch of fast-moving fungal spores has not been tested. In this paper, we use data on spore discharge processes obtained from ultra-high-speed video recordings to evaluate the effects of air viscosity predicted by Stokes' law and a commonly used non-linear drag model. We find that discharge distances predicted from launch speeds by Stokes' model provide a much better match to measured distances than estimates from the more complex drag model. Stokes' model works better over a wide range projectile sizes, launch speeds, and discharge distances, from microscopic mushroom ballistospores discharged at <1 m s(-1) over a distance of <0.1mm (Re<1.0), to macroscopic sporangia of Pilobolus that are launched at >10 m s(-1) and travel as far as 2.5m (Re>100). Copyright © 2010 The British Mycological Society. Published by Elsevier Ltd. All rights reserved.

Scattering linear polarization of late-type active stars

NASA Astrophysics Data System (ADS)

Yakobchuk, T. M.; Berdyugina, S. V.

2018-05-01

Context. Many active stars are covered in spots, much more so than the Sun, as indicated by spectroscopic and photometric observations. It has been predicted that star spots induce non-zero intrinsic linear polarization by breaking the visible stellar disk symmetry. Although small, this effect might be useful for star spot studies, and it is particularly significant for a future polarimetric atmosphere characterization of exoplanets orbiting active host stars. Aims: Using models for a center-to-limb variation of the intensity and polarization in presence of continuum scattering and adopting a simplified two-temperature photosphere model, we aim to estimate the intrinsic linear polarization for late-type stars of different gravity, effective temperature, and spottedness. Methods: We developed a code that simulates various spot configurations or uses arbitrary surface maps, performs numerical disk integration, and builds Stokes parameter phase curves for a star over a rotation period for a selected wavelength. It allows estimating minimum and maximum polarization values for a given set of stellar parameters and spot coverages. Results: Based on assumptions about photosphere-to-spot temperature contrasts and spot size distributions, we calculate the linear polarization for late-type stars with Teff = 3500 K-6000 K, log g = 1.0-5.0, using the plane-parallel and spherical atmosphere models. Employing random spot surface distribution, we analyze the relation between spot coverage and polarization and determine the influence of different input parameters on results. Furthermore, we consider spot configurations with polar spots and active latitudes and longitudes.

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

NASA Astrophysics Data System (ADS)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

A Stokes drift approximation based on the Phillips spectrum

NASA Astrophysics Data System (ADS)

Breivik, Øyvind; Bidlot, Jean-Raymond; Janssen, Peter A. E. M.

2016-04-01

A new approximation to the Stokes drift velocity profile based on the exact solution for the Phillips spectrum is explored. The profile is compared with the monochromatic profile and the recently proposed exponential integral profile. ERA-Interim spectra and spectra from a wave buoy in the central North Sea are used to investigate the behavior of the profile. It is found that the new profile has a much stronger gradient near the surface and lower normalized deviation from the profile computed from the spectra. Based on estimates from two open-ocean locations, an average value has been estimated for a key parameter of the profile. Given this parameter, the profile can be computed from the same two parameters as the monochromatic profile, namely the transport and the surface Stokes drift velocity.

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

High speed magnetized flows in the quiet Sun

NASA Astrophysics Data System (ADS)

Quintero Noda, C.; Borrero, J. M.; Orozco Suárez, D.; Ruiz Cobo, B.

2014-09-01

Context. We analyzed spectropolarimetric data recorded with Hinode/SP in quiet-Sun regions located at the disk center. We found single-lobed Stokes V profiles showing highly blue- and red-shifted signals. Oftentimes both types of events appear to be related to each other. Aims: We aim to set constraints on the nature and physical causes of these highly Doppler-shifted signals, as well as to study their spatial distribution, spectropolarimetric properties, size, and rate of occurrence. Also, we plan to retrieve the variation of the physical parameters with optical depth through the photosphere. Methods: We have examined the spatial and polarimetric properties of these events using a variety of data from the Hinode spacecraft. We have also inferred the atmospheric stratification of the physical parameters by means of the inversion of the observed Stokes profiles employing the Stokes Inversion based on Response functions (SIR) code. Finally, we analyzed their evolution using a time series from the same instrument. Results: Blue-shifted events tend to appear over bright regions at the edge of granules, while red-shifted events are seen predominantly over dark regions on intergranular lanes. Large linear polarization signals can be seen in the region that connects them. The magnetic structure inferred from the time series revealed that the structure corresponds to a Ω-loop, with one footpoint always over the edge of a granule and the other inside an intergranular lane. The physical parameters obtained from the inversions of the observed Stokes profiles in both events show an increase with respect to the Harvard-Smithonian reference atmosphere in the temperature at log τ500 ∈ (-1, -3) and a strong magnetic field, B ≥ 1 kG, at the bottom of the atmosphere that quickly decreases upward until vanishing at log τ500 ≈ -2. In the blue-shifted events, the LOS velocities change from upflows at the bottom to downflows at the top of the atmosphere. Red-shifted events display the opposite velocity stratification. The change of sign in LOS velocity happens at the same optical depth in which the magnetic field becomes zero. Conclusions: The physical mechanism that best explains the inferred magnetic field configuration and flow motions is a siphon flow along an arched magnetic flux tube. Further investigation is required, however, as the expected features of a siphon flow cannot be unequivocally identified.

Synchronous fluorescence spectroscopic study of solvatochromic curcumin dye.

PubMed

Patra, Digambara; Barakat, Christelle

2011-09-01

Curcumin, the main yellow bioactive component of turmeric, has recently acquired attention by chemists due its wide range of potential biological applications as an antioxidant, an anti-inflammatory, and an anti-carcinogenic agent. This molecule fluoresces weakly and poorly soluble in water. In this detailed study of curcumin in thirteen different solvents, both the absorption and fluorescence spectra of curcumin was found to be broad, however, a narrower and simple synchronous fluorescence spectrum of curcumin was obtained at Δλ=10-20 nm. Lippert-Mataga plot of curcumin in different solvents illustrated two sets of linearity which is consistent with the plot of Stokes' shift vs. the ET30. When Stokes's shift in wavenumber scale was replaced by synchronous fluorescence maximum in nanometer scale, the solvent polarity dependency measured by λSFSmax vs. Lippert-Mataga plot or ET30 values offered similar trends as measured via Stokes' shift for protic and aprotic solvents for curcumin. Better linear correlation of λSFSmax vs. π* scale of solvent polarity was found compared to λabsmax or λemmax or Stokes' shift measurements. In Stokes' shift measurement both absorption/excitation as well as emission (fluorescence) spectra are required to compute the Stokes' shift in wavenumber scale, but measurement could be done in a very fast and simple way by taking a single scan of SFS avoiding calculation and obtain information about polarity of the solvent. Curcumin decay properties in all the solvents could be fitted well to a double-exponential decay function. Copyright © 2011 Elsevier B.V. All rights reserved.

Intrinsic character of Stokes matrices

NASA Astrophysics Data System (ADS)

Gagnon, Jean-François; Rousseau, Christiane

2017-02-01

Two germs of linear analytic differential systems x k + 1Y‧ = A (x) Y with a non-resonant irregular singularity are analytically equivalent if and only if they have the same eigenvalues and equivalent collections of Stokes matrices. The Stokes matrices are the transition matrices between sectors on which the system is analytically equivalent to its formal normal form. Each sector contains exactly one separating ray for each pair of eigenvalues. A rotation in S allows supposing that R+ lies in the intersection of two sectors. Reordering of the coordinates of Y allows ordering the real parts of the eigenvalues, thus yielding triangular Stokes matrices. However, the choice of the rotation in x is not canonical. In this paper we establish how the collection of Stokes matrices depends on this rotation, and hence on a chosen order of the projection of the eigenvalues on a line through the origin.

Demonstration of a vectorial optical field generator with adaptive close loop control.

PubMed

Chen, Jian; Kong, Lingjiang; Zhan, Qiwen

2017-12-01

We experimentally demonstrate a vectorial optical field generator (VOF-Gen) with an adaptive close loop control. The close loop control capability is illustrated with the calibration of polarization modulation of the system. To calibrate the polarization ratio modulation, we generate 45° linearly polarized beam and make it propagate through a linear analyzer whose transmission axis is orthogonal to the incident beam. For the retardation calibration, circularly polarized beam is employed and a circular polarization analyzer with the opposite chirality is placed in front of the CCD as the detector. In both cases, the close loop control automatically changes the value of the corresponding calibration parameters in the pre-set ranges to generate the phase patterns applied to the spatial light modulators and records the intensity distribution of the output beam by the CCD camera. The optimized calibration parameters are determined corresponding to the minimum total intensity in each case. Several typical kinds of vectorial optical beams are created with and without the obtained calibration parameters, and the full Stokes parameter measurements are carried out to quantitatively analyze the polarization distribution of the generated beams. The comparisons among these results clearly show that the obtained calibration parameters could remarkably improve the accuracy of the polarization modulation of the VOF-Gen, especially for generating elliptically polarized beam with large ellipticity, indicating the significance of the presented close loop in enhancing the performance of the VOF-Gen.

A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart Finite Element Discretizations of the Incompressible Stokes Problem

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Paraschivoiu, Marius

1998-01-01

We present a finite element technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the finite element discretization is effected by Crouzeix-Raviart elements, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented Lagrangian: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the finite element equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.

Alpha models for rotating Navier-Stokes equations in geophysics with nonlinear dispersive regularization

NASA Astrophysics Data System (ADS)

Kim, Bong-Sik

Three dimensional (3D) Navier-Stokes-alpha equations are considered for uniformly rotating geophysical fluid flows (large Coriolis parameter f = 2O). The Navier-Stokes-alpha equations are a nonlinear dispersive regularization of usual Navier-Stokes equations obtained by Lagrangian averaging. The focus is on the existence and global regularity of solutions of the 3D rotating Navier-Stokes-alpha equations and the uniform convergence of these solutions to those of the original 3D rotating Navier-Stokes equations for large Coriolis parameters f as alpha → 0. Methods are based on fast singular oscillating limits and results are obtained for periodic boundary conditions for all domain aspect ratios, including the case of three wave resonances which yields nonlinear "2½-dimensional" limit resonant equations for f → 0. The existence and global regularity of solutions of limit resonant equations is established, uniformly in alpha. Bootstrapping from global regularity of the limit equations, the existence of a regular solution of the full 3D rotating Navier-Stokes-alpha equations for large f for an infinite time is established. Then, the uniform convergence of a regular solution of the 3D rotating Navier-Stokes-alpha equations (alpha ≠ 0) to the one of the original 3D rotating NavierStokes equations (alpha = 0) for f large but fixed as alpha → 0 follows; this implies "shadowing" of trajectories of the limit dynamical systems by those of the perturbed alpha-dynamical systems. All the estimates are uniform in alpha, in contrast with previous estimates in the literature which blow up as alpha → 0. Finally, the existence of global attractors as well as exponential attractors is established for large f and the estimates are uniform in alpha.

Adhesion of Mineral and Soot Aerosols can Strongly Affect their Scattering and Absorption Properties

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Jana M.

2012-01-01

We use the numerically exact superposition T-matrix method to compute the optical cross sections and the Stokes scattering matrix for polydisperse mineral aerosols (modeled as homogeneous spheres) covered with a large number of much smaller soot particles. These results are compared with the Lorenz-Mie results for a uniform external mixture of mineral and soot aerosols. We show that the effect of soot particles adhering to large mineral particles can be to change the extinction and scattering cross sections and the asymmetry parameter quite substantially. The effect on the phase function and degree of linear polarization can be equally significant.

ASTROPOP: ASTROnomical Polarimetry and Photometry pipeline

NASA Astrophysics Data System (ADS)

Campagnolo, Julio C. N.

2018-05-01

AstroPoP reduces almost any CCD photometry and image polarimetry data. For photometry reduction, the code performs source finding, aperture and PSF photometry, astrometry calibration using different automated and non-automated methods and automated source identification and magnitude calibration based on online and local catalogs. For polarimetry, the code resolves linear and circular Stokes parameters produced by image beam splitter or polarizer polarimeters. In addition to the modular functions, ready-to-use pipelines based in configuration files and header keys are also provided with the code. AstroPOP was initially developed to reduce the IAGPOL polarimeter data installed at Observatório Pico dos Dias (Brazil).

Synthesis, Spectrofluorometric Studies, Micellization and non Linear Optical Properties of Blue Emitting Quinoline (AMQC) Dye.

PubMed

Afzal, S M; Asiri, Abdullah M; Razvi, M A N; Bakry, Ahmed H; Khan, Salman A; Zayed, Mohie E M

2016-03-01

Blue emitting 2-amino-4-(3, 4, 5-tri methoxyphenyl)-9-methoxy-5,6 dihydrobenzo[f]isoquinoline-1-carbonitrile (AMQC) dye was synthesized by one-pot multicomponent reactions (MCRs) of 3,4,5-trimethoxybenzaldehyd, malononitrile, 6-methoxy-1,2,3,4-tetrahydro-naphthalin-1-one and ammonium acetate. Results obtained from spectroscopic and elemental analysis of synthesized AMQC was in good agreement with their chemical structures. Fluorescence polarity study demonstrated that AMQC was sensitive to the polarity of the microenvironment provided by different solvents. In addition, spectroscopic and physicochemical parameters, including electronic absorption, excitation coefficient, stokes shift, oscillator strength, transition dipole moment and fluorescence quantum yield were investigated in order to explore the analytical potential of AMQC. Dye undergoes solubilization in different micelles and may be used as a quencher and a probe to determine the critical micelle concentration (CMC) of SDS and CTAB. Nonlinear optical parameters of AMQC dye shows relatively lower nonlinear refractive index and nonlinear absorption coefficient at the power levels. Variation of n2 with concentration is linear in the concentration range used in the present study.

A stable penalty method for the compressible Navier-Stokes equations. 1: Open boundary conditions

NASA Technical Reports Server (NTRS)

Hesthaven, J. S.; Gottlieb, D.

1994-01-01

The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends to infinity. The versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder.

Numerical modelling of single-phase flow in rough fractures with contacts

NASA Astrophysics Data System (ADS)

Olkiewicz, Piotr; Dabrowski, Marcin

2017-04-01

Fracture flow may dominate in rocks with low porosity and it can accompany both industrial and natural processes. Typical examples of such processes are natural flows in crystalline rocks and industrial flows in oil and gas production systems or hydraulic fracturing. Fracture flow provides an important mechanism for transporting mass and energy. The distribution of the apertures of fracture and contact area are the key parameters with regard to the fracture transmissivity. We use the method of correlated random fields [Mourzenko, 1996] to generate synthetic fracture geometry in 3D. The flow of an incompressible Newtonian viscous fluid in geological formation can be approximated by the Stokes, the Stokes-Brinkman or the Reynolds models. We use our own implementation of the finite element method based on MILAMIN [Dabrowski, 2008] to solve governing partial differential equation over domain. We compare the Stokes, the Stokes-Brinkamn and the Reynolds models for fracture flow based on systematic numerical simulations for a wide range of geometric parameters. Mismatch between the Reynolds and the Stokes models becomes significant with increasing fracture roughness or contact area. The Stokes-Brinkman model is more accurate than Reynolds models due to additional Laplacian term, which allows to fulfil no-slip boundary condition. We present condition when the Reynolds and the Stokes-Brinkman models are valid. In the last three decades many authors used the Reynolds equation for studying fracture flow because of its simplicity. We recommend using the Stokes-Brinkman model for fracture flow, which allows to fulfil no-slip boundary condition on asperities boundary and is more accurate for rough fractures than the Reynolds model.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Role of excited state solvent fluctuations on time-dependent fluorescence Stokes shift

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tanping, E-mail: tanping@lsu.edu, E-mail: revatik@lsu.edu; Kumar, Revati, E-mail: tanping@lsu.edu, E-mail: revatik@lsu.edu

2015-11-07

We explore the connection between the solvation dynamics of a chromophore upon photon excitation and equilibrium fluctuations of the solvent. Using molecular dynamics simulations, fluorescence Stokes shift for the tryptophan in Staphylococcus nuclease was examined using both nonequilibrium calculations and linear response theory. When the perturbed and unperturbed surfaces exhibit different solvent equilibrium fluctuations, the linear response approach on the former surface shows agreement with the nonequilibrium process. This agreement is excellent when the perturbed surface exhibits Gaussian statistics and qualitative in the case of an isomerization induced non-Gaussian statistics. However, the linear response theory on the unperturbed surface breaksmore » down even in the presence of Gaussian fluctuations. Experiments also provide evidence of the connection between the excited state solvent fluctuations and the total fluorescence shift. These observations indicate that the equilibrium statistics on the excited state surface characterize the relaxation dynamics of the fluorescence Stokes shift. Our studies specifically analyze the Gaussian fluctuations of the solvent in the complex protein environment and further confirm the role of solvent fluctuations on the excited state surface. The results are consistent with previous investigations, found in the literature, of solutes dissolved in liquids.« less

Bandwidth optimization of femtosecond pure-rotational coherent anti-Stokes Raman scattering by pump/Stokes spectral focusing.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kearney, Sean Patrick

A simple spectral focusing scheme for bandwidth optimization of gas-phase rotational coherent anti-Stokes Raman scattering (CARS) spectra is presented. The method is useful when femtosecond pump/Stokes preparation of the Raman coherence is utilized. The approach is of practical utility when working with laser pulses that are not strictly transform limited, or when windows or other sources of pulse chirp may be present in the experiment. A delay between the femtosecond preparation pulses is introduced to shift the maximum Raman preparation away from zero frequency and toward the Stokes or anti-Stokes side of the spectrum with no loss in total preparationmore » bandwidth. Shifts of 100 cm -1 or more are attainable and allow for enhanced detection of high-energy (150-300 cm -1) rotational Raman transitions at near transform-limited optimum sensitivity. A simple theoretical treatment for the case of identical pump and Stokes pulses with linear frequency chirp is presented. The approach is then demonstrated experimentally for typical levels of transform-limited laser performance obtained our laboratory with nonresonant CARS in argon and Raman-resonant spectra from a lean H 2/air flat flame.« less

Bandwidth optimization of femtosecond pure-rotational coherent anti-Stokes Raman scattering by pump/Stokes spectral focusing.

DOE PAGES

Kearney, Sean Patrick

2014-07-01

A simple spectral focusing scheme for bandwidth optimization of gas-phase rotational coherent anti-Stokes Raman scattering (CARS) spectra is presented. The method is useful when femtosecond pump/Stokes preparation of the Raman coherence is utilized. The approach is of practical utility when working with laser pulses that are not strictly transform limited, or when windows or other sources of pulse chirp may be present in the experiment. A delay between the femtosecond preparation pulses is introduced to shift the maximum Raman preparation away from zero frequency and toward the Stokes or anti-Stokes side of the spectrum with no loss in total preparationmore » bandwidth. Shifts of 100 cm -1 or more are attainable and allow for enhanced detection of high-energy (150-300 cm -1) rotational Raman transitions at near transform-limited optimum sensitivity. A simple theoretical treatment for the case of identical pump and Stokes pulses with linear frequency chirp is presented. The approach is then demonstrated experimentally for typical levels of transform-limited laser performance obtained our laboratory with nonresonant CARS in argon and Raman-resonant spectra from a lean H 2/air flat flame.« less

X-Ray Spectro-Polarimetry with Photoelectric Polarimeters

NASA Technical Reports Server (NTRS)

Strohmayer, T. E.

2017-01-01

We derive a generalization of forward fitting for X-ray spectroscopy to include linear polarization of X-ray sources, appropriate for the anticipated next generation of space-based photoelectric polarimeters. We show that the inclusion of polarization sensitivity requires joint fitting to three observed spectra, one for each of the Stokes parameters, I(E), U(E), and Q(E). The equations for StokesI (E) (the total intensity spectrum) are identical to the familiar case with no polarization sensitivity, and for which the model-predicted spectrum is obtained by a convolution of the source spectrum, F (E), with the familiar energy response function,(E) R(E,E), where (E) and R(E,E) are the effective area and energy redistribution matrix, respectively. In addition to the energy spectrum, the two new relations for U(E) and Q(E) include the source polarization fraction and position angle versus energy, a(E), and 0(E), respectively, and the model-predicted spectra for these relations are obtained by a convolution with the modulated energy response function, (E)(E) R(E,E), where(E) is the energy-dependent modulation fraction that quantifies a polarimeters angular response to 100 polarized radiation. We present results of simulations with response parameters appropriate for the proposed PRAXyS Small Explorer observatory to illustrate the procedures and methods, and we discuss some aspects of photoelectric polarimeters with relevance to understanding their calibration and operation.

Euler/Navier-Stokes calculations of transonic flow past fixed- and rotary-wing aircraft configurations

NASA Technical Reports Server (NTRS)

Deese, J. E.; Agarwal, R. K.

1989-01-01

Computational fluid dynamics has an increasingly important role in the design and analysis of aircraft as computer hardware becomes faster and algorithms become more efficient. Progress is being made in two directions: more complex and realistic configurations are being treated and algorithms based on higher approximations to the complete Navier-Stokes equations are being developed. The literature indicates that linear panel methods can model detailed, realistic aircraft geometries in flow regimes where this approximation is valid. As algorithms including higher approximations to the Navier-Stokes equations are developed, computer resource requirements increase rapidly. Generation of suitable grids become more difficult and the number of grid points required to resolve flow features of interest increases. Recently, the development of large vector computers has enabled researchers to attempt more complex geometries with Euler and Navier-Stokes algorithms. The results of calculations for transonic flow about a typical transport and fighter wing-body configuration using thin layer Navier-Stokes equations are described along with flow about helicopter rotor blades using both Euler/Navier-Stokes equations.

Nonlinear dynamics near the stability margin in rotating pipe flow

NASA Technical Reports Server (NTRS)

Yang, Z.; Leibovich, S.

1991-01-01

The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

Investigation of the polarization state of dual APPLE-II undulators.

PubMed

Hand, Matthew; Wang, Hongchang; Dhesi, Sarnjeet S; Sawhney, Kawal

2016-01-01

The use of an APPLE II undulator is extremely important for providing a high-brilliance X-ray beam with the capability to switch between various photon beam polarization states. A high-precision soft X-ray polarimeter has been used to systematically investigate the polarization characteristics of the two helical APPLE II undulators installed on beamline I06 at Diamond Light Source. A simple data acquisition and processing procedure has been developed to determine the Stokes polarization parameters for light polarized at arbitrary linear angles emitted from a single undulator, and for circularly polarized light emitted from both undulators in conjunction with a single-period undulator phasing unit. The purity of linear polarization is found to deteriorate as the polarization angle moves away from the horizontal and vertical modes. Importantly, a negative correlation between the degree of circular polarization and the photon flux has been found when the phasing unit is used.

Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Arteaga, Santiago Egido

1998-12-01

The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the linearization strategies considered and whose computational cost is negligible. The algebraic properties of these systems depend on both the discretization and nonlinear method used. We study in detail the positive definiteness and skewsymmetry of the advection submatrices (essentially, convection-diffusion problems). We propose a discretization based on a new trilinear form for Newton's method. We solve the linear systems using three Krylov subspace methods, GMRES, QMR and TFQMR, and compare the advantages of each. Our emphasis is on parallel algorithms, and so we consider preconditioners suitable for parallel computers such as line variants of the Jacobi and Gauss- Seidel methods, alternating direction implicit methods, and Chebyshev and least squares polynomial preconditioners. These work well for moderate viscosities (moderate Reynolds number). For small viscosities we show that effective parallel solution of the advection subproblem is a critical factor to improve performance. Implementation details on a CM-5 are presented.

Stokes parameters modulator for birefringent filters

NASA Technical Reports Server (NTRS)

Dollfus, A.

1985-01-01

The Solar Birefringent Filter (Filter Polarisiant Solaire Selectif FPSS) of Meudon Observatory is presently located at the focus of a solar refractor with a 28 cm lens directly pointed at the Sun. It produces a diffraction limited image without instrumental polarization and with a spectral resolution of 46,000 in a field of 6 arc min. diameter. The instrument is calibrated for absolute Doppler velocity measurements and is presently used for quantitative imagery of the radial velocity motions in the photosphere. The short period oscillations are recorded. Work of adapting the instrument for the imagery of the solar surface in the Stokes parameters is discussed. The first polarizer of the birefringent filter, with a reference position angle 0 deg, is associated with a fixed quarter wave plate at +45 deg. A rotating quarter wave plate is set at 0 deg and can be turned by incremented steps of exactly +45 deg. Another quarter wave plate also initially set at 0 deg is simultaneously incremented by -45 deg but only on each even step of the first plate. A complete cycle of increments produces images for each of the 6 parameters I + or - Q, I + or - U and I + or - V. These images are then subtracted by pairs to produce a full image in the three Stokes parameters Q, U and V. With proper retardation tolerance and positioning accuracy of the quarter wave plates, the cross talk between the Stokes parameters was calculated and checked to be minimal.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Stokes phenomena in discrete Painlevé I.

PubMed

Joshi, N; Lustri, C J

2015-05-08

In this study, we consider the asymptotic behaviour of the first discrete Painlevé equation in the limit as the independent variable becomes large. Using an asymptotic series expansion, we identify two types of solutions which are pole-free within some sector of the complex plane containing the positive real axis. Using exponential asymptotic techniques, we determine Stokes phenomena effects present within these solutions, and hence the regions in which the asymptotic series expression is valid. From a careful analysis of the switching behaviour across Stokes lines, we find that the first type of solution is uniquely defined, while the second type contains two free parameters, and that the region of validity may be extended for appropriate choice of these parameters.

Geometric algebra description of polarization mode dispersion, polarization-dependent loss, and Stokes tensor transformations.

PubMed

Soliman, George; Yevick, David; Jessop, Paul

2014-09-01

This paper demonstrates that numerous calculations involving polarization transformations can be condensed by employing suitable geometric algebra formalism. For example, to describe polarization mode dispersion and polarization-dependent loss, both the material birefringence and differential loss enter as bivectors and can be combined into a single symmetric quantity. Their frequency and distance evolution, as well as that of the Stokes vector through an optical system, can then each be expressed as a single compact expression, in contrast to the corresponding Mueller matrix formulations. The intrinsic advantage of the geometric algebra framework is further demonstrated by presenting a simplified derivation of generalized Stokes parameters that include the electric field phase. This procedure simultaneously establishes the tensor transformation properties of these parameters.

Infrared Stokes polarimetry and spectropolarimetry

NASA Astrophysics Data System (ADS)

Kudenov, Michael William

In this work, three methods of measuring the polarization state of light in the thermal infrared (3-12 mum) are modeled, simulated, calibrated and experimentally verified in the laboratory. The first utilizes the method of channeled spectropolarimetry (CP) to encode the Stokes polarization parameters onto the optical power spectrum. This channeled spectral technique is implemented with the use of two Yttrium Vanadate (YVO4) crystal retarders. A basic mathematical model for the system is presented, showing that all the Stokes parameters are directly present in the interferogram. Theoretical results are compared with real data from the system, an improved model is provided to simulate the effects of absorption within the crystal, and a modified calibration technique is introduced to account for this absorption. Lastly, effects due to interferometer instabilities on the reconstructions, including non-uniform sampling and interferogram translations, are investigated and techniques are employed to mitigate them. Second is the method of prismatic imaging polarimetry (PIP), which can be envisioned as the monochromatic application of channeled spectropolarimetry. Unlike CP, PIP encodes the 2-dimensional Stokes parameters in a scene onto spatial carrier frequencies. However, the calibration techniques derived in the infrared for CP are extremely similar to that of the PIP. Consequently, the PIP technique is implemented with a set of four YVO4 crystal prisms. A mathematical model for the polarimeter is presented in which diattenuation due to Fresnel effects and dichroism in the crystal are included. An improved polarimetric calibration technique is introduced to remove the diattenuation effects, along with the relative radiometric calibration required for the BPIP operating with a thermal background and large detector offsets. Data demonstrating emission polarization are presented from various blackbodies, which are compared to data from our Fourier transform infrared spectropolarimeter. Additionally, limitations in the PIP technique with regards to the spectral bandwidth and F/# of the imaging system are analyzed. A model able to predict the carrier frequency's fringe visibility is produced and experimentally verified, further reinforcing the PIP's limitations. The last technique is significantly different from CP or PIP and involves the simulation and calibration of a thermal infrared division of amplitude imaging Stokes polarimeter. For the first time, application of microbolometer focal plane array (FPA) technology to polarimetry is demonstrated. The sensor utilizes a wire-grid beamsplitter with imaging systems positioned at each output to analyze two orthogonal linear polarization states simultaneously. Combined with a form birefringent wave plate, the system is capable of snapshot imaging polarimetry in any one Stokes vector (S1, S2 or S3). Radiometric and polarimetric calibration procedures for the instrument are provided and the reduction matrices from the calibration are compared to rigorous coupled wave analysis (RCWA) and raytracing simulations. The design and optimization of the sensor's wire-grid beam splitter and wave plate are presented, along with their corresponding prescriptions. Polarimetric calibration error due to the spectrally broadband nature of the instrument is also overviewed. Image registration techniques for the sensor are discussed and data from the instrument are presented, demonstrating a microbolometer's ability to measure the small intensity variations corresponding to polarized emission in natural environments.

Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

NASA Technical Reports Server (NTRS)

Marx, Yves P.

1990-01-01

An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

Polarimetric signature imaging of anisotropic bio-medical tissues

NASA Astrophysics Data System (ADS)

Wu, Stewart H.; Yang, De-Ming; Chiou, Arthur; Nee, Soe-Mie F.; Nee, Tsu-Wei

2010-02-01

Polarimetric imaging of Stokes vector (I, Q, U, V) can provide 4 independent signatures showing the linear and circular polarizations of biological tissues and cells. Using a recently developed Stokes digital imaging system, we measured the Stokes vector images of tissue samples from sections of rat livers containing normal portions and hematomas. The derived Mueller matrix elements can quantitatively provide multi-signature data of the bio-sample. This polarimetric optical technology is a new option of biosensing technology to inspect the structures of tissue samples, particularly for discriminating tumor and non-tumor biopsy. This technology is useful for critical disease discrimination and medical diagnostics applications.

Investigations of a Dual Seeded 1178 nm Raman Laser System

DTIC Science & Technology

2016-01-14

20 W. Because of the linewidth broadening, a co- pumped second Stokes Raman laser system is not useful for the sodium guidestar laser application... pumped second Stokes Raman laser system is not useful for the sodium guidestar laser application which requires narrow linewidth. Keywords: Raman...optical efficiency of 52% when pumped with a linearly polarized 1120 nm fiber laser10,11. Because of the all-polarization maintaining configuration, a

Intermittency in two-dimensional Ekman-Navier-Stokes turbulence.

PubMed

Boffetta, G; Celani, A; Musacchio, S; Vergassola, M

2002-08-01

We study the statistics of the vorticity field in two-dimensional Navier-Stokes turbulence with linear Ekman friction. We show that the small-scale vorticity fluctuations are intermittent, as conjectured by Bernard [Europhys. Lett. 50, 333 (2000)] and Nam et al. [Phys. Rev. Lett. 84, 5134 (2000)]. The small-scale statistics of vorticity fluctuations coincide with that of a passive scalar with finite lifetime transported by the velocity field itself.

Backward and forward Monte Carlo method for vector radiative transfer in a two-dimensional graded index medium

NASA Astrophysics Data System (ADS)

Qian, Lin-Feng; Shi, Guo-Dong; Huang, Yong; Xing, Yu-Ming

2017-10-01

In vector radiative transfer, backward ray tracing is seldom used. We present a backward and forward Monte Carlo method to simulate vector radiative transfer in a two-dimensional graded index medium, which is new and different from the conventional Monte Carlo method. The backward and forward Monte Carlo method involves dividing the ray tracing into two processes backward tracing and forward tracing. In multidimensional graded index media, the trajectory of a ray is usually a three-dimensional curve. During the transport of a polarization ellipse, the curved ray trajectory will induce geometrical effects and cause Stokes parameters to continuously change. The solution processes for a non-scattering medium and an anisotropic scattering medium are analysed. We also analyse some parameters that influence the Stokes vector in two-dimensional graded index media. The research shows that the Q component of the Stokes vector cannot be ignored. However, the U and V components of the Stokes vector are very small.

Comment on Modified Stokes Parameters

NASA Technical Reports Server (NTRS)

Le Vine, D.M.; Utku, C.

2009-01-01

It is common practice in passive microwave remote sensing (microwave radiometry) to express observables as temperatures and in the case of polarimetric radiometry to use what are called "Modified Stokes Parameters in Brightness Temperature" to describe the scene. However, definitions with slightly different normalization (with and without division by bandwidth) have appeared in the literature. The purpose of this manuscript is to present an analysis to clarify the meaning of terms in the definition and resolve the question of the proper normalization.

GGOS and the EOP - the key role of SLR for a stable estimation of highly accurate Earth orientation parameters

NASA Astrophysics Data System (ADS)

Bloßfeld, Mathis; Panzetta, Francesca; Müller, Horst; Gerstl, Michael

2016-04-01

The GGOS vision is to integrate geometric and gravimetric observation techniques to estimate consistent geodetic-geophysical parameters. In order to reach this goal, the common estimation of station coordinates, Stokes coefficients and Earth Orientation Parameters (EOP) is necessary. Satellite Laser Ranging (SLR) provides the ability to study correlations between the different parameter groups since the observed satellite orbit dynamics are sensitive to the above mentioned geodetic parameters. To decrease the correlations, SLR observations to multiple satellites have to be combined. In this paper, we compare the estimated EOP of (i) single satellite SLR solutions and (ii) multi-satellite SLR solutions. Therefore, we jointly estimate station coordinates, EOP, Stokes coefficients and orbit parameters using different satellite constellations. A special focus in this investigation is put on the de-correlation of different geodetic parameter groups due to the combination of SLR observations. Besides SLR observations to spherical satellites (commonly used), we discuss the impact of SLR observations to non-spherical satellites such as, e.g., the JASON-2 satellite. The goal of this study is to discuss the existing parameter interactions and to present a strategy how to obtain reliable estimates of station coordinates, EOP, orbit parameter and Stokes coefficients in one common adjustment. Thereby, the benefits of a multi-satellite SLR solution are evaluated.

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.

1990-01-01

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

Compressible Fluids Interacting with a Linear-Elastic Shell

NASA Astrophysics Data System (ADS)

Breit, Dominic; Schwarzacher, Sebastian

2018-05-01

We study the Navier-Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical domain. Its deformation is modeled by a linearized version of Koiter's elastic energy. We show the existence of weak solutions to the corresponding system of PDEs provided the adiabatic exponent satisfies {γ > 12/7} ({γ >1 } in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in Lengeler and Růžičkaka (Arch Ration Mech Anal 211(1):205-255, 2014) on incompressible Navier-Stokes equations.

Nonlinear QED effects in X-ray emission of pulsars

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shakeri, Soroush; Haghighat, Mansour; Xue, She-Sheng, E-mail: Soroush.Shakeri@ph.iut.ac.ir, E-mail: m.haghighat@shirazu.ac.ir, E-mail: xue@icra.it

2017-10-01

In the presence of strong magnetic fields near pulsars, the QED vacuum becomes a birefringent medium due to nonlinear QED interactions. Here, we explore the impact of the effective photon-photon interaction on the polarization evolution of photons propagating through the magnetized QED vacuum of a pulsar. We solve the quantum Boltzmann equation within the framework of the Euler-Heisenberg Lagrangian to find the evolution of the Stokes parameters. We find that linearly polarized X-ray photons propagating outward in the magnetosphere of a rotating neutron star can acquire high values for the circular polarization parameter. Meanwhile, it is shown that the polarizationmore » characteristics of photons besides photon energy depend strongly on parameters of the pulsars such as magnetic field strength, inclination angle and rotational period. Our results are clear predictions of QED vacuum polarization effects in the near vicinity of magnetic stars which can be tested with the upcoming X-ray polarimetric observations.« less

Vector magnetic fields in sunspots. I - Stokes profile analysis using the Marshall Space Flight Center magnetograph

NASA Technical Reports Server (NTRS)

Balasubramaniam, K. S.; West, E. A.

1991-01-01

The Marshall Space Flight Center (MSFC) vector magnetograph is a tunable filter magnetograph with a bandpass of 125 mA. Results are presented of the inversion of Stokes polarization profiles observed with the MSFC vector magnetograph centered on a sunspot to recover the vector magnetic field parameters and thermodynamic parameters of the spectral line forming region using the Fe I 5250.2 A spectral line using a nonlinear least-squares fitting technique. As a preliminary investigation, it is also shown that the recovered thermodynamic parameters could be better understood if the fitted parameters like Doppler width, opacity ratio, and damping constant were broken down into more basic quantities like temperature, microturbulent velocity, or density parameter.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Polarimetric thermal emission from periodic water surfaces

NASA Technical Reports Server (NTRS)

Yueh, S. H.; Nghiem, S. V.; Kwok, R.; Wilson, W. J.; Li, F. K.; Johnson, J. T.; Kong, J. A.

1993-01-01

Experimental results and theoretical calculations are presented to study the polarimetric emission from water surfaces with directional features. For our ground-based Ku-band radiometer measurements, a water pool was constructed on the roof of a building in the Jet Propulsion Laboratory, and a fiberglass surface with periodic corrugations in one direction was impressed on the top of the water surface to create a stationary water surface underneath it. It is observed that the measured Stokes parameters of corrugated fiberglass-covered water surfaces are functions of azimuth angles and agree very well with the theoretical calculations. The theory, after being verified by the experimental data, was then used to calculate the Stokes parameters of periodic surfaces without fiberglass surface layer and with rms height of the order of wind-generated water ripples. The magnitudes of the azimuthal variation of the calculated emissivities at horizontal and vertical polarizations corresponding to the first two Stokes parameters are found to be comparable to the values measured by airborne radiometers and SSM/I. In addition, the third Stokes parameter not shown in the literature is seen to have approximately twice the magnitude of the azimuth variation of either T(sub h) or T(sub v), which may make it more sensitive to the row direction, while less susceptive to noises because the atmospheric and system noises tend to be unpolarized and are expected to be cancelled out when the third Stokes parameter is derived as the difference of two or three power measurements, as indicated by another experiment carried out at a swimming pool with complicated surroundings. The results indicate that passive polarimetry is a potential technology in the remote sensing of ocean wind vector which is a crucial component in the understanding of global climate change. Issues related to the application of microwave passive polarimetry to ocean wind are also discussed.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

The Effect of Viscosity of a Fluid on the Frequency Response of a Viscoelastic Plate Loaded by This Fluid

NASA Astrophysics Data System (ADS)

Zamanov, A. D.; Ismailov, M. I.; Akbarov, S. D.

2018-03-01

A hydroviscoelastic system consisting of a viscoelastic plate and a half-plane filled with a viscous fluid is considered. The effect of viscosity of the fluid on the frequency response of the system and its dependence on the rheological parameters of plate material are estimated. The problem on forced vibrations of the system in the plane strain state is investigated using the exact equations of viscoelastodynamics for describing the motion of the plate and linearized Navier-Stokes equations for describing the flow of the fluid. The results found in the cases of nonviscous compressible and Newtonian compressible viscous fluids are compared.

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Detection of Linear Polarization from SNR Cassiopeia A at Low Radio Frequencies

NASA Astrophysics Data System (ADS)

Raja, Wasim; Deshpande, Avinash A.

2015-03-01

We report detection of the weak but significant linear polarization from the Supernova Remnant Cas A at low radio frequencies (327 MHz) using the GMRT. The spectro-polarimetric data (16 MHz bandwidth with 256 spectral channels) was analyzed using the technique of Faraday Tomography. Ascertaining association of this weak polarization to the source is non-trivial in the presence of the remnant instrumental polarization (<1% in our case) - the expected anti-correlation ρlp,x, between the linear polarized intensity and the soft X-ray counts gets masked by the correlation between the Stokes-I dependent instrumental leakage and the X-radiation that is spatially correlated with Stokes-I, if ρ lp,x is computed naively. Hence, we compute ρ lp,x using pixels within ultra narrow bins of Stokes-I within which the instrumental leakage is expected to remain constant, and establish the anti-correlation as well as the correspondence of this correlation with the mean X-ray profile (Figure 1). Given the angular and RM-resolution in our data, the observed depolarization relative to that at higher frequencies, implies that the mixing of thermal and non-thermal plasma within the source might be occurring on spatial scales ~ 1000 AU, assuming random superposition of polarization states.

Further comments on the effects of vacuum birefringence on the polarization of X-rays emitted from magnetic neutron stars

NASA Technical Reports Server (NTRS)

Chanan, G. A.; Novick, R.; Silver, E. H.

1979-01-01

The birefringence of the vacuum in the presence of strong (of the order of 1 teragauss) magnetic fields will in general affect the polarization of X-rays propagating through these fields. Two of the four Stokes parameters will vary so rapidly with wavelength as to be 'washed out' and unobservable, but the remaining two parameters will be unaffected. These results show that one conclusion of an earlier work is incorrect: Polarized X-ray emission from the surface of a magnetic neutron star will not in general be completely depolarized by the effects of vacuum birefringence. In particular, this birefringence has no effect on the linear polarization of cyclotron emission from the poles of magnetic neutron stars, and a similar result holds for synchrotron emission. More general cases of the propagation of polarized X-rays in magnetic fields are also discussed.

Fluid-structure interaction in Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Kempf, Martin Horst Willi

1998-10-01

The linear stability of a viscous fluid between two concentric, rotating cylinders is considered. The inner cylinder is a rigid boundary and the outer cylinder has an elastic layer exposed to the fluid. The subject is motivated by flow between two adjoining rollers in a printing press. The governing equations of the fluid layer are the incompressible Navier-Stokes equations, and the governing equations of the elastic layer are Navier's equations. A narrow gap, neutral stability, and axisymmetric disturbances are assumed. The solution involves a novel technique for treating two layer stability problems, where an exact solution in the elastic layer is used to isolate the problem in the fluid layer. The results show that the presence of the elastic layer has only a slight effect on the critical Taylor numbers for the elastic parameters of modern printing presses. However, there are parameter values where the critical Taylor number is dramatically different than the classical Taylor-Couette problem.

