Chen, Hongxia; Wang, Chengzhang; Ye, Jianzhong; Zhou, Hao; Yuan, Jiaojiao
2014-01-01
Decompressing inner ebullition (DIE) can reduce the extraction liquid boiling point and polyphenols oxidation in the extraction process. The aim of this study is to optimise the phenolic extraction process by DIE and to examine the antioxidant activities. The extraction process parameters were observed by central composite design. The antioxidant activity was measured using 1,1-diphenyl-2-picrylhydrazyl (DPPH) and ferric reducing power assays. The results showed that the optimal extraction condition is extract time of 90 min, temperature of 45°C, solid-liquid ratio of 1:20 g/mL, vacuum degree of - 0.08 MPa, ethanol concentration of 60%, while the phenolic content was 5.4%. The phenolic extracts from Rhus verniciflua Stokes bark had better antioxidant activities; the antioxidant activity (IC50) of the DIE was 20 μg/mL by the DPPH method. The reducing power of the phenolic extracts was significantly related to their total phenolic content (R = 0.9903). The results presented show that the DIE method is an effective method for polyphenols extraction.
Chen, Hongxia; Wang, Chengzhang; Zhou, Hao; Tao, Ran; Ye, Jianzhong; Li, Wenjun
2017-07-01
Ethyl acetate fraction (EAF) from Rhus verniciflua Stokes is an important source of bioactive compounds. The aim of this study was the tentative identification and quantification of phenolic compounds, comparison of the phenolic structure-antioxidant activity relationships. Twelve compounds of EAF belonging to polyphenol types were detected by high performance liquid chromatography and analysed on line with negative ion electrospray ionisation tandem mass spectrometry, which were ethoxy 3-hydroxy benzoic acid, gallic acid (GA), 3,4-dihydroxy amygdalic acid, gallic acid cetyl ester, protocatechuic acid (PA), fustin, ethyl gallate (EG), garbanzol, fisetin, sulfuretin, butin and 3,7-dihydroxyflavanone-4'-rhamnoside. The antioxidant activity were evaluated based on the different types of radical scavenging capacities, i.e. DPPH·, ABTS·+ and OH. The antioxidant capacity of EAF mainly depended on the GA, EG, PA, fisetin, sulfuretin and butin. The phenolics exhibited a dose-dependent behaviour and high antioxidant ability.
Cho, Namki; Lee, Ki Yong; Huh, Jungmoo; Choi, Ji Hoon; Yang, Heejung; Jeong, Eun Ju; Kim, Hong Pyo; Sung, Sang Hyun
2013-08-01
The neuroprotective potential of flavonoids within the brain comprises anti-apoptosis of neuronal cells, anti-neuroinflammation and enhancement of cognitive function. We reported that Rhus vernciflua inhibits glutamate-induced neurotoxicity in primary cultured rat cortical cells. Here we narrowed it down to get neuroprotective fractions from the plant yielding flavonoid-rich ethyl acetate fraction (PREF). Among its active flavonoids, fisetin exhibited not only inhibitory effect against lipopolysaccharide (LPS)-induced neuroinflammation by suppressing inducible nitric oxide synthase (iNOS) and cyclooxygenase (COX)-2 but also memory enhancing effects via reactivation of cAMP responsive element binding protein (CREB)-brain derived neurotrophic factor (BDNF) pathway in memory-impaired mice by scopolamine. Butein also showed a similar activity to fisetin even though to a lesser extent. The neuroprotection by PREF and selected flavonoids may involve maintenance of antioxidant defense mechanism including glutathione peroxidase (GSH-Px), glutathione reductase (GR) and superoxide dismutase (SOD). Conclusively, we demonstrate the R. vernciflua bark extract and its active flavonoids with potent neuroprotective and anti-inflammatory effects might be good therapeutic candidates as cognitive-enhancers. Copyright © 2013 Elsevier Ltd. All rights reserved.
van den Bremer, T. S.; Breivik, Ø.
2017-12-01
During its periodic motion, a particle floating at the free surface of a water wave experiences a net drift velocity in the direction of wave propagation, known as the Stokes drift (Stokes 1847 Trans. Camb. Philos. Soc. 8, 441-455). More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel and the average Eulerian flow velocity of the fluid. This paper reviews progress in fundamental and applied research on the induced mean flow associated with surface gravity waves since the first description of the Stokes drift, now 170 years ago. After briefly reviewing the fundamental physical processes, most of which have been established for decades, the review addresses progress in laboratory and field observations of the Stokes drift. Despite more than a century of experimental studies, laboratory studies of the mean circulation set up by waves in a laboratory flume remain somewhat contentious. In the field, rapid advances are expected due to increasingly small and cheap sensors and transmitters, making widespread use of small surface-following drifters possible. We also discuss remote sensing of the Stokes drift from high-frequency radar. Finally, the paper discusses the three main areas of application of the Stokes drift: in the coastal zone, in Eulerian models of the upper ocean layer and in the modelling of tracer transport, such as oil and plastic pollution. Future climate models will probably involve full coupling of ocean and atmosphere systems, in which the wave model provides consistent forcing on the ocean surface boundary layer. Together with the advent of new space-borne instruments that can measure surface Stokes drift, such models hold the promise of quantifying the impact of wave effects on the global atmosphere-ocean system and hopefully contribute to improved climate projections. This article is part of the theme issue 'Nonlinear water waves'.
An, Byoung-Ki; Kim, Je-Hun; Zheng, Lan; Moon, Byung-Hern; Lee, Kyung-Woo
2017-05-14
This study was conducted to investigate the effects of dietary detoxified Rhus verniciflua sap (RVS) on production performance, egg quality, lipid fractions of egg yolk, liver and serum, and the profile of cecal microflora in laying hens. Two hundred 52-week-old Hy-Line Brown layers were randomly divided into 4 groups with 5 replicates per group (2 hens per cage, 5 cages per replicate) and were provided with one of 4 experimental diets containing 0, 0.05, 0.1, or 0.2% RVS, for 6 weeks. Due to unequal intervals of RVS doses, the IML procedure of the SAS program was used to correct the contrast coefficients of orthogonal polynomial. There were no differences in feed intake and egg weight among the groups. Egg production increased (linearly and quadratically, p<0.05) with increasing levels of RVS. Eggshell thickness increased (linear, p<0.05) as the level of RVS in diets increased. The levels of blood cholesterol and activities of glutamic-oxaloacetic transaminase (GOT) and glutamic-pyruvic transaminase (GPT) were not altered by dietary treatments. Increasing level of RVS increased (linear, p<0.05) in population of cecal lactic acid bacteria. The content of yolk cholesterol decreased (linear, p<0.05) with increasing levels of dietary RVS, although there were no significant differences in each lipid fraction of liver. This study indicates that dietary RVS could improve laying performance and eggshell quality, and affect cecal lactic acid bacteria in a dose-dependent manner.
Metasurfaces: Simultaneous Stokes parameters
Lepetit, Thomas; Kanté, Boubacar
2015-11-01
Techniques for determining Stokes parameters, which fully define the polarization state of a wave, require multiple measurements, thus potentially leading to inaccuracies. Researchers now show how to simultaneously determine the parameters for visible light using periodic metal structures.
Induced Stokes or anti-Stokes nuclear transitions
Energy Technology Data Exchange (ETDEWEB)
Eliezer, S. [Madrid Polytechnical Univ. (Spain)]|[SOREQN, Yavne (Israel); Martinez-Val, J.M.; Velarde, G. [Madrid Polytechnical Univ. (Spain)] [and others
1995-11-01
It is suggested that laser-generated soft x rays can be used to induce Stokes or anti-Stokes nuclear transitions. Isomeric transitions in {sup 99}Tc and {sup 179}Hf are considered as Stokes and anti-Stokes transitions, respectively. It is shown that success of the proposed scheme may open the way for a gamma-ray laser. 18 refs., 2 figs.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Unsteady Stokes equations: Some complete general solutions
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
homogeneous unsteady Stokes equations are examined. A necessary and sufficient condition for a divergence-free vector to represent the velocity field of a possible unsteady Stokes flow in the absence of body forces is derived. Keywords. Complete ...
The Navier-Stokes Equations II
Masuda, Kyûya; Rautmann, Reimund; Solonnikov, Vsevolod
1992-01-01
V.A. Solonnikov, A. Tani: Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid.- W. Borchers, T. Miyakawa:On some coercive estimates for the Stokes problem in unbounded domains.- R. Farwig, H. Sohr: An approach to resolvent estimates for the Stokes equations in L(q)-spaces.- R. Rannacher: On Chorin's projection method for the incompressible Navier-Stokes equations.- E. S}li, A. Ware: Analysis of the spectral Lagrange-Galerkin method for the Navier-Stokes equations.- G. Grubb: Initial value problems for the Navier-Stokes equations with Neumann conditions.- B.J. Schmitt, W. v.Wahl: Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the Boussinesq-equations.- O. Walsh: Eddy solutions of the Navier-Stokesequations.- W. Xie: On a three-norm inequality for the Stokes operator in nonsmooth domains.
Space-time variational saddle point formulations of Stokes and Navier-Stokes equations
Guberovic, R.; Schwab, C.; Stevenson, R.
2014-01-01
The instationary Stokes and Navier-Stokes equations are considered in a simultaneously space-time variational saddle point formulation, so involving both velocities u and pressure p. For the instationary Stokes problem, it is shown that the corresponding operator is a boundedly invertible linear
Parametric Raman anti-Stokes laser
Energy Technology Data Exchange (ETDEWEB)
Grasiuk, A.Z.; Losev, L.L.; Lutsenko, A.P.; Sazonov, S.N. (Fizicheskii Institut, Moscow (USSR))
1990-10-01
A parametric Raman anti-Stokes laser utilizing compressed (50 atm) hydrogen is reported in which anti-Stokes emission at a wavelength of 433 nm (pulse width, 15 ns) is generated due to the parametric interaction between the pumping (530 nm, 50 ns) and Stokes (680 nm) beams. The parametric Raman coupling of the light fields is achieved by the positioning of a Stokes emission resonator at a phase synchronism angle relative to the pumping radiation. A power conversion efficiency of 6 percent has been demonstrated experimentally. Numerical calculations suggest that a conversion efficiency of 40 percent is possible in the stationary mode for pumping with a divergence of not more than 0.0001 rad. 5 refs.
Infrared hyperspectral imaging stokes polarimeter
Jones, Julia Craven
This work presents the design, development, and testing of a field portable imaging spectropolarimeter that operates over the short-wavelength and middle-wavelength portion of the infrared spectrum. The sensor includes a pair of sapphire Wollaston prisms and several high order retarders to produce the first infrared implementation of an imaging Fourier transform spectropolarimeter, providing for the measurement of the complete spectropolarimetric datacube over the passband. The Wollaston prisms serve as a birefringent interferometer with reduced sensitivity to vibration when compared to an unequal path interferometer, such as a Michelson. Polarimetric data are acquired through the use of channeled spectropolarimetry to modulate the spectrum with the Stokes parameter information. The collected interferogram is Fourier filtered and reconstructed to recover the spatially and spectrally varying Stokes vector data across the image. The intent of this dissertation is to provide the reader with a detailed understanding of the steps involved in the development of this infrared hyperspectral imaging polarimeter (IHIP) instrument. First, Chapter 1 provides an overview of the fundamental concepts relevant to this research. These include imaging spectrometers, polarimeters, and spectropolarimeters. A detailed discussion of channeled spectropolarimetry, including a historical study of previous implementations, is also presented. Next a few of the design alternatives that are possible for this work are outlined and discussed in Chapter 2. The configuration that was selected for the IHIP is then presented in detail, including the optical layout, design, and operation. Chapter 3 then presents an artifact reduction technique (ART) that was developed to improve the IHIP's spectropolarimetric reconstructions by reducing errors associated with non-band-limited spectral features. ART is experimentally verified in the infrared using a commercial Fourier transform spectrometer in
On the Coupling of Incompressible Stokes or Navier–Stokes and Darcy Flows Through Porous Media
Girault, V.
2012-11-03
In this chapter, we present the theoretical analysis of coupled incompressible Navier-Stokes (or Stokes) flows and Darcy flows with the Beavers-Joseph-Saffman interface condition. We discuss alternative interface and porous media models. We review some finite element methods used by several authors in this coupling and present numerical experiments.
Torre, F. la; Kenjeres, S.; Kleijn, C.R.; Moerel, J.L.P.A.
2009-01-01
Both the particle based Direct Simulation Monte Carlo (DSMC) method and a compressible Navier-Stokes based continuum method are used to investigate the flow inside micronozzles and to predict the performance of such devices. For the Navier-Stokes approach, both slip and no-slip boundary conditions
Stokes and anti-stokes stimulated Mie scattering on nanoparticle suspensions of latex
Burkhanov, I. S.; Krivokhizha, S. V.; Chaikov, L. L.
2016-12-01
Stokes and anti-Stokes shifts of stimulated concentration light scattering (SCLS, stimulated Mie scattering) in suspensions of various-sized latex nanoparticles in water were measured by the light guide scheme, under conditions of backscattering in the presence of convection.
Stokes image reconstruction for two-color microgrid polarization imaging systems.
Lemaster, Daniel A
2011-07-18
The Air Force Research Laboratory has developed a new microgrid polarization imaging system capable of simultaneously reconstructing linear Stokes parameter images in two colors on a single focal plane array. In this paper, an effective method for extracting Stokes images is presented for this type of camera system. It is also shown that correlations between the color bands can be exploited to significantly increase overall spatial resolution. Test data is used to show the advantages of this approach over bilinear interpolation. The bounds (in terms of available reconstruction bandwidth) on image resolution are also provided.
Full Stokes glacier model on GPU
Licul, Aleksandar; Herman, Frédéric; Podladchikov, Yuri; Räss, Ludovic; Omlin, Samuel
2015-04-01
Two different approaches are commonly used in glacier ice flow modeling: models based on asymptotic approximations of ice physics and full stokes models. Lower order models are computationally lighter but reach their limits in regions of complex flow, while full Stokes models are more exact but computationally expansive. To overcome this constrain, we investigate the potential of GPU acceleration in glacier modeling. The goal of this preliminary research is to develop a three-dimensional full Stokes numerical model and apply it to the glacier flow. We numerically solve the nonlinear Stokes momentum balance equations together with the incompressibility equation. Strong nonlinearities for the ice rheology are also taken into account. We have developed a fully three-dimensional numerical MATLAB application based on an iterative finite difference scheme. We have ported it to C-CUDA to run it on GPUs. Our model is benchmarked against other full Stokes solutions for all diagnostic ISMIP-HOM experiments (Pattyn et al.,2008). The preliminary results show good agreement with the other models. The major advantages of our programming approach are simplicity and order 10-100 times speed-up in comparison to serial CPU version of the code. Future work will include some real world applications and we will implement the free surface evolution capabilities. References: [1] F. Pattyn, L. Perichon, A. Aschwanden, B. Breuer, D.B. Smedt, O. Gagliardini, G.H. Gudmundsson, R.C.A. Hindmarsh, A. Hubbard, J.V. Johnson, T. Kleiner, Y. Konovalov, C. Martin, A.J. Payne, D. Pollard, S. Price, M. Ruckamp, F. Saito, S. Sugiyama, S., and T. Zwinger, Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP-HOM), The Cryosphere, 2 (2008), 95-108.
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly that this latter fact usually does not get within reach for students in first year calculus courses and secondly that calculus textbooks in general only just hint at the correspondence alluded...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...
DEFF Research Database (Denmark)
Pafilis, Evangelos; Buttigieg, Pier Luigi; Ferrell, Barbra
2016-01-01
The microbial and molecular ecology research communities have made substantial progress on developing standards for annotating samples with environment metadata. However, sample manual annotation is a highly labor intensive process and requires familiarity with the terminologies used. We have the...... and text-mining-assisted curation revealed that EXTRACT speeds up annotation by 15-25% and helps curators to detect terms that would otherwise have been missed.Database URL: https://extract.hcmr.gr/......., organism, tissue and disease terms. The evaluators in the BioCreative V Interactive Annotation Task found the system to be intuitive, useful, well documented and sufficiently accurate to be helpful in spotting relevant text passages and extracting organism and environment terms. Comparison of fully manual...
Energy Technology Data Exchange (ETDEWEB)
Grasiuk, A.Z.; Losev, L.L.; Lutsenko, A.P.; Sazonov, S.N. (Fizicheskii Institut, Moscow (USSR))
1990-05-01
Parametric generation of anti-Stokes radiation in a Raman amplifier was calculated and implemented experimentally. In the experiments, the external Stokes signal propagated at an angle to the pumping direction which corresponded to phase matching. It is shown that, in the amplification regime, the second harmonic radiation of an Nd laser (0.53 micron) in compressed (to about 20 atm) hydrogen can be converted into the first anti-Stokes component (0.43 micron) with efficiency of about 11 percent. 5 refs.
GASP-Galway astronomical Stokes polarimeter
Directory of Open Access Journals (Sweden)
Shearer A.
2010-06-01
Full Text Available The Galway Astronomical Stokes Polarimeter (GASP is an ultra-high-speed, full Stokes, astronomical imaging polarimeter based upon a Division of Amplitude Polarimeter. It has been developed to resolve extremely rapid stochastic (~ms variations in objects such as optical pulsars, magnetars and magnetic cataclysmic variables. The polarimeter has no moving parts or modulated components so the complete Stokes vector can be measured from just one exposure - making it unique to astronomy. The time required for the determination of the full Stokes vector is limited only by detector efficiency and photon fluxes. The polarimeter utilizes a modified Fresnel rhomb that acts as a highly achromatic quarter wave plate and a beamsplitter (referred to as an RBS. We present a description of how the DOAP works, some of the optical design for the polarimeter. Calibration is an important and difficult issue with all polarimeters, but particularly in astronomical polarimeters. We give a description of calibration techniques appropriate to this type of polarimeter.
Magnetohydrodynamic stokes problem for a dissipative heat ...
African Journals Online (AJOL)
Heat and Mass transfer MHD stokes problem for a dissipative heat generating fluid with radiation absorption, mass diffusion, Hall and ion-slip currents is presented. The set of governing equations for the problem are solved by a finite difference algorithm. Effects of the various parameters in the laminar boundary layer on ...
Understanding instrumental Stokes leakage in Murchison Widefield Array polarimetry
National Research Council Canada - National Science Library
Sutinjo, A; O'Sullivan, J; Lenc, E; Wayth, R. B; Padhi, S; Hall, P; Tingay, S. J
2015-01-01
...” with the Murchison Widefield Array (MWA) as an example. A long‐standing issue that has been seen here is significant instrumental Stokes leakage after calibration, particularly in Stokes Q at high frequencies...
Observation of anomalous Stokes versus anti-Stokes ratio in MoTe2 atomic layers
Goldstein, Thomas; Chen, Shao-Yu; Xiao, Di; Ramasubramaniam, Ashwin; Yan, Jun
We grow hexagonal molybdenum ditelluride (MoTe2), a prototypical transition metal dichalcogenide (TMDC) semiconductor, with chemical vapor transport methods and investigate its atomic layers with Stokes and anti-Stokes Raman scattering. We report observation of all six types of zone center optical phonons. Quite remarkably, the anti-Stokes Raman intensity of the low energy layer-breathing mode becomes more intense than the Stokes peak under certain experimental conditions, creating an illusion of 'negative temperature'. This effect is tunable, and can be switched from anti-Stokes enhancement to suppression by varying the excitation wavelength. We interpret this observation to be a result of resonance effects arising from the C excitons in the vicinity of the Brillouin zone center, which are robust even for multiple layers of MoTe2. The intense anti-Stokes Raman scattering provides a cooling channel for the crystal and opens up opportunities for laser cooling of atomically thin TMDC semiconductor devices. Supported by the University of Massachusetts Amherst, the National Science Foundation Center for Hierarchical Manufacturing (CMMI-1025020) and Office of Emerging Frontiers in Research and Innovation (EFRI-1433496).
Stokes-polarimetry imaging of tissue
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
Polygon reduction of 3D objects using Stokes' theorem.
Kim, Nam H; Yoo, Sun K; Lee, Kyoung S
2003-07-01
Surface over volume rendering can be useful for many applications. However, the tremendously large number of polygons composing the surface primitives should be reduced to a manageable size so as to utilize the capability of low cost hardware and software rendering engines, a standard Internet protocol and VRML format. In this paper, we propose a novel algorithm that deletes several vertices simultaneously by forming a closed arbitrary shaped boundary. The Stokes' theorem, used in electro-magnetic field analysis, was newly adapted to extract the arbitrary shaped boundary. The simultaneous deletion procedure provides a computational gain and increases the reduction ratio without sacrificing the topological distortion of the original mesh. Numerically synthesized polygonal objects and real CT data were tested to evaluate the performance of the new algorithm and to demonstrate the possibility of a medical rendering application. The new algorithm outperforms the conventional decimation algorithm in both computational and reduction efficiency.
The Galway astronomical Stokes polarimeter: optical development
Directory of Open Access Journals (Sweden)
Sheehan B.
2010-06-01
Full Text Available The acquisition time of astronomical polarimeters has in the past been restricted to by the use of polarimeters utilizing modulated or rotating components [1]. If the polarisation state being measured is changing in the order of nanoseconds, how does one measure this? The Galway Astronomical Stokes Polarimeter (GASP is an instantaneous full Stokes Division Of Amplitude Polarimeter (DOAP that has been developed for astronomical imaging polarimetry. It also uses just one camera thus restricting the acquisition time to photon statistics. Following the work of Compain and Drévillon [2], the main component - the Retarding Beam-Splitter, was redesigned and enhanced for imaging use. We present how the polarization and imaging optics were developed to create a broadband imaging instantaneous polarimeter.
Complete Solutions to Extended Stokes' Problems
Directory of Open Access Journals (Sweden)
Chi-Min Liu
2008-01-01
Full Text Available The main object of the present study is to theoretically solve the viscous flow of either a finite or infinite depth, which is driven by moving plane(s. Such a viscous flow is usually named as Stokes' first or second problems, which indicates the fluid motion driven by the impulsive or oscillating motion of the boundary, respectively. Traditional Stokes' problems are firstly revisited, and three extended problems are subsequently examined. Using some mathematical techniques and integral transforms, complete solutions which can exactly capture the flow characteristics at any time are derived. The corresponding steady-state and transient solutions are readily determined on the basis of complete solutions. Current results have wide applications in academic researches and are of significance for future studies taking more boundary conditions and non-Newtonian fluids into account.
Stokes equations with penalised slip boundary conditions
Dione, Ibrahima; Tibirna, Cristian; Urquiza, José
2013-07-01
We consider the finite-element approximation of Stokes equations with slip boundary conditions imposed with the penalty method. In the case of a smooth curved boundary, our numerical results suggest that curved finite elements, regularised normal vectors or reduced integration techniques can be used to avoid a Babuska's-type paradox and ensure the convergence of finite-element approximations to the exact solution. Convergence orders with these remedies are also compared.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....
Adrian Stokes and the portrait of Melanie Klein.
Sayers, Janet
2015-08-01
This paper focuses on the offer by the art writer Adrian Stokes to commission and pay for a portrait of the psychoanalyst Melanie Klein by the artist William Coldstream. It details some of the precursors of this offer in Stokes's preceding involvement first with Klein and then with Coldstream; her response to this offer; and its outcome and aftermath in Stokes's subsequent writing about Klein and Coldstream. Copyright © 2015 Institute of Psychoanalysis.
Clustering algorithms for Stokes space modulation format recognition
DEFF Research Database (Denmark)
Boada, Ricard; Borkowski, Robert; Tafur Monroy, Idelfonso
2015-01-01
Stokes space modulation format recognition (Stokes MFR) is a blind method enabling digital coherent receivers to infer modulation format information directly from a received polarization-division-multiplexed signal. A crucial part of the Stokes MFR is a clustering algorithm, which largely...... for discriminating between dual polarization: BPSK, QPSK, 8-PSK, 8-QAM, and 16-QAM. We determine essential performance metrics for each clustering algorithm and modulation format under test: minimum required signal-to-noise ratio, detection accuracy and algorithm complexity....
Historical revision of the differential Stokes-Mueller formalism: discussion.
Arteaga, Oriol
2017-03-01
The differential Stokes-Mueller matrix formalism expresses the local evolution of the Mueller matrix or the Stokes parameters for light propagating through a homogeneous optical medium. This paper presents a historical revision of the development of the differential Stokes-Mueller matrix formalism and highlights several important early contributions that have been overlooked. Particularly relevant is that this formalism was pioneered as early as 1929 by Paul Soleillet, almost 50 years earlier than it has been usually assumed. This historical revision demonstrates that several different authors independently formulated the differential Stokes-Mueller formalism during the 20th century and they found equivalent results studying the propagation problem from different approaches.
A fast Stokes polarimeter: preliminary design
Vaughn, Israel J.; Alenin, Andrey S.; Tyo, J. Scott
2017-09-01
Designing polarimetric systems directly in the channel space has provided insight into how to design new types of polarimetric systems, including systems which use carriers in hybrid domains of space, time, or spectrum. Utilizing linear systems theory, we present a full Stokes imaging polarimeter design which has the potential to operate at half the frame rate of the imaging sensor of the system by utilizing a hybrid spatio-temporal carrier design. The design places channels on the faces and the edges of the Nyquist cube resulting in the potential for half the Nyquist limit to be achieved, provided that the spatial frequency of the objects being imaged are bandlimited to less than 0.25 cycles per pixel. If the objects are not spatially bandlimited, then the achievable temporal bandwidth is more difficult to analyze. However, a spatio-temporal tradeoff still exists allowing for increased temporal bandwidth. We present the design of a "Fast Stokes'' polarimeter and some simulated images using this design.
Kneipp, K.; Kneipp, H.; Corio, P.; Brown, S. D. M.; Shafer, K.; Motz, J.; Perelman, L. T.; Hanlon, E. B.; Marucci, A.; Dresselhaus, G.; Dresselhaus, M. S.
2000-04-01
Surface enhancement factors of at least 1012 for the Raman scattering of single-walled carbon nanotubes in contact with fractal silver colloidal clusters result in measuring very narrow Raman bands corresponding to the homogeneous linewidth of the tangential C-C stretching mode in semiconducting nanotubes. Normal and surface-enhanced Stokes and anti-Stokes Raman spectra are discussed in the framework of selective resonant Raman contributions of semiconducting or metallic nanotubes to the Stokes or anti-Stokes spectra, respectively, of the population of vibrational levels due to the extremely strong surface-enhanced Raman process, and of phonon-phonon interactions.
Mazumder, Nirmal; Xiang, Lu Yun; Qiu, Jianjun; Kao, Fu-Jen
2017-04-01
The changes of the morphology during heating and the degree of crystallinity of dry and hydrated starch granules are investigated using second harmonic generation (SHG) based Stokes polarimetry. A spatial distribution of various polarization parameters, such as the degree of polarization (DOP), the degree of linear polarization (DOLP), and the degree of circular polarization (DOCP) are extracted and compared with the two dimensional second harmonic (SH) Stokes images of starch granules. The SH signal from hydrated and dry starch on heating differed significantly in DOLP and DOCP values, indicating that hydrated starch has a greater degree of ultrastructural amylopectin disorder. The detail of denaturation and the phase transition of hydrated starch demonstrate the significant influence of thermal processing.
Tip loss correction for actuator / Navier Stokes computations
DEFF Research Database (Denmark)
Shen, Wen Zhong; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming
2004-01-01
The new tip loss correction, initially developed for ID BEM computations [1], is now extended to 2D Actuator Disc / Navier-Stokes (AD/NS) computations and 3D Actuator Line / Navier-Stokes (AL/NS) computations. As shown in the paper, the tip loss correction is an important and necessary step...
Stokes Space in Direct-Detection Data Transmission Systems
DEFF Research Database (Denmark)
Estaran Tolosa, Jose Manuel; Lu, Xiaofeng; Zibar, Darko
2015-01-01
Stokes-based processing permits complete and phase-insensitive characterization of the field’s SOP, readily unlocking polarization diversity in transmission systems where DD is desired. We present an overview on Stokes notions and most recent achievements in this context....
Analyticity estimates for the Navier-Stokes equations
DEFF Research Database (Denmark)
Herbst, I.; Skibsted, Erik
We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in and prove a stability result...
Stokes Polarimetry at the Kodaikanal Tower Tunnel Telescope
Indian Academy of Sciences (India)
A Stokes Polarimeter has been developed using a masked CCD arrangement for the measurement of the vector magnetic field of sunspots. Charge shifting within the CCD is used to record near simultaneous orthogonal polarisation. The testing of the Stokes Polarimeter and the behavior of the integrated system combined ...
A note on the Stokes operator and its powers
Guermond, Jean-Luc
2010-04-28
The so-called Stokes operator is an important tool in the analysis of the solutions of the Navier-Stokes equations and their numerical approximation. The aim of this note is to clarify certain properties of the fractional powers of this operator which are sometimes misused. © 2010 Korean Society for Computational and Applied Mathematics.
The Proteus Navier-Stokes code
Towne, Charles E.; Bui, Trong T.; Cavicchi, Richard H.; Conley, Julianne M.; Molls, Frank B.; Schwab, John R.
1992-01-01
An effort is currently underway at NASA Lewis to develop two- and three-dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. The emphasis in the development of Proteus is not algorithm development or research on numerical methods, but rather the development of the code itself. The objective is to develop codes that are user-oriented, easily-modified, and well-documented. Well-proven, state-of-the-art solution algorithms are being used. Code readability, documentation (both internal and external), and validation are being emphasized. This paper is a status report on the Proteus development effort. The analysis and solution procedure are described briefly, and the various features in the code are summarized. The results from some of the validation cases that have been run are presented for both the two- and three-dimensional codes.
Generalized extended Navier-Stokes theory
DEFF Research Database (Denmark)
Hansen, J. S.; Daivis, Peter J.; Dyre, Jeppe C.
2013-01-01
and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies......The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present...... in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime...
Aquarius Third Stokes Parameter Measurements: Initial Results
Utku, Cuneyt; Vine, David M Le; Abraham, S.; Piepmeier, J.
2012-01-01
The Aquarius/SAC-D observatory was launched on June 10, 2011 and the Aquarius instrument has been collecting data continuously since late August. One of the unique features of the L-band radiometers comprising Aquarius is the presence of a polarimetric channel to measure the third Stokes parameter. The purpose is to provide a measure of Faraday rotation, which can be important for remote sensing at L-band, especially in the case of remote sensing of salinity which requires high precision. Initial results are presented here showing a reasonable agreement between retrieved and modeled Faraday rotation and also the "noisy" behavior at land-water boundaries and other mixed scenes predicted by theory.
Topology optimization of 3D Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan
Topology optimization has been applied to a multitude of physical systems and is now a mature technology used in industrial practice, see [1] for an overview. Borrvall and Petersson [2] introduced topology optimization of Stokes flow problems which initiated works on extending topology optimization...... to different flow problems. However, this research has focused on 2D fluid modelling, which limits the practical impact of the computed designs. The explanation of the limitation is that the finite size domain used in topology optimization problems ensures that the velocity components couples, even for Stokes...... only. The motivation for considering topology optimization in 3D Stokes flow originates from micro fluidic systems. At small scales the Stokes equations are a reasonable mathematical model to use for the fluid behavior. Physically Stokes flow is an exotic inertia free flow, which in practice...
Coherent anti-Stokes Raman scattering under electric field stimulation
Capitaine, Erwan; Ould Moussa, Nawel; Louot, Christophe; Lefort, Claire; Pagnoux, Dominique; Duclère, Jean-René; Kaneyasu, Junya F.; Kano, Hideaki; Duponchel, Ludovic; Couderc, Vincent; Leproux, Philippe
2016-12-01
We introduce an experiment using electro-CARS, an electro-optical method based on the combination of ultrabroadband multiplex coherent anti-Stokes Raman scattering (M-CARS) spectroscopy and electric field stimulation. We demonstrate that this method can effectively discriminate the resonant CARS signal from the nonresonant background owing to a phenomenon of molecular orientation in the sample medium. Such molecular orientation is intrinsically related to the induction of an electric dipole moment by the applied static electric field. Evidence of the electro-CARS effect is obtained with a solution of n -alkanes (CnH2 n +2 , 15 ≤n ≤40 ), for which an enhancement of the CARS signal-to-noise ratio is achieved in the case of CH2 and CH3 symmetric/asymmetric stretching vibrations. Additionally, an electric-field-induced second-harmonic generation experiment is performed in order to corroborate the orientational organization of molecules due to the electric field excitation. Finally, we use a simple mathematical approach to compare the vibrational information extracted from electro-CARS measurements with spontaneous Raman data and to highlight the impact of electric stimulation on the vibrational signal.
Origins of Stokes shift in PbS nanocrystals
Voznyy, Oleksandr
2017-10-27
Stokes shift, an energy difference between the excitonic absorption and emission, is a property of colloidal quantum dots (CQDs) typically ascribed to splitting between dark and bright excitons. In some materials, e.g., PbS, CuInS2, CdHgTe, a Stokes shift of up to 200 meV is observed, substantially larger than the estimates of dark-bright state splitting or vibronic relaxations. The shift origin remains highly debated, as contradictory signatures of both surface and bulk character were reported for the Stokes-shifted electronic state. Here we show that the energy transfer among CQDs in a polydispersed ensemble in solution suffices to explain the excess Stokes shift. This energy transfer is primarily due to CQD aggregation, and can be substantially eliminated by extreme dilution, higher-viscosity solvent, or better-dispersed colloids. Our findings highlight that ensemble polydispersity remains the primary source of the Stokes shift in CQDs in solution, propagating into the Stokes shift in films and the open-circuit voltage deficit in CQD solar cells. Improved synthetic control can bring notable advancements in CQD photovoltaics, and the Stokes shift continues to provide a sensitive and significant metric to monitor ensemble size distribution.
Ghassemi, P.; Shupp, J. W.; Venna, S.; Boisvert, M. E.; Flanagan, K. E.; Jordan, M. H.; Ramella-Roman, J. C.
2012-02-01
Skin cancer is the most common and most rapidly increasing form of cancer in the world. Optimal treatment of skin cancer before it reaches metastasis depends critically on early diagnosis. Usually physicians will measure some outward features to diagnose malignancy of pigmented skin lesion. These are mostly morphological features like border irregularity, size, shape, and color. Valuable information can be obtained from the analysis of skin roughness. Previously, we developed a hemispherical imaging Stokes polarimeter to monitor skin cancer based on a roughness assessment of the epidermis. In this study, Stokes images were analyzed to measure polarization properties of skin samples such as the principal angle of the polarization ellipse and the degree of polarization. A processing algorithm based on morphological operators was also developed and applied on Stokes images to extract shape information. Finally, an appropriate classifier was designed to determine the type of lesion based on morphological features as well as the roughness information. Clinical evaluation of the technique was performed on patients with benign nevi, melanocytic nevi, melanoma, and normal skin.
Full Stokes polarimeter for characterization of fiber optic gyroscope coils.
Lompado, Arthur; Reinhardt, John C; Heaton, L Chris; Williams, Jeff L; Ruffin, Paul B
2009-05-11
We describe the design, construction, calibration, and validation of a Stokes vector polarimeter for investigating the polarization characteristics of fiber optic gyroscope coils. The device measures the complete Stokes vector, and reports conventional polarization properties including the Degree of Polarization (DoP), the orientation and Degree of Linear Polarization (DoLP), and the handedness and Degree of Circular Polarization (DoCP). The sensor operates at 1550 nm and employs a division of aperture optical architecture to acquire full Stokes vectors at 8 kHz while calculating polarization properties at a rate of 200 Hz. Preliminary measurements performed on both traditionally and unconventionally wound gyroscope coils are also presented.
Preconditioning the pressure operator for the time dependent Stokes problem
Energy Technology Data Exchange (ETDEWEB)
Bramble, J.H.; Pasciak, J.E.
1994-12-31
In implicit time stepping procedures for the linearized Navier Stokes equations, a linear perturbed Stokes problem must be solved at each time step. Many methods for doing this require a good preconditioner for the resulting pressure operator (Schur complement). In contrast to the time independent Stokes equations where the pressure operator is well conditioned, the pressure operator for the perturbed system becomes more illconditioned as the time step is reduced (and/or the Reynolds number is increased). The authors describe the method for solving the coupled velocity/pressure systems and, in particular, show how to construct good preconditioners for the poorly conditioned pressure operator.
Navier-Stokes equations an introduction with applications
Łukaszewicz, Grzegorz
2016-01-01
This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior o...
Asymptotic behavior of stochastic two-dimensional Navier–Stokes ...
Indian Academy of Sciences (India)
dimensional stochastic Navier–Stokes equations in the presence of delays. The results extend some of the existing results. Author Affiliations. Huabin Chen1. Department of Mathematics, School of Science, Nanchang University, Nanchang 330031, ...
Ávila, Francisco J.; del Barco, Oscar; Bueno, Juan M.
2017-10-01
Collagen organization has been analyzed at both external and internal scales by combining Stokes-vector polarimetry and second harmonic generation microscopy. A significant linear relationship between the diattenuation and the external collagen organization was found. The dominant orientation of the collagen fibers was found to run parallel to the axis of diattenuation. Information on the collagen chirality was obtained from the circular dichroism, which showed also a strong dependence with the internal collagen organization. The results show that certain polarimetric parameters might be useful to extract quantitative information and characterize collagen arrangement.
Continuum Navier-Stokes modelling of water ow past fullerene molecules
DEFF Research Database (Denmark)
Walther, J. H.; Popadic, A.; Koumoutsakos, P.