Continuous Variable Quantum Key Distribution Using Polarized Coherent States

NASA Astrophysics Data System (ADS)

Vidiella-Barranco, A.; Borelli, L. F. M.

We discuss a continuous variables method of quantum key distribution employing strongly polarized coherent states of light. The key encoding is performed using the variables known as Stokes parameters, rather than the field quadratures. Their quantum counterpart, the Stokes operators Ŝi (i=1,2,3), constitute a set of non-commuting operators, being the precision of simultaneous measurements of a pair of them limited by an uncertainty-like relation. Alice transmits a conveniently modulated two-mode coherent state, and Bob randomly measures one of the Stokes parameters of the incoming beam. After performing reconciliation and privacy amplification procedures, it is possible to distill a secret common key. We also consider a non-ideal situation, in which coherent states with thermal noise, instead of pure coherent states, are used for encoding.

Characteristics of 1.9-μm laser emission from hydrogen-filled hollow-core fiber by vibrational stimulated Raman scattering

NASA Astrophysics Data System (ADS)

Gu, Bo; Chen, Yubin; Wang, Zefeng

2016-12-01

We report here the characteristics of 1.9-μm laser emission from a gas-filled hollow-core fiber by stimulated Raman scattering (SRS). A 6.5-m hydrogen-filled ice-cream negative curvature hollow-core fiber is pumped with a high peak-power, narrow linewidth, linearly polarized subnanosecond pulsed 1064-nm microchip laser, generating a pulsed vibrational Stokes wave at 1908.5 nm. The maximum quantum efficiency of about 48% is obtained, which is mainly limited by the mode mismatch between the pump laser beam and the Stokes wave in the hollow-core fiber. The linewidths of the pump laser and the first-order vibrational Stokes wave are measured to be about 1 and 2 GHz, respectively, by a scanning Fabry-Perot interferometer. The pressure selection phenomenon of the vibrational anti-Stokes waves is also investigated. The pulse duration of the vibrational Stokes wave is recorded to be narrower than that of the pump laser. The polarization properties of the hollow-core fiber and the polarization dependence of the vibrational and the rotational SRS are also studied. The beam profile of the vibrational Stokes wave shows good quality.

Biomechanically based simulation of brain deformations for intraoperative image correction: coupling of elastic and fluid models

NASA Astrophysics Data System (ADS)

Hagemann, Alexander; Rohr, Karl; Stiehl, H. Siegfried

2000-06-01

In order to improve the accuracy of image-guided neurosurgery, different biomechanical models have been developed to correct preoperative images w.r.t. intraoperative changes like brain shift or tumor resection. All existing biomechanical models simulate different anatomical structures by using either appropriate boundary conditions or by spatially varying material parameter values, while assuming the same physical model for all anatomical structures. In general, this leads to physically implausible results, especially in the case of adjacent elastic and fluid structures. Therefore, we propose a new approach which allows to couple different physical models. In our case, we simulate rigid, elastic, and fluid regions by using the appropriate physical description for each material, namely either the Navier equation or the Stokes equation. To solve the resulting differential equations, we derive a linear matrix system for each region by applying the finite element method (FEM). Thereafter, the linear matrix systems are linked together, ending up with one overall linear matrix system. Our approach has been tested using synthetic as well as tomographic images. It turns out from experiments, that the integrated treatment of rigid, elastic, and fluid regions significantly improves the prediction results in comparison to a pure linear elastic model.

A comparative study of Full Navier-Stokes and Reduced Navier-Stokes analyses for separating flows within a diffusing inlet S-duct

NASA Technical Reports Server (NTRS)

Anderson, B. H.; Reddy, D. R.; Kapoor, K.

1993-01-01

A three-dimensional implicit Full Navier-Stokes (FNS) analysis and a 3D Reduced Navier Stokes (RNS) initial value space marching solution technique has been applied to a class of separated flow problems within a diffusing S-duct configuration characterized by vortex-liftoff. Both the FNS and the RNS solution technique were able to capture the overall flow physics of vortex lift-off, and gave remarkably similar results which agreed reasonably well with the experimental measured averaged performance parameters of engine face total pressure recovery and distortion. However, the Full Navier-Stokes and Reduced Navier-Stokes also consistently predicted separation further downstream in the M2129 inlet S-duct than was indicated by experimental data, thus compensating errors were present in the two Navier-Stokes analyses. The difficulties encountered in the Navier-Stokes separations analyses of the M2129 inlet S-duct center primarily on turbulence model issues, and these focused on two distinct but different phenomena, namely, (1) characterization of low skin friction adverse pressure gradient flows, and (2) description of the near wall behavior of flows characterized by vortex lift-off.

Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation.

PubMed

Pesavento, Umberto; Wang, Z Jane

2004-10-01

We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around 10(3). The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotation provides a mechanism for a brief elevation of center of mass near the cusplike turning points. The Navier-Stokes solutions further provide the missing quantity in the classical theory of lift, the instantaneous circulation, and suggest a revised model for the fluid forces.

Polarimetría de las atmósferas de Urano y Neptuno

NASA Astrophysics Data System (ADS)

López Sisterna, C.; Gil-Hutton, R.

2015-08-01

We present imaging polarimetry for Uranus and Neptune, the observations were taken with the 2.15 m telescope at CASLEO. The patterns observed for both planets turn to be centro-symmetric; unlike the observations on Jupiter and Saturn. However, the Stokes parameters introduce large errors on the degree of polarization, and the radial Stokes parameters are used instead. We obtain that the radial limb polarization is about 0.20. Further, we corrected the parameters for seeing, and compared the results with analytical models of semi-infinite and finite Rayleigh scattering atmospheres. From this comparison we conclude the polarization agrees with the semi-infinite Rayleigh scattering atmosphere.

Application of boundary element method to Stokes flows over a striped superhydrophobic surface with trapped gas bubbles

NASA Astrophysics Data System (ADS)

Ageev, A. I.; Golubkina, I. V.; Osiptsov, A. N.

2018-01-01

A slow steady flow of a viscous fluid over a superhydrophobic surface with a periodic striped system of 2D rectangular microcavities is considered. The microcavities contain small gas bubbles on the curved surface of which the shear stress vanishes. The general case is analyzed when the bubble occupies only a part of the cavity, and the flow velocity far from the surface is directed at an arbitrary angle to the cavity edge. Due to the linearity of the Stokes flow problem, the solution is split into two parts, corresponding to the flows perpendicular and along the cavities. Two variants of a boundary element method are developed and used to construct numerical solutions on the scale of a single cavity with periodic boundary conditions. By averaging these solutions, the average slip velocity and the slip length tensor components are calculated over a wide range of variation of governing parameters for the cases of a shear-driven flow and a pressure-driven channel flow. For a sufficiently high pressure drop in a microchannel of finite length, the variation of the bubble surface shift into the cavities induced by the streamwise pressure variation is estimated from numerical calculations.

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2018-01-01

The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus

NASA Astrophysics Data System (ADS)

Ortega-Quijano, Noé; Fade, Julien; Roche, Muriel; Parnet, François; Alouini, Mehdi

2016-04-01

Polarimetric sensing by orthogonality breaking has been recently proposed as an alternative technique for performing direct and fast polarimetric measurements using a specific dual-frequency dual-polarization (DFDP) source. Based on the instantaneous Stokes-Mueller formalism to describe the high-frequency evolution of the DFDP beam intensity, we thoroughly analyze the interaction of such a beam with birefringent, dichroic and depolarizing samples. This allows us to confirm that orthogonality breaking is produced by the sample diattenuation, whereas this technique is immune to both birefringence and diagonal depolarization. We further analyze the robustness of this technique when polarimetric sensing is performed through a birefringent waveguide, and the optimal DFDP source configuration for fiber-based endoscopic measurements is subsequently identified. Finally, we consider a stochastic depolarization model based on an ensemble of random linear diattenuators, which makes it possible to understand the progressive vanishing of the detected orthogonality breaking signal as the spatial heterogeneity of the sample increases, thus confirming the insensitivity of this method to diagonal depolarization. The fact that the orthogonality breaking signal is exclusively due to the sample dichroism is an advantageous feature for the precise decoupled characterization of such an anisotropic parameter in samples showing several simultaneous effects.

Invariants of polarization transformations.

PubMed

Sadjadi, Firooz A

2007-05-20

The use of polarization-sensitive sensors is being explored in a variety of applications. Polarization diversity has been shown to improve the performance of the automatic target detection and recognition in a significant way. However, it also brings out the problems associated with processing and storing more data and the problem of polarization distortion during transmission. We present a technique for extracting attributes that are invariant under polarization transformations. The polarimetric signatures are represented in terms of the components of the Stokes vectors. Invariant algebra is then used to extract a set of signature-related attributes that are invariant under linear transformation of the Stokes vectors. Experimental results using polarimetric infrared signatures of a number of manmade and natural objects undergoing systematic linear transformations support the invariancy of these attributes.

Hypersonic Boundary Layer Instability Over a Corner

NASA Technical Reports Server (NTRS)

Balakumar, Ponnampalam; Zhao, Hong-Wu; McClinton, Charles (Technical Monitor)

2001-01-01

A boundary-layer transition study over a compression corner was conducted under a hypersonic flow condition. Due to the discontinuities in boundary layer flow, the full Navier-Stokes equations were solved to simulate the development of disturbance in the boundary layer. A linear stability analysis and PSE method were used to get the initial disturbance for parallel and non-parallel flow respectively. A 2-D code was developed to solve the full Navier-stokes by using WENO(weighted essentially non-oscillating) scheme. The given numerical results show the evolution of the linear disturbance for the most amplified disturbance in supersonic and hypersonic flow over a compression ramp. The nonlinear computations also determined the minimal amplitudes necessary to cause transition at a designed location.

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cortes, Adriano M.; Dalcin, Lisandro; Sarmiento, Adel F.

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf–sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show howmore » the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Lastly, besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.« less

Extended depth measurement for a Stokes sample imaging polarimeter

NASA Astrophysics Data System (ADS)

Dixon, Alexander W.; Taberner, Andrew J.; Nash, Martyn P.; Nielsen, Poul M. F.

2018-02-01

A non-destructive imaging technique is required for quantifying the anisotropic and heterogeneous structural arrangement of collagen in soft tissue membranes, such as bovine pericardium, which are used in the construction of bioprosthetic heart valves. Previously, our group developed a Stokes imaging polarimeter that measures the linear birefringence of samples in a transmission arrangement. With this device, linear retardance and optic axis orientation; can be estimated over a sample using simple vector algebra on Stokes vectors in the Poincaré sphere. However, this method is limited to a single path retardation of a half-wave, limiting the thickness of samples that can be imaged. The polarimeter has been extended to allow illumination of narrow bandwidth light of controllable wavelength through achromatic lenses and polarization optics. We can now take advantage of the wavelength dependence of relative retardation to remove ambiguities that arise when samples have a single path retardation of a half-wave to full-wave. This effectively doubles the imaging depth of this method. The method has been validated using films of cellulose of varied thickness, and applied to samples of bovine pericardium.

A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem

DOE PAGES

Cortes, Adriano M.; Dalcin, Lisandro; Sarmiento, Adel F.; ...

2016-10-19

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf–sup stable and pointwise divergence-free. When applied to the discretized Stokes problem, these spaces generate a symmetric and indefinite saddle-point linear system. The iterative method of choice to solve such system is the Generalized Minimum Residual Method. This method lacks robustness, and one remedy is to use preconditioners. For linear systems of saddle-point type, a large family of preconditioners can be obtained by using a block factorization of the system. In this paper, we show howmore » the nesting of “black-box” solvers and preconditioners can be put together in a block triangular strategy to build a scalable block preconditioner for the Stokes system discretized by divergence-conforming B-splines. Lastly, besides the known cavity flow problem, we used for benchmark flows defined on complex geometries: an eccentric annulus and hollow torus of an eccentric annular cross-section.« less

A Quasioptical Vector Interferometer for Polarization Control

NASA Technical Reports Server (NTRS)

Chuss, David T.; Wollack, Edward J.; Moseley, Harvey S.; Novak, Giles

2005-01-01

We present a mathematical description of a Quasioptical Vector Interferometer (QVI), a device that maps an input polarization state to an output polarization state by introducing a phase delay between two linear orthogonal components of the input polarization. The advantages of such a device over a spinning wave-plate modulator for measuring astronomical polarization in the far-infrared through millimeter are: 1. The use of small, linear motions eliminates the need for cryogenic rotational bearings, 2. The phase flexibility allows measurement of Stokes V as well as Q and U, and 3. The QVI allows for both multi-wavelength and broadband modulation. We suggest two implementations of this device as an astronomical polarization modulator. The first involves two such modulators placed in series. By adjusting the two phase delays, it is possible to use such a modulator to measure Stokes Q, U, and V for passbands that are not too large. Conversely, a single QVI may be used to measure Q and V independent of frequency. In this implementation, Stokes U must be measured by rotating the instrument. We conclude this paper by presenting initial laboratory results.

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

CUDA GPU based full-Stokes finite difference modelling of glaciers

NASA Astrophysics Data System (ADS)

Brædstrup, C. F.; Egholm, D. L.

2012-04-01

Many have stressed the limitations of using the shallow shelf and shallow ice approximations when modelling ice streams or surging glaciers. Using a full-stokes approach requires either large amounts of computer power or time and is therefore seldom an option for most glaciologists. Recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists. Our full-stokes ice sheet model implements a Red-Black Gauss-Seidel iterative linear solver to solve the full stokes equations. This technique has proven very effective when applied to the stokes equation in geodynamics problems, and should therefore also preform well in glaciological flow probems. The Gauss-Seidel iterator is known to be robust but several other linear solvers have a much faster convergence. To aid convergence, the solver uses a multigrid approach where values are interpolated and extrapolated between different grid resolutions to minimize the short wavelength errors efficiently. This reduces the iteration count by several orders of magnitude. The run-time is further reduced by using the GPGPU technology where each card has up to 448 cores. Researchers utilizing the GPGPU technique in other areas have reported between 2 - 11 times speedup compared to multicore CPU implementations on similar problems. The goal of these initial investigations into the possible usage of GPGPU technology in glacial modelling is to apply the enhanced resolution of a full-stokes solver to ice streams and surging glaciers. This is a area of growing interest because ice streams are the main drainage conjugates for large ice sheets. It is therefore crucial to understand this streaming behavior and it's impact up-ice.

Discrete adjoint of fractional step Navier-Stokes solver in generalized coordinates

NASA Astrophysics Data System (ADS)

Wang, Mengze; Mons, Vincent; Zaki, Tamer

2017-11-01

Optimization and control in transitional and turbulent flows require evaluation of gradients of the flow state with respect to the problem parameters. Using adjoint approaches, these high-dimensional gradients can be evaluated with a similar computational cost as the forward Navier-Stokes simulations. The adjoint algorithm can be obtained by discretizing the continuous adjoint Navier-Stokes equations or by deriving the adjoint to the discretized Navier-Stokes equations directly. The latter algorithm is necessary when the forward-adjoint relations must be satisfied to machine precision. In this work, our forward model is the fractional step solution to the Navier-Stokes equations in generalized coordinates, proposed by Rosenfeld, Kwak & Vinokur. We derive the corresponding discrete adjoint equations. We also demonstrate the accuracy of the combined forward-adjoint model, and its application to unsteady wall-bounded flows. This work has been partially funded by the Office of Naval Research (Grant N00014-16-1-2542).

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Techniques and Software for Monolithic Preconditioning of Moderately-sized Geodynamic Stokes Flow Problems

NASA Astrophysics Data System (ADS)

Sanan, Patrick; May, Dave A.; Schenk, Olaf; Bollhöffer, Matthias

2017-04-01

Geodynamics simulations typically involve the repeated solution of saddle-point systems arising from the Stokes equations. These computations often dominate the time to solution. Direct solvers are known for their robustness and ``black box'' properties, yet exhibit superlinear memory requirements and time to solution. More complex multilevel-preconditioned iterative solvers have been very successful for large problems, yet their use can require more effort from the practitioner in terms of setting up a solver and choosing its parameters. We champion an intermediate approach, based on leveraging the power of modern incomplete factorization techniques for indefinite symmetric matrices. These provide an interesting alternative in situations in between the regimes where direct solvers are an obvious choice and those where complex, scalable, iterative solvers are an obvious choice. That is, much like their relatives for definite systems, ILU/ICC-preconditioned Krylov methods and ILU/ICC-smoothed multigrid methods, the approaches demonstrated here provide a useful addition to the solver toolkit. We present results with a simple, PETSc-based, open-source Q2-Q1 (Taylor-Hood) finite element discretization, in 2 and 3 dimensions, with the Stokes and Lamé (linear elasticity) saddle point systems. Attention is paid to cases in which full-operator incomplete factorization gives an improvement in time to solution over direct solution methods (which may not even be feasible due to memory limitations), without the complication of more complex (or at least, less-automatic) preconditioners or smoothers. As an important factor in the relevance of these tools is their availability in portable software, we also describe open-source PETSc interfaces to the factorization routines.

Cutaneous porphyrins exhibit anti-stokes fluorescence that is detectable in sebum (Conference Presentation)

NASA Astrophysics Data System (ADS)

Tian, Giselle; Zeng, Haishan; Zhao, Jianhua; Wu, Zhenguo; Al Jasser, Mohammed; Lui, Harvey; Mclean, David I.

2016-02-01

Porphyrins produced by Propionibacterium acnes represent the principal fluorophore associated with acne, and appear as orange-red luminescence under the Wood's lamp. Assessment of acne based on Wood's lamp (UV) or visible light illumination is limited by photon penetration depth and has limited sensitivity for earlier stage lesions. Inducing fluorescence with near infrared (NIR) excitation may provide an alternative way to assess porphyrin-related skin disorders. We discovered that under 785 nm CW laser excitation PpIX powder exhibits fluorescence emission in the shorter wavelength range of 600-715 nm with an intensity that is linearly dependent on the excitation power. We attribute this shorter wavelength emission to anti-Stokes fluorescence. Similar anti-Stokes fluorescence was also detected focally in all skin-derived samples containing porphyrins. Regular (Stokes) fluorescence was present under UV and visible light excitation on ex vivo nasal skin and sebum from uninflamed acne, but not on nose surface smears or sebum from inflamed acne. Co-registered CW laser-excited anti-Stokes fluorescence and fs laser-excited multi-photon fluorescence images of PpIX powder showed similar features. In the skin samples because of the anti-Stokes effect, the NIR-induced fluorescence was presumably specific for porphyrins since there appeared to be no anti-Stokes emission signals from other typical skin fluorophores such as lipids, keratins and collagen. Anti-Stokes fluorescence under NIR CW excitation is more sensitive and specific for porphyrin detection than UV- or visible light-excited regular fluorescence and fs laser-excited multi-photon fluorescence. This approach also has higher image contrast compared to NIR fs laser-based multi-photon fluorescence imaging. The anti-Stokes fluorescence of porphyrins within sebum could potentially be applied to detecting and targeting acne lesions for treatment via fluorescence image guidance.

Plasmonic micropolarizers for full Stokes vector imaging

NASA Astrophysics Data System (ADS)

Peltzer, J. J.; Bachman, K. A.; Rose, J. W.; Flammer, P. D.; Furtak, T. E.; Collins, R. T.; Hollingsworth, R. E.

2012-06-01

Polarimetric imaging using micropolarizers integrated on focal plane arrays has previously been limited to the linear components of the Stokes vector because of the lack of an effective structure with selectivity to circular polarization. We discuss a plasmonic micropolarizing filter that can be tuned for linear or circular polarization as well as wavelength selectivity from blue to infrared (IR) through simple changes in its horizontal geometry. The filter consists of a patterned metal film with an aperture in a central cavity that is surrounded by gratings that couple to incoming light. The aperture and gratings are covered with a transparent dielectric layer to form a surface plasmon slab waveguide. A metal cap covers the aperture and forms a metal-insulator-metal (MIM) waveguide. Structures with linear apertures and gratings provide sensitivity to linear polarization, while structures with circular apertures and spiral gratings give circular polarization selectivity. Plasmonic TM modes are transmitted down the MIM waveguide while the TE modes are cut off due to the sub-wavelength dielectric thickness, providing the potential for extremely high extinction ratios. Experimental results are presented for micropolarizers fabricated on glass or directly into the Ohmic contact metallization of silicon photodiodes. Extinction ratios for linear polarization larger than 3000 have been measured.

Research in Computational Aeroscience Applications Implemented on Advanced Parallel Computing Systems

NASA Technical Reports Server (NTRS)

Wigton, Larry

1996-01-01

Improving the numerical linear algebra routines for use in new Navier-Stokes codes, specifically Tim Barth's unstructured grid code, with spin-offs to TRANAIR is reported. A fast distance calculation routine for Navier-Stokes codes using the new one-equation turbulence models is written. The primary focus of this work was devoted to improving matrix-iterative methods. New algorithms have been developed which activate the full potential of classical Cray-class computers as well as distributed-memory parallel computers.

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

2013-01-01

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

Solvatochromic investigation of highly fluorescent 2-aminobithiophene derivatives.

PubMed

Bolduc, Andréanne; Dong, Yanmei; Guérin, Amélie; Skene, W G

2012-05-21

The solvatochromic and electrochemical properties of electronic push-pull 2-aminobithiophenes consisting of an aldehyde and nitro withdrawing groups were examined. With the use of an integrating sphere, the absolute quantum yields of the bithiophenes were measured. They were found to be highly fluorescent (Φfl > 70%), provided the nitro group was not located in the 4'-position. High fluorescence yields were observed regardless of solvent, except for alcohols, notably methanol and ethanol. Cryofluorescence was used to probe the bithiophene temperature dependent excited state deactivation modes. The singlet excited state deactivation mode other than fluorescence was found to be internal conversion involving rotation around the thiophene-thiophene bond. Deactivation by intersystem crossing to the triplet state occurred in ca. 40% only for the unsubstituted 2-aminobithiophene. In contrast, the fluorescence was quenched by photoinduced intramolecular electron transfer when the nitro group was located in the 4'-position of the bithiophene. Both the absorbance and fluorescence of the bithiophenes were found to be solvatochromic with more pronounced solvent dependent shifts being observed with the fluorescence. In fact, both the fluorescence and Stokes shifts were linearly dependent on the ET(30) solvent parameter. Deviations from the linear trend of the Stokes shift with ET(30) were observed in ethanol and methanol as a result of intermolecular hydrogen abstraction from the solvent and by the excited nitro group. The oxidation potential of the bithiophenes was also highly dependent on the type and number of the electron withdrawing substituents, with values ranging between 0.8 and 1.2 V vs. SCE.

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Zhiqiang; Manteuffel, Thomas A.; McCormick, Stephen F.

1996-01-01

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Three-dimensional Navier-Stokes analysis of turbine passage heat transfer

NASA Technical Reports Server (NTRS)

Ameri, Ali A.; Arnone, Andrea

1991-01-01

The three-dimensional Reynolds-averaged Navier-Stokes equations are numerically solved to obtain the pressure distribution and heat transfer rates on the endwalls and the blades of two linear turbine cascades. The TRAF3D code which has recently been developed in a joint project between researchers from the University of Florence and NASA Lewis Research Center is used. The effect of turbulence is taken into account by using the eddy viscosity hypothesis and the two-layer mixing length model of Baldwin and Lomax. Predictions of surface heat transfer are made for Langston's cascade and compared with the data obtained for that cascade by Graziani. The comparison was found to be favorable. The code is also applied to a linear transonic rotor cascade to predict the pressure distributions and heat transfer rates.

Intrinsic coincident full-Stokes polarimeter using stacked organic photovoltaics and architectural comparison of polarimeter techniques

NASA Astrophysics Data System (ADS)

Yang, Ruonan; Sen, Pratik; O'Connor, B. T.; Kudenov, M. W.

2017-08-01

An intrinsic coincident full-Stokes polarimeter is demonstrated by using stain-aligned polymer-based organic photovoltaics (OPVs) which can preferentially absorb certain polarized states of incident light. The photovoltaic-based polarimeter is capable of measuring four stokes parameters by cascading four semitransparent OPVs in series along the same optical axis. Two wave plates were incorporated into the system to modulate the S3 stokes parameter so as to reduce the condition number of the measurement matrix. The model for the full-Stokes polarimeter was established and validated, demonstrating an average RMS error of 0.84%. The optimization, based on minimizing the condition number of the 4-cell OPV design, showed that a condition number of 2.4 is possible. Performance of this in-line polarimeter concept was compared to other polarimeter architectures, including Division of Time (DoT), Division of Amplitude (DoAm), Division of Focal Plane (DoFP), and Division of Aperture (DoA) from signal-to-noise ratio (SNR) perspective. This in-line polarimeter concept has the potential to enable both high temporal (as compared with a DoT polarimeter) and high spatial resolution (as compared with DoFP and DoA polarimeters). We conclude that the intrinsic design has the same √2 SNR advantage as the DoAm polarimeter, but with greater compactness.

Rapid spectro-polarimetry to probe molecular symmetry in multiplex coherent anti-Stokes Raman scattering.

PubMed

Würthwein, Thomas; Brinkmann, Maximilian; Hellwig, Tim; Fallnich, Carsten

2017-11-21

We present the simultaneous detection of the spectrum and the complete polarization state of a multiplex coherent anti-Stokes Raman scattering signal with a fast division-of-amplitude spectro-polarimeter. The spectro-polarimeter is based on a commercial imaging spectrograph, a birefringent wedge prism, and a segmented polarizer. Compared to the standard rotating-retarder fixed-analyzer spectro-polarimeter, only a single measurement is required and an up to 21-fold reduced acquisition time is shown. The measured Stokes parameters allow us to differentiate between vibrational symmetries and to determine the depolarization ratio ρ by data post-processing.

Non-Gaussian statistics and optical rogue waves in stimulated Raman scattering.

PubMed

Monfared, Yashar E; Ponomarenko, Sergey A

2017-03-20

We explore theoretically and numerically optical rogue wave formation in stimulated Raman scattering inside a hydrogen filled hollow core photonic crystal fiber. We assume a weak noisy Stokes pulse input and explicitly construct the input Stokes pulse ensemble using the coherent mode representation of optical coherence theory, thereby providing a link between optical coherence and rogue wave theories. We show that the Stokes pulse peak power probability distribution function (PDF) acquires a long tail in the limit of nearly incoherent input Stokes pulses. We demonstrate a clear link between the PDF tail magnitude and the source coherence time. Thus, the latter can serve as a convenient parameter to control the former. We explain our findings qualitatively using the concepts of statistical granularity and global degree of coherence.

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

DOE PAGES

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

2016-05-25

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

The Craik-Leibovich Vortex Force as a Skin Effect

NASA Astrophysics Data System (ADS)

Malecha, Ziemowit; Chini, Gregory; Julien, Keith

2013-11-01

The Craik-Leibovich (CL) equations are a surface-wave filtered version of the instantaneous Navier-Stokes equations in which the rectified effects of the surface waves are captured through a so-called ``vortex force'' term: the cross-product of the Stokes, or Lagrangian, mass drift associated with the filtered surface waves and the filtered vorticity vector. For locally generated wind waves, the Stokes drift is very strongly surface confined. In this scenario, the induced body force may be represented as a surface, or skin, effect. Using matched asymptotic analysis in this limit, we derive effective boundary conditions (BCs) for the flow beneath the Stokes drift layer (i.e. in the bulk of the mixed layer). We establish the regime of validity of the resulting formulation by performing linear stability analyses and numerical simulations of both the asymptotic model and the full CL equations for a variety of vertical Stokes drift profiles. The effective BC formulation offers both theoretical and computational advantages, and should be particularly useful for LES of Langmuir turbulence for which the need to resolve very small scale near-surface flow structures imposes severe computational constraints. GPC would like to acknowledge funding from the NSF award 0934827, administered by the Physical Oceanography Program.

The Galway astronomical Stokes polarimeter: an all-Stokes optical polarimeter with ultra-high time resolution

NASA Astrophysics Data System (ADS)

Collins, Patrick; Kyne, Gillian; Lara, David; Redfern, Michael; Shearer, Andy; Sheehan, Brendan

2013-12-01

Many astronomical objects emit polarised light, which can give information both about their source mechanisms, and about (scattering) geometry in their source regions. To date (mostly) only the linearly polarised components of the emission have been observed in stellar sources. Observations have been constrained because of instrumental considerations to periods of excellent observing conditions, and to steady, slowly or periodically-varying sources. This leaves a whole range of interesting objects beyond the range of observation at present. The Galway Astronomical Stokes Polarimeter (GASP) has been developed to enable us to make observations on these very sources. GASP measures the four components of the Stokes Vector simultaneously over a broad wavelength range 400-800 nm., with a time resolution of order microseconds given suitable detectors and a bright source - this is possible because the optical design contains no moving or modulating components. The initial design of GASP is presented and we include some preliminary observational results demonstrating that components of the Stokes vector can be measured to % in conditions of poor atmospheric stability. Issues of efficiency and stability are addressed. An analysis of suitable astronomical targets, demanding the unique properties of GASP, is also presented.

Summer Research Program (1992). Summer Faculty Research Program (SFRP) Reports. Volume 2. Armstrong Laboratory

DTIC Science & Technology

1992-12-01

desirable. In this study, the proposed model consists of a thick-walled, highly deformable elastic tube in which the blood flow is described by linearized ...presented a mechanical model consisting of linearized Navier-Stokes and finite elasticity equations to predict blood pooling under acceleration stress... linear multielement model of the cardiovascular system which can calculate blood pressures and flows at any point in the cardio- vascular system. It

Tuning the Quantum Efficiency of Random Lasers - Intrinsic Stokes-Shift and Gain

PubMed Central

Lubatsch, Andreas; Frank, Regine

2015-01-01

We report the theoretical analysis for tuning the quantum efficiency of solid state random lasers. Vollhardt-Wölfle theory of photonic transport in disordered non-conserving and open random media, is coupled to lasing dynamics and solved positionally dependent. The interplay of non-linearity and homogeneous non-radiative frequency conversion by means of a Stokes-shift leads to a reduction of the quantum efficiency of the random laser. At the threshold a strong decrease of the spot-size in the stationary state is found due to the increase of non-radiative losses. The coherently emitted photon number per unit of modal surface is also strongly reduced. This result allows for the conclusion that Stokes-shifts are not sufficient to explain confined and extended mode regimes. PMID:26593237

Tuning the Quantum Efficiency of Random Lasers - Intrinsic Stokes-Shift and Gain.

PubMed

Lubatsch, Andreas; Frank, Regine

2015-11-23

We report the theoretical analysis for tuning the quantum efficiency of solid state random lasers. Vollhardt-Wölfle theory of photonic transport in disordered non-conserving and open random media, is coupled to lasing dynamics and solved positionally dependent. The interplay of non-linearity and homogeneous non-radiative frequency conversion by means of a Stokes-shift leads to a reduction of the quantum efficiency of the random laser. At the threshold a strong decrease of the spot-size in the stationary state is found due to the increase of non-radiative losses. The coherently emitted photon number per unit of modal surface is also strongly reduced. This result allows for the conclusion that Stokes-shifts are not sufficient to explain confined and extended mode regimes.

The Primordial Inflation Explorer (PIXIE): A Nulling Polarimeter for Cosmic Microwave Background Observations

NASA Technical Reports Server (NTRS)

Kogut, Alan J.; Fixsen, D. J.; Chuss, D. T.; Dotson, J.; Dwek, E.; Halpern, M.; Hinshaw, G. F.; Meyer, S. M.; Moseley, S. H.; Seiffert, M. D.;

A nonlinear model for analysis of slug-test data

USGS Publications Warehouse

McElwee, C.D.; Zenner, M.A.

1998-01-01

While doing slug tests in high-permeability aquifers, we have consistently seen deviations from the expected response of linear theoretical models. Normalized curves do not coincide for various initial heads, as would be predicted by linear theories, and are shifted to larger times for higher initial heads. We have developed a general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the well bore, and a Hvorslev model for the aquifer, which explains these data features. The model produces a very good fit for both oscillatory and nonoscillatory field data, using a single set of physical parameters to predict the field data for various initial displacements at a given well. This is in contrast to linear models which have a systematic lack of fit and indicate that hydraulic conductivity varies with the initial displacement. We recommend multiple slug tests with a considerable variation in initial head displacement to evaluate the possible presence of nonlinear effects. Our conclusion is that the nonlinear model presented here is an excellent tool to analyze slug tests, covering the range from the underdamped region to the overdamped region.

Multispectral Stokes polarimetry for dermatoscopic imaging

NASA Astrophysics Data System (ADS)

Castillejos, Y.; Martínez-Ponce, Geminiano; Mora-Nuñez, Azael; Castro-Sanchez, R.

2015-12-01

Most of skin pathologies, including melanoma and basal/squamous cell carcinoma, are related to alterations in external and internal order. Usually, physicians rely on their empirical expertise to diagnose these ills normally assisted with dermatoscopes. When there exists skin cancer suspicion, a cytology or biopsy is made, but both laboratory tests imply an invasive procedure. In this regard, a number of non-invasive optical techniques have been proposed recently to improve the diagnostic certainty and assist in the early detection of cutaneous cancer. Herein, skin optical properties are derived with a multispectral polarimetric dermatoscope using three different illumination wavelength intervals centered at 470, 530 and 635nm. The optical device consist of two polarizing elements, a quarter-wave plate and a linear polarizer, rotating at a different angular velocity and a CCD array as the photoreceiver. The modulated signal provided by a single pixel in the acquired image sequence is analyzed with the aim of computing the Stokes parameters. Changes in polarization state of selected wavelengths provide information about the presence of skin pigments such as melanin and hemoglobin species as well as collagen structure, among other components. These skin attributes determine the local physiology or pathology. From the results, it is concluded that optical polarimetry will provide additional elements to dermatologists in their diagnostic task.

A computational geometry approach to pore network construction for granular packings

NASA Astrophysics Data System (ADS)

van der Linden, Joost H.; Sufian, Adnan; Narsilio, Guillermo A.; Russell, Adrian R.; Tordesillas, Antoinette

2018-03-01

Pore network construction provides the ability to characterize and study the pore space of inhomogeneous and geometrically complex granular media in a range of scientific and engineering applications. Various approaches to the construction have been proposed, however subtle implementational details are frequently omitted, open access to source code is limited, and few studies compare multiple algorithms in the context of a specific application. This study presents, in detail, a new pore network construction algorithm, and provides a comprehensive comparison with two other, well-established Delaunay triangulation-based pore network construction methods. Source code is provided to encourage further development. The proposed algorithm avoids the expensive non-linear optimization procedure in existing Delaunay approaches, and is robust in the presence of polydispersity. Algorithms are compared in terms of structural, geometrical and advanced connectivity parameters, focusing on the application of fluid flow characteristics. Sensitivity of the various networks to permeability is assessed through network (Stokes) simulations and finite-element (Navier-Stokes) simulations. Results highlight strong dependencies of pore volume, pore connectivity, throat geometry and fluid conductance on the degree of tetrahedra merging and the specific characteristics of the throats targeted by the merging algorithm. The paper concludes with practical recommendations on the applicability of the three investigated algorithms.

Optical characterization of porcine articular cartilage using a polarimetry technique with differential Mueller matrix formulism.

PubMed

Chang, Ching-Min; Lo, Yu-Lung; Tran, Nghia-Khanh; Chang, Yu-Jen

2018-03-20

A method is proposed for characterizing the optical properties of articular cartilage sliced from a pig's thighbone using a Stokes-Mueller polarimetry technique. The principal axis angle, phase retardance, optical rotation angle, circular diattenuation, diattenuation axis angle, linear diattenuation, and depolarization index properties of the cartilage sample are all decoupled in the proposed analytical model. Consequently, the accuracy and robustness of the extracted results are improved. The glucose concentration, collagen distribution, and scattering properties of samples from various depths of the articular cartilage are systematically explored via an inspection of the related parameters. The results show that the glucose concentration and scattering effect are both enhanced in the superficial region of the cartilage. By contrast, the collagen density increases with an increasing sample depth.

Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study

DOE PAGES

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan; ...

2017-09-07

In this paper, we demonstrate a statistical procedure for learning a high-order eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynolds-averaged Navier–Stokes (RANS) simulator. The method is tested in a three-dimensional (3D), transonic jet-in-crossflow (JIC) configuration. The process starts with a cubic eddy viscosity model (CEVM) developed for incompressible flows. It is fitted to limited experimental JIC data using shrinkage regression. The shrinkage process removes all the terms from the model, except an intercept, a linear term, and a quadratic one involving the square of the vorticity. The shrunk eddy viscositymore » model is implemented in an RANS simulator and calibrated, using vorticity measurements, to infer three parameters. The calibration is Bayesian and is solved using a Markov chain Monte Carlo (MCMC) method. A 3D probability density distribution for the inferred parameters is constructed, thus quantifying the uncertainty in the estimate. The phenomenal cost of using a 3D flow simulator inside an MCMC loop is mitigated by using surrogate models (“curve-fits”). A support vector machine classifier (SVMC) is used to impose our prior belief regarding parameter values, specifically to exclude nonphysical parameter combinations. The calibrated model is compared, in terms of its predictive skill, to simulations using uncalibrated linear and CEVMs. Finally, we find that the calibrated model, with one quadratic term, is more accurate than the uncalibrated simulator. The model is also checked at a flow condition at which the model was not calibrated.« less

Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan

In this paper, we demonstrate a statistical procedure for learning a high-order eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynolds-averaged Navier–Stokes (RANS) simulator. The method is tested in a three-dimensional (3D), transonic jet-in-crossflow (JIC) configuration. The process starts with a cubic eddy viscosity model (CEVM) developed for incompressible flows. It is fitted to limited experimental JIC data using shrinkage regression. The shrinkage process removes all the terms from the model, except an intercept, a linear term, and a quadratic one involving the square of the vorticity. The shrunk eddy viscositymore » model is implemented in an RANS simulator and calibrated, using vorticity measurements, to infer three parameters. The calibration is Bayesian and is solved using a Markov chain Monte Carlo (MCMC) method. A 3D probability density distribution for the inferred parameters is constructed, thus quantifying the uncertainty in the estimate. The phenomenal cost of using a 3D flow simulator inside an MCMC loop is mitigated by using surrogate models (“curve-fits”). A support vector machine classifier (SVMC) is used to impose our prior belief regarding parameter values, specifically to exclude nonphysical parameter combinations. The calibrated model is compared, in terms of its predictive skill, to simulations using uncalibrated linear and CEVMs. Finally, we find that the calibrated model, with one quadratic term, is more accurate than the uncalibrated simulator. The model is also checked at a flow condition at which the model was not calibrated.« less

Partially-Averaged Navier Stokes Model for Turbulence: Implementation and Validation

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.; Abdol-Hamid, Khaled S.

2005-01-01

Partially-averaged Navier Stokes (PANS) is a suite of turbulence closure models of various modeled-to-resolved scale ratios ranging from Reynolds-averaged Navier Stokes (RANS) to Navier-Stokes (direct numerical simulations). The objective of PANS, like hybrid models, is to resolve large scale structures at reasonable computational expense. The modeled-to-resolved scale ratio or the level of physical resolution in PANS is quantified by two parameters: the unresolved-to-total ratios of kinetic energy (f(sub k)) and dissipation (f(sub epsilon)). The unresolved-scale stress is modeled with the Boussinesq approximation and modeled transport equations are solved for the unresolved kinetic energy and dissipation. In this paper, we first present a brief discussion of the PANS philosophy followed by a description of the implementation procedure and finally perform preliminary evaluation in benchmark problems.

Coupled photonic crystal micro-cavities with ultra-low threshold power for stimulated Raman scattering.

PubMed

Liu, Qiang; Ouyang, Zhengbiao; Albin, Sacharia

2011-02-28

We propose coupled cavities to realize a strong enhancement of the Raman scattering. Five sub cavities are embedded in the photonic crystals. Simulations through finite-difference time-domain (FDTD) method demonstrate that one cavity, which is used to propagate the pump beam at the optical-communication wavelength, has a Q factor as high as 
1.254×10⁸ and modal volume as small as 0.03 μm3 (0.3192(λ/n)3). These parameters result in ultra-small threshold lasing power~17.7 nW and 2.58 nW for Stokes and anti-Stokes respectively. The cavities are designed to support the required Stokes and anti-Stokes modal spacing in silicon. The proposed structure has the potential for sensor devices, especially for biological and medical diagnoses.

The global structure of hot star winds: Constraints from spectropolarimetry

NASA Astrophysics Data System (ADS)

Eversberg, Thomas

2000-11-01

Chapter 1. We present time-series of ultra-high S/N, high resolution spectra of the He II λ 4686 Å emission line in the O4I(n)f supergiant ζ Puppis, the brightest early-type O-star in the sky. These reveal stochastic, variable substructures in the line, which tend to move away from the line-center with time. Similar scaled-up features are well established in the strong winds of Wolf-Rayet stars (the presumed descendants of O stars), where they are explained by outward moving inhomogeneities (e.g., blobs, clumps, shocks) in the winds. If all hot-star winds are clumped like that of ζ Pup, as is plausible, then mass-low rates based on recombination-line intensities will have to be revised downwards. Using a standard `β' velocity law we deduce a value of β = 1.0-1.2 to account for the kinematics of these structures in the wind of ζ Pup. In addition to the small-scale stochastic variations we also find a slow systematic variation of the mean central absorption reversal. Chapter 2. We introduce a new polarimeter unit which, mounted at the Cassegrain focus of any telescope and fiber-connected to a fixed CCD spectrograph, is able to measure all Stokes parameters I, Q, U and V across spectral lines of bright stellar targets and other point sources in a quasi-simultaneous manner. Applying standard reduction techniques for linearly and circularly polarized light we are able to obtain photon-noise limited line polarization. We briefly outline the technical design of the polarimeter unit and the linear algebraic Mueller calculus for obtaining polarization parameters of any point source. In addition, practical limitations of the optical elements are outlined. We present first results obtained with our spectropolarimeter for four bright, hot-star targets: We confirm previous results for Hα in the bright Be star γ Cas and find linear depolarization features across the emission line complex C III/C IV (λ 5696/λ 5808 Å) of the WR+O binary γ2 Vel. We also find circular line polarization in the strongly magnetic Ap star 53 Cam across its Hα absorption line. No obvious line polarization features are seen across Hα in the variable O star θ1 Ori C above the σ ~ 0.2% instrumental level. Chapter 3. We present low resolution (~6 Å), high signal-to noise spectropolarimetric observations obtained with the new William-Wehlau spectropolarimeter for the apparently brightest Wolf-Rayet star in the sky, the 78.5d WR+O binary γ2 Velorum. Quasi- simultaneous monitoring of all four Stokes parameters I(λ), q(λ), u(λ) and v(λ) was carried out over an interval of 31 nights centered on periastron. All emission lines in our observed wavelength interval (5200-6000 Å) show highly stochastic variations over the whole run. The phase-dependent behavior of the excess emission in the C III λ 5696 line can be related to the wind-wind collision phenomenon. Varying features of Stokes q and u are seen across the strong lines, probably as a result of variable electron scattering of mainly continuum light. The spherical symmetry of the WR wind is thus broken by the presence of the O companion and clumping in the WR wind. Similar features in the extended red wing of the C III λ 5696 emission line remain unexplained. No obvious circular line polarization features are seen across any emission line above the 3σ ~ 0.03% instrumental level.

More on homological supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

Behtash, Alireza

2018-03-01

In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the bosonized supersymmetric quantum mechanics on algebraic geometric grounds and report that their complex phases can be accessed through the cohomology of WKB 1-form of the underlying singular spectral curve subject to necessary cohomological corrections for nonzero genus. Motivated by Picard-Lefschetz theory, we write down a general formula for the index of N =4 quantum mechanics with background R -symmetry gauge fields. We conjecture that certain symmetries of the refined Witten index and singularities of the moduli space may be used to determine the correct intersection coefficients. A few examples, where this conjecture holds, are shown in both linear and closed quivers with rank-one quiver gauge groups. The R -anomaly removal along the "Morsified" relative homology cycles also called "Lefschetz thimbles" is shown to lead to the appearance of Stokes lines. We show that the Fayet-Iliopoulos parameters appear in the intersection coefficients for the relative homology of the quiver quantum mechanics resulting from dimensional reduction of 2 d N =(2 ,2 ) gauge theory on a circle and explicitly calculate integrals along the Lefschetz thimbles in N =4 C Pk -1 model. The Stokes jumping of coefficients and its relation to wall crossing phenomena is briefly discussed. We also find that the notion of "on-the-wall" index is related to the invariant Lefschetz thimbles under Stokes phenomena. An implication of the Lefschetz thimbles in constructing knots from quiver quantum mechanics is indicated.

Stimulated Raman scattering holography for time-resolved imaging of methane gas.

PubMed

Amer, Eynas; Gren, Per; Edenharder, Stefan; Sjödahl, Mikael

2016-05-01

In this paper, pulsed digital holographic detection is coupled to the stimulated Raman scattering (SRS) process for imaging gases. A Q-switched Nd-YAG laser (532 nm) has been used to pump methane gas (CH₄) at pressures up to 12 bars. The frequency-tripled (355 nm) beam from the same laser was used to pump an optical parametric oscillator (OPO). The Stokes beam (from the OPO) has been tuned to 629.93 nm so that the frequency difference between the pump (532 nm) and the Stokes beams fits a Raman active vibrational mode of the methane molecule (2922  cm^-1). The pump beam has been spatially modulated with fringes produced in a Michelson interferometer. The pump and the Stokes beams were overlapped in time, space, and polarization on the gas molecules, resulting in a stimulated Raman gain of the Stokes beam and a corresponding loss of the pump beam through the SRS process. The resulting gain of the Stokes beam has been detected using pulsed digital holography by blending it with a reference beam on the detector. Two holograms of the Stokes beam, without and with the pump beam fringes present, were recorded. Intensity maps calculated from the recorded digital holograms showed amplification of the Stokes beam at the position of overlap with the pump beam fringes and the gas molecules. The gain of the Stokes beam has been separated from the background in the Fourier domain. A gain of about 4.5% at a pump beam average intensity of 4  MW/cm² and a Stokes beam intensity of 0.16  MW/cm² have been recorded at a gas pressure of 12 bars. The gain decreased linearly with decreasing gas pressure. The results show that SRS holography is a promising technique to pinpoint a specific species and record its spatial and temporal distribution.

Radially polarized tip-enhanced near-field coherent anti-Stokes Raman scattering microscopy for vibrational nano-imaging

NASA Astrophysics Data System (ADS)

Lin, Jian; Zi Jian Er, Kenneth; Zheng, Wei; Huang, Zhiwei

2013-08-01

We report a radially polarized tip-enhanced near-field coherent anti-Stokes Raman scattering (RP-TE-CARS) microscopy technique for high-contrast vibrational imaging of subcellular organelles at nano-scale resolutions. The radially polarized pump and Stokes laser beams are tightly focused onto the sample while a gold-coated metallic probe is placed at the upper surface of the sample to enhance the electric field and CARS signals. The back-scattered CARS signal is measured with the gold-coated nano-tip being stationary at the focal region of laser beams. The RP-TE-CARS signal is ˜6-fold higher than that using linearly polarized laser excitation. We demonstrate the good performance of the RP-TE-CARS technique developed by imaging sub-micron polystyrene beads and mitochondria at nano-scale resolutions.

Multi-wavelength Praseodymium fiber laser using stimulated Brillouin scattering

NASA Astrophysics Data System (ADS)

Ahmad, H.; Aidit, S. N.; Tiu, Z. C.

2018-02-01

A multi-wavelength Brillouin Praseodymium fiber laser (MWBPFL) operating at 1300 nm region is demonstrated based on the hybrid scheme by utilizing Brillouin gain medium and Praseodymium-doped fluoride fiber as linear gain medium. A 15 μm air gap is incorporated into the cavity to allow the switching of Brillouin frequency spacing from double to single spacing. Under the Brillouin pump of 8 dBm and the 1020 nm pump power of 567.2 mW, 36 Stokes lines with a wavelength spacing of 0.16 nm and 24 Stokes lines with a wavelength spacing of 0.08 nm are achieved. The wavelength tunability of 8 nm is realized for both MWBPFLs by shifting the Brillouin pump wavelength. The MWBPFLs exhibit an excellent stability in the number of generated Stokes and power level over one-hour period.

Resolving the ambiguity in the relation between Stokes shift and Huang-Rhys parameter.

PubMed

de Jong, Mathijs; Seijo, Luis; Meijerink, Andries; Rabouw, Freddy T

2015-07-14

Electronic transitions in luminescent molecules or centers in crystals couple to vibrations. This results in broadening of absorption and emission bands, as well as in the occurence of a Stokes shift EStokes. In principle, one can derive from EStokes the Huang-Rhys parameter S, which describes the microscopic details of the vibrational coupling and can be related to the equilibrium position offset ΔQe between the ground state and excited state. The commonly used textbook relations EStokes = (2S - 1)ℏω and EStokes = 2Sℏω are only approximately valid. In this paper we investigate how EStokes is related to S, taking into account the effects of a finite temperature. We show that in different ranges of temperature, different approximate relations between EStokes and S are appropriate. Moreover, we demonstrate that the difference between the barycenters of absorption and emission bands can be used to determine S in an unambiguous way. The position of the barycenter is, contrary to the Stokes shift, unaffected by temperature.

Asymptotic behavior of solutions of the renormalization group K-epsilon turbulence model

NASA Technical Reports Server (NTRS)

Yakhot, A.; Staroselsky, I.; Orszag, S. A.

1994-01-01

Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.

Statistics of partially-polarized fields: beyond the Stokes vector and coherence matrix

NASA Astrophysics Data System (ADS)

Charnotskii, Mikhail

2017-08-01

Traditionally, the partially-polarized light is characterized by the four Stokes parameters. Equivalent description is also provided by correlation tensor of the optical field. These statistics specify only the second moments of the complex amplitudes of the narrow-band two-dimensional electric field of the optical wave. Electric field vector of the random quasi monochromatic wave is a nonstationary oscillating two-dimensional real random variable. We introduce a novel statistical description of these partially polarized waves: the Period-Averaged Probability Density Function (PA-PDF) of the field. PA-PDF contains more information on the polarization state of the field than the Stokes vector. In particular, in addition to the conventional distinction between the polarized and depolarized components of the field PA-PDF allows to separate the coherent and fluctuating components of the field. We present several model examples of the fields with identical Stokes vectors and very distinct shapes of PA-PDF. In the simplest case of the nonstationary, oscillating normal 2-D probability distribution of the real electrical field and stationary 4-D probability distribution of the complex amplitudes, the newly-introduced PA-PDF is determined by 13 parameters that include the first moments and covariance matrix of the quadrature components of the oscillating vector field.

Variational principle for the Navier-Stokes equations.

PubMed

Kerswell, R R

1999-05-01

A variational principle is presented for the Navier-Stokes equations in the case of a contained boundary-driven, homogeneous, incompressible, viscous fluid. Based upon making the fluid's total viscous dissipation over a given time interval stationary subject to the constraint of the Navier-Stokes equations, the variational problem looks overconstrained and intractable. However, introducing a nonunique velocity decomposition, u(x,t)=phi(x,t) + nu(x,t), "opens up" the variational problem so that what is presumed a single allowable point over the velocity domain u corresponding to the unique solution of the Navier-Stokes equations becomes a surface with a saddle point over the extended domain (phi,nu). Complementary or dual variational problems can then be constructed to estimate this saddle point value strictly from above as part of a minimization process or below via a maximization procedure. One of these reduced variational principles is the natural and ultimate generalization of the upper bounding problem developed by Doering and Constantin. The other corresponds to the ultimate Busse problem which now acts to lower bound the true dissipation. Crucially, these reduced variational problems require only the solution of a series of linear problems to produce bounds even though their unique intersection is conjectured to correspond to a solution of the nonlinear Navier-Stokes equations.

An Edge-Based Method for the Incompressible Navier-Stokes Equations on Polygonal Meshes

NASA Astrophysics Data System (ADS)

Wright, Jeffrey A.; Smith, Richard W.

2001-05-01

A pressure-based method is presented for discretizing the unsteady incompressible Navier-Stokes equations using hybrid unstructured meshes. The edge-based data structure and assembly procedure adopted lead naturally to a strictly conservative discretization, which is valid for meshes composed of n-sided polygons. Particular attention is given to the construction of a pressure-velocity coupling procedure which is supported by edge data, resulting in a relatively simple numerical method that is consistent with the boundary and initial conditions required by the incompressible Navier-Stokes equations. Edge formulas are presented for assembling the momentum equations, which are based on an upwind-biased linear reconstruction of the velocity field. Similar formulas are presented for assembling the pressure equation. The method is demonstrated to be second-order accurate in space and time for two Navier-Stokes problems admitting an exact solution. Results for several other well-known problems are also presented, including lid-driven cavity flow, impulsively started cylinder flow, and unsteady vortex shedding from a circular cylinder. Although the method is by construction minimalist, it is shown to be accurate and robust for the problems considered.

Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2014-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Stokes paradox in electronic Fermi liquids

NASA Astrophysics Data System (ADS)

Lucas, Andrew

2017-03-01

The Stokes paradox is the statement that in a viscous two-dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi liquid of electrons in two-dimensional metals. Using hydrodynamics and kinetic theory, we estimate the contribution of a single cylindrical obstacle to the global electrical resistance of a material, within linear response. Momentum relaxation, present in any realistic electron liquid, resolves the classical paradox. Nonetheless, this paradox imprints itself in the resistance, which can be parametrically larger than predicted by Ohmic transport theory. We find a remarkably rich set of behaviors, depending on whether or not the quasiparticle dynamics in the Fermi liquid should be treated as diffusive, hydrodynamic, or ballistic on the length scale of the obstacle. We argue that all three types of behavior are observable in present day experiments.

Viscous properties of isotropic fluids composed of linear molecules: departure from the classical Navier-Stokes theory in nano-confined geometries.

PubMed

Hansen, J S; Daivis, Peter J; Todd, B D

2009-10-01

In this paper we present equilibrium molecular-dynamics results for the shear, rotational, and spin viscosities for fluids composed of linear molecules. The density dependence of the shear viscosity follows a stretched exponential function, whereas the rotational viscosity and the spin viscosities show approximately power-law dependencies. The frequency-dependent shear and spin viscosities are also studied. It is found that viscoelastic behavior is first manifested in the shear viscosity and that the real part of the spin viscosities features a maximum for nonzero frequency. The calculated transport coefficients are used together with the extended Navier-Stokes equations to investigate the effect of the coupling between the intrinsic angular momentum and linear momentum for highly confined fluids. Both steady and oscillatory flows are studied. It is shown, for example, that the fluid flow rate for Poiseuille flow is reduced by up to 10% in a 2 nm channel for a buta-triene fluid at density 236 kg m(-3) and temperature 306 K. The coupling effect may, therefore, become very important for nanofluidic applications.

Oasis: A high-level/high-performance open source Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Valen-Sendstad, Kristian

2015-03-01

Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.

Covariances and spectra of the kinematics and dynamics of nonlinear waves

NASA Technical Reports Server (NTRS)

Tung, C. C.; Huang, N. E.

1985-01-01

Using the Stokes waves as a model of nonlinear waves and considering the linear component as a narrow-band Gaussian process, the covariances and spectra of velocity and acceleration components and pressure for points in the vicinity of still water level were derived taking into consideration the effects of free surface fluctuations. The results are compared with those obtained earlier using linear Gaussian waves.

The Stokes-Einstein relation at moderate Schmidt number.

PubMed

Balboa Usabiaga, Florencio; Xie, Xiaoyi; Delgado-Buscalioni, Rafael; Donev, Aleksandar

2013-12-07

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

Boltzmann equation and hydrodynamics beyond Navier-Stokes.

PubMed

Bobylev, A V

2018-04-28

We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Enhanced secure 4-D modulation space optical multi-carrier system based on joint constellation and Stokes vector scrambling.

PubMed

Liu, Bo; Zhang, Lijia; Xin, Xiangjun

2018-03-19

This paper proposes and demonstrates an enhanced secure 4-D modulation optical generalized filter bank multi-carrier (GFBMC) system based on joint constellation and Stokes vector scrambling. The constellation and Stokes vectors are scrambled by using different scrambling parameters. A multi-scroll Chua's circuit map is adopted as the chaotic model. Large secure key space can be obtained due to the multi-scroll attractors and independent operability of subcarriers. A 40.32Gb/s encrypted optical GFBMC signal with 128 parallel subcarriers is successfully demonstrated in the experiment. The results show good resistance against the illegal receiver and indicate a potential way for the future optical multi-carrier system.

Impact of firing temperature on multi-wavelength selective Stokes and anti-Stokes luminescent behavior by Gd2O2S:Er,Yb phosphor and its application in solar energy harvesting

NASA Astrophysics Data System (ADS)

Kataria, V.; Mehta, D. S.

2018-04-01

Erbium (Er3+)-ytterbium (Yb3+) doped gadolinium oxysulphide (Gd2O2S) phosphor has been developed via a facile method of solid-state flux fusion, and offers two-fold spectrum modification with highly intense Stokes and anti-Stokes shift. The effect of the firing cycle on the photoluminescent response and morphology of Gd2O2S:Er,Yb is scrutinized, wherein the firing temperature was varied (1000 °C-1250 °C), keeping firing time and all other parameters constant. Interestingly, the nanostructures fired below 1150 °C showed nanorods of diameter ~200 nm and length ~1-2 µm, whereas firing at 1150 °C and above rendered nanospheres with small diameter, ~350 nm. Highly bright upconversion (UC) emission was achieved even under an extremely low excitation power density of 800 µW cm-2 from a 980 nm laser, and was comfortably visible to the naked eye. The incident power dependent studies disclosed increase in UC-emission intensity with increasing excitation power and a quasi-linear dependence on excitation power density. Intense characteristic UC-emission of Er3+ excited states at 525 nm, 556 nm and 668 nm were observed, and the green emission band was found to be dominant over the red band in intensity. Concurrently, downconversion (DC) emission at 556 nm and 669 nm was also exhibited under ultraviolet excitation (285 nm and 380 nm), with the red band being more powerful than the green, unlike UC-emission. Firing temperature dependent studies divulged the dependence of luminescence intensity on the firing cycle of the luminophore and formation of the respective luminescent phase. The UC-emission intensity was found to be maximum for samples fired at 1150 °C, whereas samples fired at 1000 °C showed the highest DC-emission intensity. The excitation and emission profile of single Gd2O2S:Er,Yb phosphor lying in the desired spectral region and as a dual spectral converter marks its possible application for enhanced harvesting of sunlight.

Characteristic correlation study of UV disinfection performance for ballast water treatment

NASA Astrophysics Data System (ADS)

Ba, Te; Li, Hongying; Osman, Hafiiz; Kang, Chang-Wei

2016-11-01

Characteristic correlation between ultraviolet disinfection performance and operating parameters, including ultraviolet transmittance (UVT), lamp power and water flow rate, was studied by numerical and experimental methods. A three-stage model was developed to simulate the fluid flow, UV radiation and the trajectories of microorganisms. Navier-Stokes equation with k-epsilon turbulence was solved to model the fluid flow, while discrete ordinates (DO) radiation model and discrete phase model (DPM) were used to introduce UV radiation and microorganisms trajectories into the model, respectively. The UV dose statistical distribution for the microorganisms was found to move to higher value with the increase of UVT and lamp power, but moves to lower value when the water flow rate increases. Further investigation shows that the fluence rate increases exponentially with UVT but linearly with the lamp power. The average and minimum resident time decreases linearly with the water flow rate while the maximum resident time decrease rapidly in a certain range. The current study can be used as a digital design and performance evaluation tool of the UV reactor for ballast water treatment.

High-efficiency broadband polarization converter based on Ω-shaped metasurface

NASA Astrophysics Data System (ADS)

Zhang, Tianyao; Huang, Lingling; Li, Xiaowei; Liu, Juan; Wang, Yongtian

2017-11-01

The polarization state, which cannot be directly detected by human eyes, forms an important characteristic of electromagnetic waves. Control of polarization states has long been pursued for various applications. Conventional polarization converters can hardly meet the requirements in lab-on-chip systems, due to the involvement of bulk materials. Here, we propose the design and realization of a linear to circular polarization converter based on metasurfaces. The metasurface is deliberately designed using achiral two-fold mirror symmetry Ω-shaped antennas. The converter integrates a ground metal plane, a spacer dielectric layer and an antenna array, leading to a high conversion efficiency and broad operating bandwidth in the near infrared regime. The calculated Stokes parameters indicate an excellent conversion of linear to circular polarization for the reflected light. The tunability of the bandwidth by oblique incidence and by modulating the thickness of the dielectric layer is also introduced and demonstrated, which shows great flexibilities for such metasurface converters. The proposed metasurface may open up intriguing possibilities towards the realization of ultrathin nanophotonic devices for polarization manipulation and wavefront engineering.

A Si I atomic model for NLTE spectropolarimetric diagnostics of the 10 827 Å line

NASA Astrophysics Data System (ADS)

Shchukina, N. G.; Sukhorukov, A. V.; Trujillo Bueno, J.

2017-07-01

Aims: The Si I 10 827 Å line is commonly used for spectropolarimetric diagnostics of the solar atmosphere. First, we aim at quantifying the sensitivity of the Stokes profiles of this line to non-local thermodynamic equilibrium (NLTE) effects. Second, we aim at facilitating NLTE diagnostics of the Si I 10 827 Å line. To this end, we propose the use of a relatively simple silicon model atom, which allows a fast and accurate computation of Stokes profiles. The NLTE Stokes profiles calculated using this simple model atom are very similar to those obtained via the use of a very comprehensive silicon model atom. Methods: We investigate the impact of the NLTE effects on the Si I 10 827 Å line by means of multilevel radiative transfer calculations in a three-dimensional (3D) model atmosphere taken from a state-of-the-art magneto-convection simulation with small-scale dynamo action. We calculate the emergent Stokes profiles for this line at the solar disk center and for every vertical column of the 3D snapshot model, neglecting the effects of horizontal radiative transfer. Results: We find significant departures from LTE in the Si I 10 827 Å line, not only in the intensity but also in the linearly and circularly polarized profiles. At wavelengths around 0.1 Å, where most of the Stokes Q, U, and V peaks of the Si I 10 827 Å line occur, the differences between the NLTE and LTE profiles are comparable with the Stokes amplitudes themselves. The deviations from LTE increase with increasing Stokes Q, U, and V signals. Concerning the Stokes V profiles, the NLTE effects correlate with the magnetic field strength in the layers where such circular polarization signals are formed. Conclusions: The NLTE effects should be taken into account when diagnosing the emergent Stokes I profiles as well as the Stokes Q, U, and V profiles of the Si I 10 827 Å line. The sixteen-level silicon model atom proposed here, with six radiative bound-bound transitions, is suitable to account for the physics of formation of the Si I 10 827 Å line and for modeling and inverting its Stokes profiles without assuming LTE.

A finite element solution algorithm for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Langtangen, Hans Petter; Wells, Garth N.

2011-09-01

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model.

Asymptotic behaviour of Stokes flow in a thin domain with a moving rough boundary

PubMed Central

Fabricius, J.; Koroleva, Y. O.; Tsandzana, A.; Wall, P.

2014-01-01

We consider a problem that models fluid flow in a thin domain bounded by two surfaces. One of the surfaces is rough and moving, whereas the other is flat and stationary. The problem involves two small parameters ϵ and μ that describe film thickness and roughness wavelength, respectively. Depending on the ratio λ=ϵ/μ, three different flow regimes are obtained in the limit as both of them tend to zero. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high-frequency roughness regime). The derivations of the limiting equations are based on formal expansions in the parameters ϵ and μ. PMID:25002820

Design of the Polarimeter for the Fibre Arrayed Solar Optical Telescope

NASA Astrophysics Data System (ADS)

Dun, Guang-tao; Qu, Zhong-quan

2013-01-01

The theoretical design of the polarimeter used for the Fibre Arrayed Solar Optical Telescope (FASOT) is described. It has the following characteris- tics: (1) It is provided with the function of optical polarization switching, which makes the high-effciency polarimetry possible; (2) In the waveband of 750 nm, the polarimetric effciency is higher than 50% for the every Stokes parameter, and higher than 86.6% for the total polarization, thus an observer can make the simultaneous polarization measurements on multiple magnetosensitive lines in such a broad range of wavelength; (3) According to the selected photospheric and chromospheric lines, the measurement can be focused on either linear polarization or circular polarization; (4) The polarimeter has a loose tolerance on the manufacturing technology of polarimetric elements and installation errors. All this makes this polarimeter become a high-performance polarimetric device.

Model of formation of droplets during electric arc surfacing of functional coatings

NASA Astrophysics Data System (ADS)

Sarychev, Vladimir D.; Granovskii, Alexei Yu; Nevskii, Sergey A.; Gromov, Victor E.

2016-01-01

The mathematical model was developed for the initial stage of formation of an electrode metal droplet in the process of arc welding. Its essence lies in the fact that the presence of a temperature gradient in the boundary layer of the molten metal causes thermo-capillary instability, which leads to the formation of electrode metal droplets. A system of equations including Navier-Stokes equations, heat conduction and Maxwell's equations was solved as well as the boundary conditions for the system electrodes-plasma. Dispersion equation for thermo-capillary waves in the linear approximation for the plane layer was received and analyzed. The values of critical wavelengths, at which thermo-capillary instability appears in the nanometer wavelength range, were found. The parameters at which the mode of a fine-droplet transfer of the material takes place were theoretically defined.

A nanostructured surface increases friction exponentially at the solid-gas interface.

PubMed

Phani, Arindam; Putkaradze, Vakhtang; Hawk, John E; Prashanthi, Kovur; Thundat, Thomas

2016-09-06

According to Stokes' law, a moving solid surface experiences viscous drag that is linearly related to its velocity and the viscosity of the medium. The viscous interactions result in dissipation that is known to scale as the square root of the kinematic viscosity times the density of the gas. We observed that when an oscillating surface is modified with nanostructures, the experimentally measured dissipation shows an exponential dependence on kinematic viscosity. The surface nanostructures alter solid-gas interplay greatly, amplifying the dissipation response exponentially for even minute variations in viscosity. Nanostructured resonator thus allows discrimination of otherwise narrow range of gaseous viscosity making dissipation an ideal parameter for analysis of a gaseous media. We attribute the observed exponential enhancement to the stochastic nature of interactions of many coupled nanostructures with the gas media.

SEARCH FOR A MAGNETIC FIELD VIA CIRCULAR POLARIZATION IN THE WOLF-RAYET STAR EZ CMa

DOE Office of Scientific and Technical Information (OSTI.GOV)

De la Chevrotiere, A.; St-Louis, N.; Moffat, A. F. J.

We report on the first deep, direct search for a magnetic field via the circular polarization of Zeeman splitting in a Wolf-Rayet (W-R) star. Using the highly efficient ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope, we observed at three different epochs one of the best W-R candidates in the sky expected to harbor a magnetic field, the bright, highly variable WN4 star EZ CMa = WR6 = HD 50896. We looked for the characteristic circular polarization (Stokes V) pattern in strong emission lines that would arise as a consequence of a global, rotating magnetic field with a split monopole configuration. Wemore » also obtained nearly simultaneous linear polarization spectra (Stokes Q and U), which are dominated by electron scattering, most likely from a flattened wind with large-scale corotating structures. As the star rotates with a period of 3.766 days, our view of the wind changes, which in turn affects the value of the linear polarization in lines versus continuum at the {approx}0.2% level. Depending on the epoch of observation, our Stokes V data were affected by significant crosstalk from Stokes Q and U to V. We removed this spurious signal from the circular polarization data and experimented with various levels of spectral binning to increase the signal-to-noise ratio of our data. In the end, no magnetic field is unambiguously detected in EZ CMa. Assuming that the star is intrinsically magnetic and harbors a split monopole configuration, we find an upper limit of B {approx} 100 G for the intensity of its field in the line-forming regions of the stellar wind.« less

Electro-osmotic flow of couple stress fluids in a micro-channel propagated by peristalsis

NASA Astrophysics Data System (ADS)

Tripathi, Dharmendra; Yadav, Ashu; Anwar Bég, O.

2017-04-01

A mathematical model is developed for electro-osmotic peristaltic pumping of a non-Newtonian liquid in a deformable micro-channel. Stokes' couple stress fluid model is employed to represent realistic working liquids. The Poisson-Boltzmann equation for electric potential distribution is implemented owing to the presence of an electrical double layer (EDL) in the micro-channel. Using long wavelength, lubrication theory and Debye-Huckel approximations, the linearized transformed dimensionless boundary value problem is solved analytically. The influence of electro-osmotic parameter (inversely proportional to Debye length), maximum electro-osmotic velocity (a function of external applied electrical field) and couple stress parameter on axial velocity, volumetric flow rate, pressure gradient, local wall shear stress and stream function distributions is evaluated in detail with the aid of graphs. The Newtonian fluid case is retrieved as a special case with vanishing couple stress effects. With increasing the couple stress parameter there is a significant increase in the axial pressure gradient whereas the core axial velocity is reduced. An increase in the electro-osmotic parameter both induces flow acceleration in the core region (around the channel centreline) and it also enhances the axial pressure gradient substantially. The study is relevant in the simulation of novel smart bio-inspired space pumps, chromatography and medical micro-scale devices.

PHYSICS REQUIRES A SIMPLE LOW MACH NUMBER FLOW TO BE COMPRESSIBLE

EPA Science Inventory

Radial, laminar, plane, low velocity flow represents the simplest, non-linear fluid dynamics problem. Ostensibly this apparently trivial flow could be solved using the incompressible Navier-Stokes equations, universally believed to be adequate for such problems. Most researchers ...

Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements.

PubMed

Boesche, Eyk; Stammes, Piet; Ruhtz, Thomas; Preusker, Réne; Fischer, Juergen

2006-12-01

We analyze the sensitivity of the degree of linear polarization in the Sun's principal plane as a function of aerosol microphysical parameters: the real and imaginary parts of the refractive index, the median radius and geometric standard deviation of the bimodal size distribution (both fine and coarse modes), and the relative number weight of the fine mode at a wavelength of 675 nm. We use Mie theory for single-scattering simulations and the doubling-adding method with the inclusion of polarization for multiple scattering. It is shown that the behavior of the degree of linear polarization is highly sensitive to both the small mode of the bimodal size distribution and the real part of the refractive index of aerosols, as well as to the aerosol optical thickness; whereas not all parameters influence the polarization equally. A classification of the importance of the input parameters is given. This sensitivity study is applied to an analysis of ground-based polarization measurements. For the passive remote sensing of microphysical and optical properties of aerosols, a ground-based spectral polarization measuring system was built, which aims to measure the Stokes parameters I, Q, and U in the visible (from 410 to 789 nm) and near-infrared (from 674 to 995 nm) spectral range with a spectral resolution of 7 nm in the visible and 2.4 nm in the near infrared. We compare polarization measurements taken with radiative transfer simulations under both clear- and hazy-sky conditions in an urban area (Cabauw, The Netherlands, 51.58 degrees N, 4.56 degrees E). Conclusions about the microphysical properties of aerosol are drawn from the comparison.

Magnetic field topology of τ Scorpii. The uniqueness problem of Stokes V ZDI inversions

NASA Astrophysics Data System (ADS)

Kochukhov, O.; Wade, G. A.

2016-02-01

Context. The early B-type star τ Sco exhibits an unusually complex, relatively weak surface magnetic field. Its topology was previously studied with the Zeeman Doppler imaging (ZDI) modelling of high-resolution circular polarisation (Stokes V) observations. Aims: Here we assess the robustness of the Stokes V ZDI reconstruction of the magnetic field geometry of τ Sco and explore the consequences of using different parameterisations of the surface magnetic maps. Methods: This analysis is based on the archival ESPaDOnS high-resolution Stokes V observations and employs an independent ZDI magnetic inversion code. Results: We succeeded in reproducing previously published magnetic field maps of τ Sco using both general harmonic expansion and a direct, pixel-based representation of the magnetic field. These maps suggest that the field topology of τ Sco is comprised of comparable contributions of the poloidal and toroidal magnetic components. At the same time, we also found that available Stokes V observations can be successfully fitted with restricted harmonic expansions, by either neglecting the toroidal field altogether, or linking the radial and horizontal components of the poloidal field as required by the widely used potential field extrapolation technique. These alternative modelling approaches lead to a stronger and topologically more complex surface field structure. The field distributions, which were recovered with different ZDI options, differ significantly and yield indistinguishable Stokes V profiles but different linear polarisation (Stokes Q and U) signatures. Conclusions: Our investigation underscores the well-known problem of non-uniqueness of the Stokes V ZDI inversions. For the magnetic stars with properties similar to τ Sco (relatively complex field, slow rotation) the outcome of magnetic reconstruction strongly depends on the adopted field parameterisation, rendering photospheric magnetic mapping and determination of the extended magnetospheric field topology ambiguous. Stokes Q and U spectropolarimetric observations represent the only way of breaking the degeneracy of surface magnetic field models. Based on observations obtained at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii.

Separated flows near the nose of a body of revolution

NASA Technical Reports Server (NTRS)

Lin, S. P.

1986-01-01

The solution of the Navier-Stokes equations for the problem of cross-flow separataion about a deforming cylinder was achieved by iteration. It was shown that the separation starts at the rear stagnation point and the point of primary separation moves upstram along the cylinder surface. A general method of linear stability analysis for nonparallel external flows was constructed, which consists of representing the eigenfunctions with complete orthogonal sets and forms characteristic equations with the Galerkin method. The method was applied to the Kovasznay flow which is an exact solution of the Navier-Stokes equation. The results show that when the critical parameter is exceeded, there are only a few isolated unstable eigen-frequencies. Another exact solution is shown to be absolutely and monotonically stable with respect to infinitesimal disturbances of all frequencies. The flow is also globally, asymptotically, and monotonically stable in the mean with respect o three-dimensional disturbances. This result forms the sound foundation of rigorous stability analysis for nonparallel flows, and provides an invaluable test ground for future studies of nonparallel flows in which the basic states do not posses exact solutions. The application of this method to the study of the formation of spiral vorticies near the nose of a rotating body of revolution is underway. The same method will be applied to the stability analysis of reversed flow over a plate with suction.

A fast iterative scheme for the linearized Boltzmann equation

NASA Astrophysics Data System (ADS)

Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

2017-06-01

Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference between these results and those using the hard-sphere potential is discussed.

Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhalla, Amneet Pal Singh; Knepley, Matthew G.; Adams, Mark F.

2016-12-20

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular because of their simplicity and generality. In prior work (Guy et al., Adv Comput Math, 2015), some of us developed a geometric multigrid preconditioner for a stable semi-implicit IB method under Stokes flow conditions; however, this solver methodology used a Vanka-type smoother that presented limited opportunities for parallelization. This work extends this Stokes-IB solver methodology by developing smoothing techniques that are suitable for parallel implementation. Specifically,more » we demonstrate that an additive version of the Vanka smoother can yield an effective multigrid preconditioner for the Stokes-IB equations, and we introduce an efficient Schur complement-based smoother that is also shown to be effective for the Stokes-IB equations. We investigate the performance of these solvers for a broad range of material stiffnesses, both for Stokes flows and flows at nonzero Reynolds numbers, and for thick and thin structural models. We show here that linear solver performance degrades with increasing Reynolds number and material stiffness, especially for thin interface cases. Nonetheless, the proposed approaches promise to yield effective solution algorithms, especially at lower Reynolds numbers and at modest-to-high elastic stiffnesses.« less

The Aquarius Level 2 Algorithm

NASA Astrophysics Data System (ADS)

Meissner, T.; Wentz, F. J.; Hilburn, K. A.; Lagerloef, G. S.; Le Vine, D. M.

2012-12-01

The Aquarius L-band radiometer/scatterometer system is designed to provide monthly salinity maps at 150 km spatial scale to an accuracy of 0.2 psu. The sensor was launched on June 10, 2011, aboard the Argentine CONAE SAC-D spacecraft. The L-band radiometers and the scatterometer have been taking science data observations since August 25, 2011. This presentation discusses the current state of the Aquarius Level processing algorithm, which transforms radiometer counts ultimately into sea surface salinity (SSS). We focus on several topics that we have investigated since launch: 1. Updated Pointing A detailed check of the Aquarius pointing angles was performed, which consists in making adjustments of the two pointing angles, azimuth angle and off-nadir angle, for each horn. It has been found that the necessary adjustments for all 3 horns can be explained by a single offset for the antenna pointing if we introduce a constant offset in the roll angle by - 0.51 deg and the pitch angle by + 0.16 deg. 2. Antenna Patterns and Instrument Calibration In March 2012 JPL has produced a set of new antenna patterns using the GRASP software. Compared with the various pre-launch patterns those new patterns lead to an increase in the spillover coefficient by about 1%. We discuss its impact on several components of the Level 2 processing: the antenna pattern correction (APC), the correction for intrusion of galactic and solar radiation that is reflected from the ocean surface into the Aquarius field of view, and the correction of contamination from land surface radiation entering into the sidelobes. We show that the new antenna patterns result in a consistent calibration of all 3 Stokes parameters, which can be best demonstrated during spacecraft pitch maneuvers. 3. Cross Polarization Couplings of the 3rd Stokes Parameter Using the APC values for the cross polarization coupling of the 3rd Stokes parameter into the 1st and 2nd Stokes parameter lead to a spurious image of the 3rd Stokes parameter into the SSS and an unwanted bias of the SSS between the ascending and descending part of the swath. We show that in order to remove this effect it is necessary to fine tune the cross polarization coupling of the 3rd Stokes parameter. 4. Aquarius Wind Speed Retrievals and Impact on Surface Roughness Correction Backscatter measurements form the Aquarius scatterometer can be combined with radiometer observations to derive an Aquarius wind speed product. We show that if the weights for the various scatterometer and radiometer channels are chosen appropriately, this Aquarius wind speed matches the high performance of the WindSat and SSM/I retrieved wind speed. This results in an RMS accuracy of about 0.7 m/s when comparing with ground truth observations. This is a significant improvement over wind speeds from NCEP which are currently used in the Aquarius L2vel 2 processing and which have an RMS accuracy of about only 1.2 m/s. We discuss the impact of using this improved wind speed product on the Level 2 surface roughness correction and ultimately on the retrieved SSS.

Instability of the roll-streak structure induced by background turbulence in pretransitional Couette flow

NASA Astrophysics Data System (ADS)

Farrell, Brian F.; Ioannou, Petros J.; Nikolaidis, Marios-Andreas

2017-03-01

Although the roll-streak structure is ubiquitous in both observations and simulations of pretransitional wall-bounded shear flow, this structure is linearly stable if the idealization of laminar flow is made. Lacking an instability, the large transient growth of the roll-streak structure has been invoked to explain its appearance as resulting from chance occurrence in the background turbulence of perturbations configured to optimally excite it. However, there is an alternative interpretation for the role of free-stream turbulence in the genesis of the roll-streak structure, which is that the background turbulence interacts with the roll-streak structure to destabilize it. Statistical state dynamics (SSD) provides analysis methods for studying instabilities of this type that arise from interaction between the coherent and incoherent components of turbulence. SSD in the form of a closure at second order is used in this work to analyze the cooperative eigenmodes arising from interaction between the coherent streamwise invariant component and the incoherent background component of turbulence. In pretransitional Couette flow a manifold of stable modes with roll-streak form is found to exist in the presence of low-intensity background turbulence. The least stable mode of this manifold is destabilized at a critical value of a parameter controlling the background turbulence intensity and a finite-amplitude roll-streak structure arises from this instability through a bifurcation in this parameter. Although this bifurcation has analytical expression only in the infinite ensemble formulation of second order SSD, referred in this work as the S3T system, it is closely reflected in numerical simulations of both the dynamically similar quasilinear system, referred to as the restricted nonlinear (RNL) system, as well as in the full Navier-Stokes equations. This correspondence is verified using ensemble implementations of the RNL system and the Navier-Stokes equations. The S3T system also predicts a second bifurcation at a higher value of the turbulent excitation parameter that results in destabilization of the finite-amplitude roll-streak equilibria. This second bifurcation is shown to lead first to time dependence of the roll-streak structure in the S3T system and then to chaotic fluctuation corresponding to minimal channel turbulence. This transition scenario is also verified in simulations of the RNL system and of the Navier-Stokes equations. This bifurcation from a finite-amplitude roll-streak equilibrium provides a direct route to the turbulent state through the S3T roll-streak instability.

Composite solvers for linear saddle point problems arising from the incompressible Stokes equations with highly heterogeneous viscosity structure

NASA Astrophysics Data System (ADS)

Sanan, P.; Schnepp, S. M.; May, D.; Schenk, O.

2014-12-01

Geophysical applications require efficient forward models for non-linear Stokes flow on high resolution spatio-temporal domains. The bottleneck in applying the forward model is solving the linearized, discretized Stokes problem which takes the form of a large, indefinite (saddle point) linear system. Due to the heterogeniety of the effective viscosity in the elliptic operator, devising effective preconditioners for saddle point problems has proven challenging and highly problem-dependent. Nevertheless, at least three approaches show promise for preconditioning these difficult systems in an algorithmically scalable way using multigrid and/or domain decomposition techniques. The first is to work with a hierarchy of coarser or smaller saddle point problems. The second is to use the Schur complement method to decouple and sequentially solve for the pressure and velocity. The third is to use the Schur decomposition to devise preconditioners for the full operator. These involve sub-solves resembling inexact versions of the sequential solve. The choice of approach and sub-methods depends crucially on the motivating physics, the discretization, and available computational resources. Here we examine the performance trade-offs for preconditioning strategies applied to idealized models of mantle convection and lithospheric dynamics, characterized by large viscosity gradients. Due to the arbitrary topological structure of the viscosity field in geodynamical simulations, we utilize low order, inf-sup stable mixed finite element spatial discretizations which are suitable when sharp viscosity variations occur in element interiors. Particular attention is paid to possibilities within the decoupled and approximate Schur complement factorization-based monolithic approaches to leverage recently-developed flexible, communication-avoiding, and communication-hiding Krylov subspace methods in combination with `heavy' smoothers, which require solutions of large per-node sub-problems, well-suited to solution on hybrid computational clusters. To manage the combinatorial explosion of solver options (which include hybridizations of all the approaches mentioned above), we leverage the modularity of the PETSc library.

An outflow boundary condition for aeroacoustic computations

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Hagstrom, Thomas

1995-01-01

A formulation of boundary condition for flows with small disturbances is presented. The authors test their methodology in an axisymmetric jet flow calculation, using both the Navier-Stokes and Euler equations. Solutions in the far field are assumed to be oscillatory. If the oscillatory disturbances are small, the growth of the solution variables can be predicted by linear theory. Eigenfunctions of the linear theory are used explicitly in the formulation of the boundary conditions. This guarantees correct solutions at the boundary in the limit where the predictions of linear theory are valid.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1994-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.

Double Stokes-Mueller polarimetry in KTP (Potassium Titanyl Phosphate) crystal

NASA Astrophysics Data System (ADS)

Shaji, Chitra; S B, Sruthil Lal; Sharan, Alok

2017-04-01

Ultra-structural properties of material are being probed by Double Stokes-Mueller polarimetry (DSMP) technique. It makes use of higher dimensions of Stokes vector (9 X 1) and Mueller matrix (4 X9) to characterize the nonlinear optical properties of a material. Second harmonic generation (SHG) at 532nm using 1064nm as fundamental cw beam from Nd: YAG laser in type II phase matched KTP (Potassium Titanyl Phosphate) crystal is studied using DSMP. The experimental measurements for determining double Mueller matrix are carried out in the ``Polarization In Polarization Out'' (PIPO) arrangement. Nine input polarization states are incident on the sample and the linear Stokes vector of the emerging light from the sample is measured. The KTP crystal is oriented such that the SHG signal efficiency at the incident horizontal and vertical polarizations is high as compared to diagonal polarization states. The susceptibility tensor components and the phase difference between them at this orientation are determined from the double Mueller matrix elements. These determined values give information regarding the crystal axis orientations. To our knowledge, this is the first report of the use of DSMP technique to determine the crystal orientations of a biaxial crystal.