We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...... as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the computational cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently...
Continuum Navier-Stokes modelling of water flow past fullerene molecules
DEFF Research Database (Denmark)
Walther, J. H.; Popadic, A.; Koumoutsakos, P.
We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...... as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the computational cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently...
Gu, Mingming
2018-01-08
The effects of moderate levels of chirp in the pump and Stokes pulses on chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering (CPP fs CARS) were investigated. The frequency chirp in the pump and Stokes pulses was introduced by placing SF11 glass disks with thicknesses of 10 mm or 20 mm in the optical path for these beams. The magnitude of the chirp in the probe beam was much greater and was induced by placing a 30-cm rod of SF10 glass in the beam path. The temperature measurements were performed in hydrogen/air non-premixed flames stabilized on a Hencken burner at equivalence ratios of 0.3, 0.5, 0.7, and 1.0. We performed measurements with no disks in pump and Stokes beam paths, and then with disks of 10 mm and 20 mm placed in both beam paths. The spectrum of the nonresonant background four-wave mixing signal narrowed considerably with increasing pump and Stokes chirp, while the resonant CARS signal was relatively unaffected. Consequently, the interference of the nonresonant background with the resonant CARS signal in the frequency-spread dephasing region of the spectrum was minimized. The increased rate of decay of the resonant CARS signal with increasing temperature was thus readily apparent. We have started to analyze the CPP fs CARS thermometry data and initial results indicate improved accuracy and precision are obtained due to moderate chirp in the pump and Stokes laser pulses.
3D Topology optimization of Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Dammann, Bernd
The present talk is concerned with the application of topology optimization to creeping flow problems in 3D. This research is driven by the fact that topology optimization has proven very successful as a tool in academic and industrial design problems. Success stories are reported from such diverse...... fields as solid mechanics and optics and is due to the method's flexibility in the (rough) parametrization of the design, see [1] and the reference therein for an overview. Borrvall and Petersson [2] is the seminal reference for topology optimization in fluid flow problems. They considered design...... of energy efficient devices for 2D Stokes flow. Creeping flow problems are described by the Stokes equations which model very viscous fluids at macro scales or ordinary fluids at very small scales. The latter gives the motivation for topology optimization problems based on the Stokes equations being a model...
Topology optimization of 3D Stokes flow problems
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Sigmund, Ole; Bendsøe, Martin P.
The design of MEMS devices have benefitted from the topology optimization tool and complicated layout problems have been solved, see [1] for an overview. This research is aimed at micro fluidic devices known as micro-Total-Analysis-Systems (muTAS) where the main physical phenomena originate from...... optimization tool for micro fluidic design problems by considering design of energy efficient devices subjected to Stokes flow. Several researchers have elaborated on [2], however, this research has focused on 2D fluid modelling which limits the practical impact of the computed designs. This limitation...... is caused by the finite size domain used in topology optimization problems which ensures that the velocity components couples, even for Stokes flow [3]. Physically Stokes flow is an exotic inertia free flow, which in practice complicates mixing by passive devices. Passive mixing devices are relevant...
Applied Analysis of the Navier-Stokes Equations
Doering, Charles R.; Gibbon, J. D.
1995-04-01
The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the fundamental dynamics of fluid motion. They are applied routinely to problems in engineering, geophysics, astrophysics, and atmospheric science. This book is an introductory physical and mathematical presentation of the Navier-Stokes equations, focusing on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion. The goal of the book is to present a mathematically rigorous investigation of the Navier-Stokes equations that is accessible to a broader audience than just the subfields of mathematics to which it has traditionally been restricted. Therefore, results and techniques from nonlinear functional analysis are introduced as needed with an eye toward communicating the essential ideas behind the rigorous analyses. This book is appropriate for graduate students in many areas of mathematics, physics, and engineering.
Cheyne-Stokes respiration in patients hospitalised for heart failure
Directory of Open Access Journals (Sweden)
Mared Lena
2004-09-01
Full Text Available Abstract Background Previous studies showing a strong relationship between Cheyne-Stokes respiration and the severity of left ventricular systolic dysfunction have usually been done in selected patient populations with lower age and a higher proportion of males than the "typical" in-hospital patient with heart failure. The purpose of the present study was test the strength of this relationship in unselected patients admitted to hospital due to decompensated chronic heart failure. Methods We evaluated 191 patients (32% women, mean age 73 years, ready for discharge from the heart failure unit in the University Hospital of Malmö, Sweden. The patients underwent echocardiography for determination of left ventricular ejection fraction and left ventricular inner diastolic diameter. A respiratory investigation during sleep was performed the last night before discharge. Results We found that 66% of the patients had Cheyne-Stokes respiration more than 10% of the total recording time. Only 7 (3.6% of the patients had predominantly obstructive apnoeas. There was a significant but very weak relationship between left ventricular ejection fraction and left ventricular inner diastolic diameter on one hand and Cheyne-Stokes respiration on the other. Age was a stronger determinant of Cheyne-Stokes respiration than any of the cardiac or other clinical variables. Conclusion Although presence of Cheyne-Stokes respiration indicates left ventricular dysfunction, its severity seems only weakly related to the severity of heart failure. Age was found to be a stronger determinant, which may reflect the underlying age-dependency found also in healthy subjects. Due to age restrictions or other selection criteria, the importance of age may have been underestimated in many previous studies on factors associated with Cheyne-Stokes respiration.
Topology Optimization of Large Scale Stokes Flow Problems
DEFF Research Database (Denmark)
Aage, Niels; Poulsen, Thomas Harpsøe; Gersborg-Hansen, Allan
2008-01-01
This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs.......This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs....
Medidas de viscosidad: viscosímetro. Ley de Stokes
Pérez Rodríguez, Jorge; Miret Marí, Juan José; Espinosa Tomás, Julián; Caballero Caballero, María Teresa
2010-01-01
Guión de la pŕactica de Física de primero del grado de Óptica y Optometría "Medidas de viscosidad: Viscosímetro. Ley de Stokes" Objetivos - Medir la viscosidad de un líquido problema con el viscosímetro. - Señalar la ventaja de la determinación de magnitudes relativas. - Medir la viscosidad de un líquido problema aplicando la ley de Stokes.
KNOW-BLADE task-4 report: Navier-Stokes aeroelasticity
DEFF Research Database (Denmark)
Politis, E.S.; Nikolaou, I.G.; Chaviaropoulos, P.K.
2004-01-01
wind turbine blade have been combined with 2D and 3D unsteady Navier-Stokes solvers. The relative disadvantage of the quasi-3D approach (where the elastic solver is coupled with a 2D Navier-Stokes solver) isits inability to model induced flow. The lack of a validation test case did not allow...... the computations for the full blade, 2D computations for the so-called “typical section” have been carried out. The 2D aeroelastic tools resulted in similar aerodynamic damping values. Qualitative agreement was better for the lead-lagmode. The presence of roughness tapes has a small, rather negligible impact...
Cavitation Modeling in Euler and Navier-Stokes Codes
Deshpande, Manish; Feng, Jinzhang; Merkle, Charles L.
1993-01-01
Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.
Inversions of High-Cadence SOLIS-VSM Stokes Observations
Fischer, C.E.; Keller, C.U.; Snik, F.
2008-01-01
We have processed full-Stokes observations made with the SOLIS-VSM using Fe I 630.15 and Fe I 630.25 nm. The data have high spectral and temporal resolution, moderate spatial resolution, and large polarimetric sensitivity and accuracy. We use the code LILIA, an LTE inversion code written by
Stokes flow with slip and Kuwabara boundary conditions
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
But, it is sufficient to obtain a relatively simple analytical expression that takes into account the effect of the ... symmetric flow that has a simple analytical solution in closed form, and thus can be used for drag calculations. ..... [6] Stokes G G, On the effects of internal friction of fluids on pendulums, J. Trans. Camb. Philos. Soc.
An optimal adaptive finite element method for the Stokes problem
Kondratyuk, Y.; Stevenson, R.
2008-01-01
A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur
Unstructured Navier-Stokes Analysis of Full TCA Configuration
Frink, Neal T.; Pirzadeh, Shahyar Z.
1999-01-01
This paper presents an Unstructured Navier-Stokes Analysis of Full TCA (Technology Concept Airplane) Configuration. The topics include: 1) Motivation; 2) Milestone and approach; 3) Overview of the unstructured-grid system; 4) Results on full TCA W/B/N/D/E configuration; 5) Concluding remarks; and 6) Future directions.
New solutions of stokes problem for an oscillating plate using ...
African Journals Online (AJOL)
New solutions of stokes problem for an oscillating plate using Laplace transform. Ehsan Ellahi Ashraf, Muhammad R Mohyuddin. Abstract. An exact solution of the flow of a Newtonian fluid on a porous plate is obtained when the plate at y = 0 is oscillating with the amplitude β and oscillating frequency ω with the assumption ...
Topology optimization of mass distribution problems in Stokes flow
DEFF Research Database (Denmark)
Gersborg-Hansen, Allan; Berggren, Martin; Dammann, Bernd
We consider topology optimization of mass distribution problems in 2D and 3D Stokes flow with the aim of designing devices that meet target outflow rates. For the purpose of validation, the designs have been post processed using the image processing tools available in FEMLAB. In turn, this has en...
Stokes flow with slip and Kuwabara boundary conditions
Indian Academy of Sciences (India)
... distributed parallel circular cylinder or spheres in uniform viscous flow are investigated with slip boundary condition under Stokes approximation using particle-in-cell model technique and the result compared with the no-slip case. The corresponding problem of streaming flow past spheroidal particles departing but little in ...
Eulerian derivations of non-inertial Navier-Stokes equations
CSIR Research Space (South Africa)
Combrinck, MA
2014-09-01
Full Text Available The paper presents an Eulerian derivation of the non-inertial Navier-Stokes equations as an alternative to the Lagrangian fluid parcel approach. This work expands on the work of Kageyama and Hyodo [1] who derived the incompressible momentum equation...
Solutions of Navier-Stokes Equation with Coriolis Force
Directory of Open Access Journals (Sweden)
Sunggeun Lee
2017-01-01
Full Text Available We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.
Navier-Stokes Calculations of Helicopter Fuselage Flowfield and Loads
DEFF Research Database (Denmark)
M, Costes; N, Kroll; P., Renzoni
1999-01-01
This paper describes the theoretically basedactivities conducted during the first year of theBrite/Euram Helifuse Porgramme. These activitiesmainly consisted of the numerical prediction ofhelicopter fuselage flowfields with existing Navier-Stokes solvers on a number of pre-selectedcases, taken ou...
Topology optimization considering design-dependent Stokes flow loads
Picelli, R.; Vicente, W.M.; Pavanello, R.; van Keulen, A.; Li, Qing; Steven, Grant P.; Zhang, Zhongpu
2015-01-01
This article presents an evolutionary topology optimization method for mean compliance minimization of structures under design-dependent viscous fluid flow loads. The structural domain is governed by the elasticity equation and the fluid by the incompressible Stokes flow equations. When the
The Navier-Stokes Equations Theory and Numerical Methods
Masuda, Kyûya; Rautmann, Reimund; Solonnikov, Vsevolod
1990-01-01
These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.
Compact fibre-based coherent anti-Stokes Raman scattering ...
Indian Academy of Sciences (India)
Abstract. We demonstrate a new approach to CARS spectroscopy by efficiently syn- thesizing synchronized narrow-bandwidth (less than 10 cm−1) pump and Stokes pulses. (frequency difference continuously tunable upto ~3000 cm−1) based on spectral compres- sion together with second harmonic generation (in ...
Compact fibre-based coherent anti-Stokes Raman scattering ...
Indian Academy of Sciences (India)
We demonstrate a new approach to CARS spectroscopy by efficiently synthesizing synchronized narrow-bandwidth (less than 10 cm-1) pump and Stokes pulses (frequency difference continuously tunable upto ∼ 3000 cm-1) based on spectral compression together with second harmonic generation (in periodically-poled ...
Construction and application of an automatic Stokes parameters photopolarimeter
Directory of Open Access Journals (Sweden)
Soankwan, C.
2004-03-01
Full Text Available Stokes parameters are used to describe the polarization state of the beam. The Stokes parameters can be used to analyze the properties of a sample in terms of retardation and specific rotation. As several conventional instruments for measuring the Stokes parameters involve many procedures and a lot of time is required, the application area is limited. Therefore, to lessen the measuring period and widen the application area, in this research, an automatic instrument for determining the state of polarization based on a technique employing Fourier analysis coupled with some simple computer controlled electronic circuits are proposed. The technique of this measurement is called “Fourier analysis using a rotating quarter wave plate”. Thissystem is composed of a rotating quarter wave plate controlled by a stepping motor, a fixed linear horizontal polarizer and a detector. The intensities obtained from the receiving detector are analyzed with Simpson 's method and Fourier Analysis to calculate the Stokes parameters. The performance of the instrument was preliminary examined by measuring several known polarized beams. In addition, the instrument was used as a tool to determine the specific rotation of D-glucose and phase shift of known retardances. The experimentalresults were found to be in agreement with theoretical results.
Analysis of Stokes waves theory as a diffusion problem | Okeke ...
African Journals Online (AJOL)
This mathematical model concerns the theory of Stokes waves. These wave types belong to the class of ocean surface waves found in deep and intermediate waters. In this consideration, the fifth order expansion was obtained using Korteweg de Vries equation with diffusion term. This study suggests that the phase velocity ...
Further on stokes expansions for the finite amplitude water waves ...
African Journals Online (AJOL)
An analytic method is applied to study the higher order approximate solution of Stokes waves. For comparison and effective analysis, solutions of first to fifth order approximations are studied. From the various expressions derived, the numerical computations and the graphical solutions, there is a gradual increase in the ...
Getting in Shape : Swimming with Stokes and Surfing with Brinkman
Bet, B.P.|info:eu-repo/dai/nl/370530667
2018-01-01
In this dissertation, we investigate the effect of shape on the motion of microscopic particles that perform a swimming motion or ‘surf’, driven by an external flow, through microscopic channels. These motions take place in a fluid, and fluid motion is in general described by the Navier-Stokes
On iterative methods for the incompressible Stokes problem
Rehman, M. ur; Geenen, T.; Vuik, C.; Segal, G.; MacLachlan, S.P.
2011-01-01
In this paper, we discuss various techniques for solving the system of linear equations that arise from the discretization of the incompressible Stokes equations by the finite-element method. The proposed solution methods, based on a suitable approximation of the Schur-complement matrix, are shown
The Stokes-Einstein relation at moderate Schmidt number.
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.
Bohlin, Alexis; Patterson, Brian D.; Kliewer, Christopher J.
2017-11-01
In many fields of study, from coherent Raman microscopy on living cells to time-resolved coherent Raman spectroscopy of gas-phase turbulence and combustion reaction dynamics, the need for the capability to time-resolve fast dynamical and nonrepetitive processes has led to the continued development of high-speed coherent Raman methods and new high-repetition rate laser sources, such as pulse-burst laser systems. However, much less emphasis has been placed on our ability to detect shot to shot coherent Raman spectra at equivalently high scan rates, across the kilohertz to megahertz regime. This is beyond the capability of modern scientific charge coupled device (CCD) cameras, for instance, as would be employed with a Czerny-Turner type spectrograph. As an alternative detection strategy with megahertz spectral detection rate, we demonstrate dispersive Fourier transformation detection of pulsed (∼90 ps) coherent Raman signals in the time-domain. Instead of reading the frequency domain signal out using a spectrometer and CCD, the signal is transformed into a time-domain waveform through dispersive Fourier transformation in a long single-mode fiber and read-out with a fast sampling photodiode and oscilloscope. Molecular O- and S-branch rotational sideband spectra from both N2 and H2 were acquired employing this scheme, and the waveform is fitted to show highly quantitative agreement with a molecular model. The total detection time for the rotational spectrum was 20 ns, indicating an upper limit to the detection frequency of ∼50 MHz, significantly faster than any other reported spectrally-resolved coherent anti-Stokes Raman detection strategy to date.
Pure-rotational H2 thermometry by ultrabroadband coherent anti-Stokes Raman spectroscopy
Courtney, Trevor L.; Bohlin, Alexis; Patterson, Brian D.; Kliewer, Christopher J.
2017-06-01
Coherent anti-Stokes Raman spectroscopy (CARS) is a sensitive technique for probing highly luminous flames in combustion applications to determine temperatures and species concentrations. CARS thermometry has been demonstrated for the vibrational Q-branch and pure-rotational S-branch of several small molecules. Practical advantages of pure-rotational CARS, such as multi-species detection, reduction of coherent line mixing and collisional narrowing even at high pressures, and the potential for more precise thermometry, have motivated experimental and theoretical advances in S-branch CARS of nitrogen (N2), for example, which is a dominant species in air-fed combustion processes. Although hydrogen (H2) is of interest given its prevalence as a reactant and product in many gas-phase reactions, laser bandwidth limitations have precluded the extension of CARS thermometry to the H2 S-branch. We demonstrate H2 thermometry using hybrid femtosecond/picosecond pure-rotational CARS, in which a broadband pump/Stokes pulse enables simultaneous excitation of the set of H2 S-branch transitions populated at flame temperatures over the spectral region of 0-2200 cm-1. We present a pure-rotational H2 CARS spectral model for data fitting and compare extracted temperatures to those from simultaneously collected N2 spectra in two systems of study: a heated flow and a diffusion flame on a Wolfhard-Parker slot burner. From 300 to 650 K in the heated flow, the H2 and N2 CARS extracted temperatures are, on average, within 2% of the set temperature. For flame measurements, the fitted H2 and N2 temperatures are, on average, within 5% of each other from 300 to 1600 K. Our results confirm the viability of pure-rotational H2 CARS thermometry for probing combustion reactions.
Stokes phenomena in discrete Painlevé II.
Joshi, N; Lustri, C J; Luu, S
2017-02-01
We consider the asymptotic behaviour of the second discrete Painlevé equation in the limit as the independent variable becomes large. Using asymptotic power series, we find solutions that are asymptotically pole-free within some region of the complex plane. These asymptotic solutions exhibit Stokes phenomena, which is typically invisible to classical power series methods. We subsequently apply exponential asymptotic techniques to investigate such phenomena, and obtain mathematical descriptions of the rapid switching behaviour associated with Stokes curves. Through this analysis, we determine the regions of the complex plane in which the asymptotic behaviour is described by a power series expression, and find that the behaviour of these asymptotic solutions shares a number of features with the tronquée and tri-tronquée solutions of the second continuous Painlevé equation.
Transonic airfoil and wing design using Navier-Stokes codes
Yu, N. J.; Campbell, R. L.
1992-01-01
An iterative design method has been implemented into 2D and 3D Navier-Stokes codes for the design of airfoils or wings with given target pressure distributions. The method begins with the analysis of an initial geometry, and obtains the analysis pressure distributions of that geometry. The differences between analysis pressures and target pressures are used to drive geometry changes through the use of a streamline curvature method. This paper describes the procedure that makes the iterative design method work for Navier-Stokes codes. Examples of 2D airfoil design, and 3D wing design are included. It is demonstrated that the method is highly effective for airfoil or wing design at flow conditions where no substantial separation occurs. Problems encountered in the airfoil design with shock induced flow separations are discussed.
Stokes-vector and Mueller-matrix polarimetry [Invited].
Azzam, R M A
2016-07-01
This paper reviews the current status of instruments for measuring the full 4×1 Stokes vector S, which describes the state of polarization (SOP) of totally or partially polarized light, and the 4×4 Mueller matrix M, which determines how the SOP is transformed as light interacts with a material sample or an optical element or system. The principle of operation of each instrument is briefly explained by using the Stokes-Mueller calculus. The development of fast, automated, imaging, and spectroscopic instruments over the last 50 years has greatly expanded the range of applications of optical polarimetry and ellipsometry in almost every branch of science and technology. Current challenges and future directions of this important branch of optics are also discussed.
Cascaded forward Brillouin scattering to all Stokes orders
Wolff, Christian; Eggleton, Benjamin J; Steel, Michael J; Poulton, Christopher G
2016-01-01
Inelastic scattering processes such as Brillouin scattering can often function in cascaded regimes and this is likely to occur in certain integrated opto-acoustic devices. We develop a Hamiltonian formalism for cascaded Brillouin scattering valid for both quantum and classical regimes. By regarding Brillouin scattering as the interaction of a single acoustic envelope and a single optical envelope that covers all Stokes and anti-Stokes orders, we obtain a compact model that is well suited for numerical implementation, extension to include other optical nonlinearities or short pulses, and application in the quantum-optics domain. We then theoretically analyze intra-mode forward Brillouin scattering (FBS) for arbitrary waveguides with and without optical dispersion. In the absence of optical dispersion, we find an exact analytical solution. With a perturbative approach, we furthermore solve the case of weak optical dispersion. Our work leads to several key results on intra-mode FBS. For negligible dispersion, we...
Stokes phenomena in discrete Painlevé I.
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.
On Critical Spaces for the Navier-Stokes Equations
Prüss, Jan; Wilke, Mathias
2017-10-01
The abstract theory of critical spaces developed in Prüss and Wilke (J Evol Equ, 2017. doi: 10.1007/s00028-017-0382-6), Prüss et al. (Critical spaces for quasilinear parabolic evolution equations and applications, 2017) is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the L_p -L_q setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an H^∞-calculus with H^∞-angle 0, and the real and complex interpolation spaces of these operators are identified.
Polarization ellipse and Stokes parameters in geometric algebra.
Santos, Adler G; Sugon, Quirino M; McNamara, Daniel J
2012-01-01
In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.
Application of the parallel BDDC preconditioner to the Stokes flow
Czech Academy of Sciences Publication Activity Database
Šístek, Jakub; Sousedík, Bedřich; Burda, P.; Mandel, J.; Novotný, J.
2011-01-01
Roč. 46, č. 1 (2011), s. 429-435 ISSN 0045-7930 R&D Projects: GA AV ČR IAA100760702; GA ČR GA106/08/0403 Institutional research plan: CEZ:AV0Z10190503; CEZ:AV0Z20760514 Keywords : BDDC * domain decomprosition * iterative substructuring * Stokes flow Subject RIV: BA - General Mathematics Impact factor: 1.810, year: 2011 http://www.sciencedirect.com/science/article/pii/S0045793011000053
Steady State Stokes Flow Interpolation for Fluid Control
DEFF Research Database (Denmark)
Bhatacharya, Haimasree; Nielsen, Michael Bang; Bridson, Robert
2012-01-01
— suffer from a common problem. They fail to capture the rotational components of the velocity field, although extrapolation in the normal direction does consider the tangential component. We address this problem by casting the interpolation as a steady state Stokes flow. This type of flow captures...... the rotational components and is suitable for controlling liquid animations where tangential motion is pronounced, such as in a breaking wave...
Assessing the Polarization of a Quantum Field from Stokes Fluctuations
DEFF Research Database (Denmark)
Klimov, A. B.; Björk, G.; Söderholm, J.
2010-01-01
We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard...... (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees....
Probability density functions of instantaneous Stokes parameters on weak scattering
Chen, Xi; Korotkova, Olga
2017-10-01
The single-point probability density functions (PDF) of the instantaneous Stokes parameters of a polarized plane-wave light field scattered from a three-dimensional, statistically stationary, weak medium with Gaussian statistics and Gaussian correlation function have been studied for the first time. Apart from the scattering geometry the PDF distributions of the scattered light have been related to the illumination's polarization state and the correlation properties of the medium.
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Ervin, Vincent J.
2011-11-01
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.
Pourbeyram, Hamed; Mafi, Arash
2017-02-01
In this paper we study, both experimentally and by theory, a new nonlinear dynamic in multimode optical fiber where intermodal four-wave mixing (IM-FWM) and Kerr-induced nonlinear mode coupling (NLC) are strongly interacting. We show that presence of phase-matched IM-FWM and strong nonlinear mode coupling results in an unprecedented saturable mode conversion in the FWM anti-Stokes beam. We investigate the evolution of modal conversion as a function of fiber length and show that the result of this novel nonlinear dynamic is a controllable, length independent mode conversion. Our theoretical calculations suggest that the converted anti-Stokes beam can also be amplified via IM-FWM. We observe a mode conversion with an efficiency as high as 90 percent.
Second (1178 nm) and third (1242 nm) Stokes Raman fiber lasers without intermediate Stokes cavities
Mejía, E. B.; Juárez-Hernández, M.; De la Cruz-May, L.
2017-07-01
We report and propose a simple Raman fiber laser scheme that generates two or three order Raman Stokes components by using a single strong (unidirectional) cavity formed by a high-reflecting fiber Bragg grating and air-glass interface (fiber output); the intermediate cavities are non-grating, weak and bi-directional cavities that serve as ‘virtual links’ or energy reservoirs. Once the strong cavity reaches operation, it practically consumes (converts) all the energy from pump and intermediate components into a single and clamped (unidirectional) signal. For example, the use of second-Stokes fiber Bragg grating together with glass-air output operated and harvested practically all the energy. Analogously, third Stokes emission was obtained by changing the grating and hence relying on first and second non-grating formed intermediate cavities. The system uses commercial silica fiber and minimizes the use of lossy and costly fiber Bragg gratings. This proposal broadens the possibilities for covering the entire 1000-2000 nm window for applications that use silica fibers.
Feng, Qingsong; Zheng, Chunyang; Liu, Zhanjun; Xiao, Chengzhuo; Wang, Qing; Cao, Lihua; He, Xiantu
2017-10-01
The anti-Stokes scattering and Stokes scattering in stimulated Brillouin scattering (SBS) cascade have been researched by the Vlasov-Maxwell simulation. In the high-intensity laser-plasmas interaction, the stimulated anti-Stokes Brillouin scattering (SABS) will occur after the second stage SBS rescattering. The mechanism of SABS has been put forward to explain this phenomenon. In the early time of SBS evolution, only the first stage SBS appears, and the total SBS reflectivity comes from the first stage SBS. However, when the high-stage SBS and SABS occur, the SBS reflectivity will appear a burst behavior, and the total reflectivity comes from the SBS cascade and SABS superimposition. The SABS will compete with the SBS rescattering to determine the total SBS reflectivity. Thus, the SBS rescattering including the SABS is an important saturation mechanism of SBS, and should be taken into account in the high-intensity laser-plasmas interaction. This research was supported by the National Natural Science Foundation of China (Grant Nos. 11375032, 11575035, 11475030 and 11435011), National Basic Research Program of China (Grant No. 2013CB834101) and Science Challenge Project, No. TZ2016005.
Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations
Gomez, Hector
2010-05-01
This paper is devoted to the numerical simulation of the Navier-Stokes-Korteweg equations, a phase-field model for water/water-vapor two-phase flows. We develop a numerical formulation based on isogeometric analysis that permits straightforward treatment of the higher-order partial-differential operator that represents capillarity. We introduce a new refinement methodology that desensitizes the numerical solution to the computational mesh and achieves mesh invariant solutions. Finally, we present several numerical examples in two and three dimensions that illustrate the effectiveness and robustness of our approach. © 2010 Elsevier B.V.
The Stokes phenomenon and the Lerch zeta function
Directory of Open Access Journals (Sweden)
R. B. Paris
2016-05-01
Full Text Available We examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\\lambda,a,s=\\sum_{n=0}^\\infty \\exp (2\\pi ni\\lambda/(n+a^s$ for large complex values of $a$, with $\\lambda$ and $s$ regarded as parameters. It is shown that an infinite number of subdominant exponential terms switch on across the Stokes lines $\\arg\\,a=\\pm\\fs\\pi$. In addition, it is found that the transition across the upper and lower imaginary $a$-axes is associated, in general, with unequal scales. Numerical calculations are presented to confirm the theoretical predictions.
Imaging Stars by Performing Full-Stokes Optical Interferometric Polarimetry
Directory of Open Access Journals (Sweden)
Nicholas M. Elias II
2012-03-01
Full Text Available Optical interferometry and polarimetry have separately provided new insights into stellar astronomy, especially in the fields of fundamental parameters and atmospheric models. We present: scientific justifications for “full-Stokes” optical interferometric polarimetry (OIP; updated instrument requirements; preliminary beam combiner designs; polarimeter design; end-to-end OIP data reduction; and realistic reimaged full-Stokes models of Be stars with a suitable number of telescopes plus noise sources. All of this work represents preliminary research to construct an OIP beam combiner.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.
2017-05-23
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.
Double-Cut of Scattering Amplitudes and Stokes' Theorem
Mastrolia, Pierpaolo
2009-01-01
We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions in two complex-conjugated variables, which are simply computed by an indefinite integration in a single variable, followed by Cauchy's Residue integration in the conjugated one. The method is suitable for the cut-construction of the coefficients of 2-point functions entering the decomposition of one-loop amplitudes in terms of scalar master integrals.
Deriving a new domain decomposition method for the Stokes equations using the Smith factorization
Dolean, Victorita; Nataf, Frédéric; Rapin, Gerd
2009-01-01
International audience; In this paper the Smith factorization is used systematically to derive a new domain decomposition method for the Stokes problem. In two dimensions the key idea is the transformation of the Stokes problem into a scalar bi-harmonic problem. We show, how a proposed domain decomposition method for the bi-harmonic problem leads to a domain decomposition method for the Stokes equations which inherits the convergence behavior of the scalar problem. Thus, it is sufficient to s...
Time-accurate finite difference solutions to the incompressible Navier-Stokes/energy equations
Mirfakhraee, Ali; Davis, Sanford
1991-01-01
Two new algorithms for solving coupled Navier-Stokes and energy equations are presented. The algorithms are compared with available Navier-Stokes solutions for the model problem of a driven-cavity-flow over a range of Reynolds numbers. It is noted that the algorithms represent two different implementations of the fractional step approach to the solution of the coupled Navier-Stokes and energy equations using the Boussinesq approximation.
National Research Council Canada - National Science Library
I. V. Makeev; I. Y. Popov; I. V. Blinova
2016-01-01
.... We suggest exact particular solutions of Stokes and continuity equations with variable viscosity and density in spherical coordinates for the case of spherically symmetric viscosity and density distributions...
Dumbbell formation for elastic capsules in nonlinear extensional Stokes flows
Dimitrakopoulos, P.
2017-06-01
Cross-slot and four-roll-mill microdevices are commonly used for particle manipulation and characterization owing to the stagnation-point flow at the device center. Because of the solid boundaries, these devices may generate extensional Stokes flows where the velocity is a nonlinear function of position associated with a decreased pressure at the particle edges and an increased pressure at the particle middle. Our computational investigation shows that in this class of Stokes flows, an elastic capsule made of a strain-hardening membrane develops two distinct steady-state conformations at strong flows, i.e., an elongated weak dumbbell shape with rounded edges at low flow nonlinearity and a laterally extended dumbbell shape at high flow nonlinearity. These effects are more pronounced for the less strain-hardening capsules which develop a flat extended middle where the two sides of the membrane approach each other. The strong stability properties of the strain-hardening capsules (owing to the development of strong membrane tensions) contrast significantly with the behavior of droplets in these nonlinear flows which are unable to achieve highly deformed steady-state dumbbell shapes owing to their constant surface tension.
Modeling Vortex Generators in a Navier-Stokes Code
Dudek, Julianne C.
2011-01-01
A source-term model that simulates the effects of vortex generators was implemented into the Wind-US Navier-Stokes code. The source term added to the Navier-Stokes equations simulates the lift force that would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, subsonic flow in an S-duct with 22 corotating vortex generators, and supersonic flow in a rectangular duct with a counter-rotating vortex-generator pair. The model was also used to successfully simulate microramps in supersonic flow by treating each microramp as a pair of vanes with opposite angles of incidence. The validation results indicate that the source-term vortex-generator model provides a useful tool for screening vortex-generator configurations and gives comparable results to solutions computed using gridded vanes.
Preconditioned conjugate gradient methods for the Navier-Stokes equations
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.
Microscopic statistical description of incompressible Navier-Stokes granular fluids
Tessarotto, Massimo; Mond, Michael; Asci, Claudio
2017-05-01
Based on the recently established Master kinetic equation and related Master constant H-theorem which describe the statistical behavior of the Boltzmann-Sinai classical dynamical system for smooth and hard spherical particles, the problem is posed of determining a microscopic statistical description holding for an incompressible Navier-Stokes fluid. The goal is reached by introducing a suitable mean-field interaction in the Master kinetic equation. The resulting Modified Master Kinetic Equation (MMKE) is proved to warrant at the same time the condition of mass-density incompressibility and the validity of the Navier-Stokes fluid equation. In addition, it is shown that the conservation of the Boltzmann-Shannon entropy can similarly be warranted. Applications to the plane Couette and Poiseuille flows are considered showing that they can be regarded as final decaying states for suitable non-stationary flows. As a result, it is shown that an arbitrary initial stochastic 1-body PDF evolving in time by means of MMKE necessarily exhibits the phenomenon of Decay to Kinetic Equilibrium (DKE), whereby the same 1-body PDF asymptotically relaxes to a stationary and spatially uniform Maxwellian PDF.
An optimal iterative solver for the Stokes problem
Energy Technology Data Exchange (ETDEWEB)
Wathen, A. [Univ. of Bristol (United Kingdom); Silvester, D.
1994-12-31
Discretisations of the classical Stokes Problem for slow viscous incompressible flow gives rise to systems of equations in matrix form for the velocity u and the pressure p, where the coefficient matrix is symmetric but necessarily indefinite. The square submatrix A is symmetric and positive definite and represents a discrete (vector) Laplacian and the submatrix C may be the zero matrix or more generally will be symmetric positive semi-definite. For `stabilised` discretisations (C {ne} 0) and descretisations which are inherently `stable` (C = 0) and so do not admit spurious pressure components even as the mesh size, h approaches zero, the Schur compliment of the matrix has spectral condition number independent of h (given also that B is bounded). Here the authors will show how this property together with a multigrid preconditioner only for the Laplacian block A yields an optimal solver for the Stokes problem through use of the Minimum Residual iteration. That is, combining Minimum Residual iteration for the matrix equation with a block preconditioner which comprises a small number of multigrid V-cycles for the Laplacian block A together with a simple diagonal scaling block provides an iterative solution procedure for which the computational work grows only linearly with the problem size.
Discussion of Stokes' hypothesis through the smoothed particle hydrodynamics model
Colagrossi, Andrea; Durante, Danilo; Bonet Avalos, Josep; Souto-Iglesias, Antonio
2017-08-01
Stokes' hypothesis, the zeroing of the bulk viscosity in a Newtonian fluid, is discussed in this paper. To this aim, a continuum macroscopic fluid domain is initially modeled as a Hamiltonian system of discrete particles, for which the interparticle dissipative forces are required to be radial in order to conserve the angular momentum. The resulting system of particles is then reconverted to the continuum domain via the framework of the smoothed particle hydrodynamics (SPH) model. Since an SPH-consistent approximation of the Newtonian viscous term in the momentum equation incorporates interparticle radial as well as nonradial terms, it is postulated that the latter must be null. In the present work it is shown that this constraint implies that first and second viscosities are equal, resulting in a positive value for the bulk viscosity, in contradiction to the cited Stokes' hypothesis. Moreover, it is found that this postulate leads to bulk viscosity coefficients close to values found in the experimental literature for monoatomic gases and common liquids such as water.
Brain cancer probed by native fluorescence and stokes shift spectroscopy
Zhou, Yan; Liu, Cheng-hui; He, Yong; Pu, Yang; Li, Qingbo; Wang, Wei; Alfano, Robert R.
2012-12-01
Optical biopsy spectroscopy was applied to diagnosis human brain cancer in vitro. The spectra of native fluorescence, Stokes shift and excitation spectra were obtained from malignant meningioma, benign, normal meningeal tissues and acoustic neuroma benign tissues. The wide excitation wavelength ranges were used to establish the criterion for distinguishing brain diseases. The alteration of fluorescence spectra between normal and abnormal brain tissues were identified by the characteristic fluorophores under the excitation with UV to visible wavelength range. It was found that the ratios of the peak intensities and peak position in both spectra of fluorescence and Stokes shift may be used to diagnose human brain meninges diseases. The preliminary analysis of fluorescence spectral data from cancer and normal meningeal tissues by basic biochemical component analysis model (BBCA) and Bayes classification model based on statistical methods revealed the changes of components, and classified the difference between cancer and normal human brain meningeal tissues in a predictions accuracy rate is 0.93 in comparison with histopathology and immunohistochemistry reports (gold standard).
Navier–Stokes flow in converging–diverging distensible tubes
Directory of Open Access Journals (Sweden)
Taha Sochi
2015-09-01
Full Text Available We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging–diverging tubes for Navier–Stokes fluids. We employ an analytical formula derived from a one-dimensional version of the Navier–Stokes equations to describe the underlying flow model that provides the residual function. This formula correlates the flow rate to the boundary pressures in straight cylindrical elastic tubes with constant-radius. We validate our findings by the convergence toward a final solution with fine discretization as well as by comparison to the Poiseuille-type flow in its convergence toward analytic solutions found earlier in rigid converging–diverging tubes. We also tested the method on limiting special cases of cylindrical elastic tubes with constant-radius where the numerical solutions converged to the expected analytical solutions. The distensible model has also been endorsed by its convergence toward the rigid Poiseuille-type model with increasing the tube wall stiffness. Lubrication-based one-dimensional finite element method was also used for verification. In this investigation five converging–diverging geometries are used for demonstration, validation and as prototypes for modeling converging–diverging geometries in general.