Large Scale Flutter Data for Design of Rotating Blades Using Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.

2012-01-01

A procedure to compute flutter boundaries of rotating blades is presented; a) Navier-Stokes equations. b) Frequency domain method compatible with industry practice. Procedure is initially validated: a) Unsteady loads with flapping wing experiment. b) Flutter boundary with fixed wing experiment. Large scale flutter computation is demonstrated for rotating blade: a) Single job submission script. b) Flutter boundary in 24 hour wall clock time with 100 cores. c) Linearly scalable with number of cores. Tested with 1000 cores that produced data in 25 hrs for 10 flutter boundaries. Further wall-clock speed-up is possible by performing parallel computations within each case.

Reduction of the two dimensional stationary Navier-Stokes problem to a sequence of Fredholm integral equations of the second kind

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.

1981-01-01

Present approaches to solving the stationary Navier-Stokes equations are of limited value; however, there does exist an equivalent representation of the problem that has significant potential in solving such problems. This is due to the fact that the equivalent representation consists of a sequence of Fredholm integral equations of the second kind, and the solving of this type of problem is very well developed. For the problem in this form, there is an excellent chance to also determine explicit error estimates, since bounded, rather than unbounded, linear operators are dealt with.

On a strong solution of the non-stationary Navier-Stokes equations under slip or leak boundary conditions of friction type

NASA Astrophysics Data System (ADS)

Kashiwabara, Takahito

Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a variational inequality of parabolic type, to which uniqueness is established. Using Galerkin's method and deriving a priori estimates, we prove global and local existence for 2D and 3D slip problems respectively. For leak problems, under no-leak assumption at t=0 we prove local existence in 2D and 3D cases. Compatibility conditions for initial states play a significant role in the estimates.

Numerical study of a multigrid method with four smoothing methods for the incompressible Navier-Stokes equations in general coordinates

NASA Technical Reports Server (NTRS)

Zeng, S.; Wesseling, P.

1993-01-01

The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.

Control of sound radiation from a wavepacket over a curved surface

NASA Technical Reports Server (NTRS)

Maestrello, Lucio; El Hady, Nabil M.

1989-01-01

Active control of acoustic pressure in the far field resulting from the growth and decay of a wavepacket convecting in a boundary layer over a concave-convex surface is investigated numerically using direct computations of the Navier-Stokes equations. The resulting sound radiation is computed using linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. The acoustic far field exhibits directivity type of behavior that points upstream to the flow direction. A fixed control algorithm is used where the attenuation signal is synthesized by a filter which actively adapt it to the amplitude-time response of the outgoing acoustic wave.

An incremental block-line-Gauss-Seidel method for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Napolitano, M.; Walters, R. W.

1985-01-01

A block-line-Gauss-Seidel (LGS) method is developed for solving the incompressible and compressible Navier-Stokes equations in two dimensions. The method requires only one block-tridiagonal solution process per iteration and is consequently faster per step than the linearized block-ADI methods. Results are presented for both incompressible and compressible separated flows: in all cases the proposed block-LGS method is more efficient than the block-ADI methods. Furthermore, for high Reynolds number weakly separated incompressible flow in a channel, which proved to be an impossible task for a block-ADI method, solutions have been obtained very efficiently by the new scheme.

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

1998-01-01

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Simple and accurate theory for strong shock waves in a dense hard-sphere fluid.

PubMed

Montanero, J M; López de Haro, M; Santos, A; Garzó, V

1999-12-01

Following an earlier work by Holian et al. [Phys. Rev. E 47, R24 (1993)] for a dilute gas, we present a theory for strong shock waves in a hard-sphere fluid described by the Enskog equation. The idea is to use the Navier-Stokes hydrodynamic equations but taking the temperature in the direction of shock propagation rather than the actual temperature in the computation of the transport coefficients. In general, for finite densities, this theory agrees much better with Monte Carlo simulations than the Navier-Stokes and (linear) Burnett theories, in contrast to the well-known superiority of the Burnett theory for dilute gases.

Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

NASA Astrophysics Data System (ADS)

Dadzie, S. Kokou; Dongari, Nishanth

2012-11-01

We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called 'volume diffusion hydrodynamic model'. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction.

Data Assimilation and Propagation of Uncertainty in Multiscale Cardiovascular Simulation

NASA Astrophysics Data System (ADS)

Schiavazzi, Daniele; Marsden, Alison

2015-11-01

Cardiovascular modeling is the application of computational tools to predict hemodynamics. State-of-the-art techniques couple a 3D incompressible Navier-Stokes solver with a boundary circulation model and can predict local and peripheral hemodynamics, analyze the post-operative performance of surgical designs and complement clinical data collection minimizing invasive and risky measurement practices. The ability of these tools to make useful predictions is directly related to their accuracy in representing measured physiologies. Tuning of model parameters is therefore a topic of paramount importance and should include clinical data uncertainty, revealing how this uncertainty will affect the predictions. We propose a fully Bayesian, multi-level approach to data assimilation of uncertain clinical data in multiscale circulation models. To reduce the computational cost, we use a stable, condensed approximation of the 3D model build by linear sparse regression of the pressure/flow rate relationship at the outlets. Finally, we consider the problem of non-invasively propagating the uncertainty in model parameters to the resulting hemodynamics and compare Monte Carlo simulation with Stochastic Collocation approaches based on Polynomial or Multi-resolution Chaos expansions.

Contribution functions for Zeeman-split lines, and line formation in photospheric faculae

NASA Technical Reports Server (NTRS)

Vanballegooijen, A. A.

1985-01-01

The transfer of polarized light in an inhomogeneous stellar atmosphere, and the formation of magnetically sensitive spectral lines, are discussed. A new method for the solution of the transfer equations is proposed. The method gives a natural definition of the contribution functions for Stokes' parameters, i.e., functions describing the contributions from different parts along the line-of-sight (LOS). The formalism includes all magneto-optical effects, and allows for an arbitrary variation of magnetic field, velocity field, temperature, density, etc., along the LOS. The formation of FeI lambda 5250.2 in photospheric faculae is described. A potential-field model of a facular element is presented, and spectra profiles and contribution functions are computed for the Stokes parameters I, Q, and V.

Topics in viscous potential flow of two-phase systems

NASA Astrophysics Data System (ADS)

Padrino Inciarte, Juan Carlos

Two-phase flows are ubiquitous, from natural and domestic environments to industrial settings. However, due to their complexity, modeling these fluid systems remains a challenge from both the perspective of fundamental questions on the dynamics of an individual, smooth interface, and the perspective of integral analyses, which involve averaging of the conservation laws over large domains, thereby missing local details of the flow. In this work, we consider a set of five problems concerning the linear and non-linear dynamics of an interface or free surface and the study of cavitation inception. Analyses are carried out by assuming the fluid motion to be irrotational, that is, with zero vorticity, and the fluids to be viscous, although results from rotational analyses are presented for the purpose of comparison. The problems considered here are the following: First, we analyze the non-linear deformation and break-up of a bubble or drop immersed in a uniaxial extensional flow of an incompressible viscous fluid. The method of viscous potential flow, in which the flow field is irrotational and viscosity enters through the balance of normal stresses at the interface, is used in the analysis. The governing equations are solved numerically to track the motion of the interface by coupling a boundary element method with a time-integration routine. When break-up occurs, the break-up time computed here is compared with results obtained elsewhere from numerical simulations of the Navier.Stokes equations, which thus keeps vorticity in the analysis, for several combinations of the relevant dimensionless parameters of the problem. For the bubble, for Weber numbers 3 ≤ We ≤ 6, predictions from viscous potential flow shows good agreement with the results from the Navier.Stokes equations for the bubble break-up time, whereas for larger We, the former underpredicts the results given by the latter. Including viscosity increases the break-up time with respect to the inviscid case. For the drop, as expected, increasing the viscous effects of the irrotational motion produces large, elongated drops that take longer to break up in comparison with results for inviscid fluids. In the second problem, we compute the force acting on a spherical bubble of variable radius moving within a liquid with an outer spherical boundary. Viscous potential flow and the dissipation method, which is another purely irrotational approach stemming from the mechanical energy equation, are both systematically implemented. This exposes the role of the choice of the outer boundary condition for the stress on the drag, an issue not explained in the literature known to us. By means of the well-known "cell-model" analysis, the results for the drag are then applied to the case of a swarm of rising bubbles having a certain void fraction. Computations from the dissipation method for the drag coefficient and rise velocity for a bubble swarm agree with numerical solutions; evaluation against experimental data for high Reynolds and low Weber numbers shows that all the models considered, including those given in the literature, overpredict the bubble swarm rise velocity. In the next two problems, we apply the analysis of viscous potential flow and the dissipation method to study the linear dynamics of waves of "small" amplitude acting either on a plane or on a spherical interface separating a liquid from a dynamically inactive fluid. It is shown that the viscous irrational theories exhibit the features of the wave dynamics by comparing with the exact solution. The range of parameters for which good agreement with the exact solution exists is presented. The general trend shows that for long waves the dissipation method results in the best approximation, whereas for short waves, even for very viscous liquids, viscous potential flow demonstrates better agreement. Finally, the problem of cavitation inception for the flow of a viscous liquid past a stationary sphere is studied by means of the theory of stress-induced cavitation. The flow field for a single phase needed in the analysis is found from three different methods, namely, the numerical solution of the Navier--Stokes equations, the irrotational motion of a viscous fluid, and, in the limit of no inertia, the Stokes flow formulation. The new predictions are then compared with those obtained from the classical pressure criterion. The main finding is that at a fixed cavitation number more viscous liquids are at greater risk to cavitation.

Navier-Stokes and Euler solutions for lee-side flows over supersonic delta wings. A correlation with experiment

NASA Technical Reports Server (NTRS)

Mcmillin, S. Naomi; Thomas, James L.; Murman, Earll M.

1990-01-01

An Euler flow solver and a thin layer Navier-Stokes flow solver were used to numerically simulate the supersonic leeside flow fields over delta wings which were observed experimentally. Three delta wings with 75, 67.5, and 60 deg leading edge sweeps were computed over an angle-of-attack range of 4 to 20 deg at a Mach number 2.8. The Euler code and Navier-Stokes code predict equally well the primary flow structure where the flow is expected to be separated or attached at the leading edge based on the Stanbrook-Squire boundary. The Navier-Stokes code is capable of predicting both the primary and the secondary flow features for the parameter range investigated. For those flow conditions where the Euler code did not predict the correct type of primary flow structure, the Navier-Stokes code illustrated that the flow structure is sensitive to boundary layer model. In general, the laminar Navier-Stokes solutions agreed better with the experimental data, especially for the lower sweep delta wings. The computational results and a detailed re-examination of the experimental data resulted in a refinement of the flow classifications. This refinement in the flow classification results in the separation bubble with the shock flow type as the intermediate flow pattern between separated and attached flows.

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

NASA Astrophysics Data System (ADS)

Stankiewicz, Witold; Morzyński, Marek; Kotecki, Krzysztof; Noack, Bernd R.

2017-04-01

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier-Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier-Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

Method for transition prediction in high-speed boundary layers, phase 2

NASA Astrophysics Data System (ADS)

Herbert, T.; Stuckert, G. K.; Lin, N.

1993-09-01

The parabolized stability equations (PSE) are a new and more reliable approach to analyzing the stability of streamwise varying flows such as boundary layers. This approach has been previously validated for idealized incompressible flows. Here, the PSE are formulated for highly compressible flows in general curvilinear coordinates to permit the analysis of high-speed boundary-layer flows over fairly general bodies. Vigorous numerical studies are carried out to study convergence and accuracy of the linear-stability code LSH and the linear/nonlinear PSE code PSH. Physical interfaces are set up to analyze the M = 8 boundary layer over a blunt cone calculated by using a thin-layer Navier Stokes (TNLS) code and the flow over a sharp cone at angle of attack calculated using the AFWAL parabolized Navier-Stokes (PNS) code. While stability and transition studies at high speeds are far from routine, the method developed here is the best tool available to research the physical processes in high-speed boundary layers.

Evaluation of Linear, Inviscid, Viscous, and Reduced-Order Modeling Aeroelastic Solutions of the AGARD 445.6 Wing Using Root Locus Analysis

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Perry, Boyd III; Chwalowski, Pawel

2014-01-01

Reduced-order modeling (ROM) methods are applied to the CFD-based aeroelastic analysis of the AGARD 445.6 wing in order to gain insight regarding well-known discrepancies between the aeroelastic analyses and the experimental results. The results presented include aeroelastic solutions using the inviscid CAP-TSD code and the FUN3D code (Euler and Navier-Stokes). Full CFD aeroelastic solutions and ROM aeroelastic solutions, computed at several Mach numbers, are presented in the form of root locus plots in order to better reveal the aeroelastic root migrations with increasing dynamic pressure. Important conclusions are drawn from these results including the ability of the linear CAP-TSD code to accurately predict the entire experimental flutter boundary (repeat of analyses performed in the 1980's), that the Euler solutions at supersonic conditions indicate that the third mode is always unstable, and that the FUN3D Navier-Stokes solutions stabilize the unstable third mode seen in the Euler solutions.

SIMULTANEOUS LINEAR AND CIRCULAR OPTICAL POLARIMETRY OF ASTEROID (4) VESTA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiktorowicz, Sloane J.; Nofi, Larissa A., E-mail: sloanew@ucolick.org

From a single 3.8 hr observation of the asteroid (4) Vesta at 13.°7 phase angle with the POlarimeter at Lick for Inclination Studies of Hot jupiters 2 (POLISH2) at the Lick Observatory Shane 3 m telescope, we confirm rotational modulation of linear polarization in the B and V bands. We measure the peak-to-peak modulation in the degree of linear polarization to be ΔP = (294 ± 35) × 10{sup −6} (ppm) and time-averaged ΔP/P = 0.0575 ± 0.0069. After rotating the plane of linear polarization to the scattering plane, asteroidal rotational modulation is detected with 12σ confidence and observed solelymore » in Stokes Q/I. POLISH2 simultaneously measures Stokes I, Q, U (linear polarization), and V (circular polarization), but we detect no significant circular polarization with a 1σ upper limit of 78 ppm in the B band. Circular polarization is expected to arise from multiple scattering of sunlight by rough surfaces, and it has previously been detected in nearly all other classes of solar system bodies except for asteroids. Subsequent observations may be compared with surface albedo maps from the Dawn Mission, which may allow the identification of compositional variation across the asteroidal surface. These results demonstrate the high accuracy achieved by POLISH2 at the Lick 3 m telescope, which is designed to directly detect scattered light from spatially unresolvable exoplanets.« less

Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations

NASA Astrophysics Data System (ADS)

Takizawa, Kenji; Tezduyar, Tayfun E.; Otoguro, Yuto

2018-04-01

Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space-time (ST) computational methods in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.

Multispectral and polarimetric photodetection using a plasmonic metasurface

NASA Astrophysics Data System (ADS)

Pelzman, Charles; Cho, Sang-Yeon

2018-01-01

We present a metasurface-integrated Si 2-D CMOS sensor array for multispectral and polarimetric photodetection applications. The demonstrated sensor is based on the polarization selective extraordinary optical transmission from periodic subwavelength nanostructures, acting as artificial atoms, known as meta-atoms. The meta-atoms were created by patterning periodic rectangular apertures that support optical resonance at the designed spectral bands. By spatially separating meta-atom clusters with different lattice constants and orientations, the demonstrated metasurface can convert the polarization and spectral information of an optical input into a 2-D intensity pattern. As a proof-of-concept experiment, we measured the linear components of the Stokes parameters directly from captured images using a CMOS camera at four spectral bands. Compared to existing multispectral polarimetric sensors, the demonstrated metasurface-integrated CMOS system is compact and does not require any moving components, offering great potential for advanced photodetection applications.

Polarimetric receiver in the forty gigahertz band: new instrument for the Q-U-I joint Tenerife experiment

NASA Astrophysics Data System (ADS)

Villa, Enrique; Cano, Juan L.; Aja, Beatriz; Terán, J. Vicente; de la Fuente, Luisa; Mediavilla, Ángel; Artal, Eduardo

2018-03-01

This paper describes the analysis, design and characterization of a polarimetric receiver developed for covering the 35 to 47 GHz frequency band in the new instrument aimed at completing the ground-based Q-U-I Joint Tenerife Experiment. This experiment is designed to measure polarization in the Cosmic Microwave Background. The described high frequency instrument is a HEMT-based array composed of 29 pixels. A thorough analysis of the behaviour of the proposed receiver, based on electronic phase switching, is presented for a noise-like linearly polarized input signal, obtaining simultaneously I, Q and U Stokes parameters of the input signal. Wideband subsystems are designed, assembled and characterized for the polarimeter. Their performances are described showing appropriate results within the 35-to-47 GHz frequency band. Functionality tests are performed at room and cryogenic temperatures with adequate results for both temperature conditions, which validate the receiver concept and performance.

Uncertainty quantification in Eulerian-Lagrangian models for particle-laden flows

NASA Astrophysics Data System (ADS)

Fountoulakis, Vasileios; Jacobs, Gustaaf; Udaykumar, Hs

2017-11-01

A common approach to ameliorate the computational burden in simulations of particle-laden flows is to use a point-particle based Eulerian-Lagrangian model, which traces individual particles in their Lagrangian frame and models particles as mathematical points. The particle motion is determined by Stokes drag law, which is empirically corrected for Reynolds number, Mach number and other parameters. The empirical corrections are subject to uncertainty. Treating them as random variables renders the coupled system of PDEs and ODEs stochastic. An approach to quantify the propagation of this parametric uncertainty to the particle solution variables is proposed. The approach is based on averaging of the governing equations and allows for estimation of the first moments of the quantities of interest. We demonstrate the feasibility of our proposed methodology of uncertainty quantification of particle-laden flows on one-dimensional linear and nonlinear Eulerian-Lagrangian systems. This research is supported by AFOSR under Grant FA9550-16-1-0008.

A Generalized Acoustic Analogy

NASA Technical Reports Server (NTRS)

Goldstein, M. E.

2003-01-01

The purpose of this article is to show that the Navier-Stokes equations can be rewritten as a set of linearized inhomogeneous Euler equations (in convective form) with source terms that are exactly the same as those that would result from externally imposed shear stress and energy flux perturbations. These results are used to develop a mathematical basis for some existing and potential new jet noise models by appropriately choosing the base flow about which the linearization is carried out.

Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

NASA Astrophysics Data System (ADS)

Faugeras, Blaise; Blum, Jacques; Heumann, Holger; Boulbe, Cédric

2017-08-01

The modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements.

Calibration Errors in Interferometric Radio Polarimetry

NASA Astrophysics Data System (ADS)

Hales, Christopher A.

2017-08-01

Residual calibration errors are difficult to predict in interferometric radio polarimetry because they depend on the observational calibration strategy employed, encompassing the Stokes vector of the calibrator and parallactic angle coverage. This work presents analytic derivations and simulations that enable examination of residual on-axis instrumental leakage and position-angle errors for a suite of calibration strategies. The focus is on arrays comprising alt-azimuth antennas with common feeds over which parallactic angle is approximately uniform. The results indicate that calibration schemes requiring parallactic angle coverage in the linear feed basis (e.g., the Atacama Large Millimeter/submillimeter Array) need only observe over 30°, beyond which no significant improvements in calibration accuracy are obtained. In the circular feed basis (e.g., the Very Large Array above 1 GHz), 30° is also appropriate when the Stokes vector of the leakage calibrator is known a priori, but this rises to 90° when the Stokes vector is unknown. These findings illustrate and quantify concepts that were previously obscure rules of thumb.

On the drag of model dendrite fragments at low Reynolds number

NASA Technical Reports Server (NTRS)

Zakhem, R.; Weidman, P. D.; Degroh, H. C., III

1993-01-01

An experimental study of low Reynolds number drag on laboratory models of dendrite fragments has been conducted. The terminal velocities of the dendrites undergoing free fall along their axis of symmetry were measured in a large Stokes flow facility. Corrections for wall interference give nearly linear drag vs Reynolds number curves. Corrections for both wall interference and inertia effects show that the dendrite Stokes settling velocities are always less than that of a sphere of equal mass and volume. In the Stokes limit, the settling speed ratio is found to correlate well with primary dendrite arm aspect ratio and a second dimensionless shape paremeter which serves as a measure of the fractal-like nature of the dendrite models. These results can be used to estimate equiaxed grain velocities and distance of travel in metal castings. The drag measurements may be used in numerical codes to calculate the movement of grains in a convecting melt in an effort to determine macrosegregation patterns caused by the sink/float mechanism.

Polarization of light and hopf fibration

NASA Astrophysics Data System (ADS)

Jurčo, B.

1987-09-01

A set of polarization states of quasi-monochromatic light is described geometrically in terms of the Hopf fibration. Several associated alternative polarization parametrizations are given explicitly, including the Stokes parameters.

Glucose concentration measured by the hybrid coherent anti-Stokes Raman-scattering technique

NASA Astrophysics Data System (ADS)

Wang, Xi; Zhang, Aihua; Zhi, Miaochan; Sokolov, Alexei V.; Welch, George R.

2010-01-01

We investigate the possibility of using a hybrid coherent anti-Stokes Raman scattering technique for noninvasive monitoring of blood glucose levels. Our technique combines instantaneous coherent excitation of several characteristic molecular vibrations with subsequent probing of these vibrations by an optimally shaped, time-delayed, narrowband laser pulse. This pulse configuration mitigates the nonresonant four-wave mixing background while maximizing the Raman-resonant signal and allows rapid and highly specific detection even in the presence of multiple scattering. Under certain conditions we find that the measured signal is linearly proportional to the glucose concentration due to optical interference with the residual background light, which allows reliable detection of spectral signatures down to medically relevant glucose levels.

Least-squares solution of incompressible Navier-Stokes equations with the p-version of finite elements

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Sonnad, Vijay

1991-01-01

A p-version of the least squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady state incompressible viscous flow problems. The resulting system of symmetric and positive definite linear equations can be solved satisfactorily with the conjugate gradient method. In conjunction with the use of rapid operator application which avoids the formation of either element of global matrices, it is possible to achieve a highly compact and efficient solution scheme for the incompressible Navier-Stokes equations. Numerical results are presented for two-dimensional flow over a backward facing step. The effectiveness of simple outflow boundary conditions is also demonstrated.

Introduction to COFFE: The Next-Generation HPCMP CREATE-AV CFD Solver

NASA Technical Reports Server (NTRS)

Glasby, Ryan S.; Erwin, J. Taylor; Stefanski, Douglas L.; Allmaras, Steven R.; Galbraith, Marshall C.; Anderson, W. Kyle; Nichols, Robert H.

2016-01-01

HPCMP CREATE-AV Conservative Field Finite Element (COFFE) is a modular, extensible, robust numerical solver for the Navier-Stokes equations that invokes modularity and extensibility from its first principles. COFFE implores a flexible, class-based hierarchy that provides a modular approach consisting of discretization, physics, parallelization, and linear algebra components. These components are developed with modern software engineering principles to ensure ease of uptake from a user's or developer's perspective. The Streamwise Upwind/Petrov-Galerkin (SU/PG) method is utilized to discretize the compressible Reynolds-Averaged Navier-Stokes (RANS) equations tightly coupled with a variety of turbulence models. The mathematics and the philosophy of the methodology that makes up COFFE are presented.

Reduction of the Nonlinear Phase Shift Induced by Stimulated Brillouin Scattering for Bi-Directional Pumping Configuration System Using Particle Swarm Optimization Algorithm

NASA Astrophysics Data System (ADS)

Al-Asadi, H. A.

2013-02-01

We present a theoretical analysis of an additional nonlinear phase shift of backward Stokes wave based on stimulated Brillouin scattering in the system with a bi-directional pumping scheme. We optimize three parameters of the system: the numerical aperture, the optical loss and the pumping wavelength to minimize an additional nonlinear phase shift of backward Stokes waves due to stimulated Brillouin scattering. The optimization is performed with various Brillouin pump powers and the optical reflectivity values are based on the modern, global evolutionary computation algorithm, particle swarm optimization. It is shown that the additional nonlinear phase shift of backward Stokes wave varies with different optical fiber lengths, and can be minimized to less than 0.07 rad according to the particle swarm optimization algorithm for 5 km. The bi-directional pumping configuration system is shown to be efficient when it is possible to transmit the power output to advanced when frequency detuning is negative and delayed when it is positive, with the optimum values of the three parameters to achieve the reduction of an additional nonlinear phase shift.

High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

NASA Technical Reports Server (NTRS)

Carlson, John R.

1996-01-01

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

Transport of Multivalent Electrolyte Mixtures in Micro- and Nanochannels

DTIC Science & Technology

2013-11-08

equations for this process are the unsteady Navier-Stokes equations along with continuity and the Poisson- Nernst -Planck system for the electro- static part...about five times the Debye screening length D (the 1/e lengthscale for the potential from the solution of the linearized Poisson- Boltzmann equation

Rarefaction and Non-equilibrium Effects in Hypersonic Flows about Leading Edges of Small Bluntness

NASA Astrophysics Data System (ADS)

Ivanov, Mikhail; Khotyanovsky, Dmitry; Kudryavtsev, Alexey; Shershnev, Anton; Bondar, Yevgeniy; Yonemura, Shigeru

2011-05-01

A hypersonic flow about a cylindrically blunted thick plate at a zero angle of attack is numerically studied with the kinetic (DSMC) and continuum (Navier-Stokes equations) approaches. The Navier-Stokes equations with velocity slip and temperature jump boundary conditions correctly predict the flow fields and surface parameters for values of the Knudsen number (based on the radius of leading edge curvature) smaller than 0.1. The results of computations demonstrate significant effects of the entropy layer on the boundary layer characteristics.

Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.

PubMed

Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A

2016-08-01

Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.

A least-squares finite element method for incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1992-01-01

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Polarization-modulated second harmonic generation ellipsometric microscopy at video rate.

PubMed

DeWalt, Emma L; Sullivan, Shane Z; Schmitt, Paul D; Muir, Ryan D; Simpson, Garth J

2014-08-19

Fast 8 MHz polarization modulation coupled with analytical modeling, fast beam-scanning, and synchronous digitization (SD) have enabled simultaneous nonlinear optical Stokes ellipsometry (NOSE) and polarized laser transmittance imaging with image acquisition rates up to video rate. In contrast to polarimetry, in which the polarization state of the exiting beam is recorded, NOSE enables recovery of the complex-valued Jones tensor of the sample that describes all polarization-dependent observables of the measurement. Every video-rate scan produces a set of 30 images (10 for each detector with three detectors operating in parallel), each of which corresponds to a different polarization-dependent result. Linear fitting of this image set contracts it down to a set of five parameters for each detector in second harmonic generation (SHG) and three parameters for the transmittance of the incident beam. These parameters can in turn be used to recover the Jones tensor elements of the sample. Following validation of the approach using z-cut quartz, NOSE microscopy was performed for microcrystals of both naproxen and glucose isomerase. When weighted by the measurement time, NOSE microscopy was found to provide a substantial (>7 decades) improvement in the signal-to-noise ratio relative to our previous measurements based on the rotation of optical elements and a 3-fold improvement relative to previous single-point NOSE approaches.

Charge Transport in Nonaqueous Liquid Electrolytes: A Paradigm Shift

DTIC Science & Technology

2015-05-18

that provide inadequate descriptions of experimental data, often using empirical equations whose fitting parameters have no physical significance...provide inadequate descriptions of experimental data, often using empirical equations whose fitting parameters have no physical significance...Ea The hydrodynamic model, utilizing the Stokes equation describes isothermal conductivity, self-diffusion coefficient, and the dielectric

The magnetic fields of Ap stars from high resolution Stokes IQUV spectropolarimetry

NASA Astrophysics Data System (ADS)

Silvester, James

In this thesis we describe the acquisition of high resolution time resolved spectropolarimetric observations of 7 (bright and well understood) Ap stars in Stokes IQUV using the ESPaDOnS and Narval spectropolarimeters at the Canada-France-Hawaii Telescope and the 2m Telescope Bernard Lyot at Pic du Midi Observatory. We compare these observations with those obtained a decade earlier using the MuSiCoS spectropolarimeter to confirm consistency with the older data and provide evidence that both ESPaDOnS and Narval perform as expected in all Stokes parameters. We demonstrate that our refined longitudinal magnetic field and linear polarisation measurements for these 7 stars are of much greater quality than was previously obtained with MuSiCoS and that the global magnetic properties of these stars are stable over a long timescale. The ultimate aim of these new data is to provide a basis from which mapping of both the magnetic field and abundance structures can be performed on our target stars. We then describe magnetic field mapping of the Ap star alpha 2 CVn using these data. This mapping is achieved with the use of tomographic inversion of Doppler-broadened Stokes IQUV profiles of a large variety of spectral lines using the INVERS10 Magnetic Doppler imaging code. We show that not only are the new magnetic field maps of alpha 2 CVn consistent with a previous generation of maps of alpha 2 CVn, but that the same magnetic field topology can be derived from a variety of atomic line sets. This indicates that the magnetic field we derive for alpha2 CVn is a realistic representation of the star's true magnetic topology. Finally we investigate surface abundance structures for alpha 2 CVn for various chemical elements. We investigate the correlation between the location of these abundance features and the magnetic field of alpha 2 CVn. We will demonstrate that whilst the magnetic field plays a role in the formation of abundance structures, the current theoretical framework does not fully explain what we find from our maps. Ultimately this work motivates future mapping of Ap stars by confirming the reliability of both the instrument and associated data and the mapping technique itself.

Self-similarity in incompressible Navier-Stokes equations.

PubMed

Ercan, Ali; Kavvas, M Levent

2015-12-01

The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.

The Primordial Inflation Explorer (PIXIE)

NASA Technical Reports Server (NTRS)

Kogut, Alan; Chuss, David T.; Dotson, Jessie; Dwek, Eli; Fixsen, Dale J.; Halpern, Mark; Hinshaw, Gary F.; Meyer, Stephan; Moseley, S. Harvey; Seiffert, Michael D.;

Feedback stabilization of an oscillating vertical cylinder by POD Reduced-Order Model

NASA Astrophysics Data System (ADS)

Tissot, Gilles; Cordier, Laurent; Noack, Bernd R.

2015-01-01

The objective is to demonstrate the use of reduced-order models (ROM) based on proper orthogonal decomposition (POD) to stabilize the flow over a vertically oscillating circular cylinder in the laminar regime (Reynolds number equal to 60). The 2D Navier-Stokes equations are first solved with a finite element method, in which the moving cylinder is introduced via an ALE method. Since in fluid-structure interaction, the POD algorithm cannot be applied directly, we implemented the fictitious domain method of Glowinski et al. [1] where the solid domain is treated as a fluid undergoing an additional constraint. The POD-ROM is classically obtained by projecting the Navier-Stokes equations onto the first POD modes. At this level, the cylinder displacement is enforced in the POD-ROM through the introduction of Lagrange multipliers. For determining the optimal vertical velocity of the cylinder, a linear quadratic regulator framework is employed. After linearization of the POD-ROM around the steady flow state, the optimal linear feedback gain is obtained as solution of a generalized algebraic Riccati equation. Finally, when the optimal feedback control is applied, it is shown that the flow converges rapidly to the steady state. In addition, a vanishing control is obtained proving the efficiency of the control approach.

Stokes polarimetry imaging of dog prostate tissue

NASA Astrophysics Data System (ADS)

Kim, Jihoon; Johnston, William K., III; Walsh, Joseph T., Jr.

2010-02-01

Prostate cancer is the second leading cause of death in the United States in 2009. Radical prostatectomy (complete removal of the prostate) is the most common treatment for prostate cancer, however, differentiating prostate tissue from adjacent bladder, nerves, and muscle is difficult. Improved visualization could improve oncologic outcomes and decrease damage to adjacent nerves and muscle important for preservation of potency and continence. A novel Stokes polarimetry imaging (SPI) system was developed and evaluated using a dog prostate specimen in order to examine the feasibility of the system to differentiate prostate from bladder. The degree of linear polarization (DOLP) image maps from linearly polarized light illumination at different visible wavelengths (475, 510, and 650 nm) were constructed. The SPI system used the polarization property of the prostate tissue. The DOLP images allowed advanced differentiation by distinguishing glandular tissue of prostate from the muscular-stromal tissue in the bladder. The DOLP image at 650 nm effectively differentiated prostate and bladder by strong DOLP in bladder. SPI system has the potential to improve surgical outcomes in open or robotic-assisted laparoscopic removal of the prostate. Further in vivo testing is warranted.

Geologic Studies of Planetary Surfaces Using Radar Polarimetric Imaging

NASA Technical Reports Server (NTRS)

Carter, Lynn M.; Campbell, Donald B.; Campbell, Bruce A.

2010-01-01

Radar is a useful remote sensing tool for studying planetary geology because it is sensitive to the composition, structure, and roughness of the surface and can penetrate some materials to reveal buried terrain. The Arecibo Observatory radar system transmits a single sense of circular polarization, and both senses of circular polarization are received, which allows for the construction of the Stokes polarization vector. From the Stokes vector, daughter products such as the circular polarization ratio, the degree of linear polarization, and linear polarization angle are obtained. Recent polarimetric imaging using Arecibo has included Venus and the Moon. These observations can be compared to radar data for terrestrial surfaces to better understand surface physical properties and regional geologic evolution. For example, polarimetric radar studies of volcanic settings on Venus, the Moon and Earth display some similarities, but also illustrate a variety of different emplacement and erosion mechanisms. Polarimetric radar data provides important information about surface properties beyond what can be obtained from single-polarization radar. Future observations using polarimetric synthetic aperture radar will provide information on roughness, composition and stratigraphy that will support a broader interpretation of surface evolution.

Localization length and intraband scattering of excitons in linear aggregates

NASA Astrophysics Data System (ADS)

Lemaistre, J. P.

1999-07-01

A theoretical model to describe the intraband scattering of excitons in linear aggregates of finite size which exhibit strong intermolecular interactions is presented. From the calculation of the aggregate eigenstates, the localization length of excitons is evaluated for various configurations featuring physical situations like trapping, edge effects, inclusion of diagonal and/or orientational disorders. The intraband scattering is studied by considering the exciton-phonon stochastic coupling induced by the thermal bath. This coupling creates local dynamical fluctuations in the site energies which are characterized by their amplitude ( Δ) and their correlation time ( τc). Expressions of scattering rates are provided and used in a Pauli master equation to calculate the time dependence of the eigenstates populations after initial excitation of the quasi exciton-band. It is shown that the time evolution of the lowest state population as well as the Stokes shift strongly depend on τc. Comparison of the theoretical results to time-resolved experiments performed on triaryl pyrylium salts allows us to interpret the observed Stokes shift and to derive an average value of the exciton-phonon correlation time.

Optimal Growth in Hypersonic Boundary Layers

NASA Technical Reports Server (NTRS)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan

2016-01-01

The linear form of the parabolized linear stability equations is used in a variational approach to extend the previous body of results for the optimal, nonmodal disturbance growth in boundary-layer flows. This paper investigates the optimal growth characteristics in the hypersonic Mach number regime without any high-enthalpy effects. The influence of wall cooling is studied, with particular emphasis on the role of the initial disturbance location and the value of the spanwise wave number that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary-layer equations, mean flow solutions based on the full Navier-Stokes equations are used in select cases to help account for the viscous- inviscid interaction near the leading edge of the plate and for the weak shock wave emanating from that region. Using the full Navier-Stokes mean flow is shown to result in further reduction with Mach number in the magnitude of optimal growth relative to the predictions based on the self-similar approximation to the base flow.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

Scale-invariant streamline equations and strings of singular vorticity for perturbed anisotropic solutions of the Navier-Stokes equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Libin, A., E-mail: a_libin@netvision.net.il

2012-12-15

A linear combination of a pair of dual anisotropic decaying Beltrami flows with spatially constant amplitudes (the Trkal solutions) with the same eigenvalue of the curl operator and of a constant velocity orthogonal vector to the Beltrami pair yields a triplet solution of the force-free Navier-Stokes equation. The amplitudes slightly variable in space (large scale perturbations) yield the emergence of a time-dependent phase between the dual Beltrami flows and of the upward velocity, which are unstable at large values of the Reynolds number. They also lead to the formation of large-scale curved prisms of streamlines with edges being the stringsmore » of singular vorticity.« less

Instability and sound emission from a flow over a curved surface

NASA Technical Reports Server (NTRS)

Maestrello, L.; Parikh, P.; Bayliss, A.

1988-01-01

The growth and decay of a wavepacket convecting in a boundary layer over a concave-convex surface is studied numerically using direct computations of the Navier-Stokes equations. The resulting sound radiation is computed using the linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. It is shown that on the concave portion the amplitude of the wavepacket increases and its bandwidth broadens while on the convex portion some of the components in the packet are stabilized. The pressure field decays exponentially away from the surface and then algebraically exhibits a decay characteristic of acoustic waves in two dimensions. The far-field acoustic pressure exhibits a peak at a frequency corresponding to the inflow instability frequency.

A compressible solution of the Navier-Stokes equations for turbulent flow about an airfoil

NASA Technical Reports Server (NTRS)

Shamroth, S. J.; Gibeling, H. J.

1979-01-01

A compressible time dependent solution of the Navier-Stokes equations including a transition turbulence model is obtained for the isolated airfoil flow field problem. The equations are solved by a consistently split linearized block implicit scheme. A nonorthogonal body-fitted coordinate system is used which has maximum resolution near the airfoil surface and in the region of the airfoil leading edge. The transition turbulence model is based upon the turbulence kinetic energy equation and predicts regions of laminar, transitional, and turbulent flow. Mean flow field and turbulence field results are presented for an NACA 0012 airfoil at zero and nonzero incidence angles of Reynolds number up to one million and low subsonic Mach numbers.

Diode-side-pumped intracavity frequency-doubled Nd:YAG/BaWO4 Raman laser generating average output power of 3.14 W at 590 nm.

PubMed

Li, Shutao; Zhang, Xingyu; Wang, Qingpu; Zhang, Xiaolei; Cong, Zhenhua; Zhang, Huaijin; Wang, Jiyang

2007-10-15

We report a linear-cavity high-power all-solid-state Q-switched yellow laser. The laser source comprises a diode-side-pumped Nd:YAG module that produces 1064 nm fundamental radiation, an intracavity BaWO(4) Raman crystal that generates a first-Stokes laser at 1180 nm, and a KTP crystal that frequency doubles the first-Stokes laser to 590 nm. A convex-plane cavity is employed in this configuration to counteract some of the thermal effect caused by high pump power. An average output power of 3.14 W at 590 nm is obtained at a pulse repetition frequency of 10 kHz.

Influence of anisotropy on anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field.

PubMed

Jurcisinová, E; Jurcisin, M; Remecký, R

2009-10-01

The influence of weak uniaxial small-scale anisotropy on the stability of the scaling regime and on the anomalous scaling of the single-time structure functions of a passive scalar advected by the velocity field governed by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and operator-product expansion within one-loop approximation of a perturbation theory. The explicit analytical expressions for coordinates of the corresponding fixed point of the renormalization-group equations as functions of anisotropy parameters are found, the stability of the three-dimensional Kolmogorov-like scaling regime is demonstrated, and the dependence of the borderline dimension d(c) is an element of (2,3] between stable and unstable scaling regimes is found as a function of the anisotropy parameters. The dependence of the turbulent Prandtl number on the anisotropy parameters is also briefly discussed. The influence of weak small-scale anisotropy on the anomalous scaling of the structure functions of a passive scalar field is studied by the operator-product expansion and their explicit dependence on the anisotropy parameters is present. It is shown that the anomalous dimensions of the structure functions, which are the same (universal) for the Kraichnan model, for the model with finite time correlations of the velocity field, and for the model with the advection by the velocity field driven by the stochastic Navier-Stokes equation in the isotropic case, can be distinguished by the assumption of the presence of the small-scale anisotropy in the systems even within one-loop approximation. The corresponding comparison of the anisotropic anomalous dimensions for the present model with that obtained within the Kraichnan rapid-change model is done.

Marangoni bubble motion in zero gravity. [Lewis zero gravity drop tower

NASA Technical Reports Server (NTRS)

Thompson, R. L.; Dewitt, K. J.

1979-01-01

It was shown experimentally that the Marangoni phenomenon is a primary mechanism for the movement of a gas bubble in a nonisothermal liquid in a low gravity environment. A mathematical model consisting of the Navier-Stokes and thermal energy equations, together with the appropriate boundary conditions for both media, is presented. Parameter perturbation theory is used to solve this boundary value problem; the expansion parameter is the Marangoni number. The zeroth, first, and second order approximations for the velocity, temperature and pressure distributions in the liquid and in the bubble, and the deformation and terminal velocity of the bubble are determined. Experimental zero gravity data for a nitrogen bubble in ethylene glycol, ethanol, and silicone oil subjected to a linear temperature gradient were obtained using the NASA Lewis zero gravity drop tower. Comparison of the zeroth order analytical results for the bubble terminal velocity showed good agreement with the experimental measurements. The first and second order solutions for the bubble deformation and bubble terminal velocity are valid for liquids having Prandtl numbers on the order of one, but there is a lack of appropriate data to test the theory fully.

Stokes space modulation format classification based on non-iterative clustering algorithm for coherent optical receivers.