High-order Stokes and anti-Stokes Raman generation in monoisotopic CVD {sup 12}C-diamond
Energy Technology Data Exchange (ETDEWEB)
Kaminskii, Alexander A. [Institute of Crystallography, Russian Academy of Sciences, Moscow (Russian Federation); Lux, Oliver; Rhee, Hanjo; Eichler, Hans J. [Institute of Optics and Atomic Physics, Technische Universitaet Berlin (Germany); Ralchenko, Victor G.; Bolshakov, Andrey P. [General Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation); Shirakawa, Akira; Yoneda, Hitoki [Institute for Laser Science, University of Electro-Communications, Tokyo (Japan)
2016-06-15
We determined, for the first time, the room temperature phonon energy related to the F{sub 2g} vibration mode (ω{sub SRS(12C)} ∝ 1333.2 cm{sup -1}) in a mono-crystalline single-isotope CVD {sup 12}C-diamond crystal by means of stimulated Raman scattering (SRS) spectroscopy. Picosecond one-micron excitation using a Nd{sup 3+}:Y{sub 3}Al{sub 5}O{sub 12}-laser generates a nearly two-octave spanning SRS frequency comb (∝12000 cm{sup -1}) consisting of higher-order Stokes and anti-Stokes components. The spacing of the spectral lines was found to differ by Δω{sub SRS} ∝ 0.9 cm{sup -1} from the comb spacing (ω{sub SRS(natC)} ∝ 1332.3 cm{sup -1}) when pumping a conventional CVD diamond crystal with a natural composition of the two stable carbon isotopes {sup 12}C (98.93%) and {sup 13}C (1.07%). (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Directory of Open Access Journals (Sweden)
Miryam Lucía Guerra-Mazo
2016-05-01
Full Text Available Presenta los resultados de la comparación entre las ecuaciones de Stokes y de Navier-Stokes para la simulación del flujo de agua líquida, a condiciones atmosféricas, a través de una placa orificio concéntrica. A partir de los datos experimentales que fueron tomados en el banco de fluidos, se evaluaron las simulaciones de ambas ecuaciones, usando el software libre Freefem++cs, que se basa en el método de los elementos finitos; las variables evaluadas son velocidad y presión en un intervalo de tiempo. Al analizar los resultados obtenidos con las simulaciones y comparar con los datos experimentales se encontró que las ecuaciones de Navier-Stokes representan mejor el sistema que la ecuación de Stokes.
Frequency-domain 2Ã—2 MIMO equalizer with stokes space updating algorithm
DEFF Research Database (Denmark)
Vaquero Caballero, F. J.; Zanaty, A.; Pittalà, Fabio
2016-01-01
We propose a novel frequency-domain Stokes space algorithm. Its low implementation complexity architecture allows merging static and dynamic 2Ã—2 MIMO equalization in a single stage.......We propose a novel frequency-domain Stokes space algorithm. Its low implementation complexity architecture allows merging static and dynamic 2Ã—2 MIMO equalization in a single stage....
Reproductive solutions for the g-Navier-Stokes and g-Kelvin-Voight equations
Directory of Open Access Journals (Sweden)
Luis Friz
2016-01-01
Full Text Available This article presents the existence of reproductive solutions of g-Navier-Stokes and g-Kelvin-Voight equations. In this way, for weak solutions, we reach basically the same result as for classic Navier-Stokes equations.
A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions
DEFF Research Database (Denmark)
Hesthaven, Jan; Gottlieb, D.
1996-01-01
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...
Hydrodynamic cavitation in Stokes flow of anisotropic fluids
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
Spatial local solutions of the Navier-Stokes equations
Garipov, R. M.
2009-03-01
This paper considers solutions of the Navier-Stokes equations polynomial in the coordinates, which. are called local solutions. For an incompressible fluid, all higher-order terms (sums of higher-order. monomials) of degree 2 are found and it is proved that nontrivial axisymmetric higher-order terms. of degree higher than 2 do not exist. Nonsolenoidal axisymmetric solutions are listed, which can be. treated as steady-state barotropic gas flows in a potential external-force field. All elliptic vortices. generalizing the well-known Kirchhoff solution are calculated. All solutions of degree 3 with the. higher-order term of partial form are found. Some of these solutions break down in a finite time. regardless of the value and sign of viscosity.
Stokes vector analysis of LWIR polarimetric in adverse weather
Michalson, Jacob L.; Romano, Joao M.; Roth, Luz
2011-10-01
It is understood that Long Wave Infrared (LWIR) polarimetric imagery has the potential for detecting man-made objects in natural clutter backgrounds. Unlike Spectral and conventional broadband, polarimetric imagery takes advantage of the polarized signals emitted by the smooth surfaces of man-made materials. Studying the effect of how meteorological conditions affect polarization signals is imperative in order to understand where and how polarimetric technology can be beneficial to the war fighter. In this paper we intend to demonstrate the effects of weather on the performance of Stokes vector components, S0, S1, S2, and the Degree of Linear Polarization (DOLP) as detectors of man-made materials. Using the Hyperspectral Polarimetric Image Collection Experiment (SPICE) data collection, we analyze approximately one thousand images and correlate the performance of each of the detection metrics to individual meteorological measurements.
Swimming of helically-undulating rings in a Stokes fluid
Fauci, Lisa; Nguyen, Hoa; Ortiz, Ricardo; Cortez, Ricardo
2009-11-01
Dinoflagellates swim due to the action of two eucaryotic flagella - a trailing, longitundinal flagellum that propagates planar waves, and a transverse flagellum that propagates helical waves. The transverse flagellum wraps around the cell in a plane perpendicular to the trailing flagellum, and is thought to provide both forward thrust along with rotational torque. Motivated by the intriguing function of this transverse flagellum, we study the fundamental fluid dynamics of a helically-undulating ring in a Stokes fluid. We use slender-body theory to compute the steady-state transverse and rotational swimming velocities of the ring in free- space, due to an imposed helical traveling wave. In addition, we study the dynamics of an undulating, elastic ring moving in both free-space and near a plane wall using the method of regularized Stokeslets.
The Navier-Stokes equations an elementary functional analytic approach
Sohr, Hermann
2001-01-01
The primary objective of this monograph is to develop an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes. Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical generality, however, the linearized theory is expounded for general dimensions higher than one. Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces. However, for the readers’ convenience, some fundamental properties...
Navier-Stokes equations on R3 × [0, T
Stenger, Frank; Baumann, Gerd
2016-01-01
In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier–Stokes partial differential equations on (x, y, z, t) ∈ ℝ3 × [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages: The functions of S are nearly always conceptual rather than explicit Initial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation ...
Symmetry Breaking for the Incompressible Navier-Stokes Equations
Waymire, E. C.; Dascaliuc, R.; Thomann, E. A.; Michalowski, N. P.
2015-12-01
The validity of uniquely determined solutions to 3-dimensional incompressible Navier-Stokes equations for smooth initial data remains one of the great challenges since their inception. Jean Leray was among the first investigage the mathematical mysteries embodied by these equations in terms of self-similarities viewed backwards in time. However this proved to be uneventful, and recently shown to be a failed approach. Recent new developments in the mathematical representation of solutions as expected values of stochastic cascades have lead to new insights into the nature of self-similarities in forward in time solutions to these equations. The purpose of this talk is to describe some of the progress and challenges underlying these fundamentally important equations for fluid flow when viewed from this perspective.
Computerized Stokes analysis of optically active polymer films
Georgiev, Georgi
2010-01-01
Optics labs are an integral part of the advanced curriculum for physics majors. Students majoring in other disciplines, like chemistry, biology or engineering rarely have the opportunity to learn about the most recent optical techniques and mathematical representation used in todayâs science and industry optics. Stokes analysis of polarization of light is one of those methods that are increasingly necessary but are seldom taught outside advanced physics or optics classes that are limited to physics majors. On the other hand biology and chemistry majors already use matrix and polarization techniques in the labs for their specialty, which makes the transition to matrix calculations seamless. Since most of the students in those majors postpone their enrollment in physics, most of the registered in those classes are juniors and seniors, enabling them to handle those techniques. We chose to study polymer samples to aid students majoring in other disciplines, especially chemistry and engineering, with understa...
Coherent anti-Stokes Raman scattering microscopy of single nanodiamonds
Pope, Iestyn; Payne, Lukas; Zoriniants, George; Thomas, Evan; Williams, Oliver; Watson, Peter; Langbein, Wolfgang; Borri, Paola
2016-01-01
Nanoparticles have attracted enormous attention for biomedical applications as optical labels, drug delivery vehicles, and contrast agents in vivo. In the quest for superior photostability and bio-compatibility, nanodiamonds (NDs) are considered one of the best choices due to their unique structural, chemical, mechanical, and optical properties. So far, mainly fluorescent NDs have been utilized for cell imaging. However, their use is limited by the efficiency and costs in reliably producing fluorescent defect centers with stable optical properties. Here, we show that single non-fluorescing NDs exhibit strong coherent anti-Stokes Raman scattering (CARS) at the sp3 vibrational resonance of diamond. Using correlative light and electron microscopy, the relationship between CARS signal strength and ND size is quantified. The calibrated CARS signal in turn enables the analysis of the number and size of NDs internalized in living cells in situ, which opens the exciting prospect of following complex cellular trafficking pathways quantitatively. PMID:25305746
Stokes integral of economic growth. Calculus and the Solow model
Mimkes, Jürgen
2010-04-01
Economic growth depends on capital and labor and two-dimensional calculus has been applied to economic theory. This leads to Riemann and Stokes integrals and to the first and second laws of production and growth. The mathematical structure is the same as in thermodynamics, economic properties may be related to physical terms: capital to energy, production to physical work, GDP per capita to temperature, production function to entropy. This is called econophysics. Production, trade and banking may be compared to motors, heat pumps or refrigerators. The Carnot process of the first law creates two levels in each system: cold and hot in physics; buyer and seller, investor and saver, rich and poor in economics. The efficiency rises with the income difference of rich and poor. The results of econophysics are compared to neoclassical theory.
Optimal distribution of integration time for intensity measurements in Stokes polarimetry.
Li, Xiaobo; Liu, Tiegen; Huang, Bingjing; Song, Zhanjie; Hu, Haofeng
2015-10-19
We consider the typical Stokes polarimetry system, which performs four intensity measurements to estimate a Stokes vector. We show that if the total integration time of intensity measurements is fixed, the variance of the Stokes vector estimator depends on the distribution of the integration time at four intensity measurements. Therefore, by optimizing the distribution of integration time, the variance of the Stokes vector estimator can be decreased. In this paper, we obtain the closed-form solution of the optimal distribution of integration time by employing Lagrange multiplier method. According to the theoretical analysis and real-world experiment, it is shown that the total variance of the Stokes vector estimator can be significantly decreased about 40% in the case discussed in this paper. The method proposed in this paper can effectively decrease the measurement variance and thus statistically improves the measurement accuracy of the polarimetric system.
CUDA GPU based full-Stokes finite difference modelling of glaciers
DEFF Research Database (Denmark)
Brædstrup, Christian; Egholm, D.L.
speedup com- pared 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......Many have stressed the limitations of using the shallow shelf and shallow ice approxima- tions 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...... provide a po- werful 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...
High Precision Stokes Polarimetry for Scattering Light using Wide Dynamic Range Intensity Detector
Directory of Open Access Journals (Sweden)
Shibata Shuhei
2015-01-01
Full Text Available This paper proposes a Stokes polarimetry for scattering light from a sample surface. To achieve a high accuracy measurement two approaches of an intensity detector and analysis algorism of a Stokes parameter were proposed. The dynamic range of this detector can achieve up to 1010 by combination of change of neutral-density (ND filters having different density and photon counting units. Stokes parameters can be measured by dual rotating of a retarder and an analyzer. The algorism of dual rotating polarimeter can be calibrated small linear diattenuation and linear retardance error of the retarder. This system can measured Stokes parameters from −20° to 70° of its scattering angle. It is possible to measure Stokes parameters of scattering of dust and scratch of optical device with high precision. This paper shows accuracy of this system, checking the polarization change of scattering angle and influence of beam size.
Resonant anti-Stokes Raman scattering in single-walled carbon nanotubes
Gordeev, Georgy; Jorio, Ado; Kusch, Patryk; Vieira, Bruno G. M.; Flavel, Benjamin; Krupke, Ralph; Barros, Eduardo B.; Reich, Stephanie
2017-12-01
The dependence of the anti-Stokes Raman intensity on the excitation laser energy in carbon nanotubes is studied by resonant Raman spectroscopy. The complete resonant anti-Stokes and Stokes Raman profiles of the high-energy longitudinal phonon (G+) are obtained for (8,3), (7,5), (6,4), and (6,5) single chirality enriched samples. A high asymmetry between the intensity of the incoming and outgoing resonance is observed in the resonant Raman profiles. In contrast to Stokes scattering, anti-Stokes scattering is more intense at the outgoing resonance then at the incoming resonance. The resonance profiles are explained by a Raman process that includes the phonon-mediated interactions with the dark excitonic state. The chirality dependence of the Raman profiles is due to the variation in the exciton-phonon matrix elements, in agreement with tight-binding calculations. Based on the asymmetric Raman profiles we present the resonance factors for the Stokes/anti-Stokes ratios in carbon nanotubes.
Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions
Tidriri, M. D.
1995-01-01
One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.
The Navier-Stokes equations an elementary functional analytic approach
Sohr, Hermann
2001-01-01
The primary objective of this monograph is to develop an elementary and self contained approach to the mathematical theory of a viscous incompressible fluid in a domain 0 of the Euclidean space ]Rn, described by the equations of Navier Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the first two chapters we collect without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain O. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n = 2,3 that are also most significant from the physical point of view. For mathematical generality, we will develop the lin earized theory for all n 2 2. Although the functional-analytic approach developed here is, in principle, known ...
Stokes Trap: Multiplexed particle trapping and manipulation using fluidics
Shenoy, Anish; Schroeder, Charles
We report the development of the Stokes Trap, which is a multiplexed microfluidic trap for control over an arbitrary number of small particles in a microfluidic device. Our work involves the design and implementation of ``smart'' flow-based devices by coupling feedback control with microfluidics, thereby enabling new routes for the fluidic-directed assembly of particles. Here, we discuss the development of a new method to achieve multiplexed microfluidic trapping of an arbitrary number of particles using the sole action of fluid flow. In particular, we use a Hele-Shaw microfluidic cell to generate hydrodynamic forces on particles in a viscous-dominated flow defined by the microdevice geometry and imposed peripheral flow rates. This platform allows for a high degree of flow control over individual particles and can be used for manufacturing novel particles for fundamental studies, using fluidic-directed assembly. From a broader perspective, our work provides a solid framework for guiding the design of next-generation, automated on-chip assays.
Multidimensional Stability of Large-Amplitude Navier-Stokes Shocks
Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin
2017-12-01
Extending results of Humpherys-Lyng-Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the multidimensional stability of planar Navier-Stokes shocks across the full range of shock amplitudes, including the infinite-amplitude limit, for monatomic or diatomic ideal gas equations of state and viscosity and heat conduction coefficients {μ}, {μ +η}, and {ν=κ/c_v} constant and in the physical ratios predicted by statistical mechanics, and Mach number {M > 1.035}. Our results indicate unconditional stability within the parameter range considered; this agrees with the results of Erpenbeck and Majda for the corresponding inviscid case of Euler shocks. Notably, this study includes the first successful numerical computation of an Evans function associated with the multidimensional stability of a viscous shock wave. The methods introduced can be used in principle to decide stability for shocks in any polytropic gas, or indeed for shocks of other models, including in, particular, viscoelasticity, combustion, and magnetohydrodynamics (MHD).
The mixed finite element multigrid method for stokes equations.
Muzhinji, K; Shateyi, S; Motsa, S S
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results.
Hydrodynamics beyond Navier-Stokes: The slip flow model
Yudistiawan, Wahyu P.; Ansumali, Santosh; Karlin, Iliya V.
2008-07-01
Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali , Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation—the nine-bit model in two dimensions—in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.
Tricontinental Routes of Solidarity: Stokely Carmichael in Cuba
Directory of Open Access Journals (Sweden)
Sarah Seidman
2012-12-01
Full Text Available Stokely Carmichael’s visit to Cuba for three weeks in the summer of 1967 illustrates a convergence in the transnational routes of the African American freedom struggle and the Cuban Revolution. African American activists saw Cuba as a model for resisting US power, eradicating racism, and enacting societal change, while the Cuban government considered African Americans allies against US imperialism and advocates of Cuba’s antiracist stance. Amidst racial violence in the United States and Cuba’s efforts to inspire revolution, Carmichael’s presence at the Organization of Latin American Solidarity conference in Havana—and in particular his interactions with Fidel Castro—caused ripples worldwide. A shared “tricontinental” vision that promoted unity in the Global South against imperialism, capitalism, and racism facilitated Carmichael’s solidarity with Castro. Yet divergent views on the role of race in fighting oppression limited their solidarity. Carmichael and Castro’s spectacular alliance demonstrated their personal affinity and ideological commonalities but did not result in an institutional alliance between the black liberation movement and the Cuban state. Instead Carmichael’s connection with the Cuban Revolution left an underexplored legacy. Examining Carmichael’s visit to Cuba illustrates the possibilities and pitfalls of transnational solidarity and furthers our understanding of postwar struggles for change.
The Stokes boundary layer for a thixotropic or antithixotropic fluid
McArdle, Catriona R.
2012-10-01
We present a mathematical investigation of the oscillatory boundary layer in a semi-infinite fluid bounded by an oscillating wall (the so-called \\'Stokes problem\\'), when the fluid has a thixotropic or antithixotropic rheology. We obtain asymptotic solutions in the limit of small-amplitude oscillations, and we use numerical integration to validate the asymptotic solutions and to explore the behaviour of the system for larger-amplitude oscillations. The solutions that we obtain differ significantly from the classical solution for a Newtonian fluid. In particular, for antithixotropic fluids the velocity reaches zero at a finite distance from the wall, in contrast to the exponential decay for a thixotropic or a Newtonian fluid.For small amplitudes of oscillation, three regimes of behaviour are possible: the structure parameter may take values defined instantaneously by the shear rate, or by a long-term average; or it may behave hysteretically. The regime boundaries depend on the precise specification of structure build-up and breakdown rates in the rheological model, illustrating the subtleties of complex fluid models in non-rheometric settings. For larger amplitudes of oscillation the dominant behaviour is hysteretic. We discuss in particular the relationship between the shear stress and the shear rate at the oscillating wall. © 2012 Elsevier B.V.
Wall effects in Stokes experiment with a liquid foam
Gao, Haijing; Subramani, Hariprasad; Harris, Michael; Basaran, Osman
2011-11-01
Liquid foams are widely used in numerous applications ranging from the oil and gas industry to beauty, healthcare, and household products industries. A fundamental understanding of the relationships between the properties of liquid foams and their flow responses is, however, still in its infancy compared to that involving the fluid dynamics of simple fluids. In this talk, the flow of a dry liquid foam around a spherical bead, i.e. the Stokes problem for liquid foams, is studied experimentally. In contrast to previous work (cf. Cantat 2006), the focus of the present research is to probe the effect of a solid wall that is located a few bubble radii from the bead. The new experimental results show that the elastic modulus of dry liquid foams is directly proportional to the surface tension of the foaming agents and inversely proportional to the average bubble size in the foams, in agreement with previous theoretical and experimental studies. The experiments further show that the close proximity of the solid wall causes profound structural changes to the gas bubbles as the foam flows past the bead. A good understanding of these structural changes and how they can affect the elastic modulus of foams can be indispensable in formulating improved models for accurately describing the dynamical response of foams within the realm of continuum mechanics.
Stokes-vector direct detection for optical communications
Shieh, William; Li, An; Che, Di; Yuan, Feng; Khodakarami, Hamid
2017-01-01
To cope with the exponential growth of the Internet traffic, optical communications has advanced by leaps and bounds. For several decades, Intensity modulation with direct detection (IM-DD) dominates the commercial short-reach optical communications. However, when upgrading the data-rate distance product to 1000 Gb/s·km per wavelength and beyond, IM-DD faces severe performance barrier. Aiming to improve the electrical SE and extend the transmission distance, advanced DD modulation formats have been proposed through a so-called self-coherent (SCOH) approach, where a carrier is transmitted together with the signal to achieve a linear mapping between the electrical baseband signal and the optical field. In that way, the impact of the CD can be removed from the received signal, greatly extending the transmission distance of the DD system. Particularly, Stokes-vector direct detection (SV-DD) has been proposed to realize linear complex optical channels as well as enhance the electrical spectral efficiency and transmission reach. In this talk, we present the principle and discuss the performance of SV-DD systems.
Phase-Field Surface Tension Modeling for Two-Phase Navier-Stokes Flow
Jacqmin, David
1997-08-01
The phase-field method applied to the multiphase Navier-Stokes equations provides a continuum-surface-tension model that is energetically and, with care, thermodynamically consistent. The phase-field Navier-Stokes equations are the Navier-Stokes equations with continuum-surface-tension forcing derived from the phase-field free energy plus the advective Cahn-Hilliard equation for describing phase convection. This equation system appears to have O(ɛ) convergence to the true multiphase Navier-Stokes equations (ɛ is interface thickness). The talk will discuss the numerical implementation of the equations with special attention paid to convergence of numerical methods in the double limit ɛ arrow 0, h arrow 0. Results will be shown for contact line flow, for interface breakup and coalescence, and for film flow and coating flow instabilities and behavior.
Exact unsteady solutions to the Navier-Stokes and viscous MHD equations
Energy Technology Data Exchange (ETDEWEB)
Bogoyavlenskij, Oleg I
2003-02-10
Infinite-dimensional families of exact solutions that depend on all four variables t,x,y,z are derived for the Navier-Stokes equations and for viscous magnetohydrodynamics equations. Soliton-like solutions--viscons--are introduced.
Carleman estimate for the Navier-Stokes equations and an application to a lateral Cauchy problem
Bellassoued, Mourad; Imanuvilov, Oleg; Yamamoto, Masahiro
2016-02-01
We consider the nonstationary linearized Navier-Stokes equations in a bounded domain and first we prove a Carleman estimate with a regular weight function. Second we apply the Carleman estimate to a lateral Cauchy problem for the Navier-Stokes equations and prove the Hölder stability in determining the velocity and pressure field in an interior domain. In the final section, we apply the results for the linearized Navier-Stokes equations to the fully nonlinear Navier-Stokes equations and establish a similar Hölder stability estimate within sufficiently smooth solutions, and prove the uniqueness of Leray-Hopf weak solutions by surface stresses on an arbitrarily chosen sub-boundary.
Impact of Heart Transplantation on Cheyne-Stokes Respiration in a Child
Directory of Open Access Journals (Sweden)
Suhail Al-Saleh
2016-01-01
Full Text Available Sleep disordered breathing is well described in adults with heart failure but not in pediatric population. We describe a 13-year-old Caucasian male with severe heart failure related to dilated cardiomyopathy who demonstrated polysomnographic features of Cheyne-Stokes respiration, which completely resolved following cardiac transplantation. Cheyne-Stokes respiration in children with advanced heart failure and its resolution after heart transplant can be observed similar to adults.
Directory of Open Access Journals (Sweden)
Pengzhan Huang
2011-01-01
Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.
Directory of Open Access Journals (Sweden)
Mohamed Abdelwahed
2017-01-01
Full Text Available We the solvability of the two-dimensional stream function-vorticity formulation of the Navier-Stokes equations. We use the time discretization and the method of characteristics order one for solving a quasi-Stokes system that we discretize by a piecewise continuous finite element method. A stabilization technique is used to overcome the loss of optimal error estimate. Finally a parallel numerical algorithm is presented and tested.
Molitor, Andreas; Hartmann, Sébastien; Elsässer, Wolfgang
2012-11-15
We demonstrate that a full polarization analysis in terms of the Stokes vector parameters is necessary to determine the polarization state of light emitted by vertical-cavity surface-emitting lasers (VCSELs). For three selected representative VCSEL devices, we measured the injection current dependence of the three Stokes parameters and compared these results with linearly selected polarization P-I curves, clearly demonstrating that a complete polarization analysis is required to unveil the full polarization behavior.
Laser engine simulation using pressure based Navier-Stokes solver
Youssef, Hazim Saad
1994-03-01
Analysis of the flow field in a laser engine represents a difficult computational problem involving combinations of complex physical and gas-dynamical processes. Following a brief discussion of these processes a calculation procedure using primitive variables formulation on a nonstaggered grid system is introduced. Based on this procedure, a pressure based Navier-Stokes solver (PBNS) is developed using a generalized curvilinear coordinate system. The solver is first tested in application to a subsonic compressible flow over an insulated flat plate and to a flow in an axisymmetric converging-diverging nozzle. Next, the PBNS code is used to analyze the flowfield and performance of a laser thruster. The physical/numerical model includes the geometric ray tracing for the laser beam, beam power absorption, plasma radiation losses, and plasma thermophysical and optical properties. Equilibrium hydrogen is used as a flowing gas and its properties are calculated using the Hydrogen Properties Calculation (HPC) based on the methods of statistical thermodynamics. Two thrustor configurations, two laser types (CO2 and iodide), various laser power levels, and various injection conditions are tested. The results of these tests include the temperature, pressure, velocity, and Mach number contours, as well as tables of the laser beam power absorbed, radiation losses to the thrustor walls, thrust level, and specific impulse. The maximum specific impulse obtained in these tests is 1537 sec for a CO2 laser thruster and 827 sec for an iodide laser thruster. Up to 100% power absorption can be achieved; however, radiation losses from the hot plasma are quite high disallowing a full conversion of the absorbed power into the thermal energy of the propellant. The PBNS code can be used to study the effects of various design parameters on the performance of a laser thruster and provide guidelines for the preliminary design of a laser engine.
Świergiel, Jolanta; Bouteiller, Laurent; Jadżyn, Jan
2014-11-14
Impedance spectroscopy was used for the study of the static and dynamic behavior of the electrical conductivity of a hydrogen-bonded supramolecular polymer of high viscosity. The experimental data are discussed in the frame of the Stokes-Einstein and Stokes-Einstein-Debye models. It was found that the translational movement of the ions is due to normal Brownian diffusion, which was revealed by a fulfillment of Ohm's law by the electric current and a strictly exponential decay of the current after removing the electric stimulus. The dependence of the dc conductivity on the viscosity of the medium fulfills the Stokes-Einstein model quite well. An extension of the model, by including in it the conductivity relaxation time, is proposed in this paper. A breakdown of the Stokes-Einstein-Debye model is revealed by the relations of the dipolar relaxation time to the viscosity and to the dc ionic conductivity. The importance of the C=O···H-N hydrogen bonds in that breakdown is discussed.
Reformulating the full-Stokes ice sheet model for a more efficient computational solution
Directory of Open Access Journals (Sweden)
J. K. Dukowicz
2012-01-01
Full Text Available The first-order or Blatter-Pattyn ice sheet model, in spite of its approximate nature, is an attractive alternative to the full Stokes model in many applications because of its reduced computational demands. In contrast, the unapproximated Stokes ice sheet model is more difficult to solve and computationally more expensive. This is primarily due to the fact that the Stokes model is indefinite and involves all three velocity components, as well as the pressure, while the Blatter-Pattyn discrete model is positive-definite and involves just the horizontal velocity components. The Stokes model is indefinite because it arises from a constrained minimization principle where the pressure acts as a Lagrange multiplier to enforce incompressibility. To alleviate these problems we reformulate the full Stokes problem into an unconstrained, positive-definite minimization problem, similar to the Blatter-Pattyn model but without any of the approximations. This is accomplished by introducing a divergence-free velocity field that satisfies appropriate boundary conditions as a trial function in the variational formulation, thus dispensing with the need for a pressure. Such a velocity field is obtained by vertically integrating the continuity equation to give the vertical velocity as a function of the horizontal velocity components, as is in fact done in the Blatter-Pattyn model. This leads to a reduced system for just the horizontal velocity components, again just as in the Blatter-Pattyn model, but now without approximation. In the process we obtain a new, reformulated Stokes action principle as well as a novel set of Euler-Lagrange partial differential equations and boundary conditions. The model is also generalized from the common case of an ice sheet in contact with and sliding along the bed to other situations, such as to a floating ice shelf. These results are illustrated and validated using a simple but nontrivial Stokes flow problem involving a sliding
Exponential integrators for the incompressible Navier-Stokes equations.
Energy Technology Data Exchange (ETDEWEB)
Newman, Christopher K.
2004-07-01
We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size. Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step. Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L{sup 2} inner product. We examine this L{sup 2} projection and an H{sup 1} projection induced by the H{sup 1} semi-inner product. The H
DEFF Research Database (Denmark)
Machida, S.; Tadakuma, T.; Satake, A.
2005-01-01
Stokes and anti-Stokes photoluminescence (AS-PL) has been investigated in a step-graded Inx(Al0.17Ga0.83)1–xAs/Al0.17Ga0.83As quantum-well (QW) heterostructure consisting of five QWs with different x values. Stokes PL spectra of this sample show a significant difference in PL intensity between...
Spatial control of coherent anti-stokes emission with height-modulated gold zig-zag nanowires.
Kim, Hyunmin; Taggart, David K; Xiang, Chengxiang; Penner, Reginald M; Potma, Eric Olaf
2008-08-01
Intrinsic coherent anti-Stokes emission is observed in lithographically patterned gold nanowires. Polarization dependent measurements reveal that the nanostructure's anti-Stokes response is polarized in the direction of the transverse surface plasmon resonance of the wire. We have used specially fabricated gold nanozigzag wires that are modulated in height between 20 and 80 nm to demonstrate tuning of the plasmon polarizability through control of wire height. Stronger anti-Stokes emission is shown to correlate with structures that support higher plasmon polarizability, underlining the primary role of the transverse plasmon resonance in the generation of anti-Stokes radiation from gold nanostructures. Our results also point out that a potential surface-enhanced coherent anti-Stokes Raman scattering (CARS) assay for detecting the vibrational response of surface-tethered molecules needs to include a mechanism for separating the molecular response from the strong intrinsic anti-Stokes emission of the metallic nanosubstrate.
Shen, Hongbin; Wang, Qingpu; Zhang, Xingyu; Chen, Xiaohan; Cong, Zhenhua; Wu, Zhenguo; Bai, Fen; Lan, Weixia; Gao, Liang
2012-07-30
1st-Stokes and 2nd-Stokes dual-wavelength operation within a diode-side-pumped Q-switched Nd:YAG/BaWO(4) intracavity Raman laser was realized. Using an output coupler of transmission of 3.9% at 1180 nm and transmission of 60.08% at 1325 nm, the maximum output power of 8.30 W and 2.84 W at a pulse repetition rate of 15 kHz for the 1st Stokes and the 2nd Stokes laser were obtained, respectively. The corresponding optical conversion efficiency from diode laser to the 1st Stokes and 2nd Stokes laser are 5.0% and 1.4%, respectively. With the pump power of 209 W and a pulse repetition rate of 15 kHz, the 1st Stokes and the 2nd Stokes pulse widths were 20.5 ns and 5.8 ns, respectively. The stable simultaneous Q-switching and mode locking of the 2nd Stokes laser without mode locking component was obtained at the pump power of about 29~82 W. The estimated mode-locked pulse width was approximately 31 ps at the pump power of 50 W and a pulse repetition rate of 15 kHz.
A viscous compressible model of soap film flow and its equivalence with the Navier-Stokes equations
Fast, Petri
2005-01-01
We present a quasi-two dimensional model of flowing soap films that bears striking similarity to the compressible Navier-Stokes equations. The variation in soap film thickness that is commonly used for flow visualization in experiments is analogous to density variations in the Navier-Stokes equations. When the soap film flow velocity is comparable to the Marangoni elastic wave velocity we recover the compressible Navier-Stokes equations and the soap film behaves like a two-dimensional isother...
Sanchez-Romero, Alejandro; Gonzalez, Josep-Abel; Calbó, Josep
2013-04-01
Since the end of the 19th century, the Campbell-Stokes sunshine recorder (CSSR) has been the instrument used to measure the sunshine duration (SD), i.e, the length of time that the ground surface is irradiated by direct solar radiation. Due to the large number of records that exist worldwide (some of them extending over more than 100 years), valuable climatic information can be extracted from them. The World Meteorological Organization (WMO) defines the SD as the time during which the direct solar irradiance (DSI) exceeds the level of 120 W/m2. The burn is typically wider (narrower) when the direct insolation is stronger (weaker). The aim of this research is to test the impact of aerosols on the SD measurements, and to obtain a new and valuable method to extract information of the temporal evolution of aerosols. The research was carried out in Girona (NE Spain), using cloudless days since February 2011. Two CSSR with two different types of bands and a pyrheliometer from Kipp&Zonen were used to measure the SD and the DSI, respectively. Other meteorological and radiometric variables were also stored for the study. To select the cloudless days, direct and global solar irradiance measurements were considered, with the support of the whole sky camera. For each band of these days, we have measured the burned area in intervals of 30 minutes, after applying a digital image processing that increases the contrast of the burn. We assume that, if SD is indeed affected by the aerosol loading, the effect would not be punctual and the narrowing in the burning will be extended over a certain period of time. That is the reason why we are more interested in measuring areas and not widths of burning. Moreover, only cloudless days were selected in order to assure that a decrease of the burn is not due to thin clouds. We have considered that characteristics of band burns could also depend on other meteorological variables (temperature, humidity, etc.). This method has been applied to a
Secret Hidden in Navier-Stokes Equations: Singularity and Criterion of Turbulent Transition
Dou, Hua-Shu
2014-01-01
As is well known, there is discontinuity from laminar flow to turbulence in the time-averaged Navier-Stokes equations. In other words, singular point may implicitly exist in the Navier-Stokes equations for a given flow configuration. Transition of a laminar flow to a turbulent flow must be via the singular point. However, how the singularity of Navier-Stokes equations is related to the turbulent transition is not understood in the community. In this paper, a new formulation of the Navier-Stokes equation is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found. For pressure driven flows, this singular point is actually the inflection point on the velocity profile. It is found that the stability of a flow depends on the direction of the gradient of the total mechanical energy for incompressible pressure-driven flow. When this direction is nearer the normal direction of the streamline, the flow is more unstable. It is further demonstrated tha...
The effect of Stokes shift in the discrimination of urine of cervical cancer from normal subjects
Rajasekaran, Ramu; Brindha, Elumalai; Aruna, Prakasa Rao; Koteeswaran, Dornadula; Ganesan, Singaravelu
2016-03-01
Stokes shift spectroscopy has been considered as a potential tool in characterization of multiple components present in tissues and biofluids. Since, the intensity and resolution of the fluorophores depends on the Stokes shift, different opinion has been reflected by the researchers in fixing the Stokes shift. Also, not many studies have been reported on the characterization of biofluids and especially on the diagnosis of cancer. Urine is considered as an important diagnostic biofluid as it is rich in many metabolites where many of them are native fluorophores. In this study, we aimed at characterizing the urine of normal subjects and patients with cervical cancer as function of different Stokes shift. It is observed that Neopterin and Riboflavin are the main fluorophores contribute to the variation between normal and cervical cancer subjects. Ratio variables based linear discriminant analysis shows that the Stokes shift of 40 nm and 60 nm may be considered for better characterization with better signal to noise ratio when compared to others.
National Research Council Canada - National Science Library
Boy, J.-P; Chinn, D. S; Rowlands, D. D; Lemoine, F. G; McCarthy J. J; Klosko, S. M; Luthcke, S. B; 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...
Navier-Stokes-Fourier Equations A Rational Asymptotic Modelling Point of View
Zeytounian, Radyadour Kh
2012-01-01
This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.
Directory of Open Access Journals (Sweden)
Srivastava Deepak Kumar
2014-01-01
Full Text Available In this paper, Oseen’s correction to Stokes drag experienced by axially symmetric particle placed in a uniform stream perpendicular to axis of symmetry(i.e. transverse flow is obtained. For this, the linear relationship between axial and transverse Stokes drag is utilized to extend the Brenner’s formula for axial flow to transverse flow. General expression of Oseen’s correction to Stokes drag on axially symmetric particle placed in transverse flow is found to be new. This general expression is applied to some known axially symmetric bodies and obtained values of Oseen’s drag, up to first order terms in Reynolds number ‘R’, are also claimed to be new and never exist in the literature. Numerical values of Oseen drag are also evaluated and their variations with respect to Reynolds number, eccentricity and deformation parameter are depicted in figures and compared with some known values. Some important applications are also highlighted.
Analytic Semigroup Approach to Generalized Navier-Stokes Flows in Besov Spaces
Chen, Zhi-Min
2017-12-01
The energy dissipation of the Navier-Stokes equations is controlled by the viscous force defined by the Laplacian -Δ , while that of the generalized Navier-Stokes equations is determined by the fractional Laplacian (-Δ )^α . The existence and uniqueness problem is always solvable in a strong dissipation situation in the sense of large α but it becomes complicated when α is decreasing. In this paper, the well-posedness regarding to the unique existence of small time solutions and small initial data solutions is examined in critical homogeneous Besov spaces for α ≥ 1/2. An analytic semigroup approach to the understanding of the generalized Navier-Stokes equations is developed and thus the well-posedness on the equations is examined in a manner different to earlier investigations.
Bae, Kideog; Zheng, Wei; Huang, Zhiwei
2017-08-01
We report the quantitative assessment of spinal cord injury using the circularly polarized coherent anti-Stokes Raman scattering (CP-CARS) technique together with Stokes parameters in the Poincaré sphere. The pump and Stokes excitation beams are circularly polarized to suppress both the linear polarization-dependent artifacts and the nonresonant background of tissue CARS imaging, enabling quantitative CP-CARS image analysis. This study shows that CP-CARS imaging uncovers significantly increased phase retardance of injured spinal cord tissue as compared to normal tissue, suggesting that CP-CARS is an appealing label-free imaging tool for determining the degree of tissue phase retardance, which could serve as a unique diagnostic parameter associated with nervous tissue injury.
The Actuator Surface Model: A New Navier-Stokes Based Model for Rotor Computations
DEFF Research Database (Denmark)
Shen, Wen Zhong; Zhang, J.H.; Sørensen, Jens Nørkær
2009-01-01
This paper presents a new numerical technique for simulating two-dimensional wind turbine flow. The method, denoted as the 2D actuator surface technique, consists of a two-dimensional Navier-Stokes solver in which the pressure distribution is represented by body forces that are distributed along...... the chord of the airfoils. The distribution of body force is determined from a set of predefined functions that depend on angle of attack and airfoil shape. The predefined functions are curve fitted using pressure distributions obtained either from viscous-inviscid interactive codes or from full Navier-Stokes...... simulations. The actuator surface technique is evaluated by computing the two-dimensional flow past a NACA 0015 airfoil at a Reynolds number of 10(6) and an angle of attack of 10 deg and by comparing the computed streamlines with the results from a traditional Reynolds-averaged Navier-Stokes computation...
Bilateral bad pixel and Stokes image reconstruction for microgrid polarimetric imagers
LeMaster, Daniel A.; Ratliff, Bradley M.
2015-09-01
Uncorrected or poorly corrected bad pixels reduce the effectiveness of polarimetric clutter suppression. In conventional microgrid processing, bad pixel correction is accomplished as a separate step from Stokes image reconstruction. Here, these two steps are combined to speed processing and provide better estimates of the entire image, including missing samples. A variation on the bilateral filter enables both edge preservation in the Stokes imagery and bad pixel suppression. Understanding the newly presented filter requires two key insights. First, the adaptive nature of the bilateral filter is extended to correct for bad pixels by simply incorporating a bad pixel mask. Second, the bilateral filter for Stokes estimation is the sum of the normalized bilateral filters for estimating each analyzer channel individually. This paper describes the new approach and compares it to our legacy method using simulated imagery.
Sun, Yingying; Yanagisawa, Masahiro; Kunimoto, Masahiro; Nakamura, Masatoshi; Homma, Takayuki
2016-02-01
A structure's temperature can be determined from the Raman spectrum using the frequency and the ratio of the intensities of the anti-Stokes and Stokes signals (the Ias/Is ratio). In this study, we apply this approach and an equation relating the temperature, Raman frequency, and Ias/Is ratio to in-situ estimation of the phase change point of a (3-aminopropyl)triethoxysilane self-assembled monolayer (APTES SAM). Ag nanoparticles were deposited on APTES to enhance the Raman signals. A time-resolved measurement mode was used to monitor the variation in the Raman spectra in situ. Moreover, the structural change in APTES SAM (from ordered to disordered structure) under heating was discussed in detail, and the phase change point (around 118 °C) was calculated.
Mishra, Chandan K; Ganapathy, Rajesh
2015-05-15
We examine the influence of the shape of dynamical heterogeneities on the Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in quasi-two-dimensional suspensions of colloidal ellipsoids. For ellipsoids with repulsive interactions, both SE and SED relations are violated at all area fractions. On approaching the glass transition, however, the extent to which this violation occurs changes beyond a crossover area fraction. Quite remarkably, we find that it is not just the presence of dynamical heterogeneities but their change in the shape from stringlike to compact that coincides with this crossover. On introducing a suitable short-range depletion attraction between the ellipsoids, associated with the lack of morphological evolution of dynamical heterogeneities, the extent to which the SE and SED relations are violated remains unchanged even for deep supercooling.
Navier-Stokes computations of separated vortical flows past prolate spheroid at incidence
Wong, Tin-Chee; Kandil, Osama A.; Liu, C. H.
1989-01-01
The problem of steady incompressible viscous flow past prolate spheroids at incidence is formulated using the unsteady incompressible and compressible thin-layer Navier-Stokes equations. The two sets of Navier-Stokes equations are solved using a pseudotime stepping of the implicit flux-difference splitting scheme on a curvilinear grid, which is generated by a transfinite grid generator. The Baldwin and Lomax (1978) algebraic eddy-viscosity model is used to model the turbulent flow. The computational applications cover a 6:1 prolate spheroid at different angles of attack and Reynolds numbers. The results are compared with experimental data.
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.
A strongly conservative finite element method for the coupling of Stokes and Darcy flow
Kanschat, G.
2010-08-01
We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in Hdiv(Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders. © 2010 Elsevier Inc.
Anti-Stokes luminescence in the light of second order perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, Rupak, E-mail: rupak@iiserkol.ac.in; Pal, Bipul, E-mail: bipul@iiserkol.ac.in; Bansal, Bhavtosh, E-mail: bhavtosh@iiserkol.ac.in [Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia, West Bengal 741246 (India)
2014-11-10
Anti-Stokes photoluminescence is measured in high-quality GaAs quantum wells. The primary pathway for interband optical absorption and hence emission under subbandgap photoexcitation is the optical phonon-mediated second-order electric dipole transition. This conclusion is drawn from the remarkable agreement between predictions of second-order perturbation calculation and the measured intensity of anti-Stokes photoluminescence, both as function of the detuning wavelength and temperature. The results are of direct relevance to laser cooling of solids where phonon-assisted upconversion is a necessary condition.
The Compressible Stokes Flows with No-Slip Boundary Condition on Non-Convex Polygons
Kweon, Jae Ryong
2017-03-01
In this paper we study the compressible Stokes equations with no-slip boundary condition on non-convex polygons and show a best regularity result that the solution can have without subtracting corner singularities. This is obtained by a suitable Helmholtz decomposition: {{{u}}={{w}}+nablaφ_R} with div w = 0 and a potential φ_R. Here w is the solution for the incompressible Stokes problem and φ_R is defined by subtracting from the solution of the Neumann problem the leading two corner singularities at non-convex vertices.
Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations
Bessaih, Hakima
2016-01-27
We study a modified three-dimensional incompressible anisotropic Navier−Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one. This modification appears naturally in porous media when a fluid obeys the Darcy−Forchheimer law instead of the classical Darcy law. We prove global in time existence and uniqueness of solutions without assuming the smallness condition on the initial data. This improves the result obtained for the classical 3D incompressible anisotropic Navier−Stokes equations.
A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations
Zhang, Tao
2015-06-01
In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.
Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations
Directory of Open Access Journals (Sweden)
Junbai Ren
2014-01-01
Full Text Available This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t-3/4≤uL2≤C2(1+t-3/4, t>1. The decay rate is optimal since it coincides with that of heat equation.
Solutions to three-dimensional Navier-Stokes equations for incompressible fluids
Directory of Open Access Journals (Sweden)
Jorma Jormakka
2010-07-01
Full Text Available This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.
Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C., E-mail: waymire@math.oregonstate.edu [Department of Mathematics, Oregon State University, Corvallis, Oregon 97331 (United States); Michalowski, Nicholas [Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003 (United States)
2015-07-15
The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.
Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations
Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C.
2015-07-01
The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.
Multilevel solvers of first-order system least-squares for Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Lai, Chen-Yao G. [National Chung Cheng Univ., Chia-Yi (Taiwan, Province of China)
1996-12-31
Recently, The use of first-order system least squares principle for the approximate solution of Stokes problems has been extensively studied by Cai, Manteuffel, and McCormick. In this paper, we study multilevel solvers of first-order system least-squares method for the generalized Stokes equations based on the velocity-vorticity-pressure formulation in three dimensions. The least-squares functionals is defined to be the sum of the L{sup 2}-norms of the residuals, which is weighted appropriately by the Reynolds number. We develop convergence analysis for additive and multiplicative multilevel methods applied to the resulting discrete equations.
Solution of the two-dimensional Navier-Stokes equations using sparse matrix solvers
Bender, Erich E.; Khosla, Prem K.
1987-01-01
The use of direct sparse matrix solvers in the solution of the Navier-Stokes equations is investigated. The Yale Sparse Matrix Package and its implementation in the solution algorithm is described. The streamfunction-vorticity form of the Navier-Stokes equations are discretized and linearized and the resulting system of equations are solved using this package. Several viscous flow problems are investigated, including flow in a cavity and flow around a NACA0012 airfoil. Massively separated flow around a sine wave airfoil is investigated and high Reynolds number solutions are obtained. A solution of the unsteady flow around a Joukowski airfoil at high angle of attack is presented.
Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source
DEFF Research Database (Denmark)
Paulsen, H.N.; Hilligsøe, Karen Marie; Thøgersen, J.
2003-01-01
A coherent anti-Stokes Raman scattering microscope based on a Ti:sapphire femtosecond oscillator and a photonic crystal fiber is demonstrated. The nonlinear response of the fiber is used to generate the additional wavelength needed in the Raman process. The applicability of the setup is demonstra......A coherent anti-Stokes Raman scattering microscope based on a Ti:sapphire femtosecond oscillator and a photonic crystal fiber is demonstrated. The nonlinear response of the fiber is used to generate the additional wavelength needed in the Raman process. The applicability of the setup...
Mikhailov, E. A.; Teplyakov, I. O.
2017-11-01
The flow generated in the conductive medium with the electromagnetic force appearing when non-uniform electric current interacts with the own magnetic field was considered. The problem was solved analytically using Stokes approximation in a hemispherical geometry. Also numerical solution was obtained and comparing with the oldest mode of analytical one was carried out. The numerical and asymptotic results are quite similar.
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Klaij, C.M.; van der Vegt, Jacobus J.W.; van der Ven, H.
2006-01-01
A space–time discontinuous Galerkin finite element method for the compressible Navier–Stokes equations is presented. We explain the space–time setting, derive the weak formulation and discuss our choices for the numerical fluxes. The resulting numerical method allows local grid adaptation as well as
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Klaij, C.M.; van der Vegt, Jacobus J.W.; van der Ven, H.
2005-01-01
A space-time discontinuous Galerkin finite element method for the compressible Navier-Stokes equations is presented. We explain the space-time setting, derive the weak formulation and discuss our choices for the numerical fluxes. The resulting numerical method allows local grid adaptation as well as
Chang, M-C; Chantzis, A; Jacquemin, D; Otten, E.
2016-01-01
The synthesis of a series of (formazanate)boron difluorides and their 1-electron reduction products is described. The neutral compounds are fluorescent with large Stokes shifts. DFT calculations suggest that a large structural reorganization accompanies photoexictation and accounts for the large
The vibrational Stokes shift of water (HOD in D2O)
Wang, Zhaohui; Pang, Yoonsoo; Dlott, Dana D.
2004-05-01
The vibrational Stokes shift of the OH stretching transition νOH of water is the shift between the ground-state absorption and the excited-state (v=1) emission. A recent measurement on HOD in D2O solvent [S. Woutersen and H. J. Bakker, Phys. Rev. Lett. 83, 2077 (1999)] of a 70 cm-1 redshift, and a subsequent calculation of a 57 cm-1 redshift using equilibrium molecular dynamics simulations [C. P. Lawrence and J. L. Skinner, J. Chem. Phys. 117, 8847 (2002)] were in good agreement. We now report extensive measurements of the vibrational Stokes shift in HOD/D2O using an ultrafast IR pump, Raman probe method. The vibrational Stokes shift is seen to depend on the pump pulse frequency and on time delay; by varying these parameters it can be made to range from 112 to -32 cm-1 (negative values indicate a blueshift in the excited state). The equilibrium vibrational Stokes shift is actually a negative rather than a positive quantity. Possible reasons for the disagreement between experiment and theory are briefly discussed.
Effective temperatures and the breakdown of the Stokes-Einstein relation for particle suspensions.
Mendoza, Carlos I; Santamaría-Holek, I; Pérez-Madrid, A
2015-09-14
The short- and long-time breakdown of the classical Stokes-Einstein relation for colloidal suspensions at arbitrary volume fractions is explained here by examining the role that confinement and attractive interactions play in the intra- and inter-cage dynamics executed by the colloidal particles. We show that the measured short-time diffusion coefficient is larger than the one predicted by the classical Stokes-Einstein relation due to a non-equilibrated energy transfer between kinetic and configuration degrees of freedom. This transfer can be incorporated in an effective kinetic temperature that is higher than the temperature of the heat bath. We propose a Generalized Stokes-Einstein relation (GSER) in which the effective temperature replaces the temperature of the heat bath. This relation then allows to obtain the diffusion coefficient once the viscosity and the effective temperature are known. On the other hand, the temporary cluster formation induced by confinement and attractive interactions of hydrodynamic nature makes the long-time diffusion coefficient to be smaller than the corresponding one obtained from the classical Stokes-Einstein relation. Then, the use of the GSER allows to obtain an effective temperature that is smaller than the temperature of the heat bath. Additionally, we provide a simple expression based on a differential effective medium theory that allows to calculate the diffusion coefficient at short and long times. Comparison of our results with experiments and simulations for suspensions of hard and porous spheres shows an excellent agreement in all cases.
Mathematical geophysics an introduction to rotating fluids and the Navier-Stokes equations
Chemin, Jean-Yves; Gallagher, Isabelle; Grenier, Emmanuel
2006-01-01
Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.
Czech Academy of Sciences Publication Activity Database
Šístek, Jakub; Cirak, F.
2015-01-01
Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045793015003023
Symbolic-numeric stability investigations of Jameson's scheme for this-layer Navier-Stokes equations
Ganzha, V.G.; Vorozhtsov, E.V.; Boers, J.; van Hulzen, J.A.; van Hulzen, J.A.
1994-01-01
The Navier-Stokes equations governing the three-dimensional flows of viscous, compressible, heat-conducting gas and augmented by turbulence modeling present the most realistic model for gas flows around the elements of aircraft configurations. We study the stability of one of the Jameson's schemes
Vibrational Phase Contrast Microscopy by Use of Coherent Anti-Stokes Raman Scattering
Jurna, M.; Korterik, Jeroen P.; Otto, Cornelis; Herek, Jennifer Lynn; Offerhaus, Herman L.
2009-01-01
In biological samples the resonant coherent anti-Stokes Raman scattering signal of less abundant constituents can be overwhelmed by the nonresonant background, preventing detection of those molecules. We demonstrate a method to obtain the phase of the oscillators in the focal volume that allows
On solutions with infinite energy and enstrophy of the Navier-Stokes system
Energy Technology Data Exchange (ETDEWEB)
Bakhtin, Yu Yu [International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow (Russian Federation); Dinaburg, E I [Institute of Physics of the Earth, Russian Academy of Sciences, Moscow (Russian Federation); Sinai, Yakov G [Mathematics Department, Princeton University, Princeton, New Jersey (United States)
2004-12-31
The Cauchy problem is considered for the Navier-Stokes system. Local and global existence and uniqueness theorems are given for initial data whose Fourier transform decays at infinity as a power-law function with negative exponent and has a power-law singularity at zero. The paper contains a survey of known facts and some new results.
Pointwise Estimates for Bipolar Compressible Navier-Stokes-Poisson System in Dimension Three
Wu, Zhigang; Wang, Weike
2017-11-01
The Cauchy problem of the bipolar Navier-Stokes-Poisson system (1.1) in dimension three is considered. We obtain the pointwise estimates of the time-asymptotic shape of the solution, which exhibit a generalized Huygens' principle as the Navier-Stokes system. This phenomenon is the most important difference from the unipolar Navier-Stokes-Poisson system. Due to the non-conservative structure of the system (1.1) and the interplay of two carriers which counteract the influence of the electric field (a nonlocal term), some new observations are essential for the proof. We fully use the conservative structure of the system for the total density and total momentum, and the mechanism of the linearized unipolar Navier-Stokes-Poisson system together with the special form of the nonlinear terms in the system for the difference of densities and the difference of momentums. Lastly, as a byproduct, we extend the usual {L^2(R^3)}-decay rate to the {L^p(R^3)}-decay rate with {p > 1} and also improve former decay rates.
Coherent anti-Stokes Raman scattering microscopy for pharmaceutics: a shift in the right direction
Fussell, A.L.
2014-01-01
This dissertation demonstrates coherent anti-Stokes Raman scattering (CARS) microscopy as a tool in pharmaceutical solid state development. CARS microscopy is a nonlinear optical imaging technique that uses inelastic scattering of light to provide chemically specific imaging. CARS microscopy is
Time-asymptotics and the self-organization hypothesis for 2D Navier-Stokes equations
van Groesen, Embrecht W.C.
1988-01-01
In this paper we study the long-time behaviour of solutions with a two-dimensional structure of the Navier-Stokes equations on a periodic grid. From a rigorous investigation of the decrease of the energy E and the enstrophy W, it follows that the Rayleigh quotient Image is monotonically decreasing
Energy Technology Data Exchange (ETDEWEB)
Hong Luo; Luqing Luo; Robert Nourgaliev; Vincent A. Mousseau
2010-01-01
A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.
Labeur, R.J.; Wells, G.N.
2012-01-01
A hybrid method for the incompressible Navier–Stokes equations is presented. The ethod inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods hen momentum advection becomes significant, equal-order interpolations can be used for the velocity nd pressure fields, and
van der Vegt, Jacobus J.W.; Klaij, C.M.; van der Bos, F.; van der Ven, H.; Wesseling, P.; Onate, E; Periaux, J.
2006-01-01
An overview is given of a space-time discontinuous Galerkin finite element method for the compressible Navier-Stokes equations. This method is well suited for problems with moving (free) boundaries which require the use of deforming elements. In addition, due to the local discretization, the
Directory of Open Access Journals (Sweden)
I. V. Makeev
2016-01-01
Full Text Available Stokes flows in cylindrical and spherical geometry are considered. Such flows are rather natural for geophysics. We derive some exact particular solutions of Stokes and continuity equations for particular dependence of viscosity and density on cylindrical coordinates. These solutions correspond to axisymmetric flows for the case when viscosity is a function of radius. We suggest exact particular solutions of Stokes and continuity equations with variable viscosity and density in spherical coordinates for the case of spherically symmetric viscosity and density distributions. We demonstrate how these solutions can be used for creation of test problems suitable for benchmarking numerical algorithms. Examples of such benchmarking are presented. The advantage of this benchmarking approach is the ability to test numerical algorithms for variable viscosity and density gradients. We suggest numerical scheme of multigrid algorithm for solving Stokes and continuity equations with variable viscosity in a spherical coordinate system. Calculations are performed on a sequence of orthogonal staggered grids. The quality of the numerical scheme was verified by comparing the numerical solution with the analytical solution of the test problem.
Epi-detection of vibrational phase contrast coherent anti-Stokes Raman scattering
Garbacik, E.T.; Korterik, Jeroen P.; Otto, Cornelis; Herek, Jennifer Lynn; Offerhaus, Herman L.
2014-01-01
We demonstrate a system for the phase-resolved epi-detection of coherent anti-Stokes Raman scattering (CARS) signals in highly scattering and/or thick samples. With this setup, we measure the complex vibrational responses of multiple components in a thick, highly-scattering pharmaceutical tablet in
Garbacik, E.T.; Herek, Jennifer Lynn; Otto, Cornelis; Offerhaus, Herman L.
2012-01-01
For the rapid analysis of complicated heterogeneous mixtures, we have developed a method to acquire and intuitively display hyperspectral coherent anti-Stokes Raman scattering (CARS) images. The imaging is performed with a conventional optical setup based around an optical parametric oscillator.
Stokes Space-Based Optical Modulation Format Recognition for Digital Coherent Receivers
DEFF Research Database (Denmark)
Borkowski, Robert; Zibar, Darko; Caballero Jambrina, Antonio
2013-01-01
modulation formats is successfully demonstrated numerically and experimentally. The proposed method does not require training or a constellation diagram to operate, is insensitive to polarization mixing or frequency offset and can be implemented in any receiver capable of measuring Stokes parameters....
on coupled system of navier-stokes equations and temperature in ...
African Journals Online (AJOL)
Dr. Anthony Peter
ABSTRACT. This paper deals with the coupled system of Navier-Stokes equations and temperature (Thermohydraulics) in a strip in the class of spatially non-decaying (infinite-energy) solutions belonging to the properly chosen uniformly local Sobolev spaces. The global well-posedness and dissipativity of the Navier- ...
Etude de l'equation de Navier-Stokes stochastique non homogene
African Journals Online (AJOL)
Resume. Le travail de cet article consiste a etudier !'existence et l'unicite de la solution des equations de Navier-Stokes stochastiques et non homogenes selon une methode directe due a Faedo-Galerkin [1]. Cette methode consiste a approcher les solutions de ces equations dans un espace de dimension finie. Dans ce ...
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.
Directory of Open Access Journals (Sweden)
Jian Liu
2013-09-01
Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.
On the asymptotic structure of a Navier-Stokes flow past a rotating body
Kyed, Mads
2014-01-01
Consider a rigid body moving with a prescribed constant non-zero velocity and rotating with a prescribed constant non-zero angular velocity in a three-dimensional Navier-Stokes liquid. The asymptotic structure of a steady-state solution to the corresponding equations of motion is analyzed. In particular, an asymptotic expansion of the corresponding velocity field is obtained.
Stokes flow of micropolar fluid past a viscous fluid spheroid with non ...
Indian Academy of Sciences (India)
The Stokes axisymmetric flow of an incompressible micropolar fluid past a viscous fluid spheroid whose shape deviates slightly from that of a sphere is studied analytically. The boundary conditions used are the vanishing of the normal velocities, the continuity of the tangential velocities, continuity of shear stresses and ...
Directory of Open Access Journals (Sweden)
H. A. Wahab
2015-06-01
Full Text Available This paper deals with the approximate analytical solution of the Navier-Stokes equations in cylindrical coordinates. The homotopy perturbation method is used to get the analytical approximation. Depending upon different available choices for the linear operator, we also have the advantage to choose different initial approximations to start our analysis. The analysis is done without calculating the Adomian's polynomials.
A Discontinuous Finite Volume Method for the Darcy-Stokes Equations
Directory of Open Access Journals (Sweden)
Zhe Yin
2012-01-01
Full Text Available This paper proposes a discontinuous finite volume method for the Darcy-Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh-dependent norm. First-order L2-error estimates are derived for the approximations of both velocity and pressure. Some numerical examples verifying the theoretical predictions are presented.
Schafer, D.; Müller, M.; Bonn, M.; Marr, D.W.M.; van Maarseveen, J.; Squier, J.
2009-01-01
We present an optical, noninvasive and label-free approach to characterize flow profiles in microfluidic devices. Coherent anti-Stokes Raman scattering signals were used to map the mass transport in a microfluidic device that was then related back to the local flow rate of dilute solutes having
Fussell, A.L.; Mah, Pei Ting; Offerhaus, Herman L.; Niemi, Sanna-Mari; Salonen, Jarno; Santos, Helder A.; Strachan, Clare
2014-01-01
This study reports the use of variants of coherent anti-Stokes Raman scattering (CARS) microscopy as a novel method for improved physicochemical characterization of drug-loaded silica particles. Ordered mesoporous silica is a biomaterial that can be loaded to carry a number of biochemicals,
On the impact of wave-current on Stokes waves | Oyetunde | Journal ...
African Journals Online (AJOL)
This study considers the impact of wave - current on Stokes waves in deep water. Using separately, the third, fourth and fifth order approximations of wave profile functions respectively and the determined expressions for wave – current speed , it is shown that the wave - current speed is more intense on the surface of the ...
On the effects of wave steepness on higher order Stokes waves ...
African Journals Online (AJOL)
The effect of wave steepness on higher order finite amplitude Stokes waves is investigated analytically and numerically. It is shown that the phase speed increases as the wave steepness increases thereby initiating the wave instabilities. As the order increases, the phase speed also increases .However, the impact of wave ...
On the Stochastic 3D Navier-Stokes-α Model of Fluids Turbulence
Directory of Open Access Journals (Sweden)
Gabriel Deugoue
2009-01-01
Full Text Available We investigate the stochastic 3D Navier-Stokes-α model which arises in the modelling of turbulent flows of fluids. Our model contains nonlinear forcing terms which do not satisfy the Lipschitz conditions. The adequate notion of solutions is that of probabilistic weak solution. We establish the existence of a such of solution. We also discuss the uniqueness.
Page 1 Solidification modelling 545 Navier-Stokes equations, that is ...
Indian Academy of Sciences (India)
In the solid phase, where R becomes very high, the Navier-Stokes equations will be dominated by the sources and the velocity forced to a very small value. Warious permeability functions available in the literature are listed and compared by Daming. Xu and Qingchun Li (1990). 1,1c Heat transfer at mould/metal interface: ...
A Robust Two-Level Incomplete Factorization for (Navier–)Stokes Saddle Point Matrices
Wubs, Fred W.; Thies, Jonas
2011-01-01
We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier–Stokes equations on an Arakawa C-grid. The two-level method introduced here has the following properties: (i) it is very
A ROBUST TWO-LEVEL INCOMPLETE FACTORIZATION FOR (NAVIER-)STOKES SADDLE POINT MATRICES
Wubs, Fred W.; Thies, Jonas
2011-01-01
We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method introduced here has the following properties: (i) it is very
Etude de l'equation de Navier-Stokes stochastique non homogene
African Journals Online (AJOL)
incompressibles non-homogenes, Doklady Akademii. Nauk SSSR(Russie), 216, 1008-1010. [14] Cattabriga L., 1961. Su un problema al contorno relativo al sistema di equazio di Stokes. Mathematiques Universite Padova(Italie), 31, 308-. 355. [15] Yosida K., 1986. Problemes mathematiques d'hydrodynamique statistique.
A study of plunging breaker mechanics by PIV measurements and a Navier-Stokes solver
DEFF Research Database (Denmark)
Emarat, Narumon; Forehand, David I. M.; Christensen, Erik Damgaard
2000-01-01
The mechanics of a surf-zone plunging breaker are studied from Particle Image Velocimetry (PIV) measurements and a numerical model based on the Navier-Stokes equations, using a Volume of Fluid (VOF) method. An additional numerical model using a Boundary-Integral Method (BIM) is also used in order...
Some strange numerical solutions of the non-stationary Navier-Stokes equations in pipes
Energy Technology Data Exchange (ETDEWEB)
Rummler, B.
2001-07-01
A general class of boundary-pressure-driven flows of incompressible Newtonian fluids in three-dimensional pipes with known steady laminar realizations is investigated. Considering the laminar velocity as a 3D-vector-function of the cross-section-circle arguments, we fix the scale for the velocity by the L{sub 2}-norm of the laminar velocity. The usual new variables are introduced to get dimension-free Navier-Stokes equations. The characteristic physical and geometrical quantities are subsumed in the energetic Reynolds number Re and a parameter {psi}, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form u=u{sub L}+u, where u{sub L} is the scaled laminar velocity and periodical conditions in center-line-direction are prescribed for u. An autonomous system (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction is got by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u. The finite-dimensional approximations u{sub N({lambda}}{sub )} of u are defined in the usual way. (orig.)
Completely background free broadband coherent anti-Stokes Raman scattering spectroscopy
DEFF Research Database (Denmark)
Liu, Xing; Niu, Hanben; Liu, Wei
2013-01-01
For the first time it was proposed a numerical approach to obtain non-NRB time-frequency coherent anti-Stokes Raman scattering (CARS) spectrograms. In order to evaluate the validity of the CARS spectrogram for background free broadband CARS spectroscopy, the authors numerically constructed a CARS...
Analysis of a General Family of Regularized Navier-Stokes and MHD Models
Holst, Michael; Lunasin, Evelyn; Tsogtgerel, Gantumur
2010-10-01
We consider a general family of regularized Navier-Stokes and Magnetohydrodynamics (MHD) models on n-dimensional smooth compact Riemannian manifolds with or without boundary, with n≥2. This family captures most of the specific regularized models that have been proposed and analyzed in the literature, including the Navier-Stokes equations, the Navier-Stokes- α model, the Leray- α model, the modified Leray- α model, the simplified Bardina model, the Navier-Stokes-Voight model, the Navier-Stokes- α-like models, and certain MHD models, in addition to representing a larger 3-parameter family of models not previously analyzed. This family of models has become particularly important in the development of mathematical and computational models of turbulence. We give a unified analysis of the entire three-parameter family of models using only abstract mapping properties of the principal dissipation and smoothing operators, and then use assumptions about the specific form of the parameterizations, leading to specific models, only when necessary to obtain the sharpest results. We first establish existence and regularity results, and under appropriate assumptions show uniqueness and stability. We then establish some results for singular perturbations, which as special cases include the inviscid limit of viscous models and the α→0 limit in α models. Next, we show existence of a global attractor for the general model, and then give estimates for the dimension of the global attractor and the number of degrees of freedom in terms of a generalized Grashof number. We then establish some results on determining operators for the two distinct subfamilies of dissipative and non-dissipative models. We finish by deriving some new length-scale estimates in terms of the Reynolds number, which allows for recasting the Grashof number-based results into analogous statements involving the Reynolds number. In addition to recovering most of the existing results on existence, regularity
Directory of Open Access Journals (Sweden)
Thuc T Le
Full Text Available Hepatic microvesicular steatosis is a hallmark of drug-induced hepatotoxicity and early-stage fatty liver disease. Current histopathology techniques are inadequate for the clinical evaluation of hepatic microvesicular steatosis. In this paper, we explore the use of multimodal coherent anti-Stokes Raman scattering (CARS microscopy for the detection and characterization of hepatic microvesicular steatosis. We show that CARS microscopy is more sensitive than Oil Red O histology for the detection of microvesicular steatosis. Computer-assisted analysis of liver lipid level based on CARS signal intensity is consistent with triglyceride measurement using a standard biochemical assay. Most importantly, in a single measurement procedure on unprocessed and unstained liver tissues, multimodal CARS imaging provides a wealth of critical information including the detection of microvesicular steatosis and quantitation of liver lipid content, number and size of lipid droplets, and lipid unsaturation and packing order of lipid droplets. Such information can only be assessed by multiple different methods on processed and stained liver tissues or tissue extracts using current standard analytical techniques. Multimodal CARS microscopy also permits label-free identification of lipid-rich non-parenchymal cells. In addition, label-free and non-perturbative CARS imaging allow rapid screening of mitochondrial toxins-induced microvesicular steatosis in primary hepatocyte cultures. With its sensitivity and versatility, multimodal CARS microscopy should be a powerful tool for the clinical evaluation of hepatic microvesicular steatosis.
Multi-GPU three dimensional Stokes solver for simulating glacier flow
Licul, Aleksandar; Herman, Frédéric; Podladchikov, Yuri; Räss, Ludovic; Omlin, Samuel
2016-04-01
Here we present how we have recently developed a three-dimensional Stokes solver on the GPUs and apply it to a glacier flow. We numerically solve the Stokes momentum balance equations together with the incompressibility equation, while also taking into account strong nonlinearities for ice rheology. We have developed a fully three-dimensional numerical MATLAB application based on an iterative finite difference scheme with preconditioning of residuals. Differential equations are discretized on a regular staggered grid. We have ported it to C-CUDA to run it on GPU's in parallel, using MPI. We demonstrate the accuracy and efficiency of our developed model by manufactured analytical solution test for three-dimensional Stokes ice sheet models (Leng et al.,2013) and by comparison with other well-established ice sheet models on diagnostic ISMIP-HOM benchmark experiments (Pattyn et al., 2008). The results show that our developed model is capable to accurately and efficiently solve Stokes system of equations in a variety of different test scenarios, while preserving good parallel efficiency on up to 80 GPU's. For example, in 3D test scenarios with 250000 grid points our solver converges in around 3 minutes for single precision computations and around 10 minutes for double precision computations. We have also optimized the developed code to efficiently run on our newly acquired state-of-the-art GPU cluster octopus. This allows us to solve our problem on more than 20 million grid points, by just increasing the number of GPU used, while keeping the computation time the same. In future work we will apply our solver to real world applications and implement the free surface evolution capabilities. REFERENCES Leng,W.,Ju,L.,Gunzburger,M. & Price,S., 2013. Manufactured solutions and the verification of three-dimensional stokes ice-sheet models. Cryosphere 7,19-29. Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson,G.H., Hindmarsh, R
Dubolazov, O. V.; Trifonyuk, L.; Marchuk, Yu.; Ushenko, Yu. O.; Zhytaryuk, V. G.; Prydiy, O. G.; Kushnerik, L.; Meglinskiy, I.
2017-08-01
A new method of Stokes correlometry of polarization-inhomogeneous images of biological layers is presented. Analytic relations are determined for the modulus of complex parameters of the Stokes vector. A technique for measuring the coordinate distributions of the magnitude of the two-point modulus of the Stokes vector is proposed. Objective criteria for differentiating the optical anisotropy of polycrystalline urine films of healthy donors and patients with albuminuria have been found. An excellent level of balanced accuracy of differential diagnostics has been achieved.
DEFF Research Database (Denmark)
Hesthaven, Jan
1997-01-01
This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions...... and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier-Stokes equations in general curvilinear coordinates. The versatility of the proposed scheme for the compressible Navier-Stokes equations is illustrated...
Hüllemann, K D; List, M; Matthes, D; Wiese, G; Zika, D
1975-08-01
Spiroergometric and telemetric investigations were carried out on 100 paralysed athletes during the XXI International Stoke Mandeville Games in Heidelberg, 1972. The technical and organisational difficulties in carrying out these measurements were engendered by the disabilities of subjects. The maximum oxygen uptake observed and the oxygen pulse were lower than in non-disabled persons. There were no differences in the peak heart rates (180-200 beats/min.) as compared with non-disabled athletes during particular competition situations. Sports characterised by quickness, dexterity and strength are not able to train the cardiopulomnary system substantially. Swimming is recommended as beneficial. Psychological and training physiological considerations suggest that long-distance wheelchair races should be adopted as a Stoke Mandeville event.
A mechanism of the anti-Stokes luminescence of a dye-sensitized silver halide emulsion
Tyurin, A. V.; Churashov, V. P.; Zhukov, S. A.; Pavlova, O. V.
2008-02-01
A two-photon stepwise mechanism of the low-temperature anti-Stokes luminescence of a sensitized AgBrI emulsion, caused by photoexcitation of dye aggregates, is proved experimentally. According to this mechanism, the photoexcitation energy is transferred from the dye to the AgHal microcrystal through silver cluster centers. It is found that the luminescence with the maximum at λ ≈ 750 nm is caused by the recombination of an electron localized at the silver cluster with a free hole in the valence band of the AgHal microcrystal. The migration of an electron from a silver cluster to a iodine pair center with a captured hole creates a nonradiative recombination channel, which is responsible for the flare buildup of the green anti-Stokes luminescence upon excitation of dye aggregates.
DEFF Research Database (Denmark)
Kolmogorov, Dmitry
Direct numerical solutions of the Navier-Stokes equations using Computational Fluid Dynamics methods are recognized as some the most advanced and accurate methods for prediction of flows around wind turbines. The ability of these methods to capture the dynamics of the complex flow properties...... is typical for some commonly used mass flux interpolations, is estimated, and a new interpolation technique, which eliminates these errors, is developed together with fully consistent SIMPLE-like algorithms. For the algorithms, both the accuracy and the convergence rate are shown to be higher than standard...... versions of the SIMPLE algorithm. The new technique is implemented in an existing conservative 2nd order finite-volume scheme flow solver (EllipSys), which is extended to cope with grids with nonconformal interfaces. The behavior of the discrete Navier-Stokes equations is discussed in detail...
Two-Level Stabilized Finite Volume Methods for Stationary Navier-Stokes Equations
Directory of Open Access Journals (Sweden)
Anas Rachid
2012-01-01
Full Text Available We propose two algorithms of two-level methods for resolving the nonlinearity in the stabilized finite volume approximation of the Navier-Stokes equations describing the equilibrium flow of a viscous, incompressible fluid. A macroelement condition is introduced for constructing the local stabilized finite volume element formulation. Moreover the two-level methods consist of solving a small nonlinear system on the coarse mesh and then solving a linear system on the fine mesh. The error analysis shows that the two-level stabilized finite volume element method provides an approximate solution with the convergence rate of the same order as the usual stabilized finite volume element solution solving the Navier-Stokes equations on a fine mesh for a related choice of mesh widths.
Navier-Stokes-Voigt Equations with Memory in 3D Lacking Instantaneous Kinematic Viscosity
Di Plinio, Francesco; Giorgini, Andrea; Pata, Vittorino; Temam, Roger
2017-11-01
We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. Unlike the classical Navier-Stokes-Voigt system, the energy balance involves the spatial gradient of the past history of the velocity rather than providing an instantaneous control on the high modes. In spite of this difficulty, we show that our system is dissipative in the dynamical systems sense and even possesses regular global and exponential attractors of finite fractal dimension. Such features of asymptotic well-posedness in absence of instantaneous high modes dissipation appear to be unique within the realm of dynamical systems arising from fluid models.
Transition from fractional to classical Stokes-Einstein behaviour in simple fluids.
Coglitore, Diego; Edwardson, Stuart P; Macko, Peter; Patterson, Eann A; Whelan, Maurice
2017-12-01
An optical technique for tracking single particles has been used to evaluate the particle diameter at which diffusion transitions from molecular behaviour described by the fractional Stokes-Einstein relationship to particle behaviour described by the classical Stokes-Einstein relationship. The results confirm a prior prediction from molecular dynamic simulations that there is a particle size at which transition occurs and show it is inversely dependent on concentration and viscosity but independent of particle density. For concentrations in the range 5 × 10 -3 to 5 × 10 -6 mg ml -1 and viscosities from 0.8 to 150 mPa s, the transition was found to occur in the diameter range 150-300 nm.
Development of a grid generator to support 3-D multizone Navier-Stokes analysis
Holcomb, J. E.