PubMed

Mai, Xiaofeng; Liu, Jie; Wu, Xiong; Zhang, Qun; Guo, Changjian; Yang, Yanfu; Li, Zhaohui

2017-02-06

A Stokes-space modulation format classification (MFC) technique is proposed for coherent optical receivers by using a non-iterative clustering algorithm. In the clustering algorithm, two simple parameters are calculated to help find the density peaks of the data points in Stokes space and no iteration is required. Correct MFC can be realized in numerical simulations among PM-QPSK, PM-8QAM, PM-16QAM, PM-32QAM and PM-64QAM signals within practical optical signal-to-noise ratio (OSNR) ranges. The performance of the proposed MFC algorithm is also compared with those of other schemes based on clustering algorithms. The simulation results show that good classification performance can be achieved using the proposed MFC scheme with moderate time complexity. Proof-of-concept experiments are finally implemented to demonstrate MFC among PM-QPSK/16QAM/64QAM signals, which confirm the feasibility of our proposed MFC scheme.

Measurements of vector fields with diode array

NASA Technical Reports Server (NTRS)

Wiehr, E. J.; Scholiers, W.

1985-01-01

A polarimeter was designed for high spatial and spectral resolution. It consists of a quarter-wave plate alternately operating in two positions for Stoke-V measurements and an additional quarter-wave plate for Stokes-U and -Q measurements. The spatial range covers 75 arcsec, the spectral window of about 1.8 a allows the simultaneous observations of neighboring lines. The block diagram of the data processing and acquisition system consists of five memories each one having a capacity of 10 to the 4th power 16-bit words. The total time to acquire profiles of Stokes parameters can be chosen by selecting the number of successive measurements added in the memories, each individual measurement corresponding to an integration time of 0.5 sec. Typical values range between 2 and 60 sec depending on the brightness of the structure, the amount of polarization and a compromise between desired signal-to-noise ratio and spatial resolution.

Solvent relaxation of fluorescent labels as a new tool for the detection of polarity and rigidity changes in membranes

NASA Astrophysics Data System (ADS)

Hof, Martin; Hutterer, Rudi

1998-04-01

Since solvent relaxation (SR) exclusively depends on the physical properties of the dye environment, SR spectroscopy of defined located labels in amphiphilic assemblies accomplishes the characterisation of specific domains. The most accurate way to characterise SR is the determination of the time-dependent Stokes shift. The time course of the Stokes shift, expressed as a solvent relaxation time, gives information about both the rigidity and polarity of the dye environment. The absolute value of the Stokes shift following the excitation is correlated with the polarity of the probed region. The validity of this approach for the investigation of phospholipid bilayers is illustrated by listing the parameters influencing the SR kinetics of appropriate membrane labels: membrane curvature, percentage of phosphatidylserine (PS) in small unilamell vesicles (SUV), addition of Ca2+ ions, binding of vitamin-K dependent proteins, percentage of diether-lipids in phosphatidylcholine (PC)-vesicles, and temperature.

Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

On some Approximation Schemes for Steady Compressible Viscous Flow

NASA Astrophysics Data System (ADS)

Bause, M.; Heywood, J. G.; Novotny, A.; Padula, M.

This paper continues our development of approximation schemes for steady compressible viscous flow based on an iteration between a Stokes like problem for the velocity and a transport equation for the density, with the aim of improving their suitability for computations. Such schemes seem attractive for computations because they offer a reduction to standard problems for which there is already highly refined software, and because of the guidance that can be drawn from an existence theory based on them. Our objective here is to modify a recent scheme of Heywood and Padula [12], to improve its convergence properties. This scheme improved upon an earlier scheme of Padula [21], [23] through the use of a special ``effective pressure'' in linking the Stokes and transport problems. However, its convergence is limited for several reasons. Firstly, the steady transport equation itself is only solvable for general velocity fields if they satisfy certain smallness conditions. These conditions are met here by using a rescaled variant of the steady transport equation based on a pseudo time step for the equation of continuity. Another matter limiting the convergence of the scheme in [12] is that the Stokes linearization, which is a linearization about zero, has an inevitably small range of convergence. We replace it here with an Oseen or Newton linearization, either of which has a wider range of convergence, and converges more rapidly. The simplicity of the scheme offered in [12] was conducive to a relatively simple and clearly organized proof of its convergence. The proofs of convergence for the more complicated schemes proposed here are structured along the same lines. They strengthen the theorems of existence and uniqueness in [12] by weakening the smallness conditions that are needed. The expected improvement in the computational performance of the modified schemes has been confirmed by Bause [2], in an ongoing investigation.

Polarized radiance distribution measurement of skylight. II. Experiment and data.

PubMed

Liu, Y; Voss, K

1997-11-20

Measurements of the skylight polarized radiance distribution were performed at different measurement sites, atmospheric conditions, and three wavelengths with our newly developed Polarization Radiance Distribution Camera System (RADS-IIP), an analyzer-type Stokes polarimeter. Three Stokes parameters of skylight (I, Q, U), the degree of polarization, and the plane of polarization are presented in image format. The Arago point and neutral lines have been observed with RADS-IIP. Qualitatively, the dependence of the intensity and polarization data on wavelength, solar zenith angle, and surface albedo is in agreement with the results from computations based on a plane-parallel Rayleigh atmospheric model.

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

Shear Melting of a Colloidal Glass

NASA Astrophysics Data System (ADS)

Eisenmann, Christoph; Kim, Chanjoong; Mattsson, Johan; Weitz, David A.

2010-01-01

We use confocal microscopy to explore shear melting of colloidal glasses, which occurs at strains of ˜0.08, coinciding with a strongly non-Gaussian step size distribution. For larger strains, the particle mean square displacement increases linearly with strain and the step size distribution becomes Gaussian. The effective diffusion coefficient varies approximately linearly with shear rate, consistent with a modified Stokes-Einstein relationship in which thermal energy is replaced by shear energy and the length scale is set by the size of cooperatively moving regions consisting of ˜3 particles.

Hydrodynamic cavitation in Stokes flow of anisotropic fluids.

PubMed

Stieger, Tillmann; Agha, Hakam; Schoen, Martin; Mazza, Marco G; Sengupta, Anupam

2017-05-30

Cavitation, the nucleation of vapour in liquids, is ubiquitous in fluid dynamics, and is often implicated in a myriad of industrial and biomedical applications. Although extensively studied in isotropic liquids, corresponding investigations in anisotropic liquids are largely lacking. Here, by combining liquid crystal microfluidic experiments, nonequilibrium molecular dynamics simulations and theoretical arguments, we report flow-induced cavitation in an anisotropic fluid. The cavitation domain nucleates due to sudden pressure drop upon flow past a cylindrical obstacle within a microchannel. For an anisotropic fluid, the inception and growth of the cavitation domain ensued in the Stokes regime, while no cavitation was observed in isotropic liquids flowing under similar hydrodynamic parameters. Using simulations we identify a critical value of the Reynolds number for cavitation inception that scales inversely with the order parameter of the fluid. Strikingly, the critical Reynolds number for anisotropic fluids can be 50% lower than that of isotropic fluids.

Hydrodynamic cavitation in Stokes flow of anisotropic fluids

PubMed Central

Stieger, Tillmann; Agha, Hakam; Schoen, Martin; Mazza, Marco G.; Sengupta, Anupam

2017-01-01

Cavitation, the nucleation of vapour in liquids, is ubiquitous in fluid dynamics, and is often implicated in a myriad of industrial and biomedical applications. Although extensively studied in isotropic liquids, corresponding investigations in anisotropic liquids are largely lacking. Here, by combining liquid crystal microfluidic experiments, nonequilibrium molecular dynamics simulations and theoretical arguments, we report flow-induced cavitation in an anisotropic fluid. The cavitation domain nucleates due to sudden pressure drop upon flow past a cylindrical obstacle within a microchannel. For an anisotropic fluid, the inception and growth of the cavitation domain ensued in the Stokes regime, while no cavitation was observed in isotropic liquids flowing under similar hydrodynamic parameters. Using simulations we identify a critical value of the Reynolds number for cavitation inception that scales inversely with the order parameter of the fluid. Strikingly, the critical Reynolds number for anisotropic fluids can be 50% lower than that of isotropic fluids. PMID:28555615

Results from the First Two Observing Seasons of PIQUE

NASA Astrophysics Data System (ADS)

Gundersen, Joshua; Barkats, Denis; Hedman, Matt; Staggs, Suzanne; Winstein, Bruce

2001-04-01

We report on the first two seasons of the Princeton IQU Experiment (PIQUE). PIQUE is a ground-based telescope designed to measure the polarization of the Cosmic Microwave Background (CMB). During the first season (1/19/00-4/2/00), PIQUE measured the Q Stokes parameter on a ring at declination of 89 degrees from the roof of the Physics Department at Princeton University using a 90 GHz correlation polarimeter with a full-width-half maximum beam of 0.24 degrees. PIQUE's observations from the first season yielded a new limit on the polarization of the CMB in the multipole range 100

Rayleigh scattering of twisted light by hydrogenlike ions

NASA Astrophysics Data System (ADS)

Peshkov, A. A.; Volotka, A. V.; Surzhykov, A.; Fritzsche, S.

2018-02-01

The elastic Rayleigh scattering of twisted light and, in particular, the polarization (transfer) of the scattered photons have been analyzed within the framework of second-order perturbation theory and Dirac's relativistic equation. Special attention was paid hereby to the scattering on three different atomic targets: single atoms, a mesoscopic (small) target, and a macroscopic (large) target, which are all centered with regard to the beam axis. Detailed calculations of the polarization Stokes parameters were performed for C5 + ions and for twisted Bessel beams. It is shown that the polarization of scattered photons is sensitive to the size of an atomic target and to the helicity, the opening angle, and the projection of the total angular momentum of the incident Bessel beam. These computations indicate more that the Stokes parameters of the (Rayleigh) scattered twisted light may significantly differ from their behavior for an incident plane-wave radiation.

Hydrodynamic cavitation in Stokes flow of anisotropic fluids

NASA Astrophysics Data System (ADS)

Stieger, Tillmann; Agha, Hakam; Schoen, Martin; Mazza, Marco G.; Sengupta, Anupam

2017-05-01

Cavitation, the nucleation of vapour in liquids, is ubiquitous in fluid dynamics, and is often implicated in a myriad of industrial and biomedical applications. Although extensively studied in isotropic liquids, corresponding investigations in anisotropic liquids are largely lacking. Here, by combining liquid crystal microfluidic experiments, nonequilibrium molecular dynamics simulations and theoretical arguments, we report flow-induced cavitation in an anisotropic fluid. The cavitation domain nucleates due to sudden pressure drop upon flow past a cylindrical obstacle within a microchannel. For an anisotropic fluid, the inception and growth of the cavitation domain ensued in the Stokes regime, while no cavitation was observed in isotropic liquids flowing under similar hydrodynamic parameters. Using simulations we identify a critical value of the Reynolds number for cavitation inception that scales inversely with the order parameter of the fluid. Strikingly, the critical Reynolds number for anisotropic fluids can be 50% lower than that of isotropic fluids.

On the validity of Stokes-Einstein and Stokes-Einstein-Debye relations in ionic liquids and ionic-liquid mixtures.

PubMed

Köddermann, Thorsten; Ludwig, Ralf; Paschek, Dietmar

2008-09-15

Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in the neat ionic liquid (IL) [C(2)mim][NTf(2)] and IL/chloroform mixtures are studied by means of molecular dynamics (MD) simulations. For this purpose, we simulate the translational diffusion coefficients of the cations and anions, the rotational correlation times of the C(2)--H bond in the cation C(2)mim(+), and the viscosities of the whole system. We find that the SE and SED relations are not valid for the pure ionic liquid, nor for IL/chloroform mixtures down to the miscibility gap (at 50 wt % IL). The deviations from both relations could be related to dynamical heterogeneities described by the non-Gaussian parameter alpha(t). If alpha(t) is close to zero, at a concentration of 1 wt % IL in chloroform, both relations become valid. Then, the effective radii and volumes calculated from the SE and SED equations can be related to the structures found in the MD simulations, such as aggregates of ion pairs. Overall, similarities are observed between the dynamical properties of supercooled water and those of ionic liquids.

Estimating the Earth's geometry, rotation and gravity field using a multi-satellite SLR solution

NASA Astrophysics Data System (ADS)

Stefka, V.; Blossfeld, M.; Mueller, H.; Gerstl, M.; Panafidina, N.

2012-12-01

Satellite Laser Ranging (SLR) is the unique technique to determine station coordinates, Earth Orientation Parameter (EOP) and Stokes coefficients of the Earth's gravity field in one common adjustment. These parameters form the so called "three pillars" (Plag & Pearlman, 2009) of the Global Geodetic Observing System (GGOS). In its function as official analysis center of the International Laser Ranging Service (ILRS), DGFI is developing and maintaining software to process SLR observations called "DGFI Orbit and Geodetic parameter estimation Software" (DOGS). The software is used to analyze SLR observations and to compute multi-satellite solutions. To take benefit of different orbit performances (e.g. inclination and altitude), a solution using ten different spherical satellites (ETALON1/2, LAGEOS1/2, STELLA, STARLETTE, AJISAI, LARETS, LARES, BLITS) covering the period of 12 years of observations is computed. The satellites are relatively weighted using a variance component estimation (VCE). The obtained weights are analyzed w.r.t. the potential of the satellite to monitor changes in the Earths geometry, rotation and gravity field. The estimated parameters (station coordinates and EOP) are validated w.r.t. official time series of the IERS. The Stokes coefficients are compared to recent gravity field solutions.

Estimating the Earth's gravity field using a multi-satellite SLR solution

NASA Astrophysics Data System (ADS)

Bloßfeld, Mathis; Stefka, Vojtech; Müller, Horst; Gerstl, Michael

2013-04-01

Satellite Laser Ranging (SLR) is the unique technique to determine station coordinates, Earth Orientation Parameter (EOP) and Stokes coefficients of the Earth's gravity field in one common adjustment. These parameters form the so called "three pillars" (Plag & Pearlman, 2009) of the Global Geodetic Observing System (GGOS). In its function as official analysis center of the International Laser Ranging Service (ILRS), DGFI is developing and maintaining software to process SLR observations called "DGFI Orbit and Geodetic parameter estimation Software" (DOGS). The software is used to analyze SLR observations and to compute multi-satellite solutions. To take benefit of different orbit performances (e.g. inclination and altitude), a solution using ten different spherical satellites (ETALON1/2, LAGEOS1/2, STELLA, STARLETTE, AJISAI, LARETS, LARES, BLITS) covering 12 years of observations is computed. The satellites are relatively weighted using a variance component estimation (VCE). The obtained weights are analyzed w.r.t. the potential of the satellite to monitor changes in the Earths geometry, rotation and gravity field. The estimated parameters (station coordinates and EOP) are validated w.r.t. official time series of the IERS. The obtained Stokes coefficients are compared to recent gravity field solutions and discussed in detail.

Turbulent kinetic energy and a possible hierarchy of length scales in a generalization of the Navier-Stokes alpha theory.

PubMed

Fried, Eliot; Gurtin, Morton E

2007-05-01

We present a continuum-mechanical formulation and generalization of the Navier-Stokes alpha theory based on a general framework for fluid-dynamical theories with gradient dependencies. Our flow equation involves two additional problem-dependent length scales alpha and beta. The first of these scales enters the theory through the internal kinetic energy, per unit mass, alpha2|D|2, where D is the symmetric part of the gradient of the filtered velocity. The remaining scale is associated with a dissipative hyperstress which depends linearly on the gradient of the filtered vorticity. When alpha and beta are equal, our flow equation reduces to the Navier-Stokes alpha equation. In contrast to the original derivation of the Navier-Stokes alpha equation, which relies on Lagrangian averaging, our formulation delivers boundary conditions. For a confined flow, our boundary conditions involve an additional length scale l characteristic of the eddies found near walls. Based on a comparison with direct numerical simulations for fully developed turbulent flow in a rectangular channel of height 2h, we find that alphabeta approximately Re(0.470) and lh approximately Re(-0.772), where Re is the Reynolds number. The first result, which arises as a consequence of identifying the internal kinetic energy with the turbulent kinetic energy, indicates that the choice alpha=beta required to reduce our flow equation to the Navier-Stokes alpha equation is likely to be problematic. The second result evinces the classical scaling relation eta/L approximately Re(-3/4) for the ratio of the Kolmogorov microscale eta to the integral length scale L . The numerical data also suggests that l < or = beta . We are therefore led to conjecture a tentative hierarchy, l < or = beta < alpha , involving the three length scales entering our theory.

HIGH-RESOLUTION LINEAR POLARIMETRIC IMAGING FOR THE EVENT HORIZON TELESCOPE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chael, Andrew A.; Johnson, Michael D.; Narayan, Ramesh

Images of the linear polarizations of synchrotron radiation around active galactic nuclei (AGNs) highlight their projected magnetic field lines and provide key data for understanding the physics of accretion and outflow from supermassive black holes. The highest-resolution polarimetric images of AGNs are produced with Very Long Baseline Interferometry (VLBI). Because VLBI incompletely samples the Fourier transform of the source image, any image reconstruction that fills in unmeasured spatial frequencies will not be unique and reconstruction algorithms are required. In this paper, we explore some extensions of the Maximum Entropy Method (MEM) to linear polarimetric VLBI imaging. In contrast to previousmore » work, our polarimetric MEM algorithm combines a Stokes I imager that only uses bispectrum measurements that are immune to atmospheric phase corruption, with a joint Stokes Q and U imager that operates on robust polarimetric ratios. We demonstrate the effectiveness of our technique on 7 and 3 mm wavelength quasar observations from the VLBA and simulated 1.3 mm Event Horizon Telescope observations of Sgr A* and M87. Consistent with past studies, we find that polarimetric MEM can produce superior resolution compared to the standard CLEAN algorithm, when imaging smooth and compact source distributions. As an imaging framework, MEM is highly adaptable, allowing a range of constraints on polarization structure. Polarimetric MEM is thus an attractive choice for image reconstruction with the EHT.« less

On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets

DOE PAGES

Tezaur, Irina K.; Tuminaro, Raymond S.; Perego, Mauro; ...

2015-01-01

We examine the scalability of the recently developed Albany/FELIX finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete LU (ILU) factorization, and (2) a recently-developed algebraic multigrid (AMG) preconditioner, constructed using the idea of semi-coarsening. A strong scalability study on a realistic, high resolution Greenland ice sheet problem reveals that, for a given number of processor cores, the AMG preconditionermore » results in faster linear solve times but the ILU preconditioner exhibits better scalability. In addition, a weak scalability study is performed on a realistic, moderate resolution Antarctic ice sheet problem, a substantial fraction of which contains floating ice shelves, making it fundamentally different from the Greenland ice sheet problem. We show that as the problem size increases, the performance of the ILU preconditioner deteriorates whereas the AMG preconditioner maintains scalability. This is because the linear systems are extremely ill-conditioned in the presence of floating ice shelves, and the ill-conditioning has a greater negative effect on the ILU preconditioner than on the AMG preconditioner.« less

High-resolution Linear Polarimetric Imaging for the Event Horizon Telescope

NASA Astrophysics Data System (ADS)

Chael, Andrew A.; Johnson, Michael D.; Narayan, Ramesh; Doeleman, Sheperd S.; Wardle, John F. C.; Bouman, Katherine L.

2016-09-01

Images of the linear polarizations of synchrotron radiation around active galactic nuclei (AGNs) highlight their projected magnetic field lines and provide key data for understanding the physics of accretion and outflow from supermassive black holes. The highest-resolution polarimetric images of AGNs are produced with Very Long Baseline Interferometry (VLBI). Because VLBI incompletely samples the Fourier transform of the source image, any image reconstruction that fills in unmeasured spatial frequencies will not be unique and reconstruction algorithms are required. In this paper, we explore some extensions of the Maximum Entropy Method (MEM) to linear polarimetric VLBI imaging. In contrast to previous work, our polarimetric MEM algorithm combines a Stokes I imager that only uses bispectrum measurements that are immune to atmospheric phase corruption, with a joint Stokes Q and U imager that operates on robust polarimetric ratios. We demonstrate the effectiveness of our technique on 7 and 3 mm wavelength quasar observations from the VLBA and simulated 1.3 mm Event Horizon Telescope observations of Sgr A* and M87. Consistent with past studies, we find that polarimetric MEM can produce superior resolution compared to the standard CLEAN algorithm, when imaging smooth and compact source distributions. As an imaging framework, MEM is highly adaptable, allowing a range of constraints on polarization structure. Polarimetric MEM is thus an attractive choice for image reconstruction with the EHT.

Large eddy simulation in a rotary blood pump: Viscous shear stress computation and comparison with unsteady Reynolds-averaged Navier-Stokes simulation.

PubMed

Torner, Benjamin; Konnigk, Lucas; Hallier, Sebastian; Kumar, Jitendra; Witte, Matthias; Wurm, Frank-Hendrik

2018-06-01

Numerical flow analysis (computational fluid dynamics) in combination with the prediction of blood damage is an important procedure to investigate the hemocompatibility of a blood pump, since blood trauma due to shear stresses remains a problem in these devices. Today, the numerical damage prediction is conducted using unsteady Reynolds-averaged Navier-Stokes simulations. Investigations with large eddy simulations are rarely being performed for blood pumps. Hence, the aim of the study is to examine the viscous shear stresses of a large eddy simulation in a blood pump and compare the results with an unsteady Reynolds-averaged Navier-Stokes simulation. The simulations were carried out at two operation points of a blood pump. The flow was simulated on a 100M element mesh for the large eddy simulation and a 20M element mesh for the unsteady Reynolds-averaged Navier-Stokes simulation. As a first step, the large eddy simulation was verified by analyzing internal dissipative losses within the pump. Then, the pump characteristics and mean and turbulent viscous shear stresses were compared between the two simulation methods. The verification showed that the large eddy simulation is able to reproduce the significant portion of dissipative losses, which is a global indication that the equivalent viscous shear stresses are adequately resolved. The comparison with the unsteady Reynolds-averaged Navier-Stokes simulation revealed that the hydraulic parameters were in agreement, but differences for the shear stresses were found. The results show the potential of the large eddy simulation as a high-quality comparative case to check the suitability of a chosen Reynolds-averaged Navier-Stokes setup and turbulence model. Furthermore, the results lead to suggest that large eddy simulations are superior to unsteady Reynolds-averaged Navier-Stokes simulations when instantaneous stresses are applied for the blood damage prediction.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiegelmann, T.; Solanki, S. K.; Barthol, P.

Magneto-static models may overcome some of the issues facing force-free magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quiet-Sun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the Sunrise balloon-borne solar observatory in 2013 June as boundary conditions for a magneto-static model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO /HMI. This work continues our magneto-static extrapolation approach,more » which was applied earlier to a quiet-Sun region observed with Sunrise I. In an active region the signal-to-noise-ratio in the measured Stokes parameters is considerably higher than in the quiet-Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magneto-static equilibria. The high spatial resolution of IMaX (110–130 km, pixel size 40 km) enables us to model the non-force-free layer between the photosphere and the mid-chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower-resolution photospheric measurements in the past. The linear model does not, however, permit us to model intrinsic nonlinear structures like strongly localized electric currents.« less

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

NASA Astrophysics Data System (ADS)

Roos, P. A.; Murphy, S. K.; Meng, L. S.; Carlsten, J. L.; Ralph, T. C.; White, A. G.; Brasseur, J. K.

2003-07-01

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump ↔ pump, Stokes ↔ signal, and Raman coherence ↔ idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1992-01-01

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

Polarimetric passive remote sensing of periodic surfaces

NASA Technical Reports Server (NTRS)

Veysoglu, Murat E.; Yueh, H. A.; Shin, R. T.; Kong, J. A.

1991-01-01

The concept of polarimetry in active remote sensing is extended to passive remote sensing. The potential use of the third and fourth Stokes parameters U and V, which play an important role in polarimetric active remote sensing, is demonstrated for passive remote sensing. It is shown that, by the use of the reciprocity principle, the polarimetric parameters of passive remote sensing can be obtained through the solution of the associated direct scattering problem. These ideas are applied to study polarimetric passive remote sensing of periodic surfaces. The solution of the direct scattering problem is obtained by an integral equation formulation which involves evaluation of periodic Green's functions and normal derivative of those on the surface. Rapid evaluation of the slowly convergent series associated with these functions is observed to be critical for the feasibility of the method. New formulas, which are rapidly convergent, are derived for the calculation of these series. The study has shown that the brightness temperature of the Stokes parameter U can be significant in passive remote sensing. Values as high as 50 K are observed for certain configurations.

A Zonal Approach for Prediction of Jet Noise

NASA Technical Reports Server (NTRS)

Shih, S. H.; Hixon, D. R.; Mankbadi, Reda R.

1995-01-01

A zonal approach for direct computation of sound generation and propagation from a supersonic jet is investigated. The present work splits the computational domain into a nonlinear, acoustic-source regime and a linear acoustic wave propagation regime. In the nonlinear regime, the unsteady flow is governed by the large-scale equations, which are the filtered compressible Navier-Stokes equations. In the linear acoustic regime, the sound wave propagation is described by the linearized Euler equations. Computational results are presented for a supersonic jet at M = 2. 1. It is demonstrated that no spurious modes are generated in the matching region and the computational expense is reduced substantially as opposed to fully large-scale simulation.

Regular Decompositions for H(div) Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolev, Tzanio; Vassilevski, Panayot

We study regular decompositions for H(div) spaces. In particular, we show that such regular decompositions are closely related to a previously studied “inf-sup” condition for parameter-dependent Stokes problems, for which we provide an alternative, more direct, proof.

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2015-01-01

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Transition In Supersonic Flows With Corners

NASA Technical Reports Server (NTRS)

Balakumar, P.; McClinton, Charles (Technical Monitor)

2001-01-01

It is proposed to investigate the effect of sudden change in the slope of the surface on the stability and transition onset point in supersonic and hypersonic boundary layers. Since we can not use the linear stability theory in flows where there are discontinuities we have to solve the full Navier-Stokes equations to determine the amplification of the disturbances across the oblique shock which exists at the corner. We will use the Navier-Stokes code which was developed by Dr. Harold Atkins in the aerodynamic and acoustic methods branch. The code is developed using the higher order ENO scheme and is currently set up for two-dimensional flows. In the first year of our investigation, we will investigate the evolution of small amplitude two-dimensional disturbances and determine the N-factors for the most amplified disturbances. We will perform the analysis for the parameter similar to X-31 model and flight experiment conditions. From these computation we will infer what is the maximum amplification rate possible in quite environments without any tripping devices. In the second part of the investigation, we will perform nonlinear computations to determine what is the minimum amplitudes necessary to cause the transition at a designed location. In the third part, we have to determine what kind of trip devices necessary to excite the required disturbances. The principal investigator of this project is Dr. P. Balakumar, Associate Professor of Department of Aerospace Engineering, Old Dominion University. We will actively collaborate with research scientists in the Aero-Thermodynamics Branch at NASA/Langley Research Center. A half-time graduate student will also participate in the project.

A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method.

PubMed

Zhai, Peng-Wang; Hu, Yongxiang; Trepte, Charles R; Lucker, Patricia L

2009-02-16

A vector radiative transfer model has been developed for coupled atmosphere and ocean systems based on the Successive Order of Scattering (SOS) Method. The emphasis of this study is to make the model easy-to-use and computationally efficient. This model provides the full Stokes vector at arbitrary locations which can be conveniently specified by users. The model is capable of tracking and labeling different sources of the photons that are measured, e.g. water leaving radiances and reflected sky lights. This model also has the capability to separate florescence from multi-scattered sunlight. The delta - fit technique has been adopted to reduce computational time associated with the strongly forward-peaked scattering phase matrices. The exponential - linear approximation has been used to reduce the number of discretized vertical layers while maintaining the accuracy. This model is developed to serve the remote sensing community in harvesting physical parameters from multi-platform, multi-sensor measurements that target different components of the atmosphere-oceanic system.

Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence

NASA Astrophysics Data System (ADS)

Oz, Yaron

2017-11-01

We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent z=2/3 . The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.

Optomechanical transistor with mechanical gain

NASA Astrophysics Data System (ADS)

Zhang, X. Z.; Tian, Lin; Li, Yong

2018-04-01

We study an optomechanical transistor, where an input field can be transferred and amplified unidirectionally in a cyclic three-mode optomechanical system. In this system, the mechanical resonator is coupled simultaneously to two cavity modes. We show that it only requires a finite mechanical gain to achieve the nonreciprocal amplification. Here the nonreciprocity is caused by the phase difference between the linearized optomechanical couplings that breaks the time-reversal symmetry of this system. The amplification arises from the mechanical gain, which provides an effective phonon bath that pumps the mechanical mode coherently. This effect is analogous to the stimulated emission of atoms, where the probe field can be amplified when its frequency is in resonance with that of the anti-Stokes transition. We show that by choosing optimal parameters, this optomechanical transistor can reach perfect unidirectionality accompanied with strong amplification. In addition, the presence of the mechanical gain can result in ultralong delay in the phase of the probe field, which provides an alternative to controlling light transport in optomechanical systems.

Remote detection of buried land-mines and IEDs using LWIR polarimetric imaging.

PubMed

Gurton, Kristan P; Felton, Melvin

2012-09-24

We report results of an ongoing study designed to assess the ability for enhanced detection of recently buried land-mines and/or improvised explosive devices (IED) devices using passive long-wave infrared (LWIR) polarimetric imaging. Polarimetric results are presented for a series of field tests conducted at various locations and soil types. Well-calibrated Stokes images, S0, S1, S2, and the degree-of-linear-polarization (DoLP) are recorded for different line-of-sight (LOS) slant paths at varying distances. Results span a three-year time period in which three different LWIR polarimetric camera systems are used. All three polarimetric imaging platforms used a spinning-achromatic-retarder (SAR) design capable of achieving high polarimetric frame rates and good radiometric throughput without the loss of spatial resolution inherent in other optical designs. Receiver-operating-characteristic (ROC) analysis and a standardized contrast parameter are used to compare detectability between conventional LWIR thermal and polarimetric imagery. Results suggest improved detectability, regardless of geographic location or soil type.

Linear stability analysis of laminar flow near a stagnation point in the slip flow regime

NASA Astrophysics Data System (ADS)

Essaghir, E.; Oubarra, A.; Lahjomri, J.

2017-12-01

The aim of the present contribution is to analyze the effect of slip parameter on the stability of a laminar incompressible flow near a stagnation point in the slip flow regime. The analysis is based on the traditional normal mode approach and assumes parallel flow approximation. The Orr-Sommerfeld equation that governs the infinitesimal disturbance of stream function imposed to the steady main flow, which is an exact solution of the Navier-Stokes equation satisfying slip boundary conditions, is obtained by using the powerful spectral Chebyshev collocation method. The results of the effect of slip parameter K on the hydrodynamic characteristics of the base flow, namely the velocity profile, the shear stress profile, the boundary layer, displacement and momentum thicknesses are illustrated and discussed. The numerical data for these characteristics, as well as those of the eigenvalues and the corresponding wave numbers recover the results of the special case of no-slip boundary conditions. They are found to be in good agreement with previous numerical calculations. The effects of slip parameter on the neutral curves of stability, for two-dimensional disturbances in the Reynolds-wave number plane, are then obtained for the first time in the slip flow regime for stagnation point flow. Furthermore, the evolution of the critical Reynolds number against the slip parameter is established. The results show that the critical Reynolds number for instability is significantly increased with the slip parameter and the flow turn out to be more stable when the effect of rarefaction becomes important.

The Primordial Inflation Explorer (PIXIE)

NASA Technical Reports Server (NTRS)

Kogut, Alan J.

2011-01-01

The Primordial Inflation Explorer is an Explorer-class mission to measure the gravity-wave signature of primordial inflation through its distinctive imprint on the linear polarization of the cosmic microwave background. PIXIE uses an innovative optical design to achieve background-limited sensitivity in 400 spectral channels spanning 2.5 decades in frequency from 30 GHz to 6 THz (1 cm to 50 micron wavelength). Multi-moded non-imaging optics feed a polarizing Fourier Transform Spectrometer to produce a set of interference fringes, proportional to the difference spectrum between orthogonal linear polarizations from the two input beams. The differential design and multiple signal modulations spanning 11 orders of magnitude in time combine to reduce the instrumental signature and confusion from unpolarized sources to negligible levels. PIXIE will map the full sky in Stokes I, Q, and U parameters with angular resolution 2.6 deg and sensitivity 0.2 uK per 1 deg square pixel. The principal science goal is the detection and characterization of linear polarization from an inflationary epoch in the early universe, with tensor-to-scalar ratio r <10(exp -3) at 5 standard deviations. In addition, the rich PIXIE data will constrain physical processes ranging from Big Bang cosmology to the nature of the first stars to the physical conditions within the interstellar medium of the Galaxy. We describe the PIXIE instrument and mission architecture needed to detect the signature of an inflationary epoch in the early universe using only 4 semiconductor bolometers.

Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

NASA Astrophysics Data System (ADS)

Silva, Goncalo; Talon, Laurent; Ginzburg, Irina

2017-04-01

The present contribution focuses on the accuracy of reflection-type boundary conditions in the Stokes-Brinkman-Darcy modeling of porous flows solved with the lattice Boltzmann method (LBM), which we operate with the two-relaxation-time (TRT) collision and the Brinkman-force based scheme (BF), called BF-TRT scheme. In parallel, we compare it with the Stokes-Brinkman-Darcy linear finite element method (FEM) where the Dirichlet boundary conditions are enforced on grid vertices. In bulk, both BF-TRT and FEM share the same defect: in their discretization a correction to the modeled Brinkman equation appears, given by the discrete Laplacian of the velocity-proportional resistance force. This correction modifies the effective Brinkman viscosity, playing a crucial role in the triggering of spurious oscillations in the bulk solution. While the exact form of this defect is available in lattice-aligned, straight or diagonal, flows; in arbitrary flow/lattice orientations its approximation is constructed. At boundaries, we verify that such a Brinkman viscosity correction has an even more harmful impact. Already at the first order, it shifts the location of the no-slip wall condition supported by traditional LBM boundary schemes, such as the bounce-back rule. For that reason, this work develops a new class of boundary schemes to prescribe the Dirichlet velocity condition at an arbitrary wall/boundary-node distance and that supports a higher order accuracy in the accommodation of the TRT-Brinkman solutions. For their modeling, we consider the standard BF scheme and its improved version, called IBF; this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows. Our framework extends the one- and two-point families of linear and parabolic link-wise boundary schemes, respectively called B-LI and B-MLI, which avoid the interference of the Brinkman viscosity correction in their closure relations. The performance of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. II. Classification of axisymmetric no-swirl solutions

NASA Astrophysics Data System (ADS)

Li, Li; Li, YanYan; Yan, Xukai

2018-05-01

We classify all (- 1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south and north poles, parameterizing them as a four dimensional surface with boundary in appropriate function spaces. Then we establish smoothness properties of the solution surface in the four parameters. The smoothness properties will be used in a subsequent paper where we study the existence of (- 1)-homogeneous axisymmetric solutions with non-zero swirl on S2 ∖ { S , N }, emanating from the four dimensional solution surface.

Polarimetric Thermal Imaging

DTIC Science & Technology

2007-03-01

front of a large area blackbody as background. The viewing angle , defined as the angle between surface normal and camera line of sight, was varied by...and polarization angle were derived from the Stokes parameters. The dependence of these polarization characteristics on viewing angle was investigated

Panoramic Stokes-polarimeter

NASA Astrophysics Data System (ADS)

Syniavskyi, I. I.; Ivanov, Yu. S.; Vidmachenko, A. P.; Karpov, N. V.

2013-12-01

This article proposes optical layout of the imaging polarimeter based on the polarization films to measure the linear polarization of point and extended celestial objects. The spectral range of device is 420-850 nm, field of view 0.25°x0.25°. The device is designed to equip the telescope with a diameter of primary mirror about 400 mm and aperture f/12.

L1-Based Approximations of PDEs and Applications

DTIC Science & Technology

2012-09-05

the analysis of the Navier-Stokes equations. The early versions of artificial vis- cosities being overly dissipative, the interest for these technique ...Guermond, and B. Popov. Stability analysis of explicit en- tropy viscosity methods for non-linear scalar conservation equations. Math. Comp., 2012... methods for solv- ing mathematical models of nonlinear phenomena such as nonlinear conservation laws, surface/image/data reconstruction problems

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Jet Surface Interaction-Scrubbing Noise

NASA Technical Reports Server (NTRS)

Khavaran, Abbas

2013-01-01

Generation of sound due to scrubbing of a jet flow past a nearby solid surface is investigated within the framework of the generalized acoustic analogy theory. The analysis applies to the boundary layer noise generated at and near a wall, and excludes the scattered noise component that is produced at the leading or the trailing edge. While compressibility effects are relatively unimportant at very low Mach numbers, frictional heat generation and thermal gradient normal to the surface could play important roles in generation and propagation of sound in high speed jets of practical interest. A general expression is given for the spectral density of the far-field sound as governed by the variable density Pridmore- Brown equation. The propagation Green's function should be solved numerically starting with the boundary conditions on the surface and subject to specified mean velocity and temperature profiles between the surface and the observer. The equivalent sources of aerodynamic sound are associated with non-linear momentum flux and enthalpy flux terms that appear in the linearized Navier-Stokes equations. These multi-pole sources should be modeled and evaluated with input from a Reynolds-Averaged Navier-Stokes (RANS) solver with an appropriate turbulence model.

The initial regime of drop coalescence

NASA Astrophysics Data System (ADS)

Anthony, Christopher; Harris, Michael; Basaran, Osman

2017-11-01

Drop coalescence plays a key role in both industry and nature. Consequently, study of the phenomenon has been the focus of numerous experimental, computational and theoretical works to date. In coalescence, two drops come into contact and a liquid bridge forms between them. As time advances, this bridge grows from microscopic to macroscopic scales. Despite the large volume of work dedicated to this problem, currently experiment, theory, and computation are not in perfect agreement with respect to the earliest times following the initial contact of the drops. Experiments report an initial regime where the radius of the connecting bridge grows linearly in time before a transition to either a Stokes regime or an inertial regime where either viscous or inertial forces balance capillary force. In the initial linear regime, referred to as the inertially-limited viscous regime, all three forces are thought to be important. This is in contrast to theory which predicts that all coalescence events begin in the Stokes regime. We use high accuracy numerical simulation to show that the existing discrepancy in the literature can be resolved by paying careful attention to the initial conditions that set the shape and size of the bridge connecting the two drops.

An analysis of booster tone noise using a time-linearized Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Wukie, Nathan A.

This thesis details a computational investigation of tone noise generated from a booster(low-pressure compressor) in a fan test rig. The computational study consisted of sets of time-linearized Navier-Stokes simulations in the booster region to investigate the blade-wake interactions that act as the primary noise-generating mechanism for the booster blade-passing frequency and harmonics. An acoustic test database existed with data at several operating points for the fan test rig that was used to compare against the predicted noise data from the computational study. It is shown that the computational methodology is able to capture trends in sound power for the 1st and 2nd booster tones along the operating line for the rig. It is also shown that the computational study underpredicts one of the tones at low power and is not able to capture a peak in the data at the Cutback condition. Further investigation of this type is warranted to quantify the source of discrepancies between the computational and experimental data as the reflected transmisison of sound off the fan through the bypass duct was not accounted for in this study.

Inverse models of plate coupling and mantle rheology: Towards a direct link between large-scale mantle flow and mega thrust earthquakes

NASA Astrophysics Data System (ADS)

Gurnis, M.; Ratnaswamy, V.; Stadler, G.; Rudi, J.; Liu, X.; Ghattas, O.

2017-12-01

We are developing high-resolution inverse models for plate motions and mantle flow to recover the degree of mechanical coupling between plates and the non-linear and plastic parameters governing viscous flow within the lithosphere and mantle. We have developed adjoint versions of the Stokes equations with fully non-linear viscosity with a cost function that measures the fit with plate motions and with regional constrains on effective upper mantle viscosity (from post-glacial rebound and post seismic relaxation). In our earlier work, we demonstrate that when the temperature field is known, the strength of plate boundaries, the yield stress and strain rate exponent in the upper mantle are recoverable. As the plate boundary coupling drops below a threshold, the uncertainty of the inferred parameters increases due to insensitivity of plate motion to plate coupling. Comparing the trade-offs between inferred rheological parameters found from a Gaussian approximation of the parameter distribution and from MCMC sampling, we found that the Gaussian approximation—which is significantly cheaper to compute—is often a good approximation. We have extended our earlier method such that we can recover normal and shear stresses within the zones determining the interface between subducting and over-riding plates determined through seismic constraints (using the Slab1.0 model). We find that those subduction zones with low seismic coupling correspond with low inferred values of mechanical coupling. By fitting plate motion data in the optimization scheme, we find that Tonga and the Marianas have the lowest values of mechanical coupling while Chile and Sumatra the highest, among the subduction zones we have studies. Moreover, because of the nature of the high-resolution adjoint models, the subduction zones with the lowest coupling have back-arc extension. Globally we find that the non-linear stress-strain exponent, n, is about 3.0 +/- 0.25 (in the upper mantle and lithosphere) and a pressure-independent yield stress is 150 +/- 25 MPa. The stress in the shear zones is just tens of MPa, and in preliminary models, we find that both the shear and the normal stresses are elevated in the coupled compared to the uncoupled subduction zones.

The Primordial Inflation Polarization Explorer: Science from Circular Polarization Measurements

NASA Astrophysics Data System (ADS)

Switzer, Eric; Ade, P.; Benford, D. J.; Bennett, C. L.; Chuss, D. T.; Dotson, J. L.; Eimer, J.; Fixsen, D. J.; Halpern, M.; Hinshaw, G. F.; Irwin, K.; Jhabvala, C.; Johnson, B.; Kogut, A. J.; Lazear, J.; Mirel, P.; Moseley, S. H.; Staguhn, J.; Tucker, C. E.; Weston, A.; Wollack, E.