1987-01-01
A three-dimensional grid generation code has been developed to support multizone Navier-Stokes analysis of flowfields associated with complex geometries. The code includes a number of features necessary for this task, including the definition of arbitrary zonal boundary surfaces using the output from a separate surface geometry program. The interior of each zone is gridded by an efficient parabolic/elliptic partial differential equation algorithm. To test the new grid generation code, grids were successfully generated for a finned missile configuration, for a hypersonic vehicle, for a fluid dynamic vortex valve, and for a three-dimensional rocket base/nozzle/plume configuration. Navier-Stokes calculations were run on these grids, with satisfactory results. The new code is expected to provide a solid basis for the extension to optimized and solution-adaptive grid generation in the future.
Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP–HOM
Directory of Open Access Journals (Sweden)
F. Pattyn
2008-08-01
Full Text Available We present the results of the first ice sheet model intercomparison project for higher-order and full-Stokes ice sheet models. These models are compared and verified in a series of six experiments of which one has an analytical solution obtained from a perturbation analysis. The experiments are applied to both 2-D and 3-D geometries; five experiments are steady-state diagnostic, and one has a time-dependent prognostic solution. All participating models give results that are in close agreement. A clear distinction can be made between higher-order models and those that solve the full system of equations. The full-Stokes models show a much smaller spread, hence are in better agreement with one another and with the analytical solution.
Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers
Atanasov, Atanas
2016-10-17
We present an Anderson acceleration-based approach to spatially couple three-dimensional Lattice Boltzmann and Navier–Stokes (LBNS) flow simulations. This allows to locally exploit the computational features of both fluid flow solver approaches to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier–Stokes solver. We detail our coupling methodology, validate it, and study convergence and accuracy of the Anderson accelerated coupling, considering three steady-state scenarios: plane channel flow, flow around a sphere and channel flow across a porous structure. We find that the Anderson accelerated coupling yields a speed-up (in terms of iteration steps) of up to 40% in the considered scenarios, compared to strictly sequential Schwarz coupling.
Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling
Energy Technology Data Exchange (ETDEWEB)
Zhang, Huai; Ju, Lili
2011-01-01
A three-dimensional full-Stokes computational model is considered for determining the dynamics, temperature, and thickness of ice sheets. The governing thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum, an advective-diffusion energy equation for temperature evolution, and a mass conservation equation for icethickness changes. Here, we discuss the variable resolution meshes, the finite element discretizations, and the parallel algorithms employed by the model components. The solvers are integrated through a well-designed coupler for the exchange of parametric data between components. The discretization utilizes high-quality, variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers. We demonstrate the gridding technology, discretization schemes, and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.
Numerical simulation of the second-order Stokes theory using finite difference method
Directory of Open Access Journals (Sweden)
M.A. Maâtoug
2016-09-01
Full Text Available The nonlinear water waves problem is of great importance because, according to the mechanical modeling of this problem, a relationship exists between the potential flow and pressure exerted by water waves. The difficulty of this problem comes not only from the fact that the kinematic and dynamic conditions are nonlinear in relation to the velocity potential, but especially because they are applied at an unknown and variable free surface. To overcome this difficulty, Stokes used an approach consisting of perturbations series around the still water level to develop a nonlinear theory. This paper deals with computation of the second-order Stokes theory in order to simulate the potential flow and the surface elevation and then to deduct the pressure loads. The Crank–Nicholson scheme and the finite difference method are used. The modeling accuracy was proved and is of order two in time and in space. Some computational results are presented and discussed.
Steady Stokes flow past dumbbell shaped axially symmetric body of revolution: An analytic approach
Directory of Open Access Journals (Sweden)
Srivastava Kumar Deepak
2012-01-01
Full Text Available In this paper, the problem of steady Stokes flow past dumbbell-shaped axially symmetric isolated body of revolution about its axis of symmetry is considered by utilizing a method (Datta and Srivastava, 1999 based on body geometry under the restrictions of continuously turning tangent on the boundary. The relationship between drag and moment is established in transverse flow situation. The closed form expression of Stokes drag is then calculated for dumbbell-shaped body in terms of geometric parameters b, c, d and a with the aid of this linear relation and the formula of torque obtained by (Chwang and Wu, part 1, 1974 with the use of singularity distribution along axis of symmetry. Drag coefficient and moment coefficient are defined in various forms in terms of dumbbell parameters. Their numerical values are calculated and depicted in respective graphs and compared with some known values.
Tamellini, L.
2014-01-01
In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.
Chemical imaging and microspectroscopy with spectral focusing coherent anti-Stokes Raman scattering
Chen, Bi-Chang; Sung, Jiha; Wu, Xiaoxi; Lim, Sang-Hyun
2011-02-01
We demonstrate two different coherent anti-Stokes Raman scattering (CARS) microscopy and microspectroscopy methods based on the spectral focusing mechanism. The first method uses strongly chirped broadband pulses from a single Ti:sapphire laser and generates CARS signals at the fingerprint region. Fast modulation of the time delay between the pump and Stokes laser pulses coupled with lock-in signal detection significantly reduces the nonresonant background and produces Raman-like CARS signals with a spectral resolution of 20 cm-1. The second method generates CARS signals in the CH (carbon-hydrogen) stretching region with IR supercontinuum pulses from a photonic crystal fiber. The spectral resolution of 30 cm-1 is achieved. Maximum entropy method is used to retrieve a Raman-equivalent CARS spectrum from lipid membranes. Chemical imaging and microspectroscopy are demonstrated with various samples.
Tuning the Quantum Efficiency of Random Lasers - Intrinsic Stokes-Shift and Gain
Lubatsch, Andreas; Frank, Regine
2015-11-01
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.
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.
Renumbering Methods to Unleash Multi-Threaded Approaches for a General Navier-Stokes Implementation
Vezolle, Pascal; Fournier, Yvan; Tallet, Nicolas; Heymans, Jerrold; D'Amora, Bruce
2010-09-01
Our investigation leverages the general industrial Navier-Stokes open-source Computational Fluid Dynamics (CFD) application, Code_Saturne, developed by Électricité de France (EDF). We deal with how to take advantage of the emerging processor features such as many-cores, Simultaneous Multi-Threading (SMT) and Thread Level Speculation (TLS), through a mixed MPI/multithreads approach. We focus here on the per-node performance improvements and present the constraints for a multithreads implementation to solve the general 3D Navier-Stokes equations using a finite volume discretization into polyhedral cells. We describe a simple and efficient mesh numbering scheme allowing us to introduce OpenMP and Thread Level Speculation implementations with minimal impact to overall code structure.
Schomerus, H
1997-01-01
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems with one degree of freedom is presented. We derive uniform approximations to be used in semiclassical trace formulas and determine also certain global bifurcations in conjunction with Stokes transitions that become important in the ensuing diffraction catastrophe integrals.
Covariance estimation in Terms of Stokes Parameters iwth Application to Vector Sensor Imaging
2016-12-15
vector sensor imaging problem: estimating the magnitude, polarization, and direction of plane wave sources from a sample covariance matrix of vector mea...Covariance estimation in terms of Stokes parameters with application to vector sensor imaging Ryan Volz∗, Mary Knapp†, Frank D. Lind∗, Frank C. Robey...Lincoln Laboratory, Lexington, MA Abstract— Vector sensor imaging presents a challeng- ing problem in covariance estimation when allowing arbitrarily
A domain decomposition preconditioner of Neumann-Neumann type for the Stokes equations
Dolean, Victorita; Nataf, Frédéric; Rapin, Gerd
2009-01-01
In this paper we recall a new domain decomposition method for the Stokes problem obtained via the Smith factorization. From the theoretical point of view, this domain decomposition method is optimal in the sense that it converges in two iterations for a decomposition into two equal domains. Previous results illustrated the fast convergence of the proposed algorithm in some cases. Our algorithm has shown a more robust behavior than Neumann- Neumann or FETI type methods for particular decomposi...
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Farouq, S.; Neytcheva, M.
2017-01-01
Roč. 310, January 2017 (2017), s. 5-18 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : optimal control * time-harmonic Stokes problem * preconditioning Subject RIV: BA - General Mathematics Impact factor: 1.357, year: 2016 http://www.sciencedirect.com/science/article/pii/S0377042716302631?via%3Dihub
Czech Academy of Sciences Publication Activity Database
Haslinger, Jaroslav; Kučera, R.; Šátek, V.
2017-01-01
Roč. 22, October 2017 (2017), s. 1-14 ISSN 1081-2865 R&D Projects: GA MŠk LQ1602; GA ČR(CZ) GA17-01747S Institutional support: RVO:68145535 Keywords : Stokes system * threshold slip boundary conditions * solution dependent slip function Subject RIV: BA - General Mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/abs/10.1177/1081286517716222
Invariant measure for the stochastic Navier-Stokes equations in unbounded 2D domains
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Motyl, E.; Ondreját, Martin
2017-01-01
Roč. 45, č. 5 (2017), s. 3145-3201 ISSN 0091-1798 R&D Projects: GA ČR(CZ) GA15-08819S Institutional support: RVO:67985556 Keywords : Invariant measure * bw-Feller semigroup * stochastic Navier–Stokes equation Subject RIV: BA - General Mathematics Impact factor: 1.940, year: 2016 http:// library .utia.cas.cz/separaty/2017/SI/ondrejat-0478383.pdf
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.
The Navier-Stokes-Fourier system: From weak solutions to numerical analysis
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard
2015-01-01
Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml
Parallel Solvers for Incompressible Navier-Stokes Equations and Scalable Tools for FEM Applications
K. Georgiev
2012-01-01
The White Paper content is focused on: a) construction and analysis of novel scalable algorithms to enhance scientific applications based on mesh methods (mainly on finite element method (FEM) technology); b) optimization of a new class of algorithms on many core systems. From one site, the commonly accepted benchmark problem in computational fluid dynamics (CFD) – time dependent system of incompressible Navier-Stokes equations, is considered. The activities were motivated by advanced larg...
Pesch, L.
2007-01-01
Many numerical methods for fluid dynamics are suitable only for a single, idealized type of fluid. Most prominently, algorithms for compressible flow are often tailored to ideal gases and another class of schemes is designed for incompressible media. This dissertation targets a numerical method for the simulation of the flow of fluids with differing thermodynamical properties, in particular both compressible and incompressible fluids. By considering the Navier--Stokes equations in terms of ce...
Regularity criteria for the Navier–Stokes equations based on one component of velocity
Czech Academy of Sciences Publication Activity Database
Guo, Z.; Caggio, M.; Skalák, Zdeněk
2017-01-01
Roč. 35, June (2017), s. 379-396 ISSN 1468-1218 R&D Projects: GA ČR GA14-02067S Grant - others:Západočeská univerzita(CZ) SGS-2016-003; National Natural Science Foundation of China (CN) 11301394 Institutional support: RVO:67985874 Keywords : Navier–Stokes equations * regularity of solutions * regularity criteria * Anisotropic Lebesgue spaces Subject RIV: BK - Fluid Dynamics Impact factor: 1.659, year: 2016
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.
On the asymptotic behaviour of 2D stationary Navier-Stokes solutions with symmetry conditions
Decaster, Agathe; Iftimie, Dragoş
2017-10-01
We consider the 2D stationary incompressible Navier-Stokes equations in ℝ2. Under suitable symmetry, smallness and decay at infinity conditions on the forcing we determine the behaviour at infinity of the solutions. Moreover, when the forcing is small, satisfies suitable symmetry conditions and decays at infinity like a vector field homogeneous of degree -3, we show that there exists a unique small solution whose asymptotic behaviour at infinity is homogeneous of degree -1.
Error analysis for a monolithic discretization of coupled Darcy and Stokes problems
Girault, V.
2014-01-01
© de Gruyter 2014. The coupled Stokes and Darcy equations are approximated by a strongly conservative finite element method. The discrete spaces are the divergence-conforming velocity space with matching pressure space such as the Raviart-Thomas spaces. This work proves optimal error estimate of the velocity in the L2 norm in the domain and on the interface. Lipschitz regularity of the interface is sufficient to obtain the results.
Validity of the Stokes-Einstein relation in liquids: simple rules from the excess entropy.
Pasturel, A; Jakse, N
2016-12-07
It is becoming common practice to consider that the Stokes-Einstein relation D/T~ η -1 usually works for liquids above their melting temperatures although there is also experimental evidence for its failure. Here we investigate numerically this commonly-invoked assumption for simple liquid metals as well as for their liquid alloys. Using ab initio molecular dynamics simulations we show how entropy scaling relationships developed by Rosenfeld can be used to predict the conditions for the validity of the Stokes-Einstein relation in the liquid phase. Specifically, we demonstrate the Stokes-Einstein relation may break down in the liquid phase of some liquid alloys mainly due to the presence of local structural ordering as evidenced in their partial two-body excess entropies. Our findings shed new light on the understanding of transport properties of liquid materials and will trigger more experimental and theoretical studies since excess entropy and its two-body approximation are readily obtainable from standard experiments and simulations.
Analytical solution of time periodic electroosmotic flows: analogies to Stokes' second problem.
Duttat, P; Beskok, A
2001-11-01
Analytical solutions of time periodic electroosmotic flows in two-dimensional straight channels are obtained as a function of a nondimensional parameter kappa, which is based on the electric double-layer (EDL) thickness, kinematic viscosity, and frequency of the externally applied electric field. A parametric study as a function of kappa reveals interesting physics, ranging from oscillatory "pluglike" flows to cases analogous to the oscillating flat plate in a semi-infinite flow domain (Stokes' second problem). The latter case differs from the Stokes' second solution within the EDL, since the flow is driven with an oscillatory electric field rather than an oscillating plate. The analogous case of plate oscillating with the Helmholtz-Smoluchowski velocity matches our analytical solution in the bulk flow region. This indicates that the instantaneous Helmholtz-Smoluchowski velocity is the appropriate electroosmotic slip condition even for high-frequency excitations. The velocity profiles for large kappa values show inflection points very near the walls with localized vorticity extrema that are stronger than the Stokes layers. This have the potential to result in low Reynolds number flow instabilities. It is also shown that, unlike the steady pure electroosmotic flows, the bulk flow region of time periodic electroosmotic flows are rotational when the diffusion length scales are comparable to and less than the half channel height.
Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.
2015-01-01
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Relationship between Wave-Induced Diffusion Tensor and Stokes Drift for Unstable Waves
Noda, A.; Kawatani, Y.
2014-12-01
In the presence of waves, the mean fluid velocity is different depending on whether the mean is taken along a coordinate fixed in space (Eulerian mean) or along a coordinate fixed to fluid particles (Lagrangian mean). The difference (Lagrangian mean minus Eulerian mean) in the velocity is called the Stokes drift (velocity), of which theoretically precise definition was given by Andrews and McIntyre (JFM;1978). Here we give simple and intuitive graphic illustrations explaining the relationship between the wave-induced diffusion tensor and the Stokes drift. The symmetric part of the diffusion tensor is related to the temporal and spatial change of wave amplitude, while the antisymmetric part is related to the spatial change of the amplitude of gyrating motion of fluid particles. The divergence of the diffusion tensor induces an additional transport velocity in the Eulerian mean transport equation. However, the direction of the additional velocity is opposite (identical) to the Stokes drift velocity for the symmetric (antisymmetric) part. This relationship is exemplified for the theoretical Eady wave and for atmospheric eddies simulated by a GCM.
A mimetic finite difference method for the Stokes problem with elected edge bubbles
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, K [Los Alamos National Laboratory; Berirao, L [DIPARTMENTO DI MATERMATICA
2009-01-01
A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this article is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.
National Aeronautics and Space Administration — This SBIR project proposes to develop a gas-kinetic Navier-Stokes solver for simulation of hypersonic flows in thermal and chemical non-equilibrium. The...
REDUCTION TO CANONICAL-FORMS AND THE STOKES PHENOMENON IN THE THEORY OF LINEAR DIFFERENCE-EQUATIONS
IMMINK, GK
Previous results concerning the existence of right inverses of linear difference operators on Banach Spaces of holomorphic functions are extended. The Stokes phenomenon is analyzed for a class of very singular linear difference equations.
2014-11-19
The Generalized Empirical Interpolation Method: stability theory on Hilbert spaces with an application to the Stokes equation Maday, Y.a,b,c,e, Mula...interpolant (the Lebesgue constant) by relating it to an inf-sup problem in the case of Hilbert spaces . In the second part of the paper, it will be explained...SUBTITLE The Generalized Empirical Interpolation Method: stability theory on Hilbert spaces with an application to the Stokes equation 5a. CONTRACT
DEFF Research Database (Denmark)
N., Kroll; P., Renzoni; M., Amato
1998-01-01
The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage.......The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage....
Directory of Open Access Journals (Sweden)
Meng Zhi-Jun
2016-01-01
Full Text Available This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.
Jiang, Song; Li, Fucai; Xie, Feng
2015-01-01
As is well-known that the general radiation hydrodynamics models include two mainly coupled parts: one is macroscopic fluid part, which is governed by the compressible Navier-Stokes-Fourier equations, another is radiation field part, which is described by the transport equation of photons. Under the two physical approximations: "gray" approximation and P1 approximation, one can derive the so-called Navier-Stokes-Fourier-P1 approximation radiation hydrodynamics model from the general one. In t...
Brown, Donald L.
2013-01-01
Direct numerical simulation (DNS) of fluid flow in porous media with many scales is often not feasible, and an effective or homogenized description is more desirable. To construct the homogenized equations, effective properties must be computed. Computation of effective properties for nonperiodic microstructures can be prohibitively expensive, as many local cell problems must be solved for different macroscopic points. In addition, the local problems may also be computationally expensive. When the microstructure varies slowly, we develop an efficient numerical method for two scales that achieves essentially the same accuracy as that for the full resolution solve of every local cell problem. In this method, we build a dense hierarchy of macroscopic grid points and a corresponding nested sequence of approximation spaces. Essentially, solutions computed in high accuracy approximation spaces at select points in the the hierarchy are used as corrections for the error of the lower accuracy approximation spaces at nearby macroscopic points. We give a brief overview of slowly varying media and formal Stokes homogenization in such domains. We present a general outline of the algorithm and list reasonable and easily verifiable assumptions on the PDEs, geometry, and approximation spaces. With these assumptions, we achieve the same accuracy as the full solve. To demonstrate the elements of the proof of the error estimate, we use a hierarchy of macro-grid points in [0, 1]2 and finite element (FE) approximation spaces in [0, 1]2. We apply this algorithm to Stokes equations in a slowly porous medium where the microstructure is obtained from a reference periodic domain by a known smooth map. Using the arbitrary Lagrange-Eulerian (ALE) formulation of the Stokes equations (cf. [G. P. Galdi and R. Rannacher, Fundamental Trends in Fluid-Structure Interaction, Contemporary Challenges in Mathematical Fluid Dynamics and Its Applications 1, World Scientific, Singapore, 2010]), we obtain
Zeng, Jianhua; Chen, Lei; Dai, Qiaofeng; Lan, Sheng; Tie, Shaolong
2016-01-21
We proposed a scheme in which normal Raman scattering is coupled with hyper-Raman scattering for generating a strong anti-Stokes hyper-Raman scattering in nanomaterials by using femtosecond laser pulses. The proposal was experimentally demonstrated by using a single-layer MoS2 on a SiO2/Si substrate, a 17 nm-thick MoS2 on an Au/SiO2 substrate and a 9 nm-thick MoS2 on a SiO2-SnO2/Ag/SiO2 substrate which were confirmed to be highly efficient for second harmonic generation. A strong anti-Stokes hyper-Raman scattering was also observed in other nanomaterials possessing large second-order susceptibilities, such as silicon quantum dots self-assembled into "coffee" rings and tubular Cu-doped ZnO nanorods. In all the cases, many Raman inactive vibration modes were clearly revealed in the anti-Stokes hyper-Raman scattering. Apart from the strong anti-Stokes hyper-Raman scattering, Stokes hyper-Raman scattering with small Raman shifts was detected during the ablation process of thick MoS2 layers. It was also observed by slightly defocusing the excitation light. The detection of anti-Stokes hyper-Raman scattering may serve as a new technique for studying the Raman inactive vibration modes in nanomaterials.
Energy Technology Data Exchange (ETDEWEB)
Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd
2012-01-04
The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.
Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations
Le Maitre, Olivier
2014-01-06
In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.
Eigenfunction Expansions for the Stokes Flow Operators in the Inverted Oblate Coordinate System
Directory of Open Access Journals (Sweden)
Maria Hadjinicolaou
2016-01-01
Full Text Available When studying axisymmetric particle fluid flows, a scalar function, ψ, is usually employed, which is called a stream function. It serves as a velocity potential and it can be used for the derivation of significant hydrodynamic quantities. The governing equation is a fourth-order partial differential equation; namely, E4ψ=0, where E2 is the Stokes irrotational operator and E4=E2∘E2 is the Stokes bistream operator. As it is already known, E2ψ=0 in some axisymmetric coordinate systems, such as the cylindrical, spherical, and spheroidal ones, separates variables, while in the inverted prolate spheroidal coordinate system, this equation accepts R-separable solutions, as it was shown recently by the authors. Notably, the kernel space of the operator E4 does not decompose in a similar way, since it accepts separable solutions in cylindrical and spherical system of coordinates, while E4ψ=0 semiseparates variables in the spheroidal coordinate systems and it R-semiseparates variables in the inverted prolate spheroidal coordinates. In addition to these results, we show in the present work that in the inverted oblate spheroidal coordinates, the equation E′2ψ=0 also R-separates variables and we derive the eigenfunctions of the Stokes operator in this particular coordinate system. Furthermore, we demonstrate that the equation E′4ψ=0 R-semiseparates variables. Since the generalized eigenfunctions of E′2 cannot be obtained in a closed form, we present a methodology through which we can derive the complete set of the generalized eigenfunctions of E′2 in the modified inverted oblate spheroidal coordinate system.
Discretely Self-Similar Solutions to the Navier-Stokes Equations with Besov Space Data
Bradshaw, Zachary; Tsai, Tai-Peng
2017-12-01
We construct self-similar solutions to the three dimensional Navier-Stokes equations for divergence free, self-similar initial data that can be large in the critical Besov space {\\dot{B}_{p,∞}^{3/p-1}} where 3 1. These results extend those of uc(Bradshaw) and uc(Tsai) (Ann Henri Poincaré 2016. https://doi.org/10.1007/s00023-016-0519-0) which dealt with initial data in L 3 w since {L^3_w\\subsetneq \\dot{B}_{p,∞}^{3/p-1}} for p > 3. We also provide several concrete examples of vector fields in the relevant function spaces.
Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids
Energy Technology Data Exchange (ETDEWEB)
Meese, Ernst Arne
1998-07-01
Most solution methods of computational fluid dynamics (CFD) use structured grids based on curvilinear coordinates for compliance with complex geometries. In a typical industry application, about 80% of the time used to produce the results is spent constructing computational grids. Recently the use of unstructured grids has been strongly advocated. For unstructured grids there are methods for generating them automatically on quite complex domains. This thesis focuses on the design of Navier-Stokes solvers that can cope with unstructured grids and ''low quality grids'', thus reducing the need for human intervention in the grid generation.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-04-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
Reddy, K. C.
A projection method based on Gauss-Legendre quadratures for solving hyperbolic and parabolic partial differential equations is proposed. It is comparable to spectral methods in accuracy and convergence, and is more convenient to implement for non-linear problems. Results obtained with a wave equation and Burgers equation modeling a flow with sharp gradients show the high resolution achieved for a given number of nodes by using this method. Time-split implicit techniques are used for approximating the compressible Navier-Stokes equations.
Applicability of Stokes method for measuring viscosity of mixtures with concentration gradient
Directory of Open Access Journals (Sweden)
César Medina
2017-12-01
Full Text Available After measuring density and viscosity of a mixture of glycerin and water contained in a vertical pipe, a variation of these properties according to depth is observed. These gradients are typical of non-equilibrium states related to the lower density of water and the fact that relatively long times are necessary to achieve homogeneity. In the same pipe, the falling velocity of five little spheres is measured as a function of depth, and then a numerical fit is performed which agrees very well with experimental data. Based on the generalization of these results, the applicability of Stokes method is discussed for measuring viscosity of mixtures with a concentration gradient.
Identification of severe wind conditions using a Reynolds averaged Navier-Stokes solver
DEFF Research Database (Denmark)
Sørensen, Niels N.; Bechmann, Andreas; Johansen, Jeppe
2007-01-01
The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting...... the flow in the complex terrain by comparing with measurements from two meteorology masts. Next, it is illustrated how levels of turbulent kinetic energy can be used to easily identify areas with severe flow conditions, relying on a high correlation between high turbulence intensity and severe flow...
3D Navier-Stokes computations of a stall-regulated wind turbine
Energy Technology Data Exchange (ETDEWEB)
Le Pape, A.; Lecanu, J. [ONERA, Chatillon (France). Dept. of Applied Aerodynamics
2004-07-01
Several 2D and 3D Navier-Stokes computations performed with the compressible elsA solver, developed at ONERA, on the wind turbine tested by NREL in the NASA Ames large wind tunnel are presented. After a brief description of the tools and methods used, the predictions of the S809 aerofoil performance are first discussed. Full 3D computations are then presented, analysed and compared with the experimental results. The successes and failures of the computations are highlighted and explained. The analysis focuses in particular on the 3D and unsteady effects. (author)
Commentary on local and boundary regularity of weak solutions to Navier-Stokes equations
Directory of Open Access Journals (Sweden)
Zdenek Skalak
2004-01-01
Full Text Available We present results on local and boundary regularity for weak solutions to the Navier-Stokes equations. Beginning with the regularity criterion proved recently in [14] for the Cauchy problem, we show that this criterion holds also locally. This is also the case for some other results: We present two examples concerning the regularity of weak solutions stemming from the regularity of two components of the vorticity ([2] or from the regularity of the pressure ([3]. We conclude by presenting regularity criteria near the boundary based on the results in [10] and [16].
Well-posedness of the three-dimensional Lagrangian averaged Navier-Stokes equations
Peirce, James P.
In this dissertation we study the well-posedness of the three-dimensional Lagrangian averaged Navier-Stokes (LANS-alpha) equations. The LANS-alpha equations are a system of PDEs designed to capture the large scale dynamics of the incompressible Navier-Stokes equations. In the Lagrangian averaging approach, the motion at spatial scales smaller than a chosen parameter alpha > 0 is filtered without the use of artificial viscosity. There are two types of LANS-alpha equations: the anisotropic version in which the fluctuation tensor is a dynamic variable that is coupled with the evolution equations for the mean velocity, and the isotropic version in which the covariance tensor is assumed to be a constant multiple of the identity matrix. We prove the global-in-time existence and uniqueness of weak solutions to the isotropic LANS-alpha equations for the case of no-slip boundary conditions, generalizing the known periodic box result (FHT02). Our proof makes use of a formulation of the equations on bounded domains provided by Marsden and Shkoller (2001). In the anisotropic model, there are two choices for the divergence-free projection of the viscosity term. One choice is the classic Leray projector. In this case, Marsden and Shkoller (2003) have shown the local-in-time well-posedness of the anisotropic equations in the periodic box. We extend their result by considering the second choice of projector, the generalized Stokes projector. The local-in-time well-posedness of the anisotropic LANS-alpha with this viscosity term is proven by using quasi-linear PDE-type methods. We numerically compute strong solutions to the anisotropic equations in the laminar channel and pipe by considering steady fluid flow with no-slip boundary conditions. In particular, given a steady velocity vector that solves the Navier-Stokes equations, we numerically calculate the covariance tensor such that the pair solves the anisotropic LANS-alpha equations. Our solutions are in good agreement with the
Application of the Krylov subspace method to the incompressible navier-stokes equations
Energy Technology Data Exchange (ETDEWEB)
Maeng, J.S. [Hanyang University, Seoul (Korea); Choi, I.K.; Lim, Y.W. [Hanyang University Graduate School, Seoul(Korea)
2000-07-01
The preconditioned Krylov subspace methods were applied to the incompressible Navier-Stoke's equations for convergence acceleration. Three of the Krylov subspace methods combined with the five of the preconditioners were tested to solve the lid-driven cavity flow problem. The MILU preconditioned CG method showed very fast and stable convergency. The combination of GMRES/MILU-CG solver for momentum and pressure correction equations was found less dependency on the number of the grid points among them. A guide line for stopping inner iterations for each equation is offered. (author). 18 refs., 4 figs., 6 tabs.
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
Cockburn, Bernardo
2008-12-20
We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.
Large Scale Flutter Data for Design of Rotating Blades Using Navier-Stokes Equations
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.
A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations
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
MPFA algorithm for solving stokes-brinkman equations on quadrilateral grids
Iliev, Oleg
2014-01-01
This work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations, which describes a free fluid flow coupled with a flow in porous media. Quadrilateral boundary fitted grid with a sophisticated finite volume method, namely MPFA O-method, is used to discretize the system of equations. Numerical results for two examples are presented, namely, channel flow and flow in a ring with a rolled porous medium. © Springer International Publishing Switzerland 2014.
A least-squares finite element method for incompressible Navier-Stokes problems
Jiang, Bo-Nan
1989-01-01
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.
Iterative solvers for Navier-Stokes equations: Experiments with turbulence model
Energy Technology Data Exchange (ETDEWEB)
Page, M. [IREQ - Institut de Recherche d`Hydro-Quebec, Varennes (Canada); Garon, A. [Ecole Polytechnique de Montreal (Canada)
1994-12-31
In the framework of developing software for the prediction of flows in hydraulic turbine components, Reynolds averaged Navier-Stokes equations coupled with {kappa}-{omega} two-equation turbulence model are discretized by finite element method. Since the resulting matrices are large, sparse and nonsymmetric, strategies based on CG-type iterative methods must be devised. A segregated solution strategy decouples the momentum equation, the {kappa} transport equation and the {omega} transport equation. These sets of equations must be solved while satisfying constraint equations. Experiments with orthogonal projection method are presented for the imposition of essential boundary conditions in a weak sense.
Actuator line/Navier–Stokes computations for the MEXICO rotor: comparison with detailed measurements
DEFF Research Database (Denmark)
Shen, Wen Zhong; Zhu, Wei Jun; Sørensen, Jens Nørkær
2012-01-01
In the European collaborative MEXICO (Model Experiments in Controlled Conditions) project, a series of experiments was carried out on a 4.5 m diameter wind turbine rotor to validate numerical diagnostics tools. Here, some of the measured data are compared with computations of the combined actuator...... line/Navier–Stokes (AL/NS) model developed at the Technical University of Denmark. The AL/NS model was combined with a large eddy simulation technique and used to compute the flow past the MEXICO rotor in free air and in the DNW German‐Dutch wind tunnel for three commonly defined test cases at wind...
Latyshev, A. V.; Yushkanov, A. A.
2013-03-01
The second Stokes problem concerning the behavior of a rarefied gas in the half-space bounded over a plate undergoing harmonic in-plane oscillations is solved analytically using the Bhat-nagar-Gross-Krook equation with Cercignani boundary conditions for gas molecules reflecting from the wall. The distribution function of the gas molecules is constructed. The gas velocity in the half-space and near the wall, the drag force exerted by the gas on the boundary, and the energy dissipation rate per unit area of the oscillating plate are found.
Energy Technology Data Exchange (ETDEWEB)
Shen, Yujie, E-mail: styojm@physics.tamu.edu [Texas A& M University, College Station, Texas 77843 (United States); Voronine, Dmitri V.; Sokolov, Alexei V. [Texas A& M University, College Station, Texas 77843 (United States); Baylor University, Waco, Texas 76798 (United States); Scully, Marlan O. [Texas A& M University, College Station, Texas 77843 (United States); Baylor University, Waco, Texas 76798 (United States); Princeton University, Princeton, New Jersey 08544 (United States)
2015-08-15
We report a versatile setup based on the femtosecond adaptive spectroscopic techniques for coherent anti-Stokes Raman scattering. The setup uses a femtosecond Ti:Sapphire oscillator source and a folded 4f pulse shaper, in which the pulse shaping is carried out through conventional optical elements and does not require a spatial light modulator. Our setup is simple in alignment, and can be easily switched between the collinear single-beam and the noncollinear two-beam configurations. We demonstrate the capability for investigating both transparent and highly scattering samples by detecting transmitted and reflected signals, respectively.
Spectral grading and Gleason grading of malignant prostate tissue using Stokes shift spectra
Al Salhi, M.; Masilamani, V.; Rabah, D.; Farhat, K.; Liu, C. H.; Pu, Y.; Alfano, R. R.
2012-01-01
Gleason score is the most common method of grading the virulence of prostate malignancy and is based on the pathological assessment of morphology of cellular matrix. Since this involves the excision of the tissue, we are working on a new, minimally invasive, non contact, procedure of spectral diagnosis of prostate malignancy. In this preliminary in vitro study reported here, we have analyzed 27 tissue samples (normal control =7: benign=8: malignant =12) by Stokes' shift spectra (SSS) to establish a one- to- one correlation between spectral grading and Gleason grading.
Bastide, Alain; Cocquet, Pierre-Henri; Ramalingom, Delphine
2017-01-01
submitted to Mathematical Models and Methods in Applied Sciences (M3AS); Topology optimization for fluid flow aims at finding the location of a porous medium minimizing a cost functional under constraints given by the Navier-Stokes equations. The location of the porous media is usually taken into account by adding a penalization term αu, where α is a kinematic viscosity divided by a permeability and u is the velocity of the fluid. The fluid part is obtained when α = 0 while the porous (solid)...
A prospective randomized comparison of healing in Gritti-Stokes and through-knee amputations.
Campbell, W. B.; Morris, P J
1987-01-01
Twenty-two patients with a median age of 79 years had 24 amputations about knee joint level. The patients were randomised to undergo either Gritti-Stokes or through-knee amputations. In two-thirds of limbs transcutaneous oxygen was less than 4.65 KPa (35 mmHg) or there were no audible Doppler signals at the ankle, indicating that a below-knee amputation would have been at risk of failing to heal, and in the remainder an amputation at the knee joint was considered the preferable site for a var...
Stokes-Einstein relation in computer simulated bulk glass forming Cu33Zr67 melts
Energy Technology Data Exchange (ETDEWEB)
Han, Xiujun; Schober, Herbert [IFF, Forschungszentrum Juelich, 52425 Juelich (Germany)
2009-07-01
The validity of Stokes-Einstein (SE) relation in glass forming Cu33Zr67 melts is checked by studying the relationship between viscosity and self-diffusion coefficient with molecular dynamics simulation. The atomic interaction of Cu-Zr is modeled by modified-embedded-atomic method (MEAM). The self-diffusion coefficient is calculated from mean squared displacements (MSD) and the viscosity is evaluated from Green-Kubo equation. It was found that at temperatures higher than 1500K, SE relation is valid. When the temperature is further decreased, SE relation breaks down, which is an indication of dynamical heterogeneity in the melts.
From Petrov–Einstein–Dilaton–Axion to Navier–Stokes equation in anisotropic model
Directory of Open Access Journals (Sweden)
Wen-Jian Pan
2016-01-01
Full Text Available In this paper we generalize the previous works to the case that the near-horizon dynamics of the Einstein–Dilaton–Axion theory can be governed by the incompressible Navier–Stokes equation via imposing the Petrov-like boundary condition on hypersurfaces in the non-relativistic and near-horizon limit. The dynamical shear viscosity η of such dual horizon fluid in our scenario, which isotropically saturates the Kovtun–Son–Starinet (KSS bound, is independent of both the dilaton field and axion field in that limit.
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Energy Technology Data Exchange (ETDEWEB)
Kupiainen, M; Sjogreen, B
2008-03-21
We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in [6] and for the Euler equations of compressible fluid flow in [11], to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.
Study of blade-tower interaction using a 2D Navier-Stokes solver
Energy Technology Data Exchange (ETDEWEB)
Bertagnolio, F. [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)
1999-03-01
The aim of this work is to model and study the dynamic interaction of the fluid flow with the structure which occurs when the blades of a wind turbine are passing in front of (or possibly behind) the tower. In order to capture the whole complexity of this phenomenon, the full unsteady Navier-Stokes equations for an incompressible fluid are used as a model. A new computational technique is described. For the sake of simplicity, we restrict ourselves to two-dimensional cases. The present methodology is illustrated by the computation of a wind turbine-like configuration in a periodic domain. (au)
Actuator Line/Navier-Stokes Computations for Flows past the Yawed MEXICO Rotor
DEFF Research Database (Denmark)
Shen, Wen Zhong; Sørensen, Jens Nørkær; Yang, H.
2011-01-01
In the paper the Actuator Line/Navier-Stokes model has been used to simulate flows past the yawed MEXICO rotor. The computed loads as well as the velocity field behind the yawed rotor are compared to detailed pressure and PIV measurements which were carried out in the EU funded MEXICO project...... with the DNW wind tunnel for the yawed rotor are also performed and show that the tunnel effects are very small in the loading and in the near wake field behind the rotor whereas in the far wake region (>1D) the influence becomes important....
On Liouville type theorems for the steady Navier-Stokes equations in R3
Chae, Dongho; Wolf, Jörg
2016-11-01
In this paper we prove three different Liouville type theorems for the steady Navier-Stokes equations in R3. In the first theorem we improve logarithmically the well-known L9/2 (R3) result. In the second theorem we present a sufficient condition for the trivially of the solution (v = 0) in terms of the head pressure, Q =1/2 | v|2 + p. The imposed integrability condition here has the same scaling property as the Dirichlet integral. In the last theorem we present Fubini type condition, which guarantee v = 0.