2014-01-01

The Primordial Inflation Polarization Explorer (PIPER) is a balloon-borne CMB polarimeter designed to constrain the B-mode signature of cosmological inflation. Sequential one-day flights from Northern- and Southern- Hemisphere sites will yield maps of Stokes I, Q, U and V at 200, 270, 350 and 600 GHz over 85% of the sky. The full optical path is cooled to 1.5 K by liquid helium in the ARCADE bucket dewar, and a variable-delay polarization modulator (VPM) at the front of the optics modulates the polarization response. Independent Q and U cameras each have two 32x40 Transition Edge Sensor array receivers. In addition to its primary inflationary science goal, PIPER will also measure the circular (Stokes V) polarization to a depth similar to that of the primary linear polarization. The circular polarization has received relatively little attention in large-area surveys, with constraints from the 1980’s and recent results by the Milan Polarimeter. Astrophysical circular polarization is generally tied to the presence of magnetic fields, either in relativistic plasmas or Zeeman splitting of resonances. These effects are thought to be undetectable at PIPER's frequencies and resolution, despite the depth. The expectation of a null result makes the deep Stokes V map a good cross-check for experimental systematics. More fundamentally, the fact that the sky is expected to be dark in Stokes V makes it a sector sensitive to processes such as Lorentz-violating terms in the standard model or magnetic fields in the CMB era.

Adaptive and iterative methods for simulations of nanopores with the PNP-Stokes equations

NASA Astrophysics Data System (ADS)

Mitscha-Baude, Gregor; Buttinger-Kreuzhuber, Andreas; Tulzer, Gerhard; Heitzinger, Clemens

2017-06-01

We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule dynamics inside nanopore sensors. The source code is released online at http://github.com/mitschabaude/nanopores. We add to existing numerical approaches by deploying goal-oriented adaptive mesh refinement. To reduce the computation overhead of mesh adaptivity, our error estimator uses the much cheaper Poisson-Boltzmann equation as a simplified model, which is justified on heuristic grounds but shown to work well in practice. To address the nonlinearity in the full PNP-Stokes system, three different linearization schemes are proposed and investigated, with two segregated iterative approaches both outperforming a naive application of Newton's method. Numerical experiments are reported on a real-world nanopore sensor geometry. We also investigate two different models for the interaction of target molecules with the nanopore sensor through the PNP-Stokes equations. In one model, the molecule is of finite size and is explicitly built into the geometry; while in the other, the molecule is located at a single point and only modeled implicitly - after solution of the system - which is computationally favorable. We compare the resulting force profiles of the electric and velocity fields acting on the molecule, and conclude that the point-size model fails to capture important physical effects such as the dependence of charge selectivity of the sensor on the molecule radius.

Polarized radiation diagnostics of stellar magnetic fields

NASA Astrophysics Data System (ADS)

Mathys, Gautier

The main techniques used to diagnose magnetic fields in stars from polarimetric observations are presented. First, a summary of the physics of spectral line formation in the presence of a magnetic field is given. Departures from the simple case of linear Zeeman effect are briefly considered: partial Paschen-Back effect, contribution of hyperfine structure, and combined Stark and Zeeman effects. Important approximate solutions of the equation of transfer of polarized light in spectral lines are introduced. The procedure for disk-integration of emergent Stokes profiles, which is central to stellar magnetic field studies, is described, with special attention to the treatment of stellar rotation. This formalism is used to discuss the determination of the mean longitudinal magnetic field (through the photographic technique and through Balmer line photopolarimetry). This is done within the specific framework of Ap stars, which, with their unique large-scale organized magnetic fields, are an ideal laboratory for studies of stellar magnetism. Special attention is paid to those Ap stars whose magnetically split line components are resolved in high-dispersion Stokes I spectra, and to the determination of their mean magnetic field modulus. Various techniques of exploitation of the information contained in polarized spectral line profiles are reviewed: the moment technique (in particular, the determination of the crossover and of the mean quadratic field), Zeeman-Doppler imaging, and least-squares deconvolution. The prospects that these methods open for linear polarization studies are sketched. The way in which linear polarization diagnostics complement their Stokes I and V counterparts is emphasized by consideration of the results of broad band linear polarization measurements. Illustrations of the use of various diagnostics to derive properties of the magnetic fields of Ap stars are given. This is used to show the interest of deriving more physically realistic models of the geometric structure of these fields. How this can possibly be achieved is briefly discussed. An overview of the current status of polarimetric studies of magnetic fields in non-degenerate stars of other types is presented. The final section is devoted to magnetic fields of white dwarfs. Current knowledge of magnetic fields of isolated white dwarfs is briefly reviewed. Diagnostic techniques are discussed, with particular emphasis on the variety of physical processes to be considered for understanding of spectral line formation over the broad range of magnetic field strengths encountered in these stars.

Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

NASA Astrophysics Data System (ADS)

Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi

2018-05-01

An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).

A Crank–Nicolson Leapfrog stabilization: Unconditional stability and two applications

DOE PAGES

Jiang, Nan; Kubacki, Michaela; Layton, William; ...

2014-12-09

We propose and analyze a linear stabilization of the Crank-Nicolson Leapfrog (CNLF) method that removes all time step/CFL conditions for stability and controls the unstable mode. It also increases the SPD part of the linear system to be solved at each time step while increasing solution accuracy. We give a proof of unconditional stability of the method as well as a proof of unconditional, asymptotic stability of both the stable and unstable modes. As a result, we illustrate two applications of the method: uncoupling groundwater-surface water flows and Stokes flow plus a Coriolis term.

Reduced-Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.

Reduced Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of an RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 1.1)

NASA Technical Reports Server (NTRS)

Magnus, A. E.; Epton, M. A.

1981-01-01

Panel aerodynamics (PAN AIR) is a system of computer programs designed to analyze subsonic and supersonic inviscid flows about arbitrary configurations. A panel method is a program which solves a linear partial differential equation by approximating the configuration surface by a set of panels. An overview of the theory of potential flow in general and PAN AIR in particular is given along with detailed mathematical formulations. Fluid dynamics, the Navier-Stokes equation, and the theory of panel methods were also discussed.

Polarization Imaging Apparatus with Auto-Calibration

NASA Technical Reports Server (NTRS)

Zou, Yingyin Kevin (Inventor); Zhao, Hongzhi (Inventor); Chen, Qiushui (Inventor)

2013-01-01

A polarization imaging apparatus measures the Stokes image of a sample. The apparatus consists of an optical lens set, a first variable phase retarder (VPR) with its optical axis aligned 22.5 deg, a second variable phase retarder with its optical axis aligned 45 deg, a linear polarizer, a imaging sensor for sensing the intensity images of the sample, a controller and a computer. Two variable phase retarders were controlled independently by a computer through a controller unit which generates a sequential of voltages to control the phase retardations of the first and second variable phase retarders. A auto-calibration procedure was incorporated into the polarization imaging apparatus to correct the misalignment of first and second VPRs, as well as the half-wave voltage of the VPRs. A set of four intensity images, I(sub 0), I(sub 1), I(sub 2) and I(sub 3) of the sample were captured by imaging sensor when the phase retardations of VPRs were set at (0,0), (pi,0), (pi,pi) and (pi/2,pi), respectively. Then four Stokes components of a Stokes image, S(sub 0), S(sub 1), S(sub 2) and S(sub 3) were calculated using the four intensity images.

Polarization imaging apparatus with auto-calibration

DOEpatents

Zou, Yingyin Kevin; Zhao, Hongzhi; Chen, Qiushui

2013-08-20

A polarization imaging apparatus measures the Stokes image of a sample. The apparatus consists of an optical lens set, a first variable phase retarder (VPR) with its optical axis aligned 22.5.degree., a second variable phase retarder with its optical axis aligned 45.degree., a linear polarizer, a imaging sensor for sensing the intensity images of the sample, a controller and a computer. Two variable phase retarders were controlled independently by a computer through a controller unit which generates a sequential of voltages to control the phase retardations of the first and second variable phase retarders. A auto-calibration procedure was incorporated into the polarization imaging apparatus to correct the misalignment of first and second VPRs, as well as the half-wave voltage of the VPRs. A set of four intensity images, I.sub.0, I.sub.1, I.sub.2 and I.sub.3 of the sample were captured by imaging sensor when the phase retardations of VPRs were set at (0,0), (.pi.,0), (.pi.,.pi.) and (.pi./2,.pi.), respectively. Then four Stokes components of a Stokes image, S.sub.0, S.sub.1, S.sub.2 and S.sub.3 were calculated using the four intensity images.

The Kolmogorov-Obukhov Statistical Theory of Turbulence

NASA Astrophysics Data System (ADS)

Birnir, Björn

2013-08-01

In 1941 Kolmogorov and Obukhov postulated the existence of a statistical theory of turbulence, which allows the computation of statistical quantities that can be simulated and measured in a turbulent system. These are quantities such as the moments, the structure functions and the probability density functions (PDFs) of the turbulent velocity field. In this paper we will outline how to construct this statistical theory from the stochastic Navier-Stokes equation. The additive noise in the stochastic Navier-Stokes equation is generic noise given by the central limit theorem and the large deviation principle. The multiplicative noise consists of jumps multiplying the velocity, modeling jumps in the velocity gradient. We first estimate the structure functions of turbulence and establish the Kolmogorov-Obukhov 1962 scaling hypothesis with the She-Leveque intermittency corrections. Then we compute the invariant measure of turbulence, writing the stochastic Navier-Stokes equation as an infinite-dimensional Ito process, and solving the linear Kolmogorov-Hopf functional differential equation for the invariant measure. Finally we project the invariant measure onto the PDF. The PDFs turn out to be the normalized inverse Gaussian (NIG) distributions of Barndorff-Nilsen, and compare well with PDFs from simulations and experiments.

Proper Orthogonal Decomposition in Optimal Control of Fluids

NASA Technical Reports Server (NTRS)

Ravindran, S. S.

1999-01-01

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

PAB3D: Its History in the Use of Turbulence Models in the Simulation of Jet and Nozzle Flows

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Pao, S. Paul; Hunter, Craig A.; Deere, Karen A.; Massey, Steven J.; Elmiligui, Alaa

2006-01-01

This is a review paper for PAB3D s history in the implementation of turbulence models for simulating jet and nozzle flows. We describe different turbulence models used in the simulation of subsonic and supersonic jet and nozzle flows. The time-averaged simulations use modified linear or nonlinear two-equation models to account for supersonic flow as well as high temperature mixing. Two multiscale-type turbulence models are used for unsteady flow simulations. These models require modifications to the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k-epsilon) model with a RANS/LES transition function, dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes (PANS) formulation. All of these models are implemented in the three-dimensional Navier-Stokes code PAB3D. This paper discusses computational methods, code implementation, computed results for a wide range of nozzle configurations at various operating conditions, and comparisons with available experimental data. Very good agreement is shown between the numerical solutions and available experimental data over a wide range of operating conditions.

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1996-01-01

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Quantitative identification of chemical compounds by dual-soliton based coherent anti-Stokes Raman scattering spectroscopy

NASA Astrophysics Data System (ADS)

Chen, Kun; Wu, Tao; Li, Yan; Wei, Haoyun

2017-12-01

Coherent anti-Stokes Raman scattering (CARS) is a powerful nonlinear spectroscopy technique that is rapidly gaining recognition of different molecules. Unfortunately, molecular concentration information is generally not immediately accessible from the raw CARS signal due to the nonresonant background. In addition, mainstream biomedical applications of CARS are currently hampered by a complex and bulky excitation setup. Here, we establish a dual-soliton Stokes based CARS spectroscopy scheme capable of quantifying the sample molecular, using a single fiber laser. This dual-soliton CARS scheme takes advantage of a differential configuration to achieve efficient suppression of nonresonant background and therefore allows extraction of quantitative composition information. Besides, our all-fiber based excitation source can probe the most fingerprint region (1100-1800 cm-1) with a spectral resolution of 15 cm-1 under the spectral focusing mechanism, where is considerably more information contained throughout an entire spectrum than at just a single frequency within that spectrum. Systematic studies of the scope of application and several fundamental aspects are discussed. Quantitative capability is further experimentally demonstrated through the determination of oleic acid concentration based on the linear dependence of signal on different Raman vibration bands.

Reduction of the discretization stencil of direct forcing immersed boundary methods on rectangular cells: The ghost node shifting method

NASA Astrophysics Data System (ADS)

Picot, Joris; Glockner, Stéphane

2018-07-01

We present an analytical study of discretization stencils for the Poisson problem and the incompressible Navier-Stokes problem when used with some direct forcing immersed boundary methods. This study uses, but is not limited to, second-order discretization and Ghost-Cell Finite-Difference methods. We show that the stencil size increases with the aspect ratio of rectangular cells, which is undesirable as it breaks assumptions of some linear system solvers. To circumvent this drawback, a modification of the Ghost-Cell Finite-Difference methods is proposed to reduce the size of the discretization stencil to the one observed for square cells, i.e. with an aspect ratio equal to one. Numerical results validate this proposed method in terms of accuracy and convergence, for the Poisson problem and both Dirichlet and Neumann boundary conditions. An improvement on error levels is also observed. In addition, we show that the application of the chosen Ghost-Cell Finite-Difference methods to the Navier-Stokes problem, discretized by a pressure-correction method, requires an additional interpolation step. This extra step is implemented and validated through well known test cases of the Navier-Stokes equations.

Relationships for electron-vibrational coupling in conjugated π organic systems

NASA Astrophysics Data System (ADS)

O'Neill, L.; Lynch, P.; McNamara, M.; Byrne, H. J.

2005-06-01

A series of π conjugated systems were studied by absorption, photoluminescence and vibrational spectroscopy. As is common for these systems, a linear relationship between the positioning of the absorption and photoluminescence maxima plotted against inverse conjugation length is observed. The relationships are in good agreement with the simple particle in a box method, one of the earliest descriptions of the properties of one-dimensional organic molecules. In addition to the electronic transition energies, it was observed that the Stokes shift also exhibited a well-defined relationship with increasing conjugation length, implying a correlation between the electron-vibrational coupling and chain length. This correlation is further examined using Raman spectroscopy, whereby the integrated Raman scattering is seen to behave superlinearly with chain length. There is a clear indication that the vibrational activity and thus nonradiative decay processes are controllable through molecular structure. The correlations between the Stokes energies and the vibrational structure are also observed in a selection of PPV based polymers and a clear trend of increasing luminescence efficiency with decreasing vibrational activity and Stokes shift is observable. The implications of such structure property relationships in terms of materials design are discussed.

Interparticle collision of natural sediment grains in water

USGS Publications Warehouse

Schmeeckle, Mark W.; Nelson, Jonathan M.; Pitlick, John; Bennett, James P.

2001-01-01

Elastohydrodynamic theory and measurements of particle impacts on an inclined glass plane in water are used to investigate the mechanics of interparticle collisions in sediment‐transporting flows. A collision Stokes number is proposed as a measure of the momentum of an interparticle collision versus the viscous pressure force in the interstitial gap between colliding particles. The viscous pressure force opposes motion of the particles on approach and rebound. A Stokes number of between 39 and 105 is estimated as the critical range below which particle impacts are completely viscously damped and above which impacts are partially elastic. The critical Stokes number is shown to roughly coincide with the Bagnold number transition between macroviscous and grain inertial debris flows and the transition between damped and partially elastic bed load transport saltation impacts. The nonspherical nature of natural particles significantly alters the motion of the center of mass after a partially elastic collision. The normal to the point of contact between the particles does not necessarily go through the center of mass. Thus normal rebound of the center of mass may not occur. A model of particle motion after rebound for particles of arbitrary shape, conserving both linear and angular momentum, is proposed.

Polarization imaging apparatus

NASA Technical Reports Server (NTRS)

Zou, Yingyin Kevin (Inventor); Chen, Qiushui (Inventor); Zhao, Hongzhi (Inventor)

2010-01-01

A polarization imaging apparatus measures the Stokes image of a sample. The apparatus consists of an optical lens set 11, a linear polarizer 14 with its optical axis 18, a first variable phase retarder 12 with its optical axis 16 aligned 22.5.degree. to axis 18, a second variable phase retarder 13 with its optical axis 17 aligned 45.degree. to axis 18, a imaging sensor 15 for sensing the intensity images of the sample, a controller 101 and a computer 102. Two variable phase retarders 12 and 13 were controlled independently by a computer 102 through a controller unit 101 which generates a sequential of voltages to control the phase retardations of VPRs 12 and 13. A set of four intensity images, I.sub.0, I.sub.1, I.sub.2 and I.sub.3 of the sample were captured by imaging sensor 15 when the phase retardations of VPRs 12 and 13 were set at (0,0), (.pi.,0), (.pi.,.pi.) and (.pi./2,.pi.), respectively Then four Stokes components of a Stokes image, S.sub.0, S.sub.1, S.sub.2 and S.sub.3 were calculated using the four intensity images.

A Spectral Multi-Domain Penalty Method for Elliptic Problems Arising From a Time-Splitting Algorithm For the Incompressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

2017-11-01

The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods.

Existence of Optimal Controls for Compressible Viscous Flow

NASA Astrophysics Data System (ADS)

Doboszczak, Stefan; Mohan, Manil T.; Sritharan, Sivaguru S.

2018-03-01

We formulate a control problem for a distributed parameter system where the state is governed by the compressible Navier-Stokes equations. Introducing a suitable cost functional, the existence of an optimal control is established within the framework of strong solutions in three dimensions.

A rapid and selective fluorescent probe with a large Stokes shift for the detection of hydrogen sulfide.

PubMed

Chen, Song; Hou, Peng; Wang, Jing; Fu, Shuang; Liu, Lei

2018-05-28

We have successfully developed a new green-emitting H 2 S fluorescence probe employing a 2,4-dinitrophenyl ether moiety as the sensing group based on 3'-formyl-4'-hydroxybiphenyl-4-carbonitrile. This probe displayed a rapid (2 min), sensitive (the detection limit was 0.18 μM) and selective with a large Stokes shift (183 nm) in response to H 2 S, which was beneficial for fluorescence sensing and cell imaging studies. Moreover, this probe can qualitatively and quantitatively detect H 2 S with a good linearity (R 2  = 0.9991). Importantly, this probe had been used for the detection of H 2 S in living MDA-MB-231 cells with good performance. Copyright © 2018 Elsevier B.V. All rights reserved.

Ultra-narrow-linewidth Brillouin/erbium fiber laser

NASA Astrophysics Data System (ADS)

Chen, Mo; Wang, Chenyu; Wang, Jianfei; Luo, Hong; Meng, Zhou

2018-02-01

Ultra-narrow-linewidth lasers are of great interest in many applications, such as precise spectroscopy, optical communications, and sensors. Stimulated Brillouin scattering (SBS), as one of the main nonlinear effects in fibers, is capable of generating narrow-linewidth light emission. We establish a compact Brillouin/erbium fiber laser (BEFL) utilizing 4-m erbium-doped fiber as both the Brillouin gain and linear media. A 360-kHz-linewidth laser diode is injected into the cavity as the Brillouin pump (BP) light and generates Brillouin Stokes lasing light. Both of the phase noise of the BP and BEFL output are measured by a high-accuracy unbalanced Michelson interferometer. It is demonstrated that 53- dB phase noise reduction is achieved after the BP is transferred into Brillouin Stokes emission. The linewidth of the BEFL is indicated at Hz-range by both calculation and experiment.

Computational analysis of water entry of a circular section at constant velocity based on Reynold's averaged Navier-Stokes method

NASA Astrophysics Data System (ADS)

Uddin, M. Maruf; Fuad, Muzaddid-E.-Zaman; Rahaman, Md. Mashiur; Islam, M. Rabiul

2017-12-01

With the rapid decrease in the cost of computational infrastructure with more efficient algorithm for solving non-linear problems, Reynold's averaged Navier-Stokes (RaNS) based Computational Fluid Dynamics (CFD) has been used widely now-a-days. As a preliminary evaluation tool, CFD is used to calculate the hydrodynamic loads on offshore installations, ships, and other structures in the ocean at initial design stages. Traditionally, wedges have been studied more than circular cylinders because cylinder section has zero deadrise angle at the instant of water impact, which increases with increase of submergence. In Present study, RaNS based commercial code ANSYS Fluent is used to simulate the water entry of a circular section at constant velocity. It is seen that present computational results were compared with experiment and other numerical method.

External heat transfer predictions in a highly loaded transonic linear turbine guide vane cascade using an upwind biased Navier-Stokes solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gehrer, A.; Jericha, H.

External heat transfer predictions are performed for two-dimensional turbine blade cascades. The Reynolds-averaged Navier-Stokes equations with algebraic (Arnone and Pacciani, 1998), one-equation (Spalart and Allmaras, 1994), and two-equation (low-Re {kappa}-{epsilon}, Biswas and Fukuyama, 1994) turbulence closures are solved with a fully implicit time-marching finite volume method. Comparisons with measurements (Arts et al., 1990; Arts, 1994) for a highly loaded transonic turbine nozzle guide vane cascade show good agreement in some cases, but also reveal problems with transition prediction and turbulence modeling. Special attention has been focused on the low-Re {kappa}-{epsilon} model concerning the influence of the inlet boundary condition formore » the {epsilon}-equation and problems in the stagnation point region.« less

Least-squares/parabolized Navier-Stokes procedure for optimizing hypersonic wind tunnel nozzles

NASA Technical Reports Server (NTRS)

Korte, John J.; Kumar, Ajay; Singh, D. J.; Grossman, B.

1991-01-01

A new procedure is demonstrated for optimizing hypersonic wind-tunnel-nozzle contours. The procedure couples a CFD computer code to an optimization algorithm, and is applied to both conical and contoured hypersonic nozzles for the purpose of determining an optimal set of parameters to describe the surface geometry. A design-objective function is specified based on the deviation from the desired test-section flow-field conditions. The objective function is minimized by optimizing the parameters used to describe the nozzle contour based on the solution to a nonlinear least-squares problem. The effect of the changes in the nozzle wall parameters are evaluated by computing the nozzle flow using the parabolized Navier-Stokes equations. The advantage of the new procedure is that it directly takes into account the displacement effect of the boundary layer on the wall contour. The new procedure provides a method for optimizing hypersonic nozzles of high Mach numbers which have been designed by classical procedures, but are shown to produce poor flow quality due to the large boundary layers present in the test section. The procedure is demonstrated by finding the optimum design parameters for a Mach 10 conical nozzle and a Mach 6 and a Mach 15 contoured nozzle.

Reynolds-averaged Navier-Stokes investigation of high-lift low-pressure turbine blade aerodynamics at low Reynolds number

NASA Astrophysics Data System (ADS)

Arko, Bryan M.

Design trends for the low-pressure turbine (LPT) section of modern gas turbine engines include increasing the loading per airfoil, which promises a decreased airfoil count resulting in reduced manufacturing and operating costs. Accurate Reynolds-Averaged Navier-Stokes predictions of separated boundary layers and transition to turbulence are needed, as the lack of an economical and reliable computational model has contributed to this high-lift concept not reaching its full potential. Presented here for what is believed to be the first time applied to low-Re computations of high-lift linear cascade simulations is the Abe-Kondoh-Nagano (AKN) linear low-Re two-equation turbulence model which utilizes the Kolmogorov velocity scale for improved predictions of separated boundary layers. A second turbulence model investigated is the Kato-Launder modified version of the AKN, denoted MPAKN, which damps turbulent production in highly strained regions of flow. Fully Laminar solutions have also been calculated in an effort to elucidate the transitional quality of the turbulence model solutions. Time accurate simulations of three modern high-lift blades at a Reynolds number of 25,000 are compared to experimental data and higher-order computations in order to judge the accuracy of the results, where it is shown that the RANS simulations with highly refined grids can produce both quantitatively and qualitatively similar separation behavior as found in experiments. In particular, the MPAKN model is shown to predict the correct boundary layer behavior for all three blades, and evidence of transition is found through inspection of the components of the Reynolds Stress Tensor, spectral analysis, and the turbulence production parameter. Unfortunately, definitively stating that transition is occurring becomes an uncertain task, as similar evidence of the transition process is found in the Laminar predictions. This reveals that boundary layer reattachment may be a result of laminar vortex shedding interaction with the blade surface, or that application of Laminar solvers with highly refined grids may be valid for investigations of transitional flow. It is recommended that this be studied in the future along with further studies of the turbulence models presented, which have proved to be worthy of additional study in the present application.

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R.

2003-01-01

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

Calculation of Linear Stability of a Stratified Gas-Liquid Flow in an Inclined Plane Channel

NASA Astrophysics Data System (ADS)

Trifonov, Yu. Ya.

2018-01-01

Linear stability of liquid and gas counterflows in an inclined channel is considered. The full Navier-Stokes equations for both phases are linearized, and the dynamics of periodic disturbances is determined by means of solving a spectral problem in wide ranges of Reynolds numbers for the liquid and vapor velocity. Two unstable modes are found in the examined ranges: surface mode (corresponding to the Kapitsa waves at small velocities of the gas) and shear mode in the gas phase. The wave length and the phase velocity of neutral disturbances of both modes are calculated as functions of the Reynolds number for the liquid. It is shown that these dependences for the surface mode are significantly affected by the gas velocity.

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

Applications of acoustic-gravity waves numerical modeling to tsunami signals observed by gravimetry satellites in very low orbit

NASA Astrophysics Data System (ADS)

Brissaud, Q.; Garcia, R.; Sladen, A.; Martin, R.; Komatitsch, D.

2016-12-01

Acoustic and gravity waves propagating in planetary atmospheres have been studied intensively as markers of specific phenomena (tectonic events, explosions) or as contributors to atmosphere dynamics. To get a better understanding of the physics behind these dynamic processes, both acoustic and gravity waves propagation should be modeled in an attenuating and windy 3D atmosphere from the ground all the way to the upper thermosphere. Thus, in order to provide an efficient numerical tool at the regional or global scale we introduce a high-order finite-difference time domain (FDTD) approach that relies on the linearized compressible Navier-Stokes equations with spatially non constant physical parameters (density, viscosities and speed of sound) and background velocities (wind). We present applications of these simulations to the propagation of gravity waves generated by tsunamis for realistic cases for which atmospheric models are extracted from empirical models including variations with altitude of atmospheric parameters, and tsunami forcing at the ocean surface is extracted from shallow water simulations. We describe the specific difficulties induced by the size of the simulation, the boundary conditions and the spherical geometry and compare the simulation outputs to data gathered by gravimetric satellites crossing gravity waves generated by tsunamis.

Multimodal non-linear optical imaging for the investigation of drug nano-/microcrystal-cell interactions.

PubMed

Darville, Nicolas; Saarinen, Jukka; Isomäki, Antti; Khriachtchev, Leonid; Cleeren, Dirk; Sterkens, Patrick; van Heerden, Marjolein; Annaert, Pieter; Peltonen, Leena; Santos, Hélder A; Strachan, Clare J; Van den Mooter, Guy

2015-10-01

Drug nano-/microcrystals are being used for sustained parenteral drug release, but safety and efficacy concerns persist as the knowledge of the in vivo fate of long-living particulates is limited. There is a need for techniques enabling the visualization of drug nano-/microcrystals in biological matrices. The aim of this work was to explore the potential of coherent anti-Stokes Raman scattering (CARS) microscopy, supported by other non-linear optical methods, as an emerging tool for the investigation of cellular and tissue interactions of unlabeled and non-fluorescent nano-/microcrystals. Raman and CARS spectra of the prodrug paliperidone palmitate (PP), paliperidone (PAL) and several suspension stabilizers were recorded. PP nano-/microcrystals were incubated with RAW 264.7 macrophages in vitro and their cellular disposition was investigated using a fully-integrated multimodal non-linear optical imaging platform. Suitable anti-Stokes shifts (CH stretching) were identified for selective CARS imaging. CARS microscopy was successfully applied for the selective three-dimensional, non-perturbative and real-time imaging of unlabeled PP nano-/microcrystals having dimensions larger than the optical lateral resolution of approximately 400nm, in relation to the cellular framework in cell cultures and ex vivo in histological sections. In conclusion, CARS microscopy enables the non-invasive and label-free imaging of (sub)micron-sized (pro-)drug crystals in complex biological matrices and could provide vital information on poorly understood nano-/microcrystal-cell interactions in future. Copyright © 2015 Elsevier B.V. All rights reserved.

Numerical Study of Pressure Field in Laterally Closed Industrial Buildings with Curved Metallic Roofs due to the Wind Effect by FEM and European Rule Comparison

NASA Astrophysics Data System (ADS)

Nieto, P. J. García; del Coz Díaz, J. J.; Vilán, J. A. Vilán; Placer, C. Casqueiro

2009-08-01

In this paper, an evaluation of distribution of the air pressure is determined throughout the laterally closed industrial buildings with curved metallic roofs due to the wind effect by the finite element method (FEM). The non-linearity is due to Reynolds-averaged Navier-Stokes (RANS) equations that govern the turbulent flow. The Navier-Stokes equations are non-linear partial differential equations and this non-linearity makes most problems difficult to solve and is part of the cause of turbulence. The RANS equations are time-averaged equations of motion for fluid flow. They are primarily used while dealing with turbulent flows. Turbulence is a highly complex physical phenomenon that is pervasive in flow problems of scientific and engineering concern like this one. In order to solve the RANS equations a two-equation model is used: the standard k-ɛ model. The calculation has been carried out keeping in mind the following assumptions: turbulent flow, an exponential-like wind speed profile with a maximum velocity of 40 m/s at 10 m reference height, and different heights of the building ranging from 6 to 10 meters. Finally, the forces and moments are determined on the cover, as well as the distribution of pressures on the same one, comparing the numerical results obtained with the Spanish CTE DB SE-AE, Spanish NBE AE-88 and European standard rules, giving place to the conclusions that are exposed in the study.

Physics and applications of atmospheric nonlinear optics and filamentation.

PubMed

Kasparian, Jérôme; Wolf, Jean-Pierre

2008-01-07

We review the properties and applications of ultrashort laser pulses in the atmosphere, with a particular focus on filamentation. Filamentation is a non-linear propagation regime specific of ultrashort and ultraintense laser pulses in the atmosphere. Typical applications include remote sensing of atmospheric gases and aerosols, lightning control, laser-induced spectroscopy, coherent anti-stokes Raman scattering, and the generation of sub-THz radiation.

Spectropolarimetry with PEPSI at the LBT: accuracy vs. precision in magnetic field measurements

NASA Astrophysics Data System (ADS)

Ilyin, Ilya; Strassmeier, Klaus G.; Woche, Manfred; Hofmann, Axel

2009-04-01

We present the design of the new PEPSI spectropolarimeter to be installed at the Large Binocular Telescope (LBT) in Arizona to measure the full set of Stokes parameters in spectral lines and outline its precision and the accuracy limiting factors.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berrada, K., E-mail: kberrada@ictp.it; The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Miramare-Trieste; Ooi, C. H. Raymond

Robustness of the geometric phase (GP) with respect to different noise effects is a basic condition for an effective quantum computation. Here, we propose a useful quantum system with real physical parameters by studying the GP of a pair of Stokes and anti-Stokes photons, involving Raman emission processes with and without photonic band gap (PBG) effect. We show that the properties of GP are very sensitive to the change of the Rabi frequency and time, exhibiting collapse phenomenon as the time becomes significantly large. The system allows us to obtain a state which remains with zero GP for longer times.more » This result plays a significant role to enhance the stabilization and control of the system dynamics. Finally, we investigate the nonlocal correlation (entanglement) between the pair photons by taking into account the effect of different parameters. An interesting correlation between the GP and entanglement is observed showing that the PBG stabilizes the fluctuations in the system and makes the entanglement more robust against the change of time and frequency.« less

Numerical study of the motion of a flagellated swimmer inside a tube in the Stokes regime

NASA Astrophysics Data System (ADS)

Zhang, Ji; Jiao, Yusheng; Xu, Xinliang; Ding, Yang

2017-11-01

Confined environments are common to micro-swimmers such bacteria and previous studies have shown that confinements such as a wall can influenced the trajectory of the micro-swimmers. Here we study whether some micro-swimmers can achieve a higher speed and energetic efficiency within a long tube comparing to the free-space case using a numerical model. The swimmer consists of an elliptical head and two helical flagella. To solve the governing Stokes equations inside an infinite tube, we combine the method of fundamental solution (MSF) and the method of Stokeslet. The geometry parameters, including shape and size of head and flagella, and relative spatial position of these components, are varied. Our results show that the geometry of the swimmer and the tube can greatly affect the speed of the micro-swimmer. For certain geometric parameters of the micro-swimmer, a greater confinement leads to a higher speed, which is consistent with the results from our robotic experiments.

The GOSSIP on the MCV V347 Pavonis

NASA Astrophysics Data System (ADS)

Potter, S. B.; Cropper, Mark; Hakala, P. J.

Modelling of the polarized cyclotron emission from magnetic cataclysmic variables (MCVs) has been a powerful technique for determining the structure of the accretion zones on the white dwarf. Until now, this has been achieved by constructing emission regions (for example arcs and spots) put in by hand, in order to recover the polarized emission. These models were all inferred indirectly from arguments based on polarization and X-ray light curves. Potter, Hakala & Cropper (1998) presented a technique (Stokes imaging) which objectively and analytically models the polarized emission to recover the structure of the cyclotron emission region(s) in MCVs. We demonstrate this technique with the aid of a test case, then we apply the technique to polarimetric observations of the AM Her system V347 Pav. As the system parameters of V347 Pav (for example its inclination) have not been well determined, we describe an extension to the Stokes imaging technique which also searches the system parameter space (GOSSIP).

Applications of polarization speckle in skin cancer detection and monitoring

NASA Astrophysics Data System (ADS)

Lee, Tim K.; Tchvialeva, Lioudmila; Phillips, Jamie; Louie, Daniel C.; Zhao, Jianhua; Wang, Wei; Lui, Harvey; Kalia, Sunil

2018-01-01

Polarization speckle is a rapidly developed field. Unlike laser speckle, polarization speckle consists of stochastic interference patterns with spatially random polarizations, amplitudes and phases. We have been working in this exciting research field, developing techniques to generate polarization patterns from skin. We hypothesize that polarization speckle patterns could be used in biomedical applications, especially, for detecting and monitoring skin cancers, the most common neoplasmas for white populations around the world. This paper describes our effort in developing two polarization speckle devices. One of them captures the Stokes parameters So and S1 simultaneously, and another one captures all four Stokes parameters So, S1, S2, and S3 in one-shot, within milliseconds. Hence these two devices could be used in medical clinics and assessed skin conditions in-vivo. In order to validate our hypothesis, we conducted a series of three clinical studies. These are early pilot studies, and the results suggest that the devices have potential to detect and monitor skin cancers.

Thrust chamber performance using Navier-Stokes solution. [space shuttle main engine viscous nozzle calculation

NASA Technical Reports Server (NTRS)

Chan, J. S.; Freeman, J. A.

1984-01-01

The viscous, axisymmetric flow in the thrust chamber of the space shuttle main engine (SSME) was computed on the CRAY 205 computer using the general interpolants method (GIM) code. Results show that the Navier-Stokes codes can be used for these flows to study trends and viscous effects as well as determine flow patterns; but further research and development is needed before they can be used as production tools for nozzle performance calculations. The GIM formulation, numerical scheme, and computer code are described. The actual SSME nozzle computation showing grid points, flow contours, and flow parameter plots is discussed. The computer system and run times/costs are detailed.

Mirrorless Optical Parametric Oscillation with Tunable Threshold in Cold Atoms.

PubMed

Mei, Yefeng; Guo, Xianxin; Zhao, Luwei; Du, Shengwang

2017-10-13

We report the demonstration of a mirrorless optical parametric oscillator with a tunable threshold in laser-cooled atoms with four-wave mixing (FWM) using electromagnetically induced transparency. Driven by two classical laser beams, the generated Stokes and anti-Stokes fields counterpropagate and build up efficient intrinsic feedback through the nonlinear FWM process. This feedback does not involve any cavity or spatially distributed microstructures. We observe the transition of photon correlation properties from the biphoton quantum regime (below the threshold) to the oscillation regime (above the threshold). The pump threshold can be tuned by varying the operating parameters. We achieve the oscillation with a threshold as low as 15  μW.

Communication: Fast dynamics perspective on the breakdown of the Stokes-Einstein law in fragile glassformers

NASA Astrophysics Data System (ADS)

Puosi, F.; Pasturel, A.; Jakse, N.; Leporini, D.

2018-04-01

The breakdown of the Stokes-Einstein (SE) law in fragile glassformers is examined by Molecular-Dynamics simulations of atomic liquids and polymers and consideration of the experimental data concerning the archetypical ortho-terphenyl glassformer. All the four systems comply with the universal scaling between the viscosity (or the structural relaxation) and the Debye-Waller factor ⟨u2⟩, the mean square amplitude of the particle rattling in the cage formed by the surrounding neighbors. It is found that the SE breakdown is scaled in a master curve by a reduced ⟨u2⟩. Two approximated expressions of the latter, with no and one adjustable parameter, respectively, are derived.

Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier-Stokes solver

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blanchard, M., E-mail: mathieu.blanchard@ladhyx.polytechnique.fr; Schuller, T.; Centrale-Supélec, Grande Voie des Vignes, 92290 Châtenay-Malabry

2015-04-15

The response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in themore » numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated.« less

Determination of Atmospheric Aerosol Characteristics from the Polarization of Scattered Radiation

NASA Technical Reports Server (NTRS)

Harris, F. S., Jr.; McCormick, M. P.

1973-01-01

Aerosols affect the polarization of radiation in scattering, hence measured polarization can be used to infer the nature of the particles. Size distribution, particle shape, real and absorption parts of the complex refractive index affect the scattering. From Lorenz-Mie calculations of the 4-Stokes parameters as a function of scattering angle for various wavelengths the following polarization parameters were plotted: total intensity, intensity of polarization in plane of observation, intensity perpendicular to the plane of observation, polarization ratio, polarization (using all 4-Stokes parameters), plane of the polarization ellipse and its ellipticity. A six-component log-Gaussian size distribution model was used to study the effects of the nature of the polarization due to variations in the size distribution and complex refractive index. Though a rigorous inversion from measurements of scattering to detailed specification of aerosol characteristics is not possible, considerable information about the nature of the aerosols can be obtained. Only single scattering from aerosols was used in this paper. Also, the background due to Rayleigh gas scattering, the reduction of effects as a result of multiple scattering and polarization effects of possible ground background (airborne platforms) were not included.

(In)sensitivity of GNSS techniques to geocenter motion

NASA Astrophysics Data System (ADS)

Rebischung, Paul; Altamimi, Zuheir; Springer, Tim

2013-04-01

As a satellite-based technique, GNSS should be sensitive to motions of the Earth's center of mass (CM) with respect to the Earth's crust. In theory, the weekly solutions of the IGS Analysis Centers (ACs) should indeed have the "instantaneous" CM as their origin, and the net translations between the weekly AC frames and a secular frame such as ITRF2008 should thus approximate the non-linear motion of CM with respect to the Earth's center of figure. However, the comparison of the AC translation time series with each other, with SLR geocenter estimates or with geophysical models reveals that this way of observing geocenter motion with GNSS currently gives unreliable results. The fact that the origin of the weekly AC solutions shoud be CM stems from the satellite equations of motion, in which no degree-1 Stokes coefficients are included. It is therefore reasonable to think that any mis-modeling or uncertainty about the forces acting on GNSS satellites can potentially offset the network origin from CM. That is why defects in radiation pressure modeling have long been assumed to be the main origin of the GNSS geocenter errors. In particular, Meindl et al. (2012) incriminate the correlation between the Z component of the origin and the direct radiation pressure parameters D0. We review here the sensitivity of GNSS techniques to geocenter motion from a different perspective. Our approach consists in determining the signature of a geocenter error on GNSS observations, and seeing how and how well such an error can be compensated by all other usual GNSS parameters. (In other words, we look for the linear combinations of parameters which have the maximal partial correlations with each of the 3 components of the origin, and evaluate these maximal partial correlations.) Without setting up any empirical radiation pressure parameter, we obtain maximal partial correlations of 99.98 % for all 3 components of the origin: a geocenter error can almost perfectly be absorbed by the other GNSS parameters. Satellite clock offsets, if estimated epoch-wise, especially devastate the sensitivity of GNSS to geocenter motion. The numerous station-related parameters (station positions, station clock offsets, ZWDs and horizontal tropospheric gradients) do the rest of the job. The maximal partial correlations increase a bit more when the classic "ECOM" set of 5 radiation pressure parameters is set up for each satellite. But this increase is almost fully attributable to the once-per-revolution parameters BC & BS. In particular, we do not find the direct radiation pressure parameters D0 to play a predominant role in the GNSS geocenter determination problem.

Spectro-polarimetry of Ice-dust Mixtures measured in the Laboratory with Application to the Solar System and Beyond

NASA Astrophysics Data System (ADS)

Poch, O.; Schmid, H. M.; Pommerol, A.; Jost, B.; Brouet, Y.; Thomas, N.

2015-12-01

Polarimetric observations of atmosphere-less Solar System bodies can give clues on the texture and on the physico-chemical composition of their surfaces, as reviewed by Mishchenko et al. (2010) and Bagnulo et al. (2011). Measurements performed in the laboratory on carefully characterized samples can provide reference data that can be used for direct comparison with remote-sensing polarimetric observations. In particular, we want to study the spectral dependence of the polarization and the way it is correlated or not with the surface albedo. In the Laboratory for Outflow Studies of Sublimating Materials (LOSSy) at the University of Bern, we have developed the capability to prepare and analyze optically thick analogues of planetary or cometary surfaces composed of water ice, minerals and carbonaceous compounds. Water-free dust of high porosity can also be produced by sublimation of ice under space-simulated conditions (Pommerol et al., 2015). Here, we present the first results of polarization measurements performed in the LOSSy. A Stokes polarimeter is used to measure the Stokes parameters describing the polarization of the visible light scattered by icy samples illuminated with a randomly polarized light simulating the star light. Additionally, a radio-goniometer, equipped with polarizers, can also measure the phase angle dependence of the linearly polarized scattered light. These measurements could provide interesting inputs to complement the theoretical models and predict or interpret spectro-polarimetric properties of Solar System objects and circumstellar disks. Mishchenko, M., et al., 2010, Polarimetric Remote Sensing of Solar System Objects. Bagnulo, S., et al., 2011, J. Quant. Spectrosc. Ra. 112, 2059. Pommerol, A., et al., 2015, Planet. Space Sci. 109-110, 106-122.

Particle image velocimetry measurements of Mach 3 turbulent boundary layers at low Reynolds numbers

NASA Astrophysics Data System (ADS)

Brooks, J. M.; Gupta, A. K.; Smith, M. S.; Marineau, E. C.

2018-05-01

Particle image velocimetry (PIV) measurements of Mach 3 turbulent boundary layers (TBL) have been performed under low Reynolds number conditions, Re_τ =200{-}1000, typical of direct numerical simulations (DNS). Three reservoir pressures and three measurement locations create an overlap in parameter space at one research facility. This allows us to assess the effects of Reynolds number, particle response and boundary layer thickness separate from facility specific experimental apparatus or methods. The Morkovin-scaled streamwise fluctuating velocity profiles agree well with published experimental and numerical data and show a small standard deviation among the nine test conditions. The wall-normal fluctuating velocity profiles show larger variations which appears to be due to particle lag. Prior to the current study, no detailed experimental study characterizing the effect of Stokes number on attenuating wall-normal fluctuating velocities has been performed. A linear variation is found between the Stokes number ( St) and the relative error in wall-normal fluctuating velocity magnitude (compared to hot wire anemometry data from Klebanoff, Characteristics of Turbulence in a Boundary Layer with Zero Pressure Gradient. Tech. Rep. NACA-TR-1247, National Advisory Committee for Aeronautics, Springfield, Virginia, 1955). The relative error ranges from about 10% for St=0.26 to over 50% for St=1.06. Particle lag and spatial resolution are shown to act as low-pass filters on the fluctuating velocity power spectral densities which limit the measurable energy content. The wall-normal component appears more susceptible to these effects due to the flatter spectrum profile which indicates that there is additional energy at higher wave numbers not measured by PIV. The upstream inclination and spatial correlation extent of coherent turbulent structures agree well with published data including those using krypton tagging velocimetry (KTV) performed at the same facility.

Arylethynyl Substituted 9,lO-Anthraquinones: Tunable Stokes Shifts by Substitution and Solvent Polarity

NASA Technical Reports Server (NTRS)

Yang, Jinhua; Dass, Amala; Rawashdeh, Abdel-Monem M.; Sotiriou-Leventis, Chariklia; Panzner, Matthew J.; Tyson, Daniel S.; Kinder, James D.; Leventis, Nicholas

2004-01-01

2-Arylethynyl- and 2,6- and 2,7-diarylethynyl-substituted 9,lO-anthraquinones were synthesized via Sonogashira coupling reactions of 2-bromo-, 2,6-dibromo-, and 2,7-dibromo-9,10- anthraquinone with para-substituted phenylacetylenes. While the redox properties of those compounds are almost insensitive to substitution, their absorption maxima are linearly related to the Hammett constants with different slopes for electron donors and electron acceptors. ABI compounds are photoluminescent both in solution (quantum yields of emission <= 6 %), and as solids. The emission spectra have the characteristics of charge-transfer bands with large Stokes shifts (100-250 nm). The charge-transfer character of the emitting state is supported by large dipole moment differences between the ground and the excited state as concluded on the basis of molecular modeling and Lippert-Mataga correlations of the Stokes shifts with solvent polarity. Maximum Stokes shifts are attained by both electron-donating and -withdrawing groups. This is explained by a destabilization of the HOMO by electron donors and a stabilization of the LUMO by electron acceptors. X-ray crystallographic analysis of, for example, 2,7-bisphenylethynfl- 9,lO-anthraquinone reveals a monoclinic P21In space group and no indication for pi-overlap that would promote quenching, thus explaining emission from the solid state. Representative reduced forms of the title compounds were isolated as stable acetates of the corresponding dihydrs-9,10- anthraquinones. The emission of these compounds is blue-shifted relative to the parent oxidized forms and is attributed to internal transitions in the dihydro-9,lO-anthraquinone core.

Computational Aeroacoustics by the Space-time CE/SE Method

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2001-01-01

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Astronomy in Denver: Probing Interstellar Circular Polarization with Polvis, a Full Stokes Single Shot Polarimeter

NASA Astrophysics Data System (ADS)

Wolfe, Tristan; Stencel, Robert E.

2018-06-01

Measurements of optical circular polarization (Stokes V) introduced by dust grains in the ISM are important for two main reasons. First of all, the polarization itself contains information about the metallic versus dielectric composition of the dust grains themselves (H. C. van de Hulst 1957, textbook). Additionally, circular polarization can help constrain the interstellar component of the polarization of any source that may have intrinsic polarization, which needs to be calibrated for astrophysical study. Though interstellar circular polarization has been observed (P. G. Martin 1972, MNRAS 159), most broadband measurements of ISM polarization include linear polarization only (Stokes Q and U), due to the relatively low circular polarization signal and the added instrumentation complexity of including V-measurement capability. Prior circular polarization measurements have also received very little follow-up in the past several decades, even as polarimeters have become more accurate due to advances in technology. The University of Denver is pursuing these studies with POLVIS, a prototype polarimeter that utilizes a stress-engineered optic ("SEO", A. K. Spilman and T. G. Brown 2007, Applied Optics IP 46) to produce polarization-dependent PSFs (A. M. Beckley and T. G. Brown 2010, Proc SPIE 7570). These PSFs are analyzed to provide simultaneous Stokes I, Q, U, and V measurements, in a single beam and single image, along the line-of-sight to point source-like objects. Polvis is the first polarimeter to apply these optics and measurement techniques for astronomical observations. We present the first results of this instrument in B, V, and R wavebands, providing a fresh look at full Stokes interstellar polarization. Importantly, this set of efforts will constrain the ISM contribution to the polarization with respect to intrinsic stellar components. The authors are grateful to the estate of William Herschel Womble for the support of astronomy at the University of Denver, and for funding provided by the Mt. Cuba Astronomical Foundation.

On the numerical treatment of nonlinear source terms in reaction-convection equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

The objectives of this paper are to investigate how various numerical treatments of the nonlinear source term in a model reaction-convection equation can affect the stability of steady-state numerical solutions and to show under what conditions the conventional linearized analysis breaks down. The underlying goal is to provide part of the basic building blocks toward the ultimate goal of constructing suitable numerical schemes for hypersonic reacting flows, combustions and certain turbulence models in compressible Navier-Stokes computations. It can be shown that nonlinear analysis uncovers much of the nonlinear phenomena which linearized analysis is not capable of predicting in a model reaction-convection equation.

MagIC: Fluid dynamics in a spherical shell simulator

NASA Astrophysics Data System (ADS)

Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.

2017-09-01

MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.

Global solutions to random 3D vorticity equations for small initial data

NASA Astrophysics Data System (ADS)

Barbu, Viorel; Röckner, Michael

2017-11-01

One proves the existence and uniqueness in (Lp (R3)) 3, 3/2 < p < 2, of a global mild solution to random vorticity equations associated to stochastic 3D Navier-Stokes equations with linear multiplicative Gaussian noise of convolution type, for sufficiently small initial vorticity. This resembles some earlier deterministic results of T. Kato [16] and are obtained by treating the equation in vorticity form and reducing the latter to a random nonlinear parabolic equation. The solution has maximal regularity in the spatial variables and is weakly continuous in (L3 ∩L 3p/4p - 6)3 with respect to the time variable. Furthermore, we obtain the pathwise continuous dependence of solutions with respect to the initial data. In particular, one gets a locally unique solution of 3D stochastic Navier-Stokes equation in vorticity form up to some explosion stopping time τ adapted to the Brownian motion.

Enhanced facial recognition for thermal imagery using polarimetric imaging.

PubMed

Gurton, Kristan P; Yuffa, Alex J; Videen, Gorden W

2014-07-01

We present a series of long-wave-infrared (LWIR) polarimetric-based thermal images of facial profiles in which polarization-state information of the image-forming radiance is retained and displayed. The resultant polarimetric images show enhanced facial features, additional texture, and details that are not present in corresponding conventional thermal imagery. It has been generally thought that conventional thermal imagery (MidIR or LWIR) could not produce the detailed spatial information required for reliable human identification due to the so-called "ghosting" effect often seen in thermal imagery of human subjects. By using polarimetric information, we are able to extract subtle surface features of the human face, thus improving subject identification. Polarimetric image sets considered include the conventional thermal intensity image, S0, the two Stokes images, S1 and S2, and a Stokes image product called the degree-of-linear-polarization image.

Numerical Simulations of Two-Phase Reacting Flow in a Single-Element Lean Direct Injection (LDI) Combustor Using NCC

NASA Technical Reports Server (NTRS)

Liu, Nan-Suey; Shih, Tsan-Hsing; Wey, C. Thomas

2011-01-01

A series of numerical simulations of Jet-A spray reacting flow in a single-element lean direct injection (LDI) combustor have been conducted by using the National Combustion Code (NCC). The simulations have been carried out using the time filtered Navier-Stokes (TFNS) approach ranging from the steady Reynolds-averaged Navier-Stokes (RANS), unsteady RANS (URANS), to the dynamic flow structure simulation (DFS). The sub-grid model employed for turbulent mixing and combustion includes the well-mixed model, the linear eddy mixing (LEM) model, and the filtered mass density function (FDF/PDF) model. The starting condition of the injected liquid spray is specified via empirical droplet size correlation, and a five-species single-step global reduced mechanism is employed for fuel chemistry. All the calculations use the same grid whose resolution is of the RANS type. Comparisons of results from various models are presented.

Chromospheric LAyer SpectroPolarimeter (CLASP2)

NASA Technical Reports Server (NTRS)

Narukage, Noriyuki; Cirtain, Jonathan W.; Ishikawa, Ryoko; Trujillo-Bueno, Javier; De Pontieu, Bart; Kubo, Masahito; Ishikawa, Shinnosuke; Kano, Ryohei; Suematsu, Yoshinori; Yoshida, Masaki;

Bessel beam CARS of axially structured samples

NASA Astrophysics Data System (ADS)

Heuke, Sandro; Zheng, Juanjuan; Akimov, Denis; Heintzmann, Rainer; Schmitt, Michael; Popp, Jürgen

2015-06-01

We report about a Bessel beam CARS approach for axial profiling of multi-layer structures. This study presents an experimental implementation for the generation of CARS by Bessel beam excitation using only passive optical elements. Furthermore, an analytical expression is provided describing the generated anti-Stokes field by a homogeneous sample. Based on the concept of coherent transfer functions, the underling resolving power of axially structured geometries is investigated. It is found that through the non-linearity of the CARS process in combination with the folded illumination geometry continuous phase-matching is achieved starting from homogeneous samples up to spatial sample frequencies at twice of the pumping electric field wave. The experimental and analytical findings are modeled by the implementation of the Debye Integral and scalar Green function approach. Finally, the goal of reconstructing an axially layered sample is demonstrated on the basis of the numerically simulated modulus and phase of the anti-Stokes far-field radiation pattern.

Bessel beam CARS of axially structured samples.

PubMed

Heuke, Sandro; Zheng, Juanjuan; Akimov, Denis; Heintzmann, Rainer; Schmitt, Michael; Popp, Jürgen

2015-06-05

We report about a Bessel beam CARS approach for axial profiling of multi-layer structures. This study presents an experimental implementation for the generation of CARS by Bessel beam excitation using only passive optical elements. Furthermore, an analytical expression is provided describing the generated anti-Stokes field by a homogeneous sample. Based on the concept of coherent transfer functions, the underling resolving power of axially structured geometries is investigated. It is found that through the non-linearity of the CARS process in combination with the folded illumination geometry continuous phase-matching is achieved starting from homogeneous samples up to spatial sample frequencies at twice of the pumping electric field wave. The experimental and analytical findings are modeled by the implementation of the Debye Integral and scalar Green function approach. Finally, the goal of reconstructing an axially layered sample is demonstrated on the basis of the numerically simulated modulus and phase of the anti-Stokes far-field radiation pattern.

Numerical solutions of Navier-Stokes equations for compressible turbulent two/three dimensional flows in terminal shock region of an inlet/diffuser

NASA Technical Reports Server (NTRS)

Liu, N. S.; Shamroth, S. J.; Mcdonald, H.

1983-01-01

The multidimensional ensemble averaged compressible time dependent Navier Stokes equations in conjunction with mixing length turbulence model and shock capturing technique were used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations were carried out: (1) 2 D, steady, subsonic; (2) 2 D, steady, transonic with normal shock; (3) 2 D, steady, supersonic with terminal shock; (4) 2 D, transient process of shock development and (5) 3 D, steady, transonic with normal shock. The numerical results obtained for the 2 D and 3 D transonic shocked flows were compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data.

On Bifurcating Time-Periodic Flow of a Navier-Stokes Liquid Past a Cylinder

NASA Astrophysics Data System (ADS)

Galdi, Giovanni P.

2016-10-01

We provide general sufficient conditions for the existence and uniqueness of branching out of a time-periodic family of solutions from steady-state solutions to the two-dimensional Navier-Stokes equations in the exterior of a cylinder. By separating the time-independent averaged component of the velocity field from its oscillatory one, we show that the problem can be formulated as a coupled elliptic-parabolic nonlinear system in appropriate and distinct function spaces, with the property that the relevant linearized operators become Fredholm of index 0. In this functional setting, the notorious difficulty of 0 being in the essential spectrum entirely disappears and, in fact, it is even meaningless. Our approach is different and, we believe, more natural and simpler than those proposed by previous authors discussing similar questions. Moreover, the latter all fail, when applied to the problem studied here.

Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres

NASA Astrophysics Data System (ADS)

Tzang, Omer; Caravaca-Aguirre, Antonio M.; Wagner, Kelvin; Piestun, Rafael

2018-06-01

Recent progress in wavefront shaping has enabled control of light propagation inside linear media to focus and image through scattering objects. In particular, light propagation in multimode fibres comprises complex intermodal interactions and rich spatiotemporal dynamics. Control of physical phenomena in multimode fibres and its applications are in their infancy, opening opportunities to take advantage of complex nonlinear modal dynamics. Here, we demonstrate a wavefront shaping approach for controlling nonlinear phenomena in multimode fibres. Using a spatial light modulator at the fibre input, real-time spectral feedback and a genetic algorithm optimization, we control a highly nonlinear multimode stimulated Raman scattering cascade and its interplay with four-wave mixing via a flexible implicit control on the superposition of modes coupled into the fibre. We show versatile spectrum manipulations including shifts, suppression, and enhancement of Stokes and anti-Stokes peaks. These demonstrations illustrate the power of wavefront shaping to control and optimize nonlinear wave propagation.

L(2) stability for weak solutions of the Navier-Stokes equations in R(3)

NASA Astrophysics Data System (ADS)

Secchi, P.

1985-11-01

We consider the motion of a viscous fluid filling the whole space R3, governed by the classical Navier-Stokes equations (1). Existence of global (in time) regular solutions for that system of non-linear partial differential equations is still an open problem. Up to now, the only available global existence theorem (other than for sufficiently small initial data) is that of weak (turbulent) solutions. From both the mathematical and the physical point of view, an interesting property is the stability of such weak solutions. We assume that v(t,x) is a solution, with initial datum vO(x). We suppose that the initial datum is perturbed and consider one weak solution u corresponding to the new initial velocity. Then we prove that, due to viscosity, the perturbed weak solution u approaches in a suitable norm the unperturbed one, as time goes to + infinity, without smallness assumptions on the initial perturbation.

Navier-Stokes simulation of the crossflow instability in swept-wing flows

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1989-01-01

The computational modeling of the transition process characteristic of flows over swept wings are described. Specifically, the crossflow instability and crossflow/T-S wave interactions are analyzed through the numerical solution of the full three-dimensional Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiments. The leading edge region of a swept wing is considered in a three-dimensional spatial simulation with random disturbances as the initial conditions. The work has been closely coordinated with the experimental program of Professor William Saric, examining the same problem. Comparisons with NASA flight test data and the experiments at Arizona State University were a necessary and an important integral part of this work.

Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows

NASA Technical Reports Server (NTRS)

Warsi, Z. U. A.; Devarayalu, K.; Thompson, J. F.

1978-01-01

A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.

A least-squares finite element method for 3D incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

Numerical Study of Hydrothermal Wave Suppression in Thermocapillary Flow Using a Predictive Control Method

NASA Astrophysics Data System (ADS)

Muldoon, F. H.

2018-04-01

Hydrothermal waves in flows driven by thermocapillary and buoyancy effects are suppressed by applying a predictive control method. Hydrothermal waves arise in the manufacturing of crystals, including the "open boat" crystal growth process, and lead to undesirable impurities in crystals. The open boat process is modeled using the two-dimensional unsteady incompressible Navier-Stokes equations under the Boussinesq approximation and the linear approximation of the surface thermocapillary force. The flow is controlled by a spatially and temporally varying heat flux density through the free surface. The heat flux density is determined by a conjugate gradient optimization algorithm. The gradient of the objective function with respect to the heat flux density is found by solving adjoint equations derived from the Navier-Stokes ones in the Boussinesq approximation. Special attention is given to heat flux density distributions over small free-surface areas and to the maximum admissible heat flux density.

Unsteady aerodynamic analyses for turbomachinery aeroelastic predictions

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Barnett, M.; Ayer, T. C.

1994-01-01

Applications for unsteady aerodynamics analysis in this report are: (1) aeroelastic: blade flutter and forced vibration; (2) aeroacoustic: noise generation; (3) vibration and noise control; and (4) effects of unsteadiness on performance. This requires that the numerical simulations and analytical modeling be accurate and efficient and contain realistic operating conditions and arbitrary modes of unsteady excitation. The assumptions of this application contend that: (1) turbulence and transition can be modeled with the Reynolds averaged and using Navier-Stokes equations; (2) 'attached' flow with high Reynolds number will require thin-layer Navier-Stokes equations, or inviscid/viscid interaction analyses; (3) small-amplitude unsteady excitations will need nonlinear steady and linearized unsteady analyses; and (4) Re to infinity will concern inviscid flow. Several computer programs (LINFLO, CLT, UNSVIS, AND SFLOW-IVI) are utilized for these analyses. Results and computerized grid examples are shown. This report was given during NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Validity of Darcy's law under transient conditions

USGS Publications Warehouse

Mongan, C.E.

1985-01-01

Darcy 's Law, which describes fluid flow through porous materials, was developed for steady flow conditions. The validity of applying this law to transient flows has been mathematically verified for most ground-water flow conditions. The verification was accomplished through application of Hankel transforms to linearized Navier-Stokes equations which described flow in a small diameter cylindrical tube. The tube was chosen to represent a single pore in a porous medium. (USGS)

Investigation of flow turning phenomenon - Effect of upstream and downstream propagation

NASA Astrophysics Data System (ADS)

Baum, Joseph D.

1988-01-01

Upstream acoustic-wave propagation in flow injected laterally through the boundary layer of a tube (simulating the flow in a solid-rocket motor) is investigated analytically. A noniterative linearized-block implicit scheme is used to solve the time-dependent compressible Navier-Stokes equations, and the results are presented in extensive graphs and characterized. Acoustic streaming interaction is shown to be significantly greater for upstream than for downstream propagation.

A Numerical Testbed for Remote Sensing of Aerosols, and its Demonstration for Evaluating Retrieval Synergy from a Geostationary Satellite Constellation of GEO-CAPE and GOES-R

NASA Technical Reports Server (NTRS)

Wang, Jun; Xu, Xiaoguang; Ding, Shouguo; Zeng, Jing; Spurr, Robert; Liu, Xiong; Chance, Kelly; Mishchenko, Michael I.

2014-01-01

We present a numerical testbed for remote sensing of aerosols, together with a demonstration for evaluating retrieval synergy from a geostationary satellite constellation. The testbed combines inverse (optimal-estimation) software with a forward model containing linearized code for computing particle scattering (for both spherical and non-spherical particles), a kernel-based (land and ocean) surface bi-directional reflectance facility, and a linearized radiative transfer model for polarized radiance. Calculation of gas absorption spectra uses the HITRAN (HIgh-resolution TRANsmission molecular absorption) database of spectroscopic line parameters and other trace species cross-sections. The outputs of the testbed include not only the Stokes 4-vector elements and their sensitivities (Jacobians) with respect to the aerosol single scattering and physical parameters (such as size and shape parameters, refractive index, and plume height), but also DFS (Degree of Freedom for Signal) values for retrieval of these parameters. This testbed can be used as a tool to provide an objective assessment of aerosol information content that can be retrieved for any constellation of (planned or real) satellite sensors and for any combination of algorithm design factors (in terms of wavelengths, viewing angles, radiance and/or polarization to be measured or used). We summarize the components of the testbed, including the derivation and validation of analytical formulae for Jacobian calculations. Benchmark calculations from the forward model are documented. In the context of NASA's Decadal Survey Mission GEOCAPE (GEOstationary Coastal and Air Pollution Events), we demonstrate the use of the testbed to conduct a feasibility study of using polarization measurements in and around the O2 A band for the retrieval of aerosol height information from space, as well as an to assess potential improvement in the retrieval of aerosol fine and coarse mode aerosol optical depth (AOD) through the synergic use of two future geostationary satellites, GOES-R (Geostationary Operational Environmental Satellite R-series) and TEMPO (Tropospheric Emissions: Monitoring of Pollution). Strong synergy between GEOS-R and TEMPO are found especially in their characterization of surface bi-directional reflectance, and thereby, can potentially improve the AOD retrieval to the accuracy required by GEO-CAPE.

A straightforward characterization of non-modal effects from the evolution of linear dynamical systems

NASA Astrophysics Data System (ADS)

Arratia, Cristobal

2014-11-01

A simple construction will be shown, which reveals a general property satisfied by the evolution in time of a state vector composed by a superposition of orthogonal eigenmodes of a linear dynamical system. This property results from the conservation of the inner product between such state vectors evolving forward and backwards in time, and it can be simply evaluated from the state vector and its first and second time derivatives. This provides an efficient way to characterize, instantaneously along any specific phase-space trajectory of the linear system, the relevance of the non-normality of the linearized Navier-Stokes operator on the energy (or any other norm) gain or decay of small perturbations. Examples of this characterization applied to stationary or time dependent base flows will be shown. CONICYT, Concurso de Apoyo al Retorno de Investigadores del Extranjero, folio 821320055.

A numerical study of linear and nonlinear kinematic models in fish swimming with the DSD/SST method

NASA Astrophysics Data System (ADS)

Tian, Fang-Bao

2015-03-01

Flow over two fish (modeled by two flexible plates) in tandem arrangement is investigated by solving the incompressible Navier-Stokes equations numerically with the DSD/SST method to understand the differences between the geometrically linear and nonlinear models. In the simulation, the motions of the plates are reconstructed from a vertically flowing soap film tunnel experiment with linear and nonlinear kinematic models. Based on the simulations, the drag, lift, power consumption, vorticity and pressure fields are discussed in detail. It is found that the linear and nonlinear models are able to reasonably predict the forces and power consumption of a single plate in flow. Moreover, if multiple plates are considered, these two models yield totally different results, which implies that the nonlinear model should be used. The results presented in this work provide a guideline for future studies in fish swimming.

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel.

PubMed

Marcos; Yang, C; Ooi, K T; Wong, T N; Masliyah, J H

2004-07-15

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study. Copyright 2004 Elsevier Inc.

Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows

NASA Astrophysics Data System (ADS)

Ladiges, Daniel R.; Sader, John E.

2018-05-01

Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.

Identification of geostationary satellites using polarization data from unresolved images

NASA Astrophysics Data System (ADS)

Speicher, Andy

In order to protect critical military and commercial space assets, the United States Space Surveillance Network must have the ability to positively identify and characterize all space objects. Unfortunately, positive identification and characterization of space objects is a manual and labor intensive process today since even large telescopes cannot provide resolved images of most space objects. Since resolved images of geosynchronous satellites are not technically feasible with current technology, another method of distinguishing space objects was explored that exploits the polarization signature from unresolved images. The objective of this study was to collect and analyze visible-spectrum polarization data from unresolved images of geosynchronous satellites taken over various solar phase angles. Different collection geometries were used to evaluate the polarization contribution of solar arrays, thermal control materials, antennas, and the satellite bus as the solar phase angle changed. Since materials on space objects age due to the space environment, it was postulated that their polarization signature may change enough to allow discrimination of identical satellites launched at different times. The instrumentation used in this experiment was a United States Air Force Academy (USAFA) Department of Physics system that consists of a 20-inch Ritchey-Chretien telescope and a dual focal plane optical train fed with a polarizing beam splitter. A rigorous calibration of the system was performed that included corrections for pixel bias, dark current, and response. Additionally, the two channel polarimeter was calibrated by experimentally determining the Mueller matrix for the system and relating image intensity at the two cameras to Stokes parameters S0 and S1. After the system calibration, polarization data was collected during three nights on eight geosynchronous satellites built by various manufacturers and launched several years apart. Three pairs of the eight satellites were identical buses to determine if identical buses could be correctly differentiated. When Stokes parameters were plotted against time and solar phase angle, the data indicates that there were distinguishing features in S0 (total intensity) and S1 (linear polarization) that may lead to positive identification or classification of each satellite.

Erratum: Correction to: Polarisation vision: overcoming challenges of working with a property of light we barely see

NASA Astrophysics Data System (ADS)

Foster, James J.; Temple, Shelby E.; How, Martin J.; Daly, Ilse M.; Sharkey, Camilla R.; Wilby, David; Roberts, Nicholas W.

2018-06-01

In "Polarisation vision: overcoming challenges of working with a property of light we barely see" (Foster et al. 2018) we provide a basic description of how Stokes parameters can be estimated and used to calculate the angle of polarisation (AoP).

Digital Holographic Interferometry for Airborne Particle Characterization

DTIC Science & Technology

2015-03-19

Interferometry and polarimetry for aerosol particle characterization, Bioaerosols: Characterization and Environmental Impact, Austin, TX (2014) [organizer...and conference chair]. 6. Invited talk: Holographic Interferometry and polarimetry for aerosol particle characterization, Optical...Stokes parameters, NATO Advanced Science Institute on Special Detection Technique ( Polarimetry ) and Remote Sensing, Kyiv, Ukraine (2010). (c

Y spaces and global smooth solution of fractional Navier-Stokes equations with initial value in the critical oscillation spaces

NASA Astrophysics Data System (ADS)

Yang, Qixiang; Yang, Haibo

2018-04-01

For fractional Navier-Stokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in C (R+ , X). In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces Y m , β where Y m , β is not contained in C (R+, B˙∞ 1 - 2 β , ∞). Consequently, for 1/2 < β < 1, we establish the global well-posedness of fractional Navier-Stokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any Besov-Morrey spaces (B˙p,q γ1 ,γ2 (Rn)) n or any Triebel-Lizorkin-Morrey spaces (F˙p,q γ1 ,γ2 (Rn)) n where 1 ≤ p , q ≤ ∞ , 0 ≤γ2 ≤ n/p, γ1 -γ2 = 1 - 2 β. These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel-Lizorkin spaces etc.

Stokes parameter studies of spontaneous emission from chiral nematic liquid crystals as a one-dimensional photonic stopband crystal: experiment and theory.

PubMed

Woon, Kai L; O'Neill, Mary; Richards, Gary J; Aldred, Matthew P; Kelly, Stephen M

2005-04-01

The helical structure of uniformly aligned chiral nematic liquid crystals results in a photonic stopband for only one sense of circular polarization. The spectroscopic Stokes polarimeter is used to analyze spontaneous emission in the stopband. Highly polarized photoluminescence is found and the polarization properties vary with the excitation wavelength. Spontaneous emission is enhanced at the stopband edge and this Purcell effect is greater on excitation at wavelengths where the absorption coefficient is low. This is interpreted as greater overlap between the excited molecules and the electrical modal field of the resonant modes at the stopband edge. Photoluminescence detected from the excitation face of the liquid crystal cell is less polarized because of photon tunneling. Fermi's golden rule in conjunction with Stokes vectors is used to model the polarization of emission taking multiple reflections at the interfaces of the cell into account. The discrepancy between the experiment and the theoretical model is interpreted as direct experimental evidence that virtual photons, which originate from zero point fluctuations of quantum space, are randomly polarized.

Second-degree Stokes coefficients from multi-satellite SLR

NASA Astrophysics Data System (ADS)

Bloßfeld, Mathis; Müller, Horst; Gerstl, Michael; Štefka, Vojtěch; Bouman, Johannes; Göttl, Franziska; Horwath, Martin

2015-09-01

The long wavelength part of the Earth's gravity field can be determined, with varying accuracy, from satellite laser ranging (SLR). In this study, we investigate the combination of up to ten geodetic SLR satellites using iterative variance component estimation. SLR observations to different satellites are combined in order to identify the impact of each satellite on the estimated Stokes coefficients. The combination of satellite-specific weekly or monthly arcs allows to reduce parameter correlations of the single-satellite solutions and leads to alternative estimates of the second-degree Stokes coefficients. This alternative time series might be helpful for assessing the uncertainty in the impact of the low-degree Stokes coefficients on geophysical investigations. In order to validate the obtained time series of second-degree Stokes coefficients, a comparison with the SLR RL05 time series of the Center of Space Research (CSR) is done. This investigation shows that all time series are comparable to the CSR time series. The precision of the weekly/monthly and coefficients is analyzed by comparing mass-related equatorial excitation functions with geophysical model results and reduced geodetic excitation functions. In case of , the annual amplitude and phase of the DGFI solution agrees better with three of four geophysical model combinations than other time series. In case of , all time series agree very well to each other. The impact of on the ice mass trend estimates for Antarctica are compared based on CSR GRACE RL05 solutions, in which different monthly time series are used for replacing. We found differences in the long-term Antarctic ice loss of Gt/year between the GRACE solutions induced by the different SLR time series of CSR and DGFI, which is about 13 % of the total ice loss of Antarctica. This result shows that Antarctic ice mass loss quantifications must be carefully interpreted.

Calibration and Stokes Imaging with Full Embedded Element Primary Beam Model for the Murchison Widefield Array

NASA Astrophysics Data System (ADS)

Sokolowski, M.; Colegate, T.; Sutinjo, A. T.; Ung, D.; Wayth, R.; Hurley-Walker, N.; Lenc, E.; Pindor, B.; Morgan, J.; Kaplan, D. L.; Bell, M. E.; Callingham, J. R.; Dwarakanath, K. S.; For, Bi-Qing; Gaensler, B. M.; Hancock, P. J.; Hindson, L.; Johnston-Hollitt, M.; Kapińska, A. D.; McKinley, B.; Offringa, A. R.; Procopio, P.; Staveley-Smith, L.; Wu, C.; Zheng, Q.

2017-11-01

The Murchison Widefield Array (MWA), located in Western Australia, is one of the low-frequency precursors of the international Square Kilometre Array (SKA) project. In addition to pursuing its own ambitious science programme, it is also a testbed for wide range of future SKA activities ranging from hardware, software to data analysis. The key science programmes for the MWA and SKA require very high dynamic ranges, which challenges calibration and imaging systems. Correct calibration of the instrument and accurate measurements of source flux densities and polarisations require precise characterisation of the telescope's primary beam. Recent results from the MWA GaLactic Extragalactic All-sky Murchison Widefield Array (GLEAM) survey show that the previously implemented Average Embedded Element (AEE) model still leaves residual polarisations errors of up to 10-20% in Stokes Q. We present a new simulation-based Full Embedded Element (FEE) model which is the most rigorous realisation yet of the MWA's primary beam model. It enables efficient calculation of the MWA beam response in arbitrary directions without necessity of spatial interpolation. In the new model, every dipole in the MWA tile (4 × 4 bow-tie dipoles) is simulated separately, taking into account all mutual coupling, ground screen, and soil effects, and therefore accounts for the different properties of the individual dipoles within a tile. We have applied the FEE beam model to GLEAM observations at 200-231 MHz and used false Stokes parameter leakage as a metric to compare the models. We have determined that the FEE model reduced the magnitude and declination-dependent behaviour of false polarisation in Stokes Q and V while retaining low levels of false polarisation in Stokes U.

Evidence for equivalence of diffusion processes of passive scalar and magnetic fields in anisotropic Navier-Stokes turbulence.

PubMed

Jurčišinová, E; Jurčišin, M

2017-05-01

The influence of the uniaxial small-scale anisotropy on the kinematic magnetohydrodynamic turbulence is investigated by using the field theoretic renormalization group technique in the one-loop approximation of a perturbation theory. The infrared stable fixed point of the renormalization group equations, which drives the scaling properties of the model in the inertial range, is investigated as the function of the anisotropy parameters and it is shown that, at least at the one-loop level of approximation, the diffusion processes of the weak passive magnetic field in the anisotropically driven kinematic magnetohydrodynamic turbulence are completely equivalent to the corresponding diffusion processes of passively advected scalar fields in the anisotropic Navier-Stokes turbulent environments.

Experimental study of spin-wave dispersion in Py/Pt film structures in the presence of an interface Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

Stashkevich, A. A.; Belmeguenai, M.; Roussigné, Y.; Cherif, S. M.; Kostylev, M.; Gabor, M.; Lacour, D.; Tiusan, C.; Hehn, M.

2015-06-01

Brillouin light scattering (BLS), complemented by ferromagnetic resonance (FMR) characterization, has been used for studying spin-wave (SW) propagation in Py (L )/Pt (6 -nm ) bilayers of various Py thicknesses (4 nm ≤L ≤10 nm ) . The FMR measurements allowed determination of the pertinent magnetic parameters and revealed the existence of a normal surface anisotropy. A pronounced asymmetry of Damon-Eshbach (DE) wave frequencies has been evidenced by BLS. Therefore, the difference between Stokes and anti-Stokes DE frequencies has been measured versus SW wave number for all the samples. A detailed discussion about the origin of this frequency difference is reported, which concludes that this is due to interface Dzyaloshinskii-Moriya interaction (IDMI).

A bifunctional amorphous polymer exhibiting equal linear and circular photoinduced birefringences.

PubMed

Royes, Jorge; Provenzano, Clementina; Pagliusi, Pasquale; Tejedor, Rosa M; Piñol, Milagros; Oriol, Luis

2014-11-01

The large and reversible photoinduced linear and circular birefringences in azo-compounds are at the basis of the interest in these materials, which are potentially useful for several applications. Since the onset of the linear and circular anisotropies relies on orientational processes, which typically occur on the molecular and supramolecular length scale, respectively, a circular birefringence at least one order of magnitude lower than the linear one is usually observed. Here, the synthesis and characterization of an amorphous polymer with a dimeric repeating unit containing a cyanoazobenzene and a cyanobiphenyl moiety are reported, in which identical optical linear and circular birefringences are induced for proper light dose and ellipticity. A pump-probe technique and an analytical method based on the Stokes-Mueller formalism are used to investigate the photoinduced effects and to evaluate the anisotropies. The peculiar photoresponse of the polymer makes it a good candidate for applications in smart functional devices. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Burnett-Cattaneo continuum theory for shock waves.

PubMed

Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

2011-02-01

We model strong shock-wave propagation, both in the ideal gas and in the dense Lennard-Jones fluid, using a refinement of earlier work, which accounts for the cold compression in the early stages of the shock rise by a nonlinear, Burnett-like, strain-rate dependence of the thermal conductivity, and relaxation of kinetic-temperature components on the hot, compressed side of the shock front. The relaxation of the disequilibrium among the three components of the kinetic temperature, namely, the difference between the component in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, is accomplished at a much more quantitative level by a rigorous application of the Cattaneo-Maxwell relaxation equation to a reference solution, namely, the steady shock-wave solution of linear Navier-Stokes-Fourier theory, along with the nonlinear Burnett heat-flux term. Our new continuum theory is in nearly quantitative agreement with nonequilibrium molecular-dynamics simulations under strong shock-wave conditions, using relaxation parameters obtained from the reference solution. ©2011 American Physical Society

A rotating, expanding disk in the Wolf-Rayet star EZ Canis Majoris?

NASA Technical Reports Server (NTRS)

Schulte-Ladbeck, R. E.; Nordsieck, K. H.; Nook, M. A.; Magalhaes, A. M.; Taylor, M.

1990-01-01

The discovery of linear polarization changes across the extended wings of He II lines, mainly the strong 4-3 transition at 4686 A, in the WN5 star EZ CMa, is reported. When the polarization across the line profiles is plotted in the Stokes parameters plane, it traces loops clockwise from the blue wing through line center to the red, rather than straight lines. Such polarization loops are reminiscent of what is observed in the Balmer lines of Be stars. The continuum polarization in EZ CMa can be understood by an axisymmetric, electron-scattering envelope, with the decrease in polarization in He II being caused by an increase in absorptive opacity in the lines and dilution by unpolarized line emission, while the variations in position angle are due to the Doppler-shifted absorptive opacity and/or scattered line photons. As the sense of rotation in the loops is also independent of phase of this alleged Wolf-Rayet + compact binary, the polarized line profiles are the signature of a rotating, expanding wind geometry around a single star.

Hydrodynamic coupling of two sharp-edged beams vibrating in a viscous fluid

PubMed Central

Intartaglia, Carmela; Soria, Leonardo; Porfiri, Maurizio

2014-01-01

In this paper, we study flexural vibrations of two thin beams that are coupled through an otherwise quiescent viscous fluid. While most of the research has focused on isolated beams immersed in placid fluids, inertial and viscous hydrodynamic coupling is ubiquitous across a multitude of engineering and natural systems comprising arrays of flexible structures. In these cases, the distributed hydrodynamic loading experienced by each oscillating structure is not only related to its absolute motion but is also influenced by its relative motion with respect to the neighbouring structures. Here, we focus on linear vibrations of two identical beams for low Knudsen, Keulegan–Carpenter and squeeze numbers. Thus, we describe the fluid flow using unsteady Stokes hydrodynamics and we propose a boundary integral formulation to compute pertinent hydrodynamic functions to study the fluid effect. We validate the proposed theoretical approach through experiments on centimetre-size compliant cantilevers that are subjected to underwater base-excitation. We consider different geometric arrangements, beam interdistances and excitation frequencies to ascertain the model accuracy in terms of the relevant non-dimensional parameters. PMID:24511249

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. PMID:29261776

Static response of deformable microchannels

NASA Astrophysics Data System (ADS)

Christov, Ivan C.; Sidhore, Tanmay C.

2017-11-01

Microfluidic channels manufactured from PDMS are a key component of lab-on-a-chip devices. Experimentally, rectangular microchannels are found to deform into a non-rectangular cross-section due to fluid-structure interactions. Deformation affects the flow profile, which results in a nonlinear relationship between the volumetric flow rate and the pressure drop. We develop a framework, within the lubrication approximation (l >> w >> h), to self-consistently derive flow rate-pressure drop relations. Emphasis is placed on handling different types of elastic response: from pure plate-bending, to half-space deformation, to membrane stretching. The ``simplest'' model (Stokes flow in a 3D rectangular channel capped with a linearly elastic Kirchhoff-Love plate) agrees well with recent experiments. We also simulate the static response of such microfluidic channels under laminar flow conditions using ANSYSWorkbench. Simulations are calibrated using experimental flow rate-pressure drop data from the literature. The simulations provide highly resolved deformation profiles, which are difficult to measure experimentally. By comparing simulations, experiments and our theoretical models, we show good agreement in many flow/deformation regimes, without any fitting parameters.

Detection of partial-thickness tears in ligaments and tendons by Stokes-polarimetry imaging

NASA Astrophysics Data System (ADS)

Kim, Jihoon; John, Raheel; Walsh, Joseph T.

2008-02-01

A Stokes polarimetry imaging (SPI) system utilizes an algorithm developed to construct degree of polarization (DoP) image maps from linearly polarized light illumination. Partial-thickness tears of turkey tendons were imaged by the SPI system in order to examine the feasibility of the system to detect partial-thickness rotator cuff tear or general tendon pathology. The rotating incident polarization angle (IPA) for the linearly polarized light provides a way to analyze different tissue types which may be sensitive to IPA variations. Degree of linear polarization (DoLP) images revealed collagen fiber structure, related to partial-thickness tears, better than standard intensity images. DoLP images also revealed structural changes in tears that are related to the tendon load. DoLP images with red-wavelength-filtered incident light may show tears and related organization of collagen fiber structure at a greater depth from the tendon surface. Degree of circular polarization (DoCP) images exhibited well the horizontal fiber orientation that is not parallel to the vertically aligned collagen fibers of the tendon. The SPI system's DOLP images reveal alterations in tendons and ligaments, which have a tissue matrix consisting largely of collagen, better than intensity images. All polarized images showed modulated intensity as the IPA was varied. The optimal detection of the partial-thickness tendon tears at a certain IPA was observed. The SPI system with varying IPA and spectral information can improve the detection of partial-thickness rotator cuff tears by higher visibility of fiber orientations and thereby improve diagnosis and treatment of tendon related injuries.

Trajectory Prediction of Spin-Stabilized Projectiles With a Steady Liquid Payload

DTIC Science & Technology

2011-11-01

analysis assumes the effect of a liquid payload is similar to the Magnus effect . Spectral analysis used to numerically compute liquid-fill induced...the internal motion of a liquid payload can induce destabilizing moments on the projectile. This report creates a method to include the effect of... effect , liquid payload moments are added to the applied loads on the projectile. These loads are computed by solving the linearized Navier-Stokes

Study of three-dimensional effects on vortex breakdown

NASA Technical Reports Server (NTRS)

Salas, M. D.; Kuruvila, G.

1988-01-01

The incompressible axisymmetric steady Navier-Stokes equations in primitive variables are used to simulate vortex breakdown. The equations, discretized using a second-order, central-difference scheme, are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers, based on vortex-core radius, as high as 1500. An attempt to study the stability of the axisymmetric solutions against three-dimensional perturbations is discussed.