3-D Navier-Stokes Analysis of Blade Root Aerodynamics for a Tiltrotor Aircraft In Cruise
Romander, Ethan
2006-01-01
The blade root area of a tiltrotor aircraft's rotor is constrained by a great many factors, not the least of which is aerodynamic performance in cruise. For this study, Navier-Stokes CFD techniques are used to study the aerodynamic performance in cruise of a rotor design as a function of airfoil thickness along the blade and spinner shape. Reducing airfoil thickness along the entire blade will be shown to have the greatest effect followed by smaller but still significant improvements achieved by reducing the thickness of root airfoils only. Furthermore, altering the shape of the spinner will be illustrated as a tool to tune the aerodynamic performance very near the blade root.
DEFF Research Database (Denmark)
Huang, Chuixiu; Chen, Zhiliang; Gjelstad, Astrid
2017-01-01
Electromembrane extraction (EME) was inspired by solid-phase microextraction and developed from hollow fiber liquid-phase microextraction in 2006 by applying an electric field over the supported liquid membrane (SLM). EME provides rapid extraction, efficient sample clean-up and selectivity based...
DEFF Research Database (Denmark)
Maagaard, Mathilde; Oestergaard, Jeanett; Johansen, Marianne
2012-01-01
Objectives. To develop and validate an Objective Structured Assessment of Technical Skills (OSATS) scale for vacuum extraction. Design. Two part study design: Primarily, development of a procedure-specific checklist for vacuum extraction. Hereafter, validationof the developed OSATS scale for vacuum...
Conducting drops subject to electric fields in 2D Stokes flows
Crowdy, Darren
2008-10-01
This paper presents an analysis of a variety of problems of electrohydrodynamics involving conducting uncharged drops (or bubbles) in 2D Stokes flow. The assumption of an uncharged droplet implies that there is no net force on the bubble and, hence, that a solution to this 2D problem is not disqualified by a Stokes paradox' phenomenon. We first study the dynamics of conducting, incompressible bubbles subject to electric fields and ambient straining flows and then extend the scope to include compressible bubbles containing ideal gas. The free boundary problems are first studied using full numerical simulations based on a complex variable formulation coupled with conformal mapping theory. It is found that even under the combined effects of surface tension, electric field effects, compressibility and ambient strain flows, there exist equilibria for the bubble shape which are remarkably close to elliptical. Therefore, in each case, a simple model system of (at most two) non-linear, non-local ordinary differential equations is proposed which is found to approximate the dynamics up to equilibrium to high accuracy.
A simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations
Directory of Open Access Journals (Sweden)
Yibao Li
2017-01-01
Full Text Available Many researchers have proposed special treatments for outlet boundary conditions owing to lack of information at the outlet. Among them, the simplest method requires a large enough computational domain to prevent or reduce numerical errors at the boundaries. However, an efficient method generally requires special treatment to overcome the problems raised by the outlet boundary condition used. For example, mass flux is not conserved and the fluid field is not divergence-free at the outlet boundary. Overcoming these problems requires additional computational cost. In this paper, we present a simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations, aiming to reduce the computational domain for simulating flow inside a long channel in the streamwise direction. The proposed outflow boundary condition is based on the transparent equation, where a weak formulation is used. The pressure boundary condition is derived by using the Navier–Stokes equations and the outlet flow boundary condition. In the numerical algorithm, a staggered marker-and-cell grid is used and temporal discretization is based on a projection method. The intermediate velocity boundary condition is consistently adopted to handle the velocity–pressure coupling. Characteristic numerical experiments are presented to demonstrate the robustness and accuracy of the proposed numerical scheme. Furthermore, the agreement of computational results from small and large domains suggests that our proposed outflow boundary condition can significantly reduce computational domain sizes.
Charge Transfer Molecular Rotor DCVJ Investigated by Coherent Anti-Stokes Raman Spectroscopy
Ujj, Laszlo; Miller, Scott; Welch, Jonathan; Amos, Charles; Prayaga, Chandra
2009-05-01
Coherent anti-Stokes Raman Spectroscopy (CARS) has been shown to be one of the most powerful experimental methodologies for obtaining vibrational information from both stable and transient molecular species^1. The electronically enhanced polarization sensitive version of CARS is even more effective for measuring molecular vibrational information not easily reachable by spontaneous Raman spectroscopy. Theoretical and experimental principles associated with CARS with an emphasis on points relevant to the interpretation of experimental spectra will be presented. The method is applied to measure the vibrational manifold of DCVJ for the first time. DCVJ is a charge transfer molecular rotor showing a viscosity dependent fluorescence quantum yield. Based upon the measured CARS spectra, the effect of inhibition of the internal rotation on the vibrational motion of the molecule will be discussed. The design and operation of an all solid-state broadband nanosecond CARS system will be also presented. An overview of applications of molecular rotors in biology and information technology will be outlined. Ref.: 1. L. Ujj and G. H. Atkinson, ``Coherent Anti-Stokes Raman Spectroscopy'', in Handbook of Vibr. Spect., Wiley & Sons, Ltd., (2002).
Farnesi, Daniele; Berneschi, Simone; Cosi, Franco; Righini, Giancarlo C; Soria, Silvia; Nunzi Conti, Gualtiero
2016-04-04
Dielectric microspheres can confine light and sound for a length of time through high quality factor whispering gallery modes (WGM). Glass microspheres can be thought as a store of energy with a huge variety of applications: compact laser sources, highly sensitive biochemical sensors and nonlinear phenomena. A protocol for the fabrication of both the microspheres and coupling system is given. The couplers described here are tapered fibers. Efficient generation of nonlinear phenomena related to third order optical non-linear susceptibility Χ((3)) interactions in triply resonant silica microspheres is presented in this paper. The interactions here reported are: Stimulated Raman Scattering (SRS), and four wave mixing processes comprising Stimulated Anti-stokes Raman Scattering (SARS). A proof of the cavity-enhanced phenomenon is given by the lack of correlation among the pump, signal and idler: a resonant mode has to exist in order to obtain the pair of signal and idler. In the case of hyperparametric oscillations (four wave mixing and stimulated anti-stokes Raman scattering), the modes must fulfill the energy and momentum conservation and, last but not least, have a good spatial overlap.
Di Mascio, A.; Zaghi, S.; Muscari, R.; Broglia, R.; Cavallini, E.; Favini, B.; Scaccia, A.
2011-05-01
The results of accurate compressible Navier-Stokes simulations of aerodynamic heating of the Vega launcher are presented. Three selected steady conditions of the Vega mission profile are considered: the first corresponding to the altitude of 18 km, the second to 25 km and the last to 33 km. The numerical code is based on the Favre- Average Navier-Stokes equations; the turbulent model chosen for closure is the one-equation model by Spalart- Allmaras. The equations are discretized by a finite volume approach, that can handle block-structured meshes with partial overlap (“Chimera” grid-overlapping technique). The isothermal boundary condition has been applied to the lancher wall. Particular care was devoted to the construction of the discrete model; indeed, the launcher is equipped with many protrusions and geometrical peculiarities (as antennas, raceways, inter-stage connection flanges and retrorockets) that are expected to affect considerably the local thermal flow-field and the level of heat fluxes, because the flow have to undergo strong variation in space; con- sequently, special attention was devoted to the definition of a tailored mesh, capable of catching local details of the aerothermal flow field (shocks, expansion fans, boundary layer, etc..). The computed results are reported together with uncertainty and actual convergence order, that were estimated by the standard procedures suggested by AIAA [Ame98].
Acoustic-mean flow interaction in solid rocket motors using Navier-Stokes equations
Vuillot, F.; Avalon, G.
1988-07-01
The presented numerical solution of laminar, two-dimensional, compressible and unsteady Navier-Stokes equations is aimed at a complete description of acoustic boundary layers that develop above a burning propellant. Such acoustic boundary layers are responsible for the so-called flow turning losses and also govern the local unsteady flow conditions that are seen by the burning propellant and to which it finally responds. In those respects, a complete understanding of such acoustic boundary layers is essential to improve existing solid rocket stability prediction codes. The full numerical solution of the Navier-Stokes equations permits to naturally incorporate into the analysis all the features of two-dimensional rocket chamber mean flow field. After a standing wave pattern is established through forcing at a given frequency, a special Fourier treatment is used to put the numerical results in a form directly comparable to available linear acoustic data. The presented results indicate that the acoustic boundary layer is substantially thinner than predicted by simplified models. Moreover, its acoustic admittance is found to significantly vary along the chamber, a result that is of major importance to stability predictions. Finally, the acoustic field is found to be rotational over a significant volume of the chamber, leading to a volume flow turning loss, rather than to a pure surface effect as usually assumed.
Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil
2015-11-01
We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.
A point implicit unstructured grid solver for the Euler and Navier-Stokes equations
Thareja, Rajiv R.; Stewart, James R.; Hassan, Obey; Morgan, Ken; Peraire, Jaime
1988-01-01
An upwind finite element technique that uses cell centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured triangular grids. A structured grid of quadrilaterals is laid out near the body surface. For inviscid flows the method is stable at Courant numbers of over 100,000. A first order basic scheme and a higher order flux corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view of simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively generated grids. The adaptive mesh generator and the upwind Navier-Stokes solver are combined in a set of programs called LARCNESS, an acronym for Langley Adaptive Remeshing Code and Navier-Stokes Solver.
Lattice Boltzmann method simulations of Stokes number effects on particle motion in a channel flow
Zhang, Lenan; Jebakumar, Anand Samuel; Abraham, John
2016-06-01
In a recent experimental study by Lau and Nathan ["Influence of Stokes number on the velocity and concentration distributions in particle-laden jets," J. Fluid Mech. 757, 432 (2014)], it was found that particles in a turbulent pipe flow tend to migrate preferentially toward the wall or the axis depending on their Stokes number (St). Particles with a higher St (>10) are concentrated near the axis while those with lower St (plane. They have explained this behavior in terms of the Saffman lift, Magnus lift, and wall repulsion forces acting on the particle. The present work extends the previous work done by Jebakumar et al. and aims to study the behavior of particles at intermediate St ranging from 10 to 20. It is in this range where the equilibrium position of the particle changes from near the wall to the axis and the particle starts oscillating about the axis. The Lattice Boltzmann method is employed to carry out this study. It is shown that the change in mean equilibrium position is related to increasing oscillations of the particle with mean position near the wall which results in the particle moving past the center plane to the opposite side. The responsible mechanisms are explained in detail.
Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations
Hafez, Mohammed; Dacles, Jennifer
1989-01-01
The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.
The Proteus Navier-Stokes code. [two and three dimensional computational fluid dynamics
Towne, Charles E.; Schwab, John R.
1992-01-01
An effort is currently underway at NASA Lewis to develop two and three dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. Proteus solves the Reynolds-averaged, unsteady, compressible Navier-Stokes equations in strong conservation law form. Turbulence is modeled using a Baldwin-Lomax based algebraic eddy viscosity model. In addition, options are available to solve thin layer or Euler equations, and to eliminate the energy equation by assuming constant stagnation enthalpy. An extensive series of validation cases have been run, primarily using the two dimensional planar/axisymmetric version of the code. Several flows were computed that have exact solution such as: fully developed channel and pipe flow; Couette flow with and without pressure gradients; unsteady Couette flow formation; flow near a suddenly accelerated flat plate; flow between concentric rotating cylinders; and flow near a rotating disk. The two dimensional version of the Proteus code has been released, and the three dimensional code is scheduled for release in late 1991.
Polarization demultiplexing in stokes space for coherent optical PDM-OFDM.
Yu, Zhenming; Yi, Xingwen; Yang, Qi; Luo, Ming; Zhang, Jing; Chen, Lei; Qiu, Kun
2013-02-11
We propose a polarization demultiplexing method for coherent optical PDM-OFDM based on Stokes space, without inserting training symbols. The proposed approach performs well for different modulation formats of OFDM subcarrier, and shows comparable performances with that of conventional methods, but with a fast convergence speed and reduced overhead. The OFDM signal in the time domain cannot satisfy the conditions of SS-PDM accurately. Therefore, we first digitally convert the received OFDM signals to the frequency domain using fast Fourier transform (FFT). Each subcarrier of the OFDM signal has a much lower speed and narrower bandwidth, the polarization effects that it experiences can be treated as flat. Consequently, we can apply the polarization demultiplexing in Stokes space (SS-PDM) on per subcarrier basis. We verify this method in experiment by transmitting 66.6-Gb/s PDM-OFDM signal with 4QAM subcarrier modulation over 5440km SSMF and 133.3-Gb/s PDM-OFDM signal with 16QAM subcarrier modulation over 960km SSMF respectively. We also compare the results with those of training symbols. Finally, we analyze of the convergence speed of this method.
Ducted-Fan Engine Acoustic Predictions using a Navier-Stokes Code
Rumsey, C. L.; Biedron, R. T.; Farassat, F.; Spence, P. L.
1998-01-01
A Navier-Stokes computer code is used to predict one of the ducted-fan engine acoustic modes that results from rotor-wake/stator-blade interaction. A patched sliding-zone interface is employed to pass information between the moving rotor row and the stationary stator row. The code produces averaged aerodynamic results downstream of the rotor that agree well with a widely used average-passage code. The acoustic mode of interest is generated successfully by the code and is propagated well upstream of the rotor; temporal and spatial numerical resolution are fine enough such that attenuation of the signal is small. Two acoustic codes are used to find the far-field noise. Near-field propagation is computed by using Eversman's wave envelope code, which is based on a finite-element model. Propagation to the far field is accomplished by using the Kirchhoff formula for moving surfaces with the results of the wave envelope code as input data. Comparison of measured and computed far-field noise levels show fair agreement in the range of directivity angles where the peak radiation lobes from the inlet are observed. Although only a single acoustic mode is targeted in this study, the main conclusion is a proof-of-concept: Navier-Stokes codes can be used both to generate and propagate rotor/stator acoustic modes forward through an engine, where the results can be coupled to other far-field noise prediction codes.
Musharbash, Eleonora; Nobile, Fabio
2018-02-01
In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational principle can be set in the constrained manifold of all S rank random fields with a prescribed value on the boundary, expressed in low rank format, with rank smaller then S. We characterize the tangent space to the constrained manifold by means of a Dual Dynamically Orthogonal (Dual DO) formulation, in which the stochastic modes are kept orthonormal and the deterministic modes satisfy suitable boundary conditions, consistent with the original problem. The Dual DO formulation is also convenient to include the incompressibility constraint, when dealing with incompressible Navier Stokes equations. We show the performance of the proposed Dual DO approximation on two numerical test cases: the classical benchmark of a laminar flow around a cylinder with random inflow velocity, and a biomedical application for simulating blood flow in realistic carotid artery reconstructed from MRI data with random inflow conditions coming from Doppler measurements.
Manufactured analytical solutions for isothermal full-Stokes ice sheet models
Directory of Open Access Journals (Sweden)
A. Sargent
2010-08-01
Full Text Available We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed.
The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions.
Blanchet, Adrien
2009-01-01
A periodic perturbation of a Gaussian measure modifies the sharp constants in Poincarae and logarithmic Sobolev inequalities in the homogeniz ation limit, that is, when the period of a periodic perturbation converges to zero. We use variational techniques to determine the homogenized constants and get optimal convergence rates toward s equilibrium of the solutions of the perturbed diffusion equations. The study of these sharp constants is motivated by the study of the stochastic Stokes\\' drift. It also applies to Brownian ratchets and molecular motors in biology. We first establish a transport phenomenon. Asymptotically, the center of mass of the solution moves with a constant velocity, which is determined by a doubly periodic problem. In the reference frame attached to the center of mass, the behavior of the solution is governed at large scale by a diffusion with a modified diffusion coefficient. Using the homogenized logarithmic Sobolev inequality, we prove that the solution converges in self-similar variables attached to t he center of mass to a stationary solution of a Fokker-Planck equation modulated by a periodic perturbation with fast oscillations, with an explicit rate. We also give an asymptotic expansion of the traveling diffusion front corresponding to the stochastic Stokes\\' drift with given potential flow. © 2009 Society for Industrial and Applied Mathematics.
On Inviscid Limits for the Stochastic Navier-Stokes Equations and Related Models
Glatt-Holtz, Nathan; Šverák, Vladimír; Vicol, Vlad
2015-08-01
We study inviscid limits of invariant measures for the 2D stochastic Navier-Stokes equations. As shown by Kuksin (J Stat Phys 115(1-2):469-492, 2004), the noise scaling is the only one which leads to non-trivial limiting measures, which are invariant for the 2D Euler equations. Using a Moser-type iteration for stochastic drift-diffusion equations, we show that any limiting measure is in fact supported on bounded vorticities. Relationships of to the long term dynamics of 2D Euler in with the weak* topology are discussed. We also obtain a drift-independent modulus of continuity for a stationary deterministic model problem, which leads us to conjecture that in fact is supported on . Moreover, in view of the Batchelor-Krainchnan 2D turbulence theory, we consider inviscid limits for a weakly damped stochastic Navier-Stokes equation. In this setting we show that only an order zero noise scaling (with respect to ν) leads to a nontrivial limiting measure in the inviscid limit.
An introduction to the mathematical theory of the Navier-Stokes equations
Galdi, Giovanni P
1994-01-01
Undoubtedly, the Navier-Stokes equations are of basic importance within the context of modern theory of partial differential equations. Although the range of their applicability to concrete problems has now been clearly recognised to be limited, as my dear friend and bright colleague K.R. Ra jagopal has showed me by several examples during the past six years, the mathematical questions that remain open are of such a fascinating and challenging nature that analysts and applied mathematicians cannot help being attracted by them and trying to contribute to their resolution. Thus, it is not a coincidence that over the past ten years more than seventy sig nificant research papers have appeared concerning the well-posedness of boundary and initial-boundary value problems. In this monograph I shall perform a systematic and up-to-date investiga tion of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions and, whenever the region of flow is unbou...
Li, Zhaorui; Livescu, Daniel
2014-11-01
By using the second-law of thermodynamics and the Onsager reciprocal method for irreversible processes, we have developed a set of physically consistent multicomponent compressible generalized Cahn-Hilliard Navier-Stokes (CGCHNS) equations from basic thermodynamics. The new equations can describe not only flows with pure miscible and pure immiscible materials but also complex flows in which mass diffusion and surface tension or Korteweg stresses effects may coexist. Furthermore, for the first time, the incompressible generalized Cahn-Hilliard Navier-Stokes (IGCHNS) equations are rigorously derived from the incompressible limit of the CGCHNS equations (as the infinite sound speed limit) and applied to the immiscible Rayleigh-Taylor instability problem. Extensive good agreements between numerical results and the linear stability theory (LST) predictions for the Rayleigh-Taylor instability are achieved for a wide range of wavenumber, surface tension, and viscosity values. The late-time results indicate that the IGCHNS equations can naturally capture complex interface topological changes including merging and breaking-up and are free of singularity problems.
Fast non-symmetric iterations and efficient preconditioning for Navier-Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Silvester, D. [UMIST, Manchester (United Kingdom); Elman, H. [Univ. of Maryland, College Park, MD (United States)
1994-12-31
Discretisation of the steady-state Navier-Stokes equations: (u.grad)u-{nu}{del}{sup 2}u + grad p = 0; div u = 0 [1]. in some flow domain {Omega} {contained_in} IR{sup d}, (d = 2 or 3), gives a system of non-linear algebraic equations for discretised variables u (the velocity), and p (the pressure). The authors assume that appropriate boundary conditions are imposed. The non-linear equation system can be linearised using a fixed-point (Picard) iteration to give a matrix system which must be solved at every iteration. Part of this matrix is block diagonal, and consists of d convection-diffusion operators, one for each component of velocity. Two difficulties arise when solving this matrix equation. Firstly, the block diagonal part is not symmetric, although under certain conditions the symmetric part is positive definite. Secondly, the overall system is indefinite. This makes the design of fast and efficient iterative solvers for discretised Navier-Stokes operators an extremely challenging task.
Exact Solutions on Twisted Rings for the 3D Navier-Stokes Equations
Funaro, Daniele
2011-01-01
The problem of describing the behavior of the solutions to the Navier-Stokes equations in three space dimensions has always been borderline. From one side, due to the viscosity term, smooth data seem to produce solutions with an everlasting regular behavior. On the other hand, the lack of a convincing theoretical analysis suggests the existence of possible counterexamples. In particular, one cannot exclude the blowing up of solutions in finite time even in presence of smooth data. Here we give examples of explicit solutions of the non-homogeneous equations. These are defined on a Hill's type vortex where the flow is rotating and swirling at the same time, inducing the flux to spiraling at a central node. Despite the appearance, the solution still remains very regular at the agglomeration point. The analysis may lead to a better understanding of the subtle problem of characterizing the solution space of the 3D Navier-Stokes equations. For instance, this result makes more narrow the path to the search of counte...
Removal of anti-Stokes emission background in STED microscopy by FPGA-based synchronous detection.
Castello, M; Tortarolo, G; Coto Hernández, I; Deguchi, T; Diaspro, A; Vicidomini, G
2017-05-01
In stimulated emission depletion (STED) microscopy, the role of the STED beam is to de-excite, via stimulated emission, the fluorophores that have been previously excited by the excitation beam. This condition, together with specific beam intensity distributions, allows obtaining true sub-diffraction spatial resolution images. However, if the STED beam has a non-negligible probability to excite the fluorophores, a strong fluorescent background signal (anti-Stokes emission) reduces the effective resolution. For STED scanning microscopy, different synchronous detection methods have been proposed to remove this anti-Stokes emission background and recover the resolution. However, every method works only for a specific STED microscopy implementation. Here we present a user-friendly synchronous detection method compatible with any STED scanning microscope. It exploits a data acquisition (DAQ) card based on a field-programmable gate array (FPGA), which is progressively used in STED microscopy. In essence, the FPGA-based DAQ card synchronizes the fluorescent signal registration, the beam deflection, and the excitation beam interruption, providing a fully automatic pixel-by-pixel synchronous detection method. We validate the proposed method in both continuous wave and pulsed STED microscope systems.
Zhou, Yan; Wang, Leana; Liu, Cheng-hui; He, Yong; Yu, Xinguang; Cheng, Gangge; Wang, Peng; Shu, Cheng; Alfano, Robert R.
2016-03-01
In this report, optical biopsy was applied to diagnose human brain cancer in vitro for the identification of brain cancer from normal tissues by native fluorescence and Stokes shift spectra (SSS). 77 brain specimens including three types of human brain tissues (normal, glioma and brain metastasis of lung cancers) were studied. In order to observe spectral changes of fluorophores via fluorescence, the selected excitation wavelength of UV at 300 and 340 nm for emission spectra and a different Stokes Shift spectra with intervals Δλ = 40 nm were measured. The fluorescence spectra and SSS from multiple key native molecular markers, such as tryptophan, collagen, NADH, alanine, ceroid and lipofuscin were observed in normal and diseased brain tissues. Two diagnostic criteria were established based on the ratios of the peak intensities and peak position in both fluorescence and SSS spectra. It was observed that the ratio of the spectral peak intensity of tryptophan (340 nm) to NADH (440 nm) increased in glioma, meningioma (benign), malignant meninges tumor, and brain metastasis of lung cancer tissues in comparison with normal tissues. The ratio of the SS spectral peak (Δλ = 40 nm) intensities from 292 nm to 366 nm had risen similarly in all grades of tumors.
In The Quest For Stokes V - Science Cases And Technical Challenges
Wiesemeyer, Helmut; Agudo, I.; Baudry, A.; Downes, D.; Güsten, R.; Herpin, F.; Houde, M.; Kreysa, E.; Maury, A.; Menten, K.; Morris, D.; Navarro, S.; Paubert, G.; Pillai, T.; Thum, C.; Weiß, A.
2017-10-01
Circular polarization is produced either in the emission process through the Zeeman effect, or through the transfer of polarized radiation in a magneto-active medium. While the former mechanism provides a direct access to the strength of the magnetic field along the sightline, the conversion of linear to circular polarization reveals particular magnetic field structures or magnetospheric events. In the first part I will present selected science cases. While Stokes V may be strong in OH masers forming in supernova remnants, the Zeeman effect becomes weaker in masers associated with star-forming environments or circumstellar envelopes. As masers probe restricted physical conditions, the Zeeman effect in thermal lines is a valuable analysis tool, but even more difficult to measure. In particular, the instrumental leakage from linear to circular polarization frequently exceeds the intrinsic Stokes V. This statement also holds for the Faraday conversion in AGN. A correction for instrumental polarization across the field of view is thus essential, but hindered by the lack of suitable calibrators. In the second part I will propose calibration schemes for both the image and UV plane.
Role of excited state solvent fluctuations on time-dependent fluorescence Stokes shift
Energy Technology Data Exchange (ETDEWEB)
Li, Tanping, E-mail: tanping@lsu.edu, E-mail: revatik@lsu.edu; Kumar, Revati, E-mail: tanping@lsu.edu, E-mail: revatik@lsu.edu [Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)
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 breaks 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.
Molecular-detailed simulation of red blood cells in Stokes flows
Peng, Zhangli; Zhu, Qiang
2010-11-01
The red blood cell (RBC) membrane consists of a lipid bilayer and a cytoskeleton. By coupling a multiscale approach of RBC membranes with a boundary element method (BEM) for the exterior and interior fluids, we developed a numerical capacity to relate the fluid-structure interaction of RBCs in Stokes flows with detailed mechanical loads inside its molecular architecture. Our multiscale approach includes three models: in the whole cell level, a finite element method (FEM) is employed to model the lipid bilayer and the cytoskeleton as two distinct layers of continuum shells; the mechanical properties of the cytoskeleton are obtained from a molecular-based model; the spectrin, a major protein of the cytoskeleton, is simulated using a constitutive model. BEM is applied to predict the exterior and interior Stokes flows, and is coupled with the FEM of the membrane through a staggered coupling algorithm. Using this method, we simulated the tumbling and tank-treading behaviors of RBCs in shear flows, and investigated the RBC dynamics in capillary flows. The structural deformation of the cytoskeleton and the interaction force between the lipid bilayer and the cytoskeleton are predicted.
Verification of Euler/Navier-Stokes codes using the method of manufactured solutions
Roy, C. J.; Nelson, C. C.; Smith, T. M.; Ober, C. C.
2004-02-01
The method of manufactured solutions is used to verify the order of accuracy of two finite-volume Euler and Navier-Stokes codes. The Premo code employs a node-centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second-order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier-Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given.
Discontinuous Galerkin solution of the Navier-Stokes equations on deformable domains
Energy Technology Data Exchange (ETDEWEB)
Persson, P.-O.; Bonet, J.; Peraire, J.
2009-01-13
We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain, By writing the Navier-Stokes equations as a conservation law for the independent variables in the reference configuration, the complexity introduced by variable geometry is reduced to solving a transformed conservation law in a fixed reference configuration, The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, while the time integration is performed using an explicit Runge-Kutta method, For general domain changes, the standard scheme fails to preserve exactly the free-stream solution which leads to some accuracy degradation, especially for low order approximations. This situation is remedied by adding an additional equation for the time evolution of the transformation Jacobian to the original conservation law and correcting for the accumulated metric integration errors. A number of results are shown to illustrate the flexibility of the approach to handle high order approximations on complex geometries.
Yao, Wei; Shen, Zhoufeng; Ding, Guanghong
2013-01-01
In this paper, we use Stokes, Brinkman and Darcy equations to approximate the porous continuum media of ligament tissues respectively, simulate the flow field with FLUENT software, and study the shear stress on the cell surface due to the interstitial fluid flow. Since the Brinkman equation approaches Stokes equation well in high hydraulic permeability (k p) condition (k p ≥1.0×10(-8) m(2) in our numerical simulation), and it is an approximation to Darcy model in low k p condition (k p ≤5.0×10(-12) m(2) in our numerical simulation), we used the Brinkman model to simulate the interstitial fluid flow in the ligament where k p is approximately 1.0×10(-16) m(2). It shows k p and anisotropic property have a little effect on the flow field, but have a great effect on the shear stress on the membrane of interstitial cells (τ cell). There is a linear relationship between τ cell and , when k p =1.0×10(-16) m(2) and the maximum τ cell (τ cell,max) is approximately 10 Pa. The anisotropic property will affect τ cell's distribution on the cell surface. When k x/k y>1, low τ cell dominates the cell, while when k x/k y<1, high τ cell dominants the cell.
Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo
2016-05-01
We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.
Dynamic-pressure distributions under Stokes waves with and without a current
Umeyama, Motohiko
2017-12-01
To investigate changes in the instability of Stokes waves prior to wave breaking in shallow water, pressure data were recorded vertically over the entire water depth, except in the near-surface layer (from 0 cm to -3 cm), in a recirculating channel. In addition, we checked the pressure asymmetry under several conditions. The phase-averaged dynamic-pressure values for the wave-current motion appear to increase compared with those for the wave-alone motion; however, they scatter in the experimental range. The measured vertical distributions of the dynamic pressure were plotted over one wave cycle and compared to the corresponding predictions on the basis of third-order Stokes wave theory. The dynamic-pressure pattern was not the same during the acceleration and deceleration periods. Spatially, the dynamic pressure varies according to the faces of the wave, i.e. the pressure on the front face is lower than that on the rear face. The direction of wave propagation with respect to the current directly influences the essential features of the resulting dynamic pressure. The results demonstrate that interactions between travelling waves and a current lead more quickly to asymmetry. This article is part of the theme issue 'Nonlinear water waves'.
Maldonado-Camargo, Lorena; Rinaldi, Carlos
2016-11-09
We report observations of breakdown of the Stokes-Einstein relation for the rotational diffusivity of polymer-grafted spherical nanoparticles in polymer melts. The rotational diffusivity of magnetic nanoparticles coated with poly(ethylene glycol) dispersed in poly(ethylene glycol) melts was determined through dynamic magnetic susceptibility measurements of the collective rotation of the magnetic nanoparticles due to imposed time-varying magnetic torques. These measurements clearly demonstrate the existence of a critical molecular weight for the melt polymer, below which the Stokes-Einstein relation accurately describes the rotational diffusivity of the polymer-grafted nanoparticles and above which the Stokes-Einstein relation ceases to apply. This critical molecular weight was found to correspond to a chain contour length that approximates the hydrodynamic diameter of the nanoparticles.
Niederer, P. G.; Mihora, D. J.
1972-01-01
The current design and hardware components of the patented 14 sqm Stokes flow parachute are described. The Stokes-flow parachute is a canopy of open mesh material, which is kept deployed by braces. Because of the light weight of its mesh material, and the high drag on its mesh elements when they operate in the Stokes-flow flight regime, this parachute has an extremely low ballistic coefficient. It provides a stable aerodynamic platform superior to conventional nonporous billowed parachutes, is exceptionally packable, and is easily contained within the canister of the Sidewinder Arcas or the RDT and E rockets. Thus, it offers the potential for gathering more meteorological data, especially at high altitudes, than conventional billowed parachutes. Methods for packaging the parachute are also recommended. These methods include schemes for folding the canopy and for automatically releasing the pressurizing fluid as the packaged parachute unfolds.
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.
Mu, Tingkui; Pacheco, Shaun; Chen, Zeyu; Zhang, Chunmin; Liang, Rongguang
2017-02-01
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.
Directory of Open Access Journals (Sweden)
Changfeng Xue
2008-01-01
Full Text Available The Rayleigh-Stokes problem for a generalized Maxwell fluid in a porous half-space with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and the temperature are obtained. Some classical results can be regarded as particular cases of our results, such as the classical solutions of the first problem of Stokes for Newtonian viscous fluids, Maxwell fluids, and Maxwell fluids in a porous half-space.
An Exact Mapping from Navier-Stokes Equation to Schördinger Equation via Riccati Equation
Directory of Open Access Journals (Sweden)
Christianto V.
2008-01-01
Full Text Available In the present article we argue that it is possible to write down Schrödinger representation of Navier-Stokes equation via Riccati equation. The proposed approach, while differs appreciably from other method such as what is proposed by R. M. Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko’s and Gibbon’s route. Further observation is of course recommended in order to refute or verify this proposition.
Brown, Donald L.
2011-09-11
In this paper we establish corrector estimates for Stokes flow in slowly varying perforated media via two scale asymptotic analysis. Current methods and techniques are often not able to deal with changing geometries prevalent in applied problems. For example, in a deformable porous medium environment, the geometry does not remain periodic under mechanical deformation and if slow variation in the geometry occurs. For such problems, one cannot use classical homogenization results directly and new homogenization results and estimates are needed. Our work uses asymptotic techniques of Marusic-Paloka and Mikelic (Bollettino U. M. I 7:661-671, 1996) where the authors constructed a downscaled velocity which converges to the fine-scale velocity at a rate of ε1/6 where ε is the characteristic length scale. We assume a slowly varying porous medium and study homogenization and corrector estimates for the Stokes equations. Slowly varying media arise, e. g., in fluid-structure interaction (FSI) problems (Popov et al. in Iterative upscaling of flows in deformable porous media, 2008), carbonation of porous concrete (Peter in C. R. Mecanique 335:357-362, 2007a; C. R. Mecanique 335:679-684, 2007b), and various other multiphysics processes. To homogenize Stokes flows in such media we restate the cell problems of Marusic-Paloka and Mikelic (Bollettino U. M. I 7:661-671, 1996) in a moving RVE framework. Further, to recover the same convergence properties it is necessary to solve an additional cell problem and add one more corrector term to the downscaled velocity. We further extend the framework of Marusic-Paloka and Mikelic (Bollettino U. M. I 7:661-671, 1996) to three spatial dimensions in both periodic and variable pore-space cases. Next, we also propose an efficient algorithm for computing the correctors by solving a limited number of cell problems at selected spatial locations. We present two computational examples: one for a constructed medium of elliptical perforations, and
Multiphase unsteady Stokes flow over longitudinal grooved surface: an analytical study
Mahesh, Krishnan; Li, Yixuan; Alame, Karim
2017-11-01
Motivated by recent interest in superhydrophobic technology, we study the effect of grooved multiphase textures exposed to turbulent channel flow of one fluid, while being infused with a second fluid. An analytical solution of unsteady Stokes flow in the presence of spanwise periodic grooves is derived. Comparison with volume of fluid (VOF) simulation data shows good agreement. The solution scales with ωL2 / ν , where ω is the frequency of the oscillatory slip velocity, L is the characteristic length of the groove, and ν is the kinematic viscosity of the external fluid. A parametric study of the viscosity ratio between the two types of fluid, the penetration of the outside flow, and the frequency of the oscillatory slip velocity is presented. Our theoretical analysis shows that the multiphase grooved surface produces a high-pass filter effect on turbulent flow. Supported by Office of Naval Research.
Energy Technology Data Exchange (ETDEWEB)
John, V.; Matthies, G.; Tobiska, L. [Magdeburg Univ. (Germany). Inst. fuer Analysis und Numerik
2001-07-01
For solving complex three-dimensional flow problems, many different approaches have been developed. It turns out that both the discretization concept and the solver designed for the discrete problem influences essentially the accuracy and efficiency of the method. The main objective of the paper is to compare lower and higher order finite element discretizations for the accurate and fast solution of the incompressible Navier-Stokes equation in three space dimensions. To this end, a well-defined benchmark problem of a channel flow around an obstacle is used to quantify the gain in accuracy when higher order discretizations are used. The comparison covers also the robust and efficient solution of the discretized algebraic equations. (orig.)
Ultrashort laser pulse-induced anti-Stokes photoluminescence of hot electrons in gold nanorods
Sitnikov, D. S.; Yurkevich, A. A.; Kotelev, M. S.; Ziangirova, M.; Chefonov, O. V.; Ilina, I. V.; Vinokurov, V. A.; Muradov, A. V.; Itzkan, I.; Agranat, M. B.; Perelman, L. T.
2014-07-01
We report observing anti-Stokes broadband radiation induced in gold nanorods by ultrashort laser pulses. The radiation is in the visible spectral range along with the second harmonic peak. Unlike conventional photoluminescence of metal nanoparticles, the energy of the excitation photons is smaller than the gap between the top of the d band and the Fermi level. Because the gold nanorods are irradiated with a pulse whose time is shorter than the electron-phonon equilibration time in gold, the energy is absorbed by s/p band electrons, creating a temperature difference between the electrons and the lattice, as described by the two-temperature model. Therefore, we identify the origin of the observed radiation as the recombination of hot conduction electrons with the d band holes created by the same ultrashort laser pulse.
A Navier-Stokes Solution of Hull-Ring Wing-Thruster Interaction
Yang, C.-I.; Hartwich, P.; Sundaram, P.
1991-01-01
Navier-Stokes simulations of high Reynolds number flow around an axisymmetric body supported in a water tunnel were made. The numerical method is based on a finite-differencing high resolution second-order accurate implicit upwind scheme. Four different configurations were investigated, these are: (1) barebody; (2) body with an operating propeller; (3) body with a ring wing; and (4) body with a ring wing and an operating propeller. Pressure and velocity components near the stern region were obtained computationally and are shown to compare favorably with the experimental data. The method correctly predicts the existence and extent of stern flow separation for the barebody and the absence of flow separation for the three other configurations with ring wing and/or propeller.
Investigations of the polarization behavior of quantum cascade lasers by Stokes parameters.
Janassek, Patrick; Hartmann, Sébastien; Molitor, Andreas; Michel, Florian; Elsäßer, Wolfgang
2016-01-15
We experimentally investigate the full polarization behavior of mid-infrared emitting quantum cascade lasers (QCLs) in terms of measuring the complete Stokes parameters, instead of only projecting them on a linear polarization basis. We demonstrate that besides the pre-dominant linear TM polarization of the emitted light as governed by the selection rules of the intersubband transition, small non-TM contributions, e.g., circularly polarized light, are present reflecting the birefringent behavior of the semiconductor quantum well waveguide. Surprisingly unique is the persistence of these polarization properties well below laser threshold. These investigations give further insight into understanding, manipulating, and exploiting the polarization properties of QCLs, both from a laser point of view and with respect toward applications.