Impact of polymer film thickness and cavity size on polymer flow during embossing : towards process design rules for nanoimprint lithography.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunk, Peter Randall; King, William P.; Sun, Amy Cha-Tien

2006-08-01

This paper presents continuum simulations of polymer flow during nanoimprint lithography (NIL). The simulations capture the underlying physics of polymer flow from the nanometer to millimeter length scale and examine geometry and thermophysical process quantities affecting cavity filling. Variations in embossing tool geometry and polymer film thickness during viscous flow distinguish different flow driving mechanisms. Three parameters can predict polymer deformation mode: cavity width to polymer thickness ratio, polymer supply ratio, and Capillary number. The ratio of cavity width to initial polymer film thickness determines vertically or laterally dominant deformation. The ratio of indenter width to residual film thickness measuresmore » polymer supply beneath the indenter which determines Stokes or squeeze flow. The local geometry ratios can predict a fill time based on laminar flow between plates, Stokes flow, or squeeze flow. Characteristic NIL capillary number based on geometry-dependent fill time distinguishes between capillary or viscous driven flows. The three parameters predict filling modes observed in published studies of NIL deformation over nanometer to millimeter length scales. The work seeks to establish process design rules for NIL and to provide tools for the rational design of NIL master templates, resist polymers, and process parameters.« less

A photoelectric skylight polarimeter.

PubMed

Hariharan, T A; Sekera, Z

1966-09-01

A photoelectric skylight polarimeter to measure directly the Stokes parameters for plane polarized light is described. The basic principle of the instrument consists in the simultaneous measurement of the intensity of light (in the chosen spectral region) transmitted by polarizers oriented in four specific directions. The main features and performance characteristics of the instrument are briefly discussed.

A numerical study of three-dimensional vortex breakdown

NASA Technical Reports Server (NTRS)

Spall, Robert E.; Ash, Robert L.

1987-01-01

A numerical simulation of bubble-type vortex breakdown using a unique discrete form of the full 3-D, unsteady incompressible Navier-Stokes equations was performed. The Navier-Stokes equations were written in a vorticity-velocity form and the physical problem was not restricted to axisymmetric flow. The problem was parametized on a Rossby- Reynolds-number basis. Utilization of this parameter duo was shown to dictate the form of the free-field boundary condition specification and allowed control of axial breakdown location within the computational domain. The structure of the breakdown bubble was studied through time evolution plots of planar projected velocity vectors as well as through plots of particle traces and vortex lines. These results compared favorably with previous experimental studies. In addition, profiles of all three velocity components are presented at various axial stations and a Fourier analysis was performed to identify the dominant circumferential modes. The dynamics of the breakdown process were studied through plots of axial variation of rate of change of integrated total energy and rate of change of integrated enstrophy, as well as through contour plots of velocity, vorticity and pressure.

The effect of line damping, magneto-optics and parasitic light on the derivation of sunspot vector magnetic fields

NASA Technical Reports Server (NTRS)

Skumanich, A.; Lites, B. W.

1985-01-01

The least square fitting of Stokes observations of sunspots using a Milne-Eddington-Unno model appears to lead, in many circumstances, to various inconsistencies such as anomalously large doppler widths and, hence, small magnetic fields which are significantly below those inferred solely from the Zeeman splitting in the intensity profile. It is found that the introduction of additional physics into the model such as the inclusion of damping wings and magneto-optic birefrigence significantly improves the fit to Stokes parameters. Model fits excluding the intensity profile, i.e., of both magnitude as well as spectral shape of the polarization parameters alone, suggest that parasitic light in the intensity profile may also be a source of inconsistencies. The consequences of the physical changes on the vector properties of the field derived from the Fe I lambda 6173 line for the 17 November 1975 spot as well as on the thermodynamic state are discussed. A Doppler width delta lambda (D) - 25mA is bound to be consistent with a low spot temperature and microturbulence, and a damping constant of a = 0.2.

Modelling the normal bouncing dynamics of spheres in a viscous fluid

NASA Astrophysics Data System (ADS)

Izard, Edouard; Lacaze, Laurent; Bonometti, Thomas

2017-06-01

Bouncing motions of spheres in a viscous fluid are numerically investigated by an immersed boundary method to resolve the fluid flow around solids which is combined to a discrete element method for the particles motion and contact resolution. Two well-known configurations of bouncing are considered: the normal bouncing of a sphere on a wall in a viscous fluid and a normal particle-particle bouncing in a fluid. Previous experiments have shown the effective restitution coefficient to be a function of a single parameter, namely the Stokes number which compares the inertia of the solid particle with the fluid viscous dissipation. The present simulations show a good agreement with experimental observations for the whole range of investigated parameters. However, a new definition of the coefficient of restitution presented here shows a dependence on the Stokes number as in previous works but, in addition, on the fluid to particle density ratio. It allows to identify the viscous, inertial and dry regimes as found in experiments of immersed granular avalanches of Courrech du Pont et al. Phys. Rev. Lett. 90, 044301 (2003), e.g. in a multi-particle configuration.

Numerical simulation of the deterministic vector separation of particles flowing over slanted open cavities

NASA Astrophysics Data System (ADS)

Shaqfeh, Eric S. G.; Bernate, Jorge A.; Yang, Mengfei

2016-12-01

Within the past decade, the separation of particles via continuous flow through microfluidic devices has been developed largely through an Edisonian approach whereby devices have been developed based on observation and intuition. This is particularly true in the development of vector chromatography at vanishingly small Reynolds number for non-Brownian particles. Note that this latter phenomenon has its origins in the irreversible forces that are at work in the device, since Stokes flow reversibility typically prohibits their function otherwise. We present a numerical simulation of the vector separation of non-Brownian particles of different sizes and deformabilities in the Stokes flow through channels whose lower surface is composed of slanted cavities. The simulations are designed to understand the physical principles behind the separation as well as to provide design criteria for devices for separating particles in a given size and flexibility range. The numerical simulations are Stokes flow boundary element simulations using techniques defined elsewhere in the literature, but including a close-range repulsive force between the particles and the slanted cavities. We demonstrate that over a range of repulsive force that is comparable to the roughness in the experimental devices, the separation data (particularly in particle size) are predicted quantitatively and are a very weak function of the range of the force. We then vary the geometric parameters of the simulated devices to demonstrate the sensitivity of the separation efficiency to these parameters, thus making design predictions as to which devices are appropriate for separating particles in different size, shape, and deformability ranges.

Nonreciprocal Linear Transmission of Sound in a Viscous Environment with Broken P Symmetry.

PubMed

Walker, E; Neogi, A; Bozhko, A; Zubov, Yu; Arriaga, J; Heo, H; Ju, J; Krokhin, A A

2018-05-18

Reciprocity is a fundamental property of the wave equation in a linear medium that originates from time-reversal symmetry, or T symmetry. For electromagnetic waves, reciprocity can be violated by an external magnetic field. It is much harder to realize nonreciprocity for acoustic waves. Here we report the first experimental observation of linear nonreciprocal transmission of ultrasound through a water-submerged phononic crystal consisting of asymmetric rods. Viscosity of water is the factor that breaks the T symmetry. Asymmetry, or broken P symmetry along the direction of sound propagation, is the second necessary factor for nonreciprocity. Experimental results are in agreement with numerical simulations based on the Navier-Stokes equation. Our study demonstrates that a medium with broken PT symmetry is acoustically nonreciprocal. The proposed passive nonreciprocal device is cheap, robust, and does not require an energy source.

Nonreciprocal Linear Transmission of Sound in a Viscous Environment with Broken P Symmetry

NASA Astrophysics Data System (ADS)

Walker, E.; Neogi, A.; Bozhko, A.; Zubov, Yu.; Arriaga, J.; Heo, H.; Ju, J.; Krokhin, A. A.

2018-05-01

Reciprocity is a fundamental property of the wave equation in a linear medium that originates from time-reversal symmetry, or T symmetry. For electromagnetic waves, reciprocity can be violated by an external magnetic field. It is much harder to realize nonreciprocity for acoustic waves. Here we report the first experimental observation of linear nonreciprocal transmission of ultrasound through a water-submerged phononic crystal consisting of asymmetric rods. Viscosity of water is the factor that breaks the T symmetry. Asymmetry, or broken P symmetry along the direction of sound propagation, is the second necessary factor for nonreciprocity. Experimental results are in agreement with numerical simulations based on the Navier-Stokes equation. Our study demonstrates that a medium with broken PT symmetry is acoustically nonreciprocal. The proposed passive nonreciprocal device is cheap, robust, and does not require an energy source.

Flow adjustment inside homogeneous canopies after a leading edge – An analytical approach backed by LES

DOE PAGES

Kroniger, Konstantin; Banerjee, Tirtha; De Roo, Frederik; ...

2017-10-06

A two-dimensional analytical model for describing the mean flow behavior inside a vegetation canopy after a leading edge in neutral conditions was developed and tested by means of large eddy simulations (LES) employing the LES code PALM. The analytical model is developed for the region directly after the canopy edge, the adjustment region, where one-dimensional canopy models fail due to the sharp change in roughness. The derivation of this adjustment region model is based on an analytic solution of the two-dimensional Reynolds averaged Navier–Stokes equation in neutral conditions for a canopy with constant plant area density (PAD). The main assumptionsmore » for solving the governing equations are separability of the velocity components concerning the spatial variables and the neglection of the Reynolds stress gradients. These two assumptions are verified by means of LES. To determine the emerging model parameters, a simultaneous fitting scheme was applied to the velocity and pressure data of a reference LES simulation. Furthermore a sensitivity analysis of the adjustment region model, equipped with the previously calculated parameters, was performed varying the three relevant length, the canopy height ( h), the canopy length and the adjustment length ( Lc), in additional LES. Even if the model parameters are, in general, functions of h/ Lc, it was found out that the model is capable of predicting the flow quantities in various cases, when using constant parameters. Subsequently the adjustment region model is combined with the one-dimensional model of Massman, which is applicable for the interior of the canopy, to attain an analytical model capable of describing the mean flow for the full canopy domain. As a result, the model is tested against an analytical model based on a linearization approach.« less

Flow adjustment inside homogeneous canopies after a leading edge – An analytical approach backed by LES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kroniger, Konstantin; Banerjee, Tirtha; De Roo, Frederik

A two-dimensional analytical model for describing the mean flow behavior inside a vegetation canopy after a leading edge in neutral conditions was developed and tested by means of large eddy simulations (LES) employing the LES code PALM. The analytical model is developed for the region directly after the canopy edge, the adjustment region, where one-dimensional canopy models fail due to the sharp change in roughness. The derivation of this adjustment region model is based on an analytic solution of the two-dimensional Reynolds averaged Navier–Stokes equation in neutral conditions for a canopy with constant plant area density (PAD). The main assumptionsmore » for solving the governing equations are separability of the velocity components concerning the spatial variables and the neglection of the Reynolds stress gradients. These two assumptions are verified by means of LES. To determine the emerging model parameters, a simultaneous fitting scheme was applied to the velocity and pressure data of a reference LES simulation. Furthermore a sensitivity analysis of the adjustment region model, equipped with the previously calculated parameters, was performed varying the three relevant length, the canopy height ( h), the canopy length and the adjustment length ( Lc), in additional LES. Even if the model parameters are, in general, functions of h/ Lc, it was found out that the model is capable of predicting the flow quantities in various cases, when using constant parameters. Subsequently the adjustment region model is combined with the one-dimensional model of Massman, which is applicable for the interior of the canopy, to attain an analytical model capable of describing the mean flow for the full canopy domain. As a result, the model is tested against an analytical model based on a linearization approach.« less

On recent advances and future research directions for computational fluid dynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.; Soliman, M. O.; Manhardt, P. D.

1986-01-01

This paper highlights some recent accomplishments regarding CFD numerical algorithm constructions for generation of discrete approximate solutions to classes of Reynolds-averaged Navier-Stokes equations. Following an overview of turbulent closure modeling, and development of appropriate conservation law systems, a Taylor weak-statement semi-discrete approximate solution algorithm is developed. Various forms for completion to the final linear algebra statement are cited, as are a range of candidate numerical linear algebra solution procedures. This development sequence emphasizes the key building blocks of a CFD RNS algorithm, including solution trial and test spaces, integration procedure and added numerical stability mechanisms. A range of numerical results are discussed focusing on key topics guiding future research directions.

Optical image security using Stokes polarimetry of spatially variant polarized beam

NASA Astrophysics Data System (ADS)

Fatima, Areeba; Nishchal, Naveen K.

2018-06-01

We propose a novel security scheme that uses vector beam characterized by the spatially variant polarization distribution. A vector beam is so generated that its helical components carry tailored phases corresponding to the image/images that is/are to be encrypted. The tailoring of phase has been done by employing the modified Gerchberg-Saxton algorithm for phase retrieval. Stokes parameters for the final vector beam is evaluated and is used to construct the ciphertext and one of the keys. The advantage of the proposed scheme is that it generates real ciphertext and keys which are easier to transmit and store than complex quantities. Moreover, the known plaintext attack is not applicable to this system. As a proof-of-concept, simulation results have been presented for securing single and double gray-scale images.

SSME thrust chamber simulation using Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

1984-01-01

The capability of the PHOENICS fluid dynamics code in predicting two-dimensional, compressible, and reacting flow in the combustion chamber and nozzle of the space shuttle main engine (SSME) was evaluated. A non-orthogonal body fitted coordinate system was used to represent the nozzle geometry. The Navier-Stokes equations were solved for the entire nozzle with a turbulence model. The wall boundary conditions were calculated based on the wall functions which account for pressure gradients. Results of the demonstration test case reveal all expected features of the transonic nozzle flows. Of particular interest are the locations of normal and barrel shocks, and regions of highest temperature gradients. Calculated performance (global) parameters such as thrust chamber flow rate, thrust, and specific impulse are also in good agreement with available data.

Ring-Down Spectroscopy for Characterizing a CW Raman Laser

NASA Technical Reports Server (NTRS)

Matsko, Andrey; Savchenkov, Anatoliy; Maleki, Lute

2007-01-01

.A relatively simple technique for characterizing an all-resonant intracavity continuous-wave (CW) solid-state Raman laser involves the use of ring-down spectroscopy. As used here, characterizing signifies determining such parameters as threshold pump power, Raman gain, conversion efficiency, and quality factors (Q values) of the pump and Stokes cavity modes. Heretofore, in order to characterize resonant-cavity-based Raman lasers, it has usually been necessary to manipulate the frequencies and power levels of pump lasers and, in each case, to take several sets of measurements. In cases involving ultra-high-Q resonators, it also has been desirable to lock pump lasers to resonator modes to ensure the quality of measurement data. Simpler techniques could be useful. In the present ring-down spectroscopic technique, one infers the parameters of interest from the decay of the laser out of its steady state. This technique does not require changing the power or frequency of the pump laser or locking the pump laser to the resonator mode. The technique is based on a theoretical analysis of what happens when the pump laser is abruptly switched off after the Raman generation reaches the steady state. The analysis starts with differential equations for the evolution of the amplitudes of the pump and Stokes electric fields, leading to solutions for the power levels of the pump and Stokes fields as functions of time and of the aforementioned parameters. Among other things, these solutions show how the ring-down time depends, to some extent, on the electromagnetic energy accumulated in the cavity. The solutions are readily converted to relatively simple equations for the parameters as functions of quantities that can be determined from measurements of the time-dependent power levels. For example, the steady-state intracavity conversion efficiency is given by G1/G2 1 and the threshold power is given by Pin(G2/G1)2, where Pin is the steady-state input pump power immediately prior to abrupt switch-off, G1 is the initial rate of decay of the pump field, and G2 is the final rate of decay of the pump field. Hence, it is possible to determine all the parameters from a single ring-down scan, provided that the measurements taken in that scan are sufficiently accurate and complete.

A high-fidelity method to analyze perturbation evolution in turbulent flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Unnikrishnan, S., E-mail: sasidharannair.1@osu.edu; Gaitonde, Datta V., E-mail: gaitonde.3@osu.edu

2016-04-01

Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier–Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state,more » its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted “baseline” and “twin”) of simultaneous synchronized Large-Eddy Simulations (LES). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier–Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, “native” forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous terms or turbulence closures. The method is illustrated by application to a well-validated Mach 1.3 jet. Specifically, the effects of turbulence on the jet lipline and core collapse regions on the near-acoustic field are isolated. The properties of the method, including linearity and effect of initial transients, are discussed. The results provide insight into how turbulence from different parts of the jet contribute to the observed dominance of low and high frequency content at shallow and sideline angles, respectively.« less

A high-fidelity method to analyze perturbation evolution in turbulent flows

NASA Astrophysics Data System (ADS)

Unnikrishnan, S.; Gaitonde, Datta V.

2016-04-01

Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier-Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state, its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted "baseline" and "twin") of simultaneous synchronized Large-Eddy Simulations (LES). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier-Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, "native" forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous terms or turbulence closures. The method is illustrated by application to a well-validated Mach 1.3 jet. Specifically, the effects of turbulence on the jet lipline and core collapse regions on the near-acoustic field are isolated. The properties of the method, including linearity and effect of initial transients, are discussed. The results provide insight into how turbulence from different parts of the jet contribute to the observed dominance of low and high frequency content at shallow and sideline angles, respectively.

Higgs, SUSY and the standard model at /γγ colliders

NASA Astrophysics Data System (ADS)

Hagiwara, Kaoru

2001-10-01

In this report, I surveyed physics potential of the γγ option of a linear e +e - collider with the following questions in mind: What new discovery can be expected at a γγ collider in addition to what will be learned at its ' parent' e +e -linear collider? By taking account of the hard energy spectrum and polarization of colliding photons, produced by Compton back-scattering of laser light off incoming e - beams, we find that a γγ collider is most powerful when new physics appears in the neutral spin-zero channel at an invariant mass below about 80% of the c.m. energy of the colliding e -e - system. If a light Higgs boson exists, its properties can be studied in detail, and if its heavier partners or a heavy Higgs boson exists in the above mass range, they may be discovered at a γγ collider. CP property of the scalar sector can be explored in detail by making use of linear polarization of the colliding photons, decay angular correlations of final state particles, and the pattern of interference with the Standard Model amplitudes. A few comments are given for SUSY particle studies at a γγ collider, where a pair of charged spinless particles is produced in the s-wave near the threshold. Squark-onium may be discovered. An e ±γ collision mode may measure the Higgs- Z-γ coupling accurately and probe flavor oscillations in the slepton sector. As a general remark, all the Standard Model background simulation tools should be prepared in the helicity amplitude level, so that simulation can be performed for an arbitrary set of Stokes parameters of the incoming photon beams.

A Simulation Study of the Overdetermined Geodetic Boundary Value Problem Using Collocation

DTIC Science & Technology

1989-03-01

9 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED GEOPHYSICS LABORATORY AIR FORCE SYSTEMS COMMAND UNITED STATES AIR FORCE HANSCOM AIR FORCE BASE...linearized integral equation is obtained through an infinite system of integral equations which is solved step by step by means of Stokes’ function. The...computed. Since 9 and W = W(9) 4 are known on the boundary, then the boundary is known in the new coordinate system . The serious disadvantage of this

Model Validation for Propulsion - On the TFNS and LES Subgrid Models for a Bluff Body Stabilized Flame

NASA Technical Reports Server (NTRS)

Wey, Thomas

2017-01-01

This paper summarizes the reacting results of simulating a bluff body stabilized flame experiment of Volvo Validation Rig using a releasable edition of the National Combustion Code (NCC). The turbulence models selected to investigate the configuration are the sub-grid scaled kinetic energy coupled large eddy simulation (K-LES) and the time-filtered Navier-Stokes (TFNS) simulation. The turbulence chemistry interaction used is linear eddy mixing (LEM).

Amplification of nonlinear surface waves by wind

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leblanc, Stephane

2007-10-15

A weakly nonlinear analysis is conducted to study the evolution of slowly varying wavepackets with small but finite amplitudes, that evolve at the interface between air and water under the effect of wind. In the inviscid assumption, wave envelopes are governed by cubic nonlinear Schroedinger or Davey-Stewartson equations forced by a linear term corresponding to Miles' mechanism of wave generation. Under fair wind, it is shown that Stokes waves grow exponentially and that Benjamin-Feir instability becomes explosive.

A comparative study of the spectral, fluorometric properties and photostability of natural curcumin, iron- and boron- complexed curcumin

NASA Astrophysics Data System (ADS)

Mohammed, Fatima; Rashid-Doubell, Fiza; Cassidy, Seamas; Henari, Fryad

2017-08-01

Curcumin is a yellow phenolic compound with a wide range of reported biological effects. However, two main obstacles hinder the use of curcumin therapeutically, namely its poor bioavailability and photostability. We have synthesized two curcumin complexes, the first a boron curcumin complex (B-Cur2) and the second an iron (Fe-Cur3) complex of curcumin. Both derivatives showed high fluorescence efficiency (quantum yield) and greater photostability in solution. The improved photostability could be attributed to the coordination structures and the removal of β-diketone group from curcumin. The fluorescence and ultra violet/visible absorption spectra of curcumin, B-Cur2 and Fe-Cur3 all have a similar spectral pattern when dissolved in the same organic solvent. However, a shift towards a lower wavelength was observed when moving from polar to non-polar solvents, possibly due to differences in solvent polarity. A plot of Stokes' shift vs the orientation polarity parameter (Δf) or vs the solvent polarity parameter (ET 30) showed an improved correlation between the solvent polarity parameter than with the orientation polarity parameter and indicating that the red shift observed could be due to hydrogen-bonding between the solvent molecules. A similar association was obtained when Stokes' shift was replaced by maximum synchronous fluorescence. Both B-Cur2 and Fe-Cur3 had larger quantum yields than curcumin, suggesting they may be good candidates for medical imaging and in vitro studies.

The Primordial Inflation Explorer (PIXIE)

NASA Technical Reports Server (NTRS)

Kogut, Alan; Chluba, Jens; Fixsen, Dale J.; Meyer, Stephan; Spergel, David

2016-01-01

The Primordial Inflation Explorer is an Explorer-class mission to open new windows on the early universe through measurements of the polarization and absolute frequency spectrum of the cosmic microwave background. PIXIE will measure the gravitational-wave signature of primordial inflation through its distinctive imprint in linear polarization, and characterize the thermal history of the universe through precision measurements of distortions in the blackbody spectrum. PIXIE uses an innovative optical design to achieve background-limited sensitivity in 400 spectral channels spanning over 7 octaves in frequency from 30 GHz to 6 THz (1 cm to 50 micron wavelength). Multi-moded non-imaging optics feed a polarizing Fourier Transform Spectrometer to produce a set of interference fringes, proportional to the difference spectrum between orthogonal linear polarizations from the two input beams. Multiple levels of symmetry and signal modulation combine to reduce systematic errors to negligible levels. PIXIE will map the full sky in Stokes I, Q, and U parameters with angular resolution 2.6 degrees and sensitivity 70 nK per 1degree square pixel. The principal science goal is the detection and characterization of linear polarization from an inflationary epoch in the early universe, with tensor-to-scalar ratio r < 10(exp. -3) at 5 standard deviations. The PIXIE mission complements anticipated ground-based polarization measurements such as CMBS4, providing a cosmic-variance-limited determination of the large-scale E-mode signal to measure the optical depth, constrain models of reionization, and provide a firm detection of the neutrino mass (the last unknown parameter in the Standard Model of particle physics). In addition, PIXIE will measure the absolute frequency spectrum to characterize deviations from a blackbody with sensitivity 3 orders of magnitude beyond the seminal COBE/FIRAS limits. The sky cannot be black at this level; the expected results will constrain physical processes ranging from inflation to the nature of the first stars and the physical conditions within the interstellar medium of the Galaxy. We describe the PIXIE instrument and mission architecture required to measure the CMB to the limits imposed by astrophysical foregrounds.

Validation and Performance Comparison of Numerical Codes for Tsunami Inundation

NASA Astrophysics Data System (ADS)

Velioglu, D.; Kian, R.; Yalciner, A. C.; Zaytsev, A.

2015-12-01

In inundation zones, tsunami motion turns from wave motion to flow of water. Modelling of this phenomenon is a complex problem since there are many parameters affecting the tsunami flow. In this respect, the performance of numerical codes that analyze tsunami inundation patterns becomes important. The computation of water surface elevation is not sufficient for proper analysis of tsunami behaviour in shallow water zones and on land and hence for the development of mitigation strategies. Velocity and velocity patterns are also crucial parameters and have to be computed at the highest accuracy. There are numerous numerical codes to be used for simulating tsunami inundation. In this study, FLOW 3D and NAMI DANCE codes are selected for validation and performance comparison. Flow 3D simulates linear and nonlinear propagating surface waves as well as long waves by solving three-dimensional Navier-Stokes (3D-NS) equations. FLOW 3D is used specificaly for flood problems. NAMI DANCE uses finite difference computational method to solve linear and nonlinear forms of shallow water equations (NSWE) in long wave problems, specifically tsunamis. In this study, these codes are validated and their performances are compared using two benchmark problems which are discussed in 2015 National Tsunami Hazard Mitigation Program (NTHMP) Annual meeting in Portland, USA. One of the problems is an experiment of a single long-period wave propagating up a piecewise linear slope and onto a small-scale model of the town of Seaside, Oregon. Other benchmark problem is an experiment of a single solitary wave propagating up a triangular shaped shelf with an island feature located at the offshore point of the shelf. The computed water surface elevation and velocity data are compared with the measured data. The comparisons showed that both codes are in fairly good agreement with each other and benchmark data. All results are presented with discussions and comparisons. The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement No 603839 (Project ASTARTE - Assessment, Strategy and Risk Reduction for Tsunamis in Europe)

Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices.

PubMed

Martínez, Francisco J; Márquez, Andrés; Gallego, Sergi; Ortuño, Manuel; Francés, Jorge; Pascual, Inmaculada; Beléndez, Augusto

2015-02-20

Parallel-aligned (PA) liquid-crystal on silicon (LCoS) microdisplays are especially appealing in a wide range of spatial light modulation applications since they enable phase-only operation. Recently we proposed a novel polarimetric method, based on Stokes polarimetry, enabling the characterization of their linear retardance and the magnitude of their associated phase fluctuations or flicker, exhibited by many LCoS devices. In this work we apply the calibrated values obtained with this technique to show their capability to predict the performance of spatially varying phase multilevel elements displayed onto the PA-LCoS device. Specifically we address a series of multilevel phase blazed gratings. We analyze both their average diffraction efficiency ("static" analysis) and its associated time fluctuation ("dynamic" analysis). Two different electrical configuration files with different degrees of flicker are applied in order to evaluate the actual influence of flicker on the expected performance of the diffractive optical elements addressed. We obtain a good agreement between simulation and experiment, thus demonstrating the predictive capability of the calibration provided by the average Stokes polarimetric technique. Additionally, it is obtained that for electrical configurations with less than 30° amplitude for the flicker retardance, they may not influence the performance of the blazed gratings. In general, we demonstrate that the influence of flicker greatly diminishes when the number of quantization levels in the optical element increases.

High-order random Raman lasing in a PM fiber with ultimate efficiency and narrow bandwidth

PubMed Central

Babin, Sergey A.; Zlobina, Ekaterina A.; Kablukov, Sergey I.; Podivilov, Evgeniy V.

2016-01-01

Random Raman lasers attract now a great deal of attention as they operate in non-active turbid or transparent scattering media. In the last case, single mode fibers with feedback via Rayleigh backscattering generate a high-quality unidirectional laser beam. However, such fiber lasers have rather poor spectral and polarization properties, worsening with increasing power and Stokes order. Here we demonstrate a linearly-polarized cascaded random Raman lasing in a polarization-maintaining fiber. The quantum efficiency of converting the pump (1.05 μm) into the output radiation is almost independent of the Stokes order, amounting to 79%, 83%, and 77% for the 1st (1.11 μm), 2nd (1.17 μm) and 3rd (1.23 μm) order, respectively, at the polarization extinction ratio >22 dB for all orders. The laser bandwidth grows with increasing order, but it is almost independent of power in the 1–10 W range, amounting to ~1, ~2 and ~3 nm for orders 1–3, respectively. So, the random Raman laser exhibits no degradation of output characteristics with increasing Stokes order. A theory adequately describing the unique laser features has been developed. Thus, a full picture of the cascaded random Raman lasing in fibers is shown. PMID:26940082

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Synthetic observations of wave propagation in a sunspot umbra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Felipe, T.; Socas-Navarro, H.; Khomenko, E.

2014-11-01

Spectropolarimetric temporal series from Fe I λ6301.5 Å and Ca II infrared triplet lines are obtained by applying the Stokes synthesis code NICOLE to a numerical simulation of wave propagation in a sunspot umbra from MANCHA code. The analysis of the phase difference between Doppler velocity and intensity core oscillations of the Fe I λ6301.5 Å line reveals that variations in the intensity are produced by opacity fluctuations rather than intrinsic temperature oscillations, except for frequencies between 5 and 6.5 mHz. On the other hand, the photospheric magnetic field retrieved from the weak field approximation provides the intrinsic magnetic fieldmore » oscillations associated to wave propagation. Our results suggest that this is due to the low magnetic field gradient of our sunspot model. The Stokes parameters of the chromospheric Ca II infrared triplet lines show striking variations as shock waves travel through the formation height of the lines, including emission self-reversals in the line core and highly abnormal Stokes V profiles. Magnetic field oscillations inferred from the Ca II infrared lines using the weak field approximation appear to be related with the magnetic field strength variation between the photosphere and the chromosphere.« less

A Framework for Segmentation Using Physical Models of Image Formation

DTIC Science & Technology

1993-12-10

light incoming to the point (vy,z) from direction (Ox, 0e) of wavelength x and Stokes parameter s at time t. This function is similar to the plenoptic ... Plenoptic Function and the Elements of Early Vision," in Computational Models of ivnal Processing, ed. M. S. Landy, and J. A. Movshon, Cambridge, MIT

A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; Lee, Henry

2014-01-01

The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no indication in Ref. II that the gaps are explicitly modeled as in Ref. 6. Computations using overset grids are reported in Ref. 12 for a case by adding moving control surface to an existing blade but with no validation either with an experiment or another computation.

Estimation of k-ε parameters using surrogate models and jet-in-crossflow data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lefantzi, Sophia; Ray, Jaideep; Arunajatesan, Srinivasan

2014-11-01

We demonstrate a Bayesian method that can be used to calibrate computationally expensive 3D RANS (Reynolds Av- eraged Navier Stokes) models with complex response surfaces. Such calibrations, conditioned on experimental data, can yield turbulence model parameters as probability density functions (PDF), concisely capturing the uncertainty in the parameter estimates. Methods such as Markov chain Monte Carlo (MCMC) estimate the PDF by sampling, with each sample requiring a run of the RANS model. Consequently a quick-running surrogate is used instead to the RANS simulator. The surrogate can be very difficult to design if the model's response i.e., the dependence of themore » calibration variable (the observable) on the parameter being estimated is complex. We show how the training data used to construct the surrogate can be employed to isolate a promising and physically realistic part of the parameter space, within which the response is well-behaved and easily modeled. We design a classifier, based on treed linear models, to model the "well-behaved region". This classifier serves as a prior in a Bayesian calibration study aimed at estimating 3 k - ε parameters ( C μ, C ε2 , C ε1 ) from experimental data of a transonic jet-in-crossflow interaction. The robustness of the calibration is investigated by checking its predictions of variables not included in the cal- ibration data. We also check the limit of applicability of the calibration by testing at off-calibration flow regimes. We find that calibration yield turbulence model parameters which predict the flowfield far better than when the nomi- nal values of the parameters are used. Substantial improvements are still obtained when we use the calibrated RANS model to predict jet-in-crossflow at Mach numbers and jet strengths quite different from those used to generate the ex- perimental (calibration) data. Thus the primary reason for poor predictive skill of RANS, when using nominal values of the turbulence model parameters, was parametric uncertainty, which was rectified by calibration. Post-calibration, the dominant contribution to model inaccuraries are due to the structural errors in RANS.« less

Influence of wave modelling on the prediction of fatigue for offshore wind turbines

NASA Astrophysics Data System (ADS)

Veldkamp, H. F.; van der Tempel, J.

2005-01-01

Currently it is standard practice to use Airy linear wave theory combined with Morison's formula for the calculation of fatigue loads for offshore wind turbines. However, offshore wind turbines are typically placed in relatively shallow water depths of 5-25 m where linear wave theory has limited accuracy and where ideally waves generated with the Navier-Stokes approach should be used. This article examines the differences in fatigue for some representative offshore wind turbines that are found if first-order, second-order and fully non-linear waves are used. The offshore wind turbines near Blyth are located in an area where non-linear wave effects are common. Measurements of these waves from the OWTES project are used to compare the different wave models with the real world in spectral form. Some attention is paid to whether the shape of a higher-order wave height spectrum (modified JONSWAP) corresponds to reality for other places in the North Sea, and which values for the drag and inertia coefficients should be used. Copyright

Formation of Linear Gradient of Antibiotics on Microfluidic Chips for High-throughput Antibiotic Susceptibility Testing

NASA Astrophysics Data System (ADS)

Kim, Seunggyu; Lee, Seokhun; Jeon, Jessie S.

2017-11-01

To determine the most effective antimicrobial treatments of infectious pathogen, high-throughput antibiotic susceptibility test (AST) is critically required. However, the conventional AST requires at least 16 hours to reach the minimum observable population. Therefore, we developed a microfluidic system that allows maintenance of linear antibiotic concentration and measurement of local bacterial density. Based on the Stokes-Einstein equation, the flow rate in the microchannel was optimized so that linearization was achieved within 10 minutes, taking into account the diffusion coefficient of each antibiotic in the agar gel. As a result, the minimum inhibitory concentration (MIC) of each antibiotic against P. aeruginosa could be immediately determined 6 hours after treatment of the linear antibiotic concentration. In conclusion, our system proved the efficacy of a high-throughput AST platform through MIC comparison with Clinical and Laboratory Standards Institute (CLSI) range of antibiotics. This work was supported by the Climate Change Research Hub (Grant No. N11170060) of the KAIST and by the Brain Korea 21 Plus project.

Boundary-Layer Receptivity and Integrated Transition Prediction

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan

2005-01-01

The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

Study of non-linear deformation of vocal folds in simulations of human phonation

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Bodony, Daniel

2014-11-01

Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).

Hybrid single-source online Fourier transform coherent anti-Stokes Raman scattering/optical coherence tomography.

PubMed

Kamali, Tschackad; Považay, Boris; Kumar, Sunil; Silberberg, Yaron; Hermann, Boris; Werkmeister, René; Drexler, Wolfgang; Unterhuber, Angelika

2014-10-01

We demonstrate a multimodal optical coherence tomography (OCT) and online Fourier transform coherent anti-Stokes Raman scattering (FTCARS) platform using a single sub-12 femtosecond (fs) Ti:sapphire laser enabling simultaneous extraction of structural and chemical ("morphomolecular") information of biological samples. Spectral domain OCT prescreens the specimen providing a fast ultrahigh (4×12  μm axial and transverse) resolution wide field morphologic overview. Additional complementary intrinsic molecular information is obtained by zooming into regions of interest for fast label-free chemical mapping with online FTCARS spectroscopy. Background-free CARS is based on a Michelson interferometer in combination with a highly linear piezo stage, which allows for quick point-to-point extraction of CARS spectra in the fingerprint region in less than 125 ms with a resolution better than 4  cm(-1) without the need for averaging. OCT morphology and CARS spectral maps indicating phosphate and carbonate bond vibrations from human bone samples are extracted to demonstrate the performance of this hybrid imaging platform.

Numerical simulation of the processes in the normal incidence tube for high acoustic pressure levels

NASA Astrophysics Data System (ADS)

Fedotov, E. S.; Khramtsov, I. V.; Kustov, O. Yu.

2016-10-01

Numerical simulation of the acoustic processes in an impedance tube at high levels of acoustic pressure is a way to solve a problem of noise suppressing by liners. These studies used liner specimen that is one cylindrical Helmholtz resonator. The evaluation of the real and imaginary parts of the liner acoustic impedance and sound absorption coefficient was performed for sound pressure levels of 130, 140 and 150 dB. The numerical simulation used experimental data having been obtained on the impedance tube with normal incidence waves. At the first stage of the numerical simulation it was used the linearized Navier-Stokes equations, which describe well the imaginary part of the liner impedance whatever the sound pressure level. These equations were solved by finite element method in COMSOL Multiphysics program in axisymmetric formulation. At the second stage, the complete Navier-Stokes equations were solved by direct numerical simulation in ANSYS CFX in axisymmetric formulation. As the result, the acceptable agreement between numerical simulation and experiment was obtained.

Near-Infrared Fluorescent Turn-on Probe with a Remarkable Large Stokes Shift for Imaging Selenocysteine in Living Cells and Animals.

PubMed

Feng, Weiyong; Li, Meixing; Sun, Yao; Feng, Guoqiang

2017-06-06

Selenocysteine (Sec) is the 21st naturally occurring amino acid and has emerged as an important sensing target in recent years. However, fluorescent detection of Sec in living systems is challenging. To date, very few fluorescent Sec probes have been reported and most of them respond fluorescence to Sec in the visible region. In this paper, a very promising near-infrared fluorescent probe for Sec was developed. This probe works in aqueous solution over a wide pH range under mild conditions and can be used for rapid, highly selective and sensitive detection of Sec with significant near-infrared fluorescent turn-on signal changes. In addition, it features a remarkable large Stokes shift (192 nm) and a low detection limit (60 nM) for Sec with a wide linear range (0-70 μM). Moreover, this probe can be conveniently used to detect Sec in serum samples, living cells, and animals, indicating it holds great promise for biological applications.

A study of infrasound propagation based on high-order finite difference solutions of the Navier-Stokes equations.

PubMed

Marsden, O; Bogey, C; Bailly, C

2014-03-01

The feasibility of using numerical simulation of fluid dynamics equations for the detailed description of long-range infrasound propagation in the atmosphere is investigated. The two dimensional (2D) Navier Stokes equations are solved via high fidelity spatial finite differences and Runge-Kutta time integration, coupled with a shock-capturing filter procedure allowing large amplitudes to be studied. The accuracy of acoustic prediction over long distances with this approach is first assessed in the linear regime thanks to two test cases featuring an acoustic source placed above a reflective ground in a homogeneous and weakly inhomogeneous medium, solved for a range of grid resolutions. An atmospheric model which can account for realistic features affecting acoustic propagation is then described. A 2D study of the effect of source amplitude on signals recorded at ground level at varying distances from the source is carried out. Modifications both in terms of waveforms and arrival times are described.

Simplified demultiplexing scheme for two PDM-IM/DD systems utilizing a single Stokes analyzer over 25-km SMF.

PubMed

Pan, Yan; Yan, Lianshan; Yi, Anlin; Jiang, Lin; Pan, Wei; Luo, Bin; Zou, Xihua

2017-10-15

We propose a four-linear state of polarization multiplexed intensity modulation and direct detection (IM/DD) scheme based on two orthogonal polarization division multiplexing (PDM) on-off keying systems. We also experimentally demonstrate a simple demultiplexing algorithm for this scheme by utilizing only a single Stokes analyzer. At the rate of 4×10  Gbit/s, the experimental results show that the power penalty of the proposed scheme is about 1.5 dB, compared to the single PDM-IM/DD for back-to-back (B2B) transmission. Compared to B2B, just about 1.7 dB power penalty is required after 25 km Corning LEAF optical fiber transmission. Meanwhile, the performance of the polarization tracking is evaluated, and the results show that the BER fluctuation is less than 0.5 dB with a polarization scrambling rate up to 708.75 deg/s.

Computation of multi-dimensional viscous supersonic jet flow

NASA Technical Reports Server (NTRS)

Kim, Y. N.; Buggeln, R. C.; Mcdonald, H.

1986-01-01

A new method has been developed for two- and three-dimensional computations of viscous supersonic flows with embedded subsonic regions adjacent to solid boundaries. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases relevant to internal supersonic flow is presented and compared with data. Comparison between data and computation are in general excellent thus indicating that the computational technique has great promise as a tool for calculating supersonic flow with embedded subsonic regions. Finally, a User's Manual is presented for the computer code used to perform the calculations.

Computation of multi-dimensional viscous supersonic flow

NASA Technical Reports Server (NTRS)

Buggeln, R. C.; Kim, Y. N.; Mcdonald, H.

1986-01-01

A method has been developed for two- and three-dimensional computations of viscous supersonic jet flows interacting with an external flow. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases associated with supersonic jet flow is presented and compared with other calculations for axisymmetric cases. Demonstration calculations indicate that the computational technique has great promise as a tool for calculating a wide range of supersonic flow problems including jet flow. Finally, a User's Manual is presented for the computer code used to perform the calculations.

A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Yidong; Liu, Xiaodong; Luo, Hong

2015-06-01

Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time,more » while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.« less

Fast preconditioned multigrid solution of the Euler and Navier-Stokes equations for steady, compressible flows

NASA Astrophysics Data System (ADS)

Caughey, David A.; Jameson, Antony

2003-10-01

New versions of implicit algorithms are developed for the efficient solution of the Euler and Navier-Stokes equations of compressible flow. The methods are based on a preconditioned, lower-upper (LU) implementation of a non-linear, symmetric Gauss-Seidel (SGS) algorithm for use as a smoothing algorithm in a multigrid method. Previously, this method had been implemented for flows in quasi-one-dimensional ducts and for two-dimensional flows past airfoils on boundary-conforming O-type grids for a variety of symmetric limited positive (SLIP) spatial approximations, including the scalar dissipation and convective upwind split pressure (CUSP) schemes. Here results are presented for both inviscid and viscous (laminar) flows past airfoils on boundary-conforming C-type grids. The method is significantly faster than earlier explicit or implicit methods for inviscid problems, allowing solution of these problems to the level of truncation error in three to five multigrid cycles. Viscous solutions still require as many as twenty multigrid cycles.