A Split-Step Scheme for the Incompressible Navier-Stokes
Energy Technology Data Exchange (ETDEWEB)
Henshaw, W; Petersson, N A
2001-06-12
We describe a split-step finite-difference scheme for solving the incompressible Navier-Stokes equations on composite overlapping grids. The split-step approach decouples the solution of the velocity variables from the solution of the pressure. The scheme is based on the velocity-pressure formulation and uses a method of lines approach so that a variety of implicit or explicit time stepping schemes can be used once the equations have been discretized in space. We have implemented both second-order and fourth-order accurate spatial approximations that can be used with implicit or explicit time stepping methods. We describe how to choose appropriate boundary conditions to make the scheme accurate and stable. A divergence damping term is added to the pressure equation to keep the numerical dilatation small. Several numerical examples are presented.
Pang, Leo
2017-12-01
The sameness of eating out has been criticised in some quarters of food media in recent years. In this paper I demonstrate through the case of three chefs in Hong Kong how this sameness is the product of global gastronomic discourse. I suggest that chefs play a crucial role in providing the content that fuels gastronomic discourses and also in delivering the experiences of the discourse on the plate to diners. The experience of chefs in cuisines such as Thai, Vietnamese and Spanish allows them to prepare dishes that attract plaudits from food media and fuel the imagination of potential diners. This experience includes professional training in a cuisine under a well-known exponent of the cuisine, which allows them to be associated with the image of their mentor. The other route is vocational culinary training, which gives the chefs the ability to create dishes that stoke the imagination of diners. Copyright © 2017 Elsevier Ltd. All rights reserved.
Design and Optimization of a Complete Stokes Polarimeter for the MWIR
Energy Technology Data Exchange (ETDEWEB)
DERENIAK,E.L.; SABATKE,D.S.; LOCKE,A.M.; DESCOUR,M.R.; SWEATT,WILLIAM C.; GARCIA,J.P.; SASS,D.; HAMILTON,T.; KEMME,SHANALYN A.; PHIPPS,GARY S.
2000-08-11
A figure of merit for optimization of a complete Stokes polarimeter based on its measurement matrix is described from the standpoint of singular value decomposition and analysis of variance. It is applied to optimize a system featuring a rotatable retarder and fixed polarizer, and to study the effects of non-ideal retarder properties. A retardance of 132{degree} (approximately three-eighths wave) and retarder orientation angles of {+-}51.7{degree} and {+-}15.1{degree} are favorable when four measurements are used. An achromatic, form-birefringent retarder for the 3--5 {micro}m spectral region has been fabricated and characterized. The effects of non-idealities in the form-birefringent retarder are moderate, and performance superior to that of a quarter-wave plate is expected.
Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver
Sørensen, N. N.; Bechmann, A.; Johansen, J.; Myllerup, L.; Botha, P.; Vinther, S.; Nielsen, B. S.
2007-07-01
The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting the flow in the complex terrain by comparing with measurements from two meteorology masts. Next, it is illustrated how levels of turbulent kinetic energy can be used to easily identify areas with severe flow conditions, relying on a high correlation between high turbulence intensity and severe flow conditions, in the form of high wind shear and directional shear which may seriously lower the lifetime of a wind turbine.
An Asymptotic-Preserving Method for a Relaxation of the Navier-Stokes-Korteweg Equations
Chertock, Alina; Neusser, Jochen
2015-01-01
The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flow. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To overcome this restriction, we propose an implicit-explicit asymptotic-preserving finite volume method. We prove that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and demonstrate that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths.
A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques
Kaul, U. K.; Chaussee, D. S.
1985-01-01
The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching-step sizes with the implicit shock fitting procedure. A correlation is found between the marching-step size, Reynolds number and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.
Ortega-Quijano, Noé; Roche, Muriel; Parnet, François; Alouini, Mehdi
2015-01-01
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 progress...
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation
Directory of Open Access Journals (Sweden)
Yuncheng You
2008-12-01
Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.
Stochastic Navier-Stokes Equations in Unbounded Channel Domains (Open Source)
2014-09-17
t h(t) = −8ν ∞∑ n=0 e−ν(2n+1) 2π2t. 58 U. Manna et al. JMFM From (3.20), denoting ∂∂th(t− τ) as H(t− τ), we obtain the Volterra integral equation of...L2(Ω; L2(0, T )) be given. Then there exists a unique solution f(·, ·) ∈ L2(Ω; L2(0, T )) for the integral equation (3.21) in the form f(t, ω...domains. Differ. Integral Equ. 23(3-4), 223–235 (2010) [23] Fernando, B.P.W., Sritharan, S.S.: Nonlinear filtering of stochastic Navier–Stokes equation with
Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review
Directory of Open Access Journals (Sweden)
Bermejo Rodolfo
2016-09-01
Full Text Available We review in this paper the development of Lagrange-Galerkin (LG methods to integrate the incompressible Navier-Stokes equations (NSEs for engineering applications. These methods were introduced in the computational fluid dynamics community in the early eighties of the past century, and at that time they were considered good methods for both their theoretical stability properties and the way of dealing with the nonlinear terms of the equations; however, the numerical experience gained with the application of LG methods to different problems has identified drawbacks of them, such as the calculation of specific integrals that arise in their formulation and the calculation of the ow trajectories, which somehow have hampered the applicability of LG methods. In this paper, we focus on these issues and summarize the convergence results of LG methods; furthermore, we shall briefly introduce a new stabilized LG method suitable for high Reynolds numbers.
Thermocapillary migration of a spherical drop in an arbitrary transient Stokes flow
Sharanya, V.; Raja Sekhar, G. P.
2015-06-01
The present problem is concerned with an arbitrary transient Stokes flow past a viscous drop. The interfacial tension gradient is assumed to be dependent on temperature which is unsteady and hence governed by unsteady heat conduction equation. Solenoidal decomposition method is used to solve the hydrodynamic problem. The unknown coefficients have been computed by using non-isothermal boundary conditions. The drag force and torque exerted on the surface of the drop are computed in the form of Faxen's laws. Some special cases like flow due to an unsteady Stokeslet and thermal field due to a heat source have been discussed. Asymptotic expansions for drag and torque have been calculated. Further, we have computed migration velocity.
A comparison of two incompressible Navier-Stokes algorithms for unsteady internal flow
Wiltberger, N. Lyn; Rogers, Stuart E.; Kwak, Dochan
1993-01-01
A comparative study of two different incompressible Navier-Stokes algorithms for solving an unsteady, incompressible, internal flow problem is performed. The first algorithm uses an artificial compressibility method coupled with upwind differencing and a line relaxation scheme. The second algorithm uses a fractional step method with a staggered grid, finite volume approach. Unsteady, viscous, incompressible, internal flow through a channel with a constriction is computed using the first algorithm. A grid resolution study and parameter studies on the artificial compressibility coefficient and the maximum allowable residual of the continuity equation are performed. The periodicity of the solution is examined and several periodic data sets are generated using the first algorithm. These computational results are compared with previously published results computed using the second algorithm and experimental data.
Guruswamy, Guru P.; Byun, Chansup
1993-01-01
A computational procedure is presented to study fluid-structural interaction problems for three-dimensional aerospace structures. The flow is modeled using the three-dimensional unsteady Euler/Navier-Stokes equations and solved using the finite-difference approach. The three dimensional structure is modeled using shell/plate finite-element formulation. The two disciplines are coupled using a domain decomposition approach. Accurate procedures both in time and space are developed to combine the solutions from the flow equations with those of the structural equations. Time accuracy is maintained using aeroelastic configuration-adaptive moving grids that are computed every time step. The work done by aerodynamic forces due to structural deformations is preserved using consistent loads. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Results are illustrated for a typical wing-body configuration.
Single-pulse coherent anti-Stokes Raman scattering microscopy employing an octave spanning pulse.
Isobe, Keisuke; Suda, Akira; Tanaka, Masahiro; Hashimoto, Hiroshi; Kannari, Fumihiko; Kawano, Hiroyuki; Mizuno, Hideaki; Miyawaki, Atsushi; Midorikawa, Katsumi
2009-07-06
We demonstrate two complementary types of microscopy using an identical setup for single-pulse coherent anti-Stokes Raman scattering (CARS) imaging, which employs an ultrabroadband laser pulse with a spectral bandwidth of 4800 cm(-1) and enables the suppression of nonresonant CARS signals. One is a novel type of microscopy that uses spectral phase modulation for the selective excitation of a single Raman mode. The selective excitation is achieved by the modulated pulse focusing its difference-frequency spectrum into a narrow spectral region. Another type is Fourier-transform CARS (FT-CARS) microspectroscopy based on the measurement of the CARS spectrum obtained from the Fourier-transform of the interferometric autocorrelation (IAC) signal. Vibrational spectral imaging of chemical and biological samples is demonstrated using the two types of microscopy.
Mohamed, Mamdouh S; Samtaney, Ravi
2015-01-01
A conservative discretization of incompressible Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the contraction operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second ord...
The FMM-BEM Method for the 3D Particulate Stokes Flow
Directory of Open Access Journals (Sweden)
Hassib Selmi
2014-01-01
Full Text Available This work introduces new functions based on the spherical harmonics and the solid harmonics which have been used to construct a multipole development for the 3D Stokes problem in order to reduce the operations costs in the BEM method. We show that the major properties of those functions are inherited from the solid harmonics. The contribution of this paper is the introduction of new formulas that serve to calculate the multipole moments and the transfer functions that are necessary for the schemes of order O(NlogN. Moreover, new translation formulas are introduced to obtain an O(N scheme. The error truncation of the resulting scheme is discussed. In comparison to the BEM that attains a limit storage at O(104, we present here a method based on FMM-BEM that attains a storage at a limit of O(106. The implementation of the method achieves a high accuracy level at a reasonable cost.
Kiris, Cetin; Kwak, Dochan
1995-01-01
The fractional step and the pseudocompressibility methods for the solution of the incompressible Navier-Stokes equations are outlined. The fractional step method is based on finite-volume formulation and uses the pressure and the volume fluxes across the faces of each cell as dependent variables. The momentum equations are solved implicitly and the Poisson equation for the pressure is solved by using the multigrid method. The pseudocompressibility approach uses an implicit-higher-order-upwind differencing scheme for the convective terms together with the Gauss-Seidel line relaxation method. The dependent variables in the pseudocompressibility approach are the pressure and the cartesian velocity components in unstaggered mesh orientation. The 90-degree square duct flow, the wing-tip vortex wake flow and unsteady turbulent flows over an oscillating NACA 0015 airfoil are computed using both the fractional step and the pseudocompressibility methods. The results obtained from two different schemes are compared against experimental measurements.
Distributed parallel processing applied to an implicit multigrid Euler/Navier-Stokes algorithm
Tysinger, T. L.; Caughey, D. A.
1993-01-01
An implicit multigrid algorithm for the solution of the Euler and Navier-Stokes equations has been implemented within the framework of multiple block-structured grids in which the physical domain is spatially decomposed into several blocks and the solution is advanced in parallel on each block. Utilities have been developed to implement such a scheme in a distributed computing environment. The multi-block algorithm is designed so that the explicit residual calculation is identical to that of single-block scheme, and therefore converged solutions for both schemes must be the same. To accelerate convergence, synchronous and asynchronous multigrid strategies are implemented. Significant speedups have been achieved in a multiple processor environment, while convergence rates similar to those of the single-block scheme are observed.
Characterization of photodamage in coherent anti-Stokes Raman scattering microscopy
Fu, Yan; Wang, Haifeng; Shi, Riyi; Cheng, Ji-Xin
2006-05-01
We report a mechanistic analysis of photodamage in coherent anti-Stokes Raman scattering (CARS) microscopy. Photodamage to the myelin sheath in spinal tissues is induced by using the point scan mode and is featured by myelin splitting and shockwaves with broadband emission. Our measurement of photodamage rate versus the excitation power reveals that both linear and nonlinear mechanisms are involved. Moreover, we show that vibrational absorption induced by coherent Raman processes significantly contributes to the nonlinear damage at high peak powers. For CARS imaging of cultured cells, the photodamage is characterized by plasma membrane blebbing and is dominated by a second order mechanism. Our study suggests that for dense samples such as the myelin sheath, CARS imaging induced photodamage can be minimized by using laser beams with relatively long near IR wavelengths and a repetition rate of a few MHz. For less dense samples such as cultured cells, laser pulses of higher repetition rates are preferred.
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.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
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.
Directory of Open Access Journals (Sweden)
Ping Zhang
2014-01-01
Full Text Available The variational multiscale element free Galerkin method is extended to simulate the Stokes flow problems in a circular cavity as an irregular geometry. The method is combined with Hughes’s variational multiscale formulation and element free Galerkin method; thus it inherits the advantages of variational multiscale and meshless methods. Meanwhile, a simple technique is adopted to impose the essential boundary conditions which makes it easy to solve problems with complex area. Finally, two examples are solved and good results are obtained as compared with solutions of analytical and numerical methods, which demonstrates that the proposed method is an attractive approach for solving incompressible fluid flow problems in terms of accuracy and stability, even for complex irregular boundaries.
Three-Component Decomposition Based on Stokes Vector for Compact Polarimetric SAR
Directory of Open Access Journals (Sweden)
Hanning Wang
2015-09-01
Full Text Available In this paper, a three-component decomposition algorithm is proposed for processing compact polarimetric SAR images. By using the correspondence between the covariance matrix and the Stokes vector, three-component scattering models for CTLR and DCP modes are established. The explicit expression of decomposition results is then derived by setting the contribution of volume scattering as a free parameter. The degree of depolarization is taken as the upper bound of the free parameter, for the constraint that the weighting factor of each scattering component should be nonnegative. Several methods are investigated to estimate the free parameter suitable for decomposition. The feasibility of this algorithm is validated by AIRSAR data over San Francisco and RADARSAT-2 data over Flevoland.
Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries
Williams-Rioux, Bertrand
2012-01-12
Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.
Effects of tissue fixation on coherent anti-Stokes Raman scattering images of brain
Galli, Roberta; Uckermann, Ortrud; Koch, Edmund; Schackert, Gabriele; Kirsch, Matthias; Steiner, Gerald
2014-07-01
Coherent anti-Stokes Raman scattering (CARS) microscopy is an emerging multiphoton technique for the label-free histopathology of the central nervous system, by imaging the lipid content within the tissue. In order to apply the technique on standard histology sections, it is important to know the effects of tissue fixation on the CARS image. Here, we report the effects of two common fixation methods, namely with formalin and methanol-acetone, on mouse brain and human glioblastoma tissue. The variations induced by fixation on the CARS contrast and intensity were compared and interpreted using Raman microspectroscopy. The results show that, whenever unfixed cryosections cannot be used, fixation with formalin constitutes an alternative which does not deteriorate substantially the contrast generated by the different brain structures in the CARS image. Fixation with methanol-acetone strongly modifies the tissue lipid content and is therefore incompatible with the CARS imaging.
Validation of the actuator line/Navier Stokes technique using mexico measurements
DEFF Research Database (Denmark)
Shen, Wen Zhong; Zhu, Wei Jun; Sørensen, Jens Nørkær
2010-01-01
This paper concerns the contribution of DTU MEK in the international research collaboration project (MexNext) within the framework of IEA Annex 29 to validate aerodynamic models or CFD codes using the existing measurements made in the previous EU funded projectMEXICO (Model Experiments in Control......This paper concerns the contribution of DTU MEK in the international research collaboration project (MexNext) within the framework of IEA Annex 29 to validate aerodynamic models or CFD codes using the existing measurements made in the previous EU funded projectMEXICO (Model Experiments...... in Controlled Conditions). The Actuator Line/Navier Stokes (AL/NS) technique developed at DTU is validated against the detailed MEXICO measurements. The AL/NS computations without the DNW wind tunnel with speeds of 10m/s, 15m/s and 24m/s. Comparisons of blade loading between computations and measurements show...
Towards a Navier Stokes-Darcy Upscaling Based on Permeability Tensor Computation
Lieb, M.
2012-06-02
The micro scale simulation of CO2 sequestration involves complex, porous-like geometries. For the generation of such geometries, we present two approaches: In 2D, we construct a fractured domain by channel networks. In 3D, we approximate sand grain-like scenarios by dense sphere packings. The ﬂow through these structures is simulated with the incompressible Navier-Stokes solver of the PDE framework Peano. Using an upscaling scheme, the results of the micro scale are used as input data for a Darcy solver on the coarse scales. The coupling concept and the scenario generators are presented together with ﬁrst simulation results showing the validity of the approach.
Broadband coherent anti-Stokes Raman spectroscopy with a modeless dye laser.
Hahn, J W; Park, C W; Park, S N
1997-09-20
We develop a modeless dye laser for broadband coherent anti-Stokes Raman spectroscopy (CARS) and investigate the operational characteristics of the modeless laser. The energy efficiency of the modeless laser is 6%, and the beam divergence is 0.65 mrad. We construct a compact movable CARS system with the modeless laser and a graphite tube furnace to assess the accuracy of the CARS temperature. It is found that the difference between the averaged CARS temperature and the radiation temperature measured with an optical pyrometer is <2% at a temperature range from 1000 to 2400 K. We also measure the averaged CARS temperature drift owing to the variation of the spectral distribution of the modeless laser, which is <1.5% during 5 h of operation.
Novel equalization techniques for space division multiplexing based on stokes space update rule
DEFF Research Database (Denmark)
Caballero, Francisco Javier Vaquero; Pittalà, Fabio; Goeger, Gernot
2017-01-01
for space division multiplexing (SDM). Although different papers have been published about the SSA and its MIMO implementation, we provide for the first time an analysis of the of the convergence speed and frequency offset of the SSA compared to the least mean square (LMS). SSA algorithm can deal......Space division multiplexing (SDM) is a promising technology that aims to overcome the capacity crunch of optical communications. In this paper, we introduce the multiple-input multiple-output (MIMO) Stokes Space Algorithm (SSA) implemented in frequency domain, a novel equalization technique...... with higher frequency offsets and linewidths than LMS, being suitable for optical communications with higher phase noise. SSA does not need pre-compensation of frequency offset, which can be compensated after equalization without penalties. On the other hand, due to reduced convergence speed, SSA requires...
Novel Equalization Techniques for Space Division Multiplexing Based on Stokes Space Update Rule
Directory of Open Access Journals (Sweden)
Francisco Javier Vaquero Caballero
2017-02-01
Full Text Available Space division multiplexing (SDM is a promising technology that aims to overcome the capacity crunch of optical communications. In this paper, we introduce the multiple-input multiple-output (MIMO Stokes Space Algorithm (SSA implemented in frequency domain, a novel equalization technique for space division multiplexing (SDM. Although different papers have been published about the SSA and its MIMO implementation, we provide for the first time an analysis of the of the convergence speed and frequency offset of the SSA compared to the least mean square (LMS. SSA algorithm can deal with higher frequency offsets and linewidths than LMS, being suitable for optical communications with higher phase noise. SSA does not need pre-compensation of frequency offset, which can be compensated after equalization without penalties. On the other hand, due to reduced convergence speed, SSA requires longer training sequences than LMS.
Fractional calculus transmutation for the Airy WKB solutions and Stokes phenomenon
Kiryakova, Virginia
2016-12-01
We apply the transmutation method to give a new explanation of the Stokes phenomenon for the Airy differential equation and of the change of the coeffcients in its asymptotic solutions for large values of argument in different parts of the complex plane. As a transmutation operator, a Weyl type fractional order integral is used. But this scheme is a special case of the so-called Poisson- Sonine-Dimovski transmutation operators related to the hyper-Bessel differential equations of arbitrary integer order, and of the generalized fractional calculus operators related to differential equations of fractional multi-order and their solutions, including a number of special functions. We analyze also the previous results of other authors and suggest some perspectives to use the same method in more general cases.
PARALLEL ALGORITHM FOR THREE-DIMENSIONAL STOKES FLOW SIMULATION USING BOUNDARY ELEMENT METHOD
Directory of Open Access Journals (Sweden)
D. G. Pribytok
2016-01-01
Full Text Available Parallel computing technique for modeling three-dimensional viscous flow (Stokes flow using direct boundary element method is presented. The problem is solved in three phases: sampling and construction of system of linear algebraic equations (SLAE, its decision and finding the velocity of liquid at predetermined points. For construction of the system and finding the velocity, the parallel algorithms using graphics CUDA cards programming technology have been developed and implemented. To solve the system of linear algebraic equations the implemented software libraries are used. A comparison of time consumption for three main algorithms on the example of calculation of viscous fluid motion in three-dimensional cavity is performed.
Dimensional dependence of the Stokes-Einstein relation and its violation.
Charbonneau, Benoit; Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco
2013-10-28
We generalize to higher spatial dimensions the Stokes-Einstein relation (SER) as well as the leading correction to diffusivity in finite systems with periodic boundary conditions, and validate these results with numerical simulations. We then investigate the evolution of the high-density SER violation with dimension in simple hard sphere glass formers. The analysis suggests that this SER violation disappears around dimension d(u) = 8, above which it is not observed. The critical exponent associated with the violation appears to evolve linearly in 8 - d, below d = 8, as predicted by Biroli and Bouchaud [J. Phys.: Condens. Matter 19, 205101 (2007)], but the linear coefficient is not consistent with the prediction. The SER violation with d establishes a new benchmark for theory, and its complete description remains an open problem.
Reynolds-averaged Navier-Stokes and Large-Eddy Simulation Over and Inside Inhomogeneous Forests
DEFF Research Database (Denmark)
Boudreault, Louis-Etienne
the performance of wind models in such environment.A systematic method to acquire gridded input of canopy structure from aircraft based LiDAR scans of heterogeneous forests is defined. An extensive validation against ground-based measurements of the vertically summed frontal area density(or plant area index......) and tree height is performed. The method is optimized both in terms of plant area index magnitude and spatial variability. A forest grid is generated from the LiDAR method using airplane scans of a 5×5 km2 forested site in Sweden. The grid serves as the basis for Reynolds-averaged Navier-Stokes (RANS......) simulations. Wind observations from an instrumented mast are used for validation where a good correlation is found for the mean wind speed of two contrasting wind directions with different influences from the upstream forest. The effects of successive simplifications of the forest representation show...
Numerical solutions of Navier-Stokes equations for a Butler wing
Abolhassani, Jamshid S.; Tiwari, Surendra N.; Smith, Robert E.
1987-01-01
The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and Reynolds number of 2,000,000. The simulation is done by integrating the viscous Navier-Stokes equations. These equations govern the unsteady, viscous, compressible and heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. The O-type and H-type grids have been used for this study, and results are compared. The governing equations are solved by the MacCormack time-split method, and the results are compared with other theoretical and experimental results. The codes are written in FORTRAN, vectorized and currently run on the CDC Vector Processing System (VPS-32) computer.
Mohamed, Mamdouh S.
2016-02-11
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Heat or mass transfer from a sphere in Stokes flow at low Péclet number
Bell, Christopher G.
2013-04-01
We consider the low Péclet number, Pe≪1, asymptotic solution for steady-state heat or mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of Van Dyke\\'s rule up to terms of O(Pe3) shows that the O(Pe3logPe) terms in the expression for the average Nusselt/Sherwood number are twice those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase the range of validity of the expansion. © 2012 Elsevier Ltd. All rights reserved.
Navier-Stokes Entropy Controlled Combustion Instability Analysis for Liquid Propellants
Chung, T. J.; Yoon, W. S.
1990-01-01
Navier-Stokes solutions are used to calculate oscillatory components of pressure, velocity, and density, which in turn provide necessary data to compute energy growth factors to determine combustion instability. It is shown that wave instabilities are associated with changes in entropy and the space and time averages of oscillatory components of pressure, velocity and density, together with the mean flow field in the energy equation. Compressible laminar and turbulent flows and reacting flows with hydrogen/oxygen combustion are considered. The SSME combustion/thrust chamber is used for illustration of the theory. The analysis shows that the increase of mean pressure and disturbances consistently results in the increase of instability. It is shown that adequate combustion instability analysis requires at least third order nonlinearity in energy growth or decay.
The commutation error of the space averaged Navier-Stokes equations on a bounded domain
Energy Technology Data Exchange (ETDEWEB)
Dunca, A.; Layton, W.J. [Pittsburgh Univ., PA (United States). Dept. of Mathematics; John, V. [Magdeburg Univ. (Germany). Inst. fuer Analysis und Numerik
2002-01-01
In Large Eddy Simulation of turbulent flows, the Navier-Stokes equations are convolved with a filter and differentiation and convolution are interchanged, introducing an extra commutation error term, which is nearly universally dropped from the resulting equations. We show that the commutation error is asymptotically negligible in L{sup p}(R{sup d}) (i.e., it vanishes as the averaging radius {delta}{yields}0) if and only if the fluid and the boundary exert exactly zero force on each other. Next, we show that the commutation error tends to zero in H{sup -1}({omega}) as {delta}{yields}0. Convergence is proven also for a weak form of the commutation error. The order of convergence is studied in both cases. Last, we study the influence of the commutation error on the energy balance of the filtered equations. (orig.)
Analytical solution for viscous incompressible Stokes flow in a spherical shell
Thieulot, Cedric
2017-11-01
I present a new family of analytical flow solutions to the incompressible Stokes equation in a spherical shell. The velocity is tangential to both inner and outer boundaries, the viscosity is radial and of the power-law type, and the solution has been designed so that the expressions for velocity, pressure, and body force are simple polynomials and therefore simple to implement in (geodynamics) codes. Various flow average values, e.g., the root mean square velocity, are analytically computed. This forms the basis of a numerical benchmark for convection codes and I have implemented it in two finite-element codes: ASPECT and ELEFANT. I report error convergence rates for velocity and pressure.
Breakdown of Stokes-Einstein relation in the supercooled liquid state of phase change materials
Sosso, G. C.; Behler, J.; Bernasconi, M.
2012-10-01
The application of amorphous chalcogenide alloys as data-storage media relies on their ability to undergo an extremely fast (10-100 ns) crystallisation once heated at sufficiently high temperature. However, the peculiar features that make these materials so attractive for memory devices still lack a comprehensive microscopic understanding. By means of large scale molecular dynamics simulations, we demonstrate that the supercooled liquid of the prototypical compound GeTe shows a very high atomic mobility (D \\sim 10^(-6) cm2/s) down to temperatures close to the glass transition temperatures. This behaviour leads to a breakdown of the Stokes-Einstein relation between the self- diffusion coefficient and the viscosity in the supercooled liquid. The results suggest that the fragility of the supercooled liquid is the key to understand the fast crystallisation process in this class of materials.
LANDSLIDE-TYPE TSUNAMI MODELLING BASED ON THE NAVIER - STOKES EQUATIONS
Directory of Open Access Journals (Sweden)
A.S. Kozelkov
2016-11-01
Full Text Available The paper presents a unified computing technology for all stages of landslide-type tsunami. The computing technology is based on the numerical solution of the Navier – Stokes equations for multiphase flows. The method of numerical solution of the Navier – Stokes equations uses a fully implicit algorithm. This algorithm removes stiff restrictions on the time steps and allows simulating a tsunami propagation in arbitrarily large water basins. The basic sampling equation formulas, coefficient types as well as the basic steps of the computational procedure are presented. The landslide is modeled by a single phase with its density and viscosity, which is separated by the interface from water and air phases. A parallel algorithm of the method implementation based on an algebraic multigrid method is proposed for the effective usage of the method to calculate the tsunami in large water areas. The multigrid method of implementation is based on algorithms of global level and cascading collection. These algorithms do not impose restrictions on the scale parallelization and allow the use of the proposed technology in petaflop class systems. It shows the possibility ofsimulating all the stages of the landslide-type tsunamis: generation, propagation and runup. The verification of the method is carried out by using the tests provided by the experimental data. The mechanism of bathymetric data accounting and the technology of constructing three-dimensional grid models are described. The results of the comparison with the non-linear dispersion theory are presented for the historical tsunami that resulted from a volcanic eruption on the island of Montserrat, the Caribbean. The results of this comparison are in good agreement.
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.
M2Di: Concise and efficient MATLAB 2-D Stokes solvers using the Finite Difference Method
Räss, Ludovic; Duretz, Thibault; Podladchikov, Yury Y.; Schmalholz, Stefan M.
2017-02-01
Recent development of many multiphysics modeling tools reflects the currently growing interest for studying coupled processes in Earth Sciences. The core of such tools should rely on fast and robust mechanical solvers. Here we provide M2Di, a set of routines for 2-D linear and power law incompressible viscous flow based on Finite Difference discretizations. The 2-D codes are written in a concise vectorized MATLAB fashion and can achieve a time to solution of 22 s for linear viscous flow on 10002 grid points using a standard personal computer. We provide application examples spanning from finely resolved crystal-melt dynamics, deformation of heterogeneous power law viscous fluids to instantaneous models of mantle flow in cylindrical coordinates. The routines are validated against analytical solution for linear viscous flow with highly variable viscosity and compared against analytical and numerical solutions of power law viscous folding and necking. In the power law case, both Picard and Newton iterations schemes are implemented. For linear Stokes flow and Picard linearization, the discretization results in symmetric positive-definite matrix operators on Cartesian grids with either regular or variable grid spacing allowing for an optimized solving procedure. For Newton linearization, the matrix operator is no longer symmetric and an adequate solving procedure is provided. The reported performance of linear and power law Stokes flow is finally analyzed in terms of wall time. All MATLAB codes are provided and can readily be used for educational as well as research purposes. The M2Di routines are available from Bitbucket and the University of Lausanne Scientific Computing Group website, and are also supplementary material to this article.
A Novel Approach to Fast SOLIS Stokes Inversion for Photospheric Vector Magnetography.
Harker, Brian; Mighell, K.
2009-05-01
The SOLIS (Synoptic Optical Long-term Investigations of the Sun) Vector Spectromagnetograph (VSM) is a full-disc spectropolarimeter, located at Kitt Peak National Observatory, which records Zeeman-induced polarization in the magnetically-sensitive FeI spectral lines at 630.15 nm and 630.25 nm. A SOLIS VSM full-disc dataset consists of 2048 scanlines, with each scanline containing the Stokes I, Q, U, and V spectral line profiles in 128 unique wavelength bins for all 2048 pixels in the scanline. These Stokes polarization profiles are inverted to obtain the magnetic and thermodynamic structure of the observations, based on a model Milne-Eddington plane-parallel atmosphere. Until recently, this has been a compute-intensive, relatively slow process. This poster presents a novel method of producing such model-based characterizations of the photospheric magnetic field by utilizing an inversion engine based on a genetic algorithm. The algorithm executes in a heterogeneous compute environment composed of both a CPU and a graphics processing unit (GPU). Using the cutting-edge NVIDIA CUDA platform, we are able to offload the compute-intensive portions of the inversion code to the GPU, which results in significant speedup. This speedup provides the impetus which has driven the development of this strategy. Currently, SOLIS vector magnetic field products are generated with a modified version of the HAO ASP inversion code developed by Skumanich & Lites (1987), and these data products are made available to the scientific community 24 hours after the actual observation(s). With this work, we aim to drastically reduce this waiting period to allow near real-time characterizations of the photospheric vector magnetic field. Here, we here detail the inversion method we have pioneered, present preliminary results on the derived full-disc magnetic field as well as timing/speedup considerations, and finally offer some outlooks on the future direction of this work.
Gayley, Kenneth G.
2017-12-01
Derived here is a more conceptually intuitive means of interpreting magnetic-field diagnostics from circularly polarized lines in a wide array of astrophysical applications. The method applies to individual “Stokes V” profile snapshots and complements standard Zeeman Doppler imaging techniques by providing the explicit form of the averaging kernel for the magnetic field that the polarization diagnostic is sensitive to. This new perspective centers on the antiderivative, or cumulative integral with respect to frequency, of the Stokes V profile. The new approach would not yield different answers for magnetic field determinations, but rather presents a more directly conceptual means of understanding the connection between what is observed and what types of fields produce it. In particular, it elucidates how lateral and line-of-sight field gradients affect the Zeeman profile. This approach is especially useful when the Zeeman shift varies in a way that correlates with the Doppler shift, as then spectral resolution serves as a proxy for spatial imaging in each polarization snapshot. Hence, the perspective is particularly useful for rapidly rotating stars, hypersonic winds, galactic rotation, and large-amplitude turbulence, when the longitudinal field varies across the source or with depth. The approach also generates an improved unsigned mean-field diagnostic that suffers less polarity cancellation than the commonly used center-of-gravity diagnostic. Reduced cancellation produces a better estimate of the field magnitude in toroidal, spotty, or dipolar fields, and a complementary comparison with the current unsigned diagnostic can help characterize the degree of field polarity reversal concealed within integrated diagnostics.
Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition
Bessaih, Hakima
2015-11-02
The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.
Vorticity-velocity formulation of the Navier-Stokes equations for aerodynamic flows
Energy Technology Data Exchange (ETDEWEB)
Hansen, M.O.L.
1994-05-01
The aim of this Ph.D. thesis was to produce a numerical model to compute the flow past a wind turbine rotor. This thesis is divided into three separate reports. The first report is called Vorticity-Velocity Formulation of the Navier-Stokes Equations and is a feasibility study to see whether this formulation is suitable to compute three-dimensional, incompressible and unsteady viscous fluid flow. The vorticity-velocity formulation is discussed, and on this basis a numerical scheme is implemented to compute 3-D viscous flows. The velocity field is found by solving the Cauchy-Riemann equations, which turn out to give an overdetermined system of linear algebraic equations. Two iterative methods for solving this system is investigated: CGNR and the Kaczmarz algorithm. To advance the solution in time the ADI technique is applied on the vorticity transport equations. In the next report, Flow Simulation of a Wind Turbine Rotor by Numerical Solution of the Euler Equations, the governing equations are transformed into a general curvilinear coordinate system. As a test case the two-dimensional potential flow past a NACA0012 airfoil is computed for different angles of attack. For the attached flow, i.e. angles of attack below approximately 14 degrees, excellent agreement with measurements is found. Furthermore, qualitatively good results for the inviscid flow past the Nibe A turbine is computed. Finally, a model for the viscous flow past a wing is described in the report Navier-Stokes Solver for a Rotating Wing. To allow computations at realistic Reynolds numbers the algebraic Baldwin-Lomax turbulence model is implemented. (EG)
DEFF Research Database (Denmark)
Wang, W.; Ishijima, R.; Matsuda, A.
2010-01-01
of the intensity speckle pattern, which converts the original real-valued signal into a complex signal. In closest analogy to the polarisation of a vector wave, the Stokes-like vector constructed from the spatial derivative of the generated complex signal has been applied for correlation. Experimental results...
van den Bremer, Ton S.; Taylor, Paul H.
2014-11-01
Although the literature has examined Stokes drift, the net Lagrangian transport by particles due to of surface gravity waves, in great detail, the motion of fluid particles transported by surface gravity wave groups has received considerably less attention. In practice nevertheless, the wave field on the open sea often has a group-like structure. The motion of particles is different, as particles at sufficient depth are transported backwards by the Eulerian return current that was first described by Longuet-Higgins & Stewart (1962) and forms an inseparable counterpart of Stokes drift for wave groups ensuring the (irrotational) mass balance holds. We use WKB theory to study the variation of the Lagrangian transport by the return current with depth distinguishing two-dimensional seas, three-dimensional seas, infinite depth and finite depth. We then provide dimensional estimates of the net horizontal Lagrangian transport by the Stokes drift on the one hand and the return flow on the other hand for realistic sea states in all four cases. Finally we propose a simple scaling relationship for the transition depth: the depth above which Lagrangian particles are transported forwards by the Stokes drift and below which such particles are transported backwards by the return current.
Stokes shift and fine-structure splitting in CdSe/CdTe invert type-II ...
Indian Academy of Sciences (India)
Using the atomistic tight-binding (TB) theory and configuration interaction (CI) description, it is showed that the Stokes shift and fine-structure splitting (FSS) in semiconductor core/shell nanocrystals are predominantly affected by the shell thickness and band profiles. CdSe/CdTe invert type-II and CdTe/CdSe type-II core/shell ...
1992-10-01
and in the interest of getting this technology out to the users, the text was not edited by TESCO . Inc. 12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b...Separation Euler Equations Computational Fluid Dynamics 16. PRICE CODE Navier-Stokes Equations 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19
Czech Academy of Sciences Publication Activity Database
Guo, Z.; Kučera, P.; Skalák, Zdeněk
2018-01-01
Roč. 458, č. 1 (2018), s. 755-766 ISSN 0022-247X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985874 Keywords : Navier Stokes equations * conditional regularity * regularity criteria * vorticity * Besov spaces * bony decomposition Subject RIV: BA - General Mathematics Impact factor: 1.064, year: 2016
Beeker, Willem; Beeker, W.P.; Lee, Christopher James; Boller, Klaus J.; Gross, P.; Cleff, Carsten; Fallnich, Carsten; Offerhaus, Herman L.; Herek, Jennifer Lynn
2010-01-01
We present a theoretical investigation of coherent anti-Stokes Raman scattering (CARS) that is modulated by periodically depleting the ground-state population through Rabi oscillations driven by an additional control laser. We find that such a process generates optical sidebands in the CARS spectrum
Irwin, R.M.; Visser, A.J.W.G.; Lee, J.; Carreira, L.A.
1980-01-01
The resonance coherent anti-Stokes Raman technique was used to obtain vibrational spectra of flavin in flavodoxins from Desulfovibrio gigas and Desulfovibrio vulgaris and of the simpler 6,7-dimethyl-8-ribityllumazine chromophore in the blue fluorescence lumazine protein from the bioluminescent
Jurna, M.; Garbacik, E.T.; Korterik, Jeroen P.; Herek, Jennifer Lynn; Otto, Cornelis; Offerhaus, Herman L.
2010-01-01
In coherent anti-Stokes Raman scattering (CARS), the emitted signal carries both amplitude and phase information of the molecules in the focal volume. Most CARS experiments ignore the phase component, but its detection allows for two advantages over intensity-only CARS. First, the pure resonant
Guermond, Jean-Luc
2012-01-01
We provide a convergence analysis for a new fractional timestepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. © 2012 American Mathematical Society.
Global Well-Posedness of the Two-Dimensional Exterior Navier-Stokes Equations for Non-decaying Data
Abe, Ken
2017-07-01
We prove global well-posedness of the two-dimensional exterior Navier-Stokes equations for bounded initial data with a finite Dirichlet integral, subject to the non-slip boundary condition. As an application, we construct global solutions for asymptotically constant initial data and arbitrary large Reynolds numbers.
Global well-posedness of the two-dimensional exterior Navier-Stokes equations for non-decaying data
Abe, Ken
2016-01-01
We prove global well-posedness of the two-dimensional exterior Navier-Stokes equations for bounded initial data with a finite Dirichlet integral, subject to the non-slip boundary condition. As an application, we construct global solutions for asymptotically constant initial data and arbitrary large Reynolds numbers.
Directory of Open Access Journals (Sweden)
Juergen Saal
2007-02-01
Full Text Available It is proved under mild regularity assumptions on the data that the Navier-Stokes equations in bounded and unbounded noncylindrical regions admit a unique local-in-time strong solution. The result is based on maximal regularity estimates for the in spatial regions with a moving boundary obtained in [16] and the contraction mapping principle.
On large-time energy concentration in solutions to the Navier-Stokes equations in the whole 3D space
Czech Academy of Sciences Publication Activity Database
Skalák, Zdeněk
2012-01-01
Roč. 92, č. 10 (2012), s. 801-815 ISSN 0044-2267 R&D Projects: GA AV ČR IAA200600801 Institutional research plan: CEZ:AV0Z20600510 Keywords : Navier-Stokes equations * large-time behavior of solutions * energy concentration Subject RIV: BA - General Mathematics Impact factor: 0.948, year: 2012
Nakao, Kohei; Taniuchi, Yasushi
2017-12-01
We shall find the weakest norm that satisfies the Brezis-Gallouet-Wainger type inequality, under some conditions. As an application of the Brezis-Gallouet-Wainger type inequality, we shall establish Beale-Kato-Majda type blow-up criteria of smooth solutions to the 3-D Navier-Stokes equations in unbounded domains.
IDENTIFICATION OF AN UNKNOWN PART OF THE BOUNDARY OF AN NAVIER-STOKES SYSTEM BY PUNCTUAL SENTINEL
Directory of Open Access Journals (Sweden)
IMAD REZZOUG
2012-06-01
Full Text Available In this work one interests a method for the identification of a part of the boundary in a parabolic equation (Navier-Stokes equations. By the means of the controllability of an adjoint system one has to identify this part while basing on an observation made on part of the boundary known.
O'Halloran, C; Walsh, N; O'Grady, M C; Barry, L; Hooton, C; Corcoran, G D; Lucey, B
2018-01-01
As many clinical laboratories convert between Stokes, Clinical and Laboratory Standards Institute (CLSI) and European Committee for Antimicrobial Susceptibility Testing (EUCAST) methods, the problem of comparing differently derived sets of antimicrobial susceptibility testing (AST) data with each other arises, owing to a scarcity of knowledge of inter-method comparability. The purpose of the current study was to determine the comparability of CLSI, EUCAST and Stokes AST methods for determining susceptibility of uropathogenic Escherichia coli to ampicillin, amoxicillin-clavulanate, trimethoprim, cephradine/cephalexin, ciprofloxacin and nitrofurantoin. A total of 100 E. coli isolates were obtained from boric acid urine samples from patients attending GP surgeries. For EUCAST and CLSI, the Kirby-Bauer disc diffusion method was used and results interpreted using the respective breakpoint guidelines. For the Stokes method, direct susceptibility testing was performed on the urine samples. The lowest levels of agreement were for amoxicillin-clavulanate (60%) and ciprofloxacin (89%) between the three AST methods, when using 2017 interpretive guidelines for CLSI and EUCAST. A comparison of EUCAST and CLSI without Stokes showed 82% agreement for amoxicillin-clavulanate and 94% agreement for ciprofloxacin. Discrepancies were compounded by varying breakpoint susceptibility guidelines issued during the period 2011-2017, and through the inclusion of a definition of intermediate susceptibility in some cases. Our data indicate that the discrepancies generated through using different AST methods and different interpretive guidelines may result in confusion and inaccuracy when prescribing treatment for urinary tract infection.
Ophaug, Vegard; Gerlach, Christian
2017-11-01
This work is an investigation of three methods for regional geoid computation: Stokes's formula, least-squares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223-232, 1995. doi: 10.1007/BF00806734) that the equivalence of Stokes's formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes's formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level.
Klaij, C.M.; van der Vegt, Jacobus J.W.; van der Ven, H.
2005-01-01
The space-time discontinuous Galerkin discretization of the compressible Navier-Stokes equations results in a non-linear system of algebraic equations, which we solve with a local pseudo-time stepping method. Explicit Runge-Kutta methods developed for the Euler equations are unsuitable for this
Ohkitani, Koji
2017-01-01
We make a detailed comparison between the Navier-Stokes equations and their dynamically scaled counterpart, the so-called Leray equations. The Navier-Stokes equations are invariant under static scaling transforms, but are not generally invariant under dynamic scaling transforms. We will study how closely they can be brought together using the critical dependent variables and discuss the implications on the regularity problems. Assuming that the Navier-Stokes equations written in the vector potential have a solution that blows up at t = 1, we derive the Leray equations by dynamic scaling. We observe: (1) the Leray equations have only one term extra on top of those of the Navier-Stokes equations (2) we can recast the Navier-Stokes equations as a Wiener path integral and the Leray equations as another Ornstein-Uhlenbeck path integral. Using the Maruyama-Girsanov theorem, both equations take the identical form modulo the Maruyama-Girsanov density, which is valid up to t=2\\sqrt{2} by the Novikov condition (3) the global solution of the Leray equations is given by a finite-dimensional projection {\\boldsymbol{R}} of a functional of an Ornstein-Uhlenbeck process and a probability measure. If {\\boldsymbol{R}} remains smooth beyond t = 1 under an absolute continuous change of the probability measure, we can rule out finite-time blowup by contradiction. There are two cases: (A) {\\boldsymbol{R}} given by a finite number of Wiener integrals, and (B) otherwise. Ruling out blowup in (A) is straightforward. For (B), a condition based on a limit passage in the Picard iterations is identified for such a contradiction to come out. The whole argument equally holds in {{{R}}}d for any d≥slant 2.
Dietzenbacher, Erik; Lahr, Michael L.
2013-01-01
In this paper, we generalize hypothetical extraction techniques. We suggest that the effect of certain economic phenomena can be measured by removing them from an input-output (I-O) table and by rebalancing the set of I-O accounts. The difference between the two sets of accounts yields the
African Journals Online (AJOL)
limited to high oleic acid oil and water purification property (Katayon et al., 2006; Foid et al., 2001 and. Folkard et al., 1993), whereas it contains up to. 332.5 g of crude protein per kg of sample (Jose et al., 1999). Studies to characterize the interaction effects of pH and salts on the extraction of. PROTEIN EXTRACTABILITY ...
A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers
Marshall, John; Adcroft, Alistair; Hill, Chris; Perelman, Lev; Heisey, Curt
1997-03-01
The numerical implementation of an ocean model based on the incompressible Navier Stokes equations which is designed for studies of the ocean circulation on horizontal scales less than the depth of the ocean right up to global scale is described. A "pressure correction" method is used which is solved as a Poisson equation for the pressure field with Neumann boundary conditions in a geometry as complicated as that of the ocean basins. A major objective of the study is to make this inversion, and hence nonhydrostatic ocean modeling, efficient on parallel computers. The pressure field is separated into surface, hydrostatic, and nonhydrostatic components. First, as in hydrostatic models, a two-dimensional problem is inverted for the surface pressure which is then made use of in the three-dimensional inversion for the nonhydrostatic pressure. Preconditioned conjugate-gradient iteration is used to invert symmetric elliptic operators in both two and three dimensions. Physically motivated preconditioners are designed which are efficient at reducing computation and minimizing communication between processors. Our method exploits the fact that as the horizontal scale of the motion becomes very much larger than the vertical scale, the motion becomes more and more hydrostatic and the three-dimensional Poisson operator becomes increasingly anisotropic and dominated by the vertical axis. Accordingly, a preconditioner is used which, in the hydrostatic limit, is an exact integral of the Poisson operator and so leads to a single algorithm that seamlessly moves from nonhydrostatic to hydrostatic limits. Thus in the hydrostatic limit the model is "fast," competitive with the fastest ocean climate models in use today based on the hydrostatic primitive equations. But as the resolution is increased, the model dynamics asymptote smoothly to the Navier Stokes equations and so can be used to address small-scale processes. A "finite-volume" approach is employed to discretize the model in
Energy Technology Data Exchange (ETDEWEB)
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.
Sulfuretin has therapeutic activity against acquired lymphedema by reducing adipogenesis.
Roh, Kangsan; Kim, Suji; Kang, Hee; Ku, Jin-Mo; Park, Kye Won; Lee, Sukchan
2017-07-01
Acquired lymphedema is a pathological condition associated with lymphatic dysfunction caused by surgical treatments for cancer. Although global estimates of the prevalence of acquired lymphedema have been rising, there are currently no effective therapeutics available. Since adipose tissue accumulation is a clinical hallmark of lymphedema, we hypothesized that regulation of adipogenesis in lymphedematous tissue could be used as a therapeutic intervention against lymphedema. Toward this, we investigated the possibility of anti-adipogenic 30% ethanol Rhus verniciflua Stokes (RVS) extract as a potential lymphedema treatment. Oral administration of RVS extract ameliorated volumetric symptoms of lymphedema in a mouse model. RVS administration also reduced adipose tissue accumulation in lymphedematous tissue and downregulated expression of adipocyte markers, including Pparγ and Fabp4. Sulfuretin was identified as a major bioactive compound in the 30% ethanol RVS extract in liquid chromatography-mass spectrometry analysis. Similar to the activities of RVS, sulfuretin inhibited adipocyte differentiation in 3T3-L1 preadipocytes. Moreover, treatment with sulfuretin on lymphedema-induced mice reduced lymphedema volume, decreased the expression of adipogenic markers, but induced the expression of markers associated with lymphangiogenesis. Taken together, our data raise the possibility that sulfuretin might be used in therapeutic interventions against acquired lymphedema. Copyright © 2017. Published by Elsevier Ltd.
Effect of Scatterering on Coherent Anti-Stokes Raman Scattering (CARS) signals
Ranasinghesagara, Janaka C; Piazza, Vincenzo; Potma, Eric O; Venugopalan, Vasan
2016-01-01
We develop a computational framework to examine the factors responsible for scattering-induced distortions of coherent anti-Stokes Raman scattering (CARS) signals in turbid samples. We use the Huygens-Fresnel Wave-based Electric Field Superposition (HF-WEFS) method combined with the radiating dipole approximation to compute the effects of scattering-induced distortions of focal excitation fields on the far-field CARS signal. We analyze the effect of spherical scatterers, placed in the vicinity of the focal volume, on the CARS signal emitted by different objects (2{\\mu}m diameter solid sphere, 2{\\mu}m diameter myelin cylinder and 2{\\mu}m diameter myelin tube). We find that distortions in the CARS signals arise not only from attenuation of the focal field but also from scattering-induced changes in the spatial phase that modifies the angular distribution of the CARS emission. Our simulations further show that CARS signal attenuation can be minimized by using a high numerical aperture condenser. Moreover, unlike...
You, Sixian; Liu, Yuan; Arp, Zane; Zhao, Youbo; Chaney, Eric J.; Marjanovic, Marina; Boppart, Stephen A.
2017-07-01
Docosanol is an over-the-counter topical agent that has proved to be one of the most effective therapies for treating herpes simplex labialis. However, the mechanism by which docosanol suppresses lesion formation remains poorly understood. To elucidate its mechanism of action, we investigated the uptake of docosanol in living cells using coherent anti-Stokes Raman scattering microscopy. Based on direct visualization of the deuterated docosanol, we observed highly concentrated docosanol inside living cells 24 h after drug treatment. In addition, different spatial patterns of drug accumulation were observed in different cell lines. In keratinocytes, which are the targeted cells of docosanol, the drug molecules appeared to be docking at the periphery of the cell membrane. In contrast, the drug molecules in fibroblasts appeared to accumulate in densely packed punctate regions throughout the cytoplasm. These results suggest that this molecular imaging approach is suitable for the longitudinal tracking of drug molecules in living cells to identify cell-specific trafficking and may also have implications for elucidating the mechanism by which docosanol suppresses lesion formation.
Byun, Chansup; Farhangnia, Mehrdad; Bhatia, Kumar; Guruswamy, Guru; VanDalsem, William R. (Technical Monitor)
1996-01-01
Modem design requirements for an aircraft push current technologies used in the design process to their limit or sometimes require more advanced technologies to meet the requirement. New design requirements always demand to improve the operational performance. Accurate prediction of aerodynamic coefficients is essential to improve the performance. For example, in the design of an advanced subsonic civil transport, since the fluid flow at transonic regime shows strong nonlinearities, high fidelity equations, such as the Euler or Navier-Stokes equations predict flow characteristics more accurately than the linear aerodynamics, which are widely used in the current design process However, high fidelity flow equations are computationally expensive and require an order of magnitude longer time to obtain aerodynamic coefficients required in the design. Parallel computing is one possibility to cut down the computational turn-around time in using high fidelity equations so that high fidelity equations would be incorporated into the design process. By doing so, high fidelity equations would be used in the routine design process. This work will demonstrate the feasibility of using high fidelity flow equations in a design process by computing aerodynamic influence coefficients of a wing-body-empennage configuration on a multiple-instruction, multiple-data parallel computer.
An analysis of the Rayleigh–Stokes problem for a generalized second-grade fluid
Bazhlekova, Emilia
2014-11-26
© 2014, The Author(s). We study the Rayleigh–Stokes problem for a generalized second-grade fluid which involves a Riemann–Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations. We establish the Sobolev regularity of the homogeneous problem for both smooth and nonsmooth initial data v, including v∈^{L2}(Ω). A space semidiscrete Galerkin scheme using continuous piecewise linear finite elements is developed, and optimal with respect to initial data regularity error estimates for the finite element approximations are derived. Further, two fully discrete schemes based on the backward Euler method and second-order backward difference method and the related convolution quadrature are developed, and optimal error estimates are derived for the fully discrete approximations for both smooth and nonsmooth initial data. Numerical results for one- and two-dimensional examples with smooth and nonsmooth initial data are presented to illustrate the efficiency of the method, and to verify the convergence theory.
Saarinen, Jukka; Sözeri, Erkan; Fraser-Miller, Sara J; Peltonen, Leena; Santos, Hélder A; Isomäki, Antti; Strachan, Clare J
2017-05-15
We have used coherent anti-Stokes Raman scattering (CARS) microscopy as a novel and rapid, label-free and non-destructive imaging method to gain structural insights into live intestinal epithelial cell cultures used for drug permeability testing. Specifically we have imaged live Caco-2 cells in (bio)pharmaceutically relevant conditions grown on membrane inserts. Imaging conditions were optimized, including evaluation of suitable membrane materials and media solutions, as well as tolerable laser powers for non-destructive imaging of the live cells. Lipid structures, in particular lipid droplets, were imaged within the cells on the insert membranes. The size of the individual lipid droplets increased substantially over the 21-day culturing period up to approximately 10% of the volume of the cross section of individual cells. Variation in lipid content has important implications for intestinal drug permeation testing during drug development but has received limited attention to date due to a lack of suitable analytical techniques. CARS microscopy was shown to be well suited for such analysis with the potential for in situ imaging of the same individual cell-cultures that are used for permeation studies. Overall, the method may be used to provide important information about cell monolayer structure to better understand drug permeation results. Copyright © 2017 Elsevier B.V. All rights reserved.
A full Stokes vector ellipsometry measurement system for in situ diagnostics in dynamic experiments.
Bakshi, L; Eliezer, S; Appelbaum, G; Nissim, N; Perelmutter, L; Mond, M
2012-05-01
A fast ellipsometry system with a resolution of only a few nanoseconds that can simultaneously measure all four Stokes parameters was developed for use in dynamic experiments. Due to its fine temporal resolution, the system is useful for a wide variety of dynamic setups, two of which are presented, fast foil heating and shock compression. As a test case the optical properties of nickel were measured in a fast foil heating setup. The complex index of refraction and emissivity at 532 nm and in the range of 1000-1900 K are presented. It was found that the emissivity monotonously increases below and above the melting point while an abrupt increase of about 2% was observed at the phase transition. These results are in accordance with the literature. Shock compression experiments included sample-free surface measurements. Samples of 1020 steel were shocked up to 25 GPa on the Hugoniot curve. The measured optical properties under these conditions showed a significant change; the value of the emissivity was doubled.
Label-free imaging of human breast tissues using coherent anti-Stokes Raman scattering microscopy
Yang, Yaliang; Gao, Liang; Wang, Zhiyong; Thrall, Michael J.; Luo, Pengfei; Wong, Kelvin K.; Wong, Stephen T.
2011-03-01
Breast cancer is a common disease in women. Current imaging and diagnostic methods for breast cancer confront several limitations, like time-consuming, invasive and with a high cost. Alternative strategies are in high demand to alleviate patients' trauma and lower medical expenses. Coherent anti-Stokes Raman scattering (CARS) imaging technique offers many advantages, including label-free, sub-wavelength spatial resolution and video-rate imaging speed. Therefore, it has been demonstrated as a powerful tool for various biomedical applications. In this study, we present a label-free fast imaging method to identify breast cancer and its subtypes using CARS microscopy. Human breast tissues, including normal, benign and invasive carcinomas, were imaged ex vivo using a custom-built CARS microscope. Compared with results from corresponding hematoxylin and eosin (H&E) stains, the CARS technique has demonstrated its capability in identifying morphological features in a similar way as in H&E stain. These features can be used to distinguish breast cancer from normal and benign tissues, and further separate cancer subtypes from each other. Our pilot study suggests that CARS microscopy could be used as a routine examination tool to characterize breast cancer ex vivo. Moreover, its label-free and fast imaging properties render this technique as a promising approach for in vivo and real-time imaging and diagnosis of breast cancer.
Detection of cervical cancer by fluorescence emission and stokes' shift spectra of blood and urine
Masilamani, V.; Vijmasi, T.; AlSalhi, M.; Govindarajan, K.; VijayaRaghavan, A. P.; Rai, Ram Rathan
2011-03-01
In this paper we present the results of a study to distinguish cervical cancer patients [ N=50] from healthy subjects [N=50] based on the Fluorescence Emission Spectra [FES] and Stokes' Shift Spectra [SSS] of blood and urine. FES was obtained from the cellular fraction of blood and urine by excitation at 400 nm. SSS was obtained from blood plasma and urine with Δλ of 70nm. In the FES of blood cellular fraction, the ratio of intensity of the two bands due to neutral porphyrin and basic porphyrin [I630 / I580] was 1 for normal controls and 3 for cervical cancers. In the SSS of plasma, the average ratio of intensity of the two bands due to tryptophan and collagen [I305 nm / I340 nm] was 1.9 for normal controls, 1.1 for early cervical cancers and 0.9 for advanced cervical cancers In the SSS of urine, the ratio of intensity of the two bands due to flavin and NADH [I450 nm / I360 nm] was 0.2 for normal controls and 0.8 for cancer patients. A discriminant analysis combining all three parameters showed a sensitivity of 80% and specificity of 78% for this technique. In this study we show that fluorescence spectroscopy of blood and urine could develop into a promising technique for non-invasive diagnosis and screening of cervical cancers and would appropriately supplement or complement currently used techniques.
The use of a Navier-Stokes code in the wing design process
Mcmillin, S. Naomi
1989-01-01
The feasibility was determined of incorporating the Navier-Stokes computational code, CFL3D, into the supersonic wing design process. The approach taken is of two steps. The first step was to calibrate CFL3D against existing experimental data sets obtained on thin sharp edged delta wings. The experimental data identified six flow types which are dependent on the similarity parameters of Mach number and angle of attack normal to the leading edge. The calibration showed CFL3D capable of simulating these various separated and attached flow conditions. The second step was to use CFL3D to study the initial formation of leading edge separation over delta wings at supersonic speeds. This consisted of examining solutions obtained on a 65 deg delta wing at Mach number of 1.6 with varying cross sectional shapes. Reynolds number was held constant at 1000000 and the Baldwin-Lomax turbulence model was used. The study showed that through the use of leading edge radius and/or camber, the onset of leading edge separation can be delayed to a higher angle of attack than observed on a flat sharp edged wing. Based on the geometries studied, three wind tunnel models are being designed to verify these results.
Full-Stokes, Multi-Frequency Radio Polarimetry of Fermi Blazars; Monitoring and Modelling
Directory of Open Access Journals (Sweden)
Emmanouil Angelakis
2017-11-01
Full Text Available The polarised emission from active galactic nuclei (AGN jets carries information about the physical conditions at the emitting plasma elements, while its temporal evolution probes the physical processes that introduce variability and dynamically modify the local conditions. Here we present the analysis of multi-frequency radio linear and circular polarisation datasets with the aim of exactly quantifying the conditions in blazar jets. Our analysis includes both the careful treatment of observational datasets and numerical modelling for the reproduction of synthetic polarisation curves that can be compared to the observed ones. In our approach, the variability is attributed to traveling shocks. The emission from the cells of our jet model is computed with radiative transfer of all Stokes parameters. The model also accounts for Faraday effects which map the low-energy particle populations. We present two extreme cases in terms of the significance of Faraday conversion in the production of circular polarisation. As we show, in both regimes the model gives a realistic reproduction of the observed emission.
Axisymmetric Stokes flow past a composite spheroidal shell of immiscible fluids
Krishna Prasad, M.; Manpreet Kaur, G.
2017-11-01
We study the flow of an incompressible Newtonian fluid past a composite spheroidal shell whose shape deviates slightly from that of a sphere. A composite particle referred to in this paper is a spheroidal liquid core covered with a porous layer. The Brinkman equation is used for the flow inside the porous medium and the Stokes equation is used for the flow in the fluid region. We assume that the external and internal viscous fluids are immiscible and the viscosity of the porous medium is different than the viscosity of pure liquid. The Ochoa-Tapia and Whitaker's stress jump boundary condition for tangential stress is applied on the porous-fluid interface. Velocity and pressure distributions are found and the drag force acting on the spheroidal shell is evaluated. The analytical solution is obtained by dividing the flow into three regions. Both type of spheroids, oblate and prolate are considered. Numerical results of the normalized hydrodynamic drag force acting on the spheroidal shell are tabulated and represented graphically for different values of the parameters characterizing the stress jump coefficient, separation parameter, permeability, deformation parameter, and viscosity ratios. The analysis of the flow pattern is done by plotting streamlines and several renowned cases are deduced.
Modeling and theoretical study of electronic anti-Stokes Raman scattering in quantum cascade lasers
Yousefvand, Hossein Reza
2017-04-01
This paper presents a self-consistent model for studying the electronic anti-Stokes (AS) Raman scattering in quantum cascade lasers (QCLs). The model is developed by employing a five-level rate-equation for the carrier dynamics in whole of the device and a two-level energy balance equations to adopt the electron-temperature in the pump and AS active regions. Using the presented model, the effect of temperature on the steady and transient characteristics of the device is investigated. Because of considering the parametric interaction between the incident and the scattered lights in the stimulated Raman process, the model accurately predicts the existence of Raman gain's saturation in both the steady and transient regimes. Additionally, using a steady-state analysis of the rate equations in the nonlinear region, an expression for the threshold current of the AS Raman laser is derived and the effects of pump power and temperature are examined. It is found that the electronic AS Raman scattering is affected by interplay between the various temperature-dependent parameters such as the pump intensity, the intrinsic gain of the nonlinear optical medium, and the longitudinal optical (LO) phonon scattering times between the states involved in the stimulated Raman process.
Structural origin of fractional Stokes-Einstein relation in glass-forming liquids
Pan, Shaopeng; Wu, Z. W.; Wang, W. H.; Li, M. Z.; Xu, Limei
2017-01-01
In many glass-forming liquids, fractional Stokes-Einstein relation (SER) is observed above the glass transition temperature. However, the origin of such phenomenon remains elusive. Using molecular dynamics simulations, we investigate the break- down of SER and the onset of fractional SER in a model of metallic glass-forming liquid. We find that SER breaks down when the size of the largest cluster consisting of trapped atoms starts to increase sharply at which the largest cluster spans half of the simulations box along one direction, and the fractional SER starts to follows when the largest cluster percolates the entire system and forms 3-dimentional network structures. Further analysis based on the percolation theory also confirms that percolation occurs at the onset of the fractional SER. Our results directly link the breakdown of the SER with structure inhomogeneity and onset of the fraction SER with percolation of largest clusters, thus provide a possible picture for the break- down of SER and onset of fractional SER in glass-forming liquids, which is is important for the understanding of the dynamic properties in glass-forming liquids.
Comparison of sunshine duration measurements from Campbell-Stokes sunshine recorder and CSD1 sensor
Urban, Grzegorz; Zając, Ireneusz
2017-07-01
Paper presents comparative analysis of sunshine duration measurement results obtained using Campbell-Stokes sunshine recorder (CS) and electronic sensor (CSD1). The comparison is based on data from 2009 to 2010 collected at seven weather stations (Leszno, Wrocław-Strachowice, Legnica, Opole, Zielona Góra, Jelenia Góra, Kłodzko) operated by the Institute of Meteorology and Water Management—National Research Institute (IMWM-NRI) in south-western Poland. Results obtained in Opole and Legnica stations are erroneous. In case of other stations, the relationship between daily total sunshine duration as measured by CS and CSD1 was strong. Coefficients of determination were 0.96-0.97. Mean differences in daily totals of sunshine duration were ±0.3 h. Differences of mean monthly and annual totals were both positive and negative with no pattern of occurrences. Implementation of permanent corrections is not possible. The highest consistency between both measurement devices was found during winter months.
Cheyne-Stokes Respiration in Patients with First-Ever Lacunar Stroke
Directory of Open Access Journals (Sweden)
Marc Bonnin-Vilaplana
2012-01-01
Full Text Available The aim of this single-center prospective study was to assess the presence of Cheyne-Stokes respiration (CSR and CSR-related variables in 68 consecutive patients with radiologically proven first-ever lacunar stroke undergoing a respiratory sleep study using a portable respiratory polygraph within the first 48 hours of stroke onset. CSR was diagnosed in 14 patients (20.6%. Patients with CSR as compared with those without CSR showed a significantly higher mean (standard deviation, SD apnea-hypopnea index (AHI (34.9 (21.7 versus 18.5 (14.4, P=0.001 and central apnea index (13.1 (13.8 versus 1.8 (3.4, P=0.0001 as well as higher scores of the Barthel index and the Canadian Neurological scale as a measure of stroke severity, and longer hospital stay. CSR was present in one of each five patients with lacunar stroke. The presence of CSR was associated with a trend towards a higher functional stroke severity and worse prognosis.
Unstructed Navier-Stokes Analysis of Wind-Tunnel Aeroelastic Effects on TCA Model 2
Frink, Neal T.; Allison, Dennis O.; Parikh, Paresh C.
1999-01-01
The aim of this work is to demonstrate a simple technique which accounts for aeroelastic deformations experienced by HSR wind-tunnel models within CFD computations. With improved correlations, CFD can become a more effective tool for augmenting the post-test understanding of experimental data. The present technique involves the loose coupling of a low-level structural representation within the ELAPS code, to an unstructured Navier-Stokes flow solver, USM3Dns. The ELAPS model is initially calibrated against bending characteristics of the wind-tunnel model. The strength of this method is that, with a single point calibration of a simple structural representation, the static aeroelastic effects can be accounted for in CFD calculations across a range of test conditions. No prior knowledge of the model deformation during the wind-on test is required. This approach has been successfully applied to the high aspect-ratio planforms of subsonic transports. The current challenge is to adapt the procedure to low aspect-ratio planforms typical of HSR configurations.
Femtosecond Coherent Anti-Stokes Raman Scattering Gas Phase Thermometry at 5 kHz
Fineman, Claresta; Lucht, Robert
2014-05-01
Understanding the thermal instabilities occurring in turbulent combustion, such as in modern gas turbine combustors, is critical for more reliable and fuel-efficient operation. Non-intrusive laser based spectroscopy methods have been documented as the techniques of choice for turbulent combustion diagnostics. Specifically, femtosecond coherent anti-Stokes Raman scattering (fs-CARS) thermometry has been established for temporal resolution of turbulent fluctuations in flame structure and provides accurate measurements across a wide range of temperatures. Experiments performed to date include 5 kHz pure vibrational N2 chirped probe-pulse fs-CARS thermometry on non-premixed hydrogen jet diffusion flames, methane jet diffusion flames, and the DLR gas turbine model combustor (GTMC). The fs-CARS signal generation process requires precise spatial and temporal overlap of tightly focused pulsed laser beams of less than 100 fs pulse duration. Here, signal loss due to beam steering, pressure fluctuations, or shear layer density gradients can become a problem. The effect of such interferences has been investigated using high velocity flow of compressed nitrogen gas from a converging-diverging nozzle. Resulting changes in fs-CARS spectra have been studied. Funding for this work was provided by the U.S. Department of Energy, Division of Chemical Sciences, Geosciences and Biosciences.
Yang, Chao-Bo; He, Ping; Escofet-Martin, David; Peng, Jiang-Bo; Fan, Rong-Wei; Yu, Xin; Dunn-Rankin, Derek
2018-01-10
In this paper, three ultrashort-pulse coherent anti-Stokes Raman scattering (CARS) thermometry approaches are summarized with a theoretical time-domain model. The difference between the approaches can be attributed to variations in the input field characteristics of the time-domain model. That is, all three approaches of ultrashort-pulse (CARS) thermometry can be simulated with the unified model by only changing the input fields features. As a specific example, the hybrid femtosecond/picosecond CARS is assessed for its use in combustion flow diagnostics; thus, the examination of the input field has an impact on thermometry focuses on vibrational hybrid femtosecond/picosecond CARS. Beginning with the general model of ultrashort-pulse CARS, the spectra with different input field parameters are simulated. To analyze the temperature measurement error brought by the input field impacts, the spectra are fitted and compared to fits, with the model neglecting the influence introduced by the input fields. The results demonstrate that, however the input pulses are depicted, temperature errors still would be introduced during an experiment. With proper field characterization, however, the significance of the error can be reduced.
Generalized conjugate-gradient methods for the Navier-Stokes equations
Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing
1991-01-01
A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.
Mimetic finite difference method for the stokes problem on polygonal meshes
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA
2009-01-01
Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.
Navier-Stokes Simulation of a Heavy Lift Slowed-Rotor Compound Helicopter Configuration
Allan, Brian G.; Jenkins, Luther N.; Yao, Chung-Sheng; Bartram, Scott M.; Hallissy, Jim B.; Harris, Jerome; Noonan, Kevin W.; Wong, Oliver D.; Jones, Henry E.; Malovrh, Brendon D.;
2009-01-01
Time accurate numerical simulations were performed using the Reynolds-averaged Navier-Stokes (RANS) flow solver OVERFLOW for a heavy lift, slowed-rotor, compound helicopter configuration, tested at the NASA Langley 14- by 22-Foot Subsonic Tunnel. The primary purpose of these simulations is to provide support for the development of a large field of view Particle Imaging Velocimetry (PIV) flow measurement technique supported by the Subsonic Rotary Wing (SRW) project under the NASA Fundamental Aeronautics program. These simulations provide a better understanding of the rotor and body wake flows and helped to define PIV measurement locations as well as requirements for validation of flow solver codes. The large field PIV system can measure the three-dimensional velocity flow field in a 0.914m by 1.83m plane. PIV measurements were performed upstream and downstream of the vertical tail section and are compared to simulation results. The simulations are also used to better understand the tunnel wall and body/rotor support effects by comparing simulations with and without tunnel floor/ceiling walls and supports. Comparisons are also made to the experimental force and moment data for the body and rotor.
Development of Multigrid Methods for diffusion, Advection, and the incompressible Navier-Stokes Equations
Energy Technology Data Exchange (ETDEWEB)
Gjesdal, Thor
1997-12-31
This thesis discusses the development and application of efficient numerical methods for the simulation of fluid flows, in particular the flow of incompressible fluids. The emphasis is on practical aspects of algorithm development and on application of the methods either to linear scalar model equations or to the non-linear incompressible Navier-Stokes equations. The first part deals with cell centred multigrid methods and linear correction scheme and presents papers on (1) generalization of the method to arbitrary sized grids for diffusion problems, (2) low order method for advection-diffusion problems, (3) attempt to extend the basic method to advection-diffusion problems, (4) Fourier smoothing analysis of multicolour relaxation schemes, and (5) analysis of high-order discretizations for advection terms. The second part discusses a multigrid based on pressure correction methods, non-linear full approximation scheme, and papers on (1) systematic comparison of the performance of different pressure correction smoothers and some other algorithmic variants, low to moderate Reynolds numbers, and (2) systematic study of implementation strategies for high order advection schemes, high-Re flow. An appendix contains Fortran 90 data structures for multigrid development. 160 refs., 26 figs., 22 tabs.
Energy Technology Data Exchange (ETDEWEB)
Xiaodong Liu; Lijun Xuan; Hong Luo; Yidong Xia
2001-01-01
A reconstructed discontinuous Galerkin (rDG(P1P2)) method, originally introduced for the compressible Euler equations, is developed for the solution of the compressible Navier- Stokes equations on 3D hybrid grids. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for the computation of the inviscid fluxes and the viscous fluxes using the second formulation of Bassi and Reay (Bassi-Rebay II). The developed rDG(P1P2) method is used to compute a variety of flow problems to assess its accuracy, efficiency, and robustness. The numerical results demonstrate that the rDG(P1P2) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the large eddy simulation (LES) and direct numerical simulation (DNS) of compressible turbulent flows.
Reynolds-Averaged Navier-Stokes Simulation of a 2D Circulation Control Wind Tunnel Experiment
Allan, Brian G.; Jones, Greg; Lin, John C.
2011-01-01
Numerical simulations are performed using a Reynolds-averaged Navier-Stokes (RANS) flow solver for a circulation control airfoil. 2D and 3D simulation results are compared to a circulation control wind tunnel test conducted at the NASA Langley Basic Aerodynamics Research Tunnel (BART). The RANS simulations are compared to a low blowing case with a jet momentum coefficient, C(sub u), of 0:047 and a higher blowing case of 0.115. Three dimensional simulations of the model and tunnel walls show wall effects on the lift and airfoil surface pressures. These wall effects include a 4% decrease of the midspan sectional lift for the C(sub u) 0.115 blowing condition. Simulations comparing the performance of the Spalart Allmaras (SA) and Shear Stress Transport (SST) turbulence models are also made, showing the SST model compares best to the experimental data. A Rotational/Curvature Correction (RCC) to the turbulence model is also evaluated demonstrating an improvement in the CFD predictions.
Navier-Stokes Simulation of UH-60A Rotor/Wake Interaction Using Adaptive Mesh Refinement
Chaderjian, Neal M.
2017-01-01
High-resolution simulations of rotor/vortex-wake interaction for a UH60-A rotor under BVI and dynamic stallconditions were carried out with the OVERFLOW Navier-Stokes code.a. The normal force and pitching moment variation with azimuth angle were in good overall agreementwith flight-test data, similar to other CFD results reported in the literature.b. The wake-grid resolution did not have a significant effect on the rotor-blade airloads. This surprisingresult indicates that a wake grid spacing of (Delta)S=10% ctip is sufficient for engineering airloads predictionfor hover and forward flight. This assumes high-resolution body grids, high-order spatial accuracy, anda hybrid RANS/DDES turbulence model.c. Three-dimensional dynamic stall was found to occur due the presence of blade-tip vortices passing overa rotor blade on the retreating side. This changed the local airfoil angle of attack, causing stall, unlikethe 2D perspective of pure pitch oscillation of the local airfoil section.
On a pure hyperbolic alternative to the Navier-Stokes equations
Peshkov, Ilya
2014-01-01
We discuss a pure hyperbolic alternative to the Navier-Stokes equations, which are of parabolic type. As a result of the substitution of the concept of the viscosity coefficient by a microphysics-based temporal characteristic, particle settled life (PSL) time, it becomes possible to formulate a model for viscous fluids in a form of first order hyperbolic partial differential equations. Moreover, the concept of PSL time allows the use the same model for flows of viscous fluids (Newtonian or non-Newtonian) as well as irreversible deformation of solids. In the theory presented, a continuum is interpreted as a system of particles, or in the case of fluids, fluid parcels connected by bonds; the internal resistance to flow is interpreted as elastic stretching of the particle bonds; and a flow is a result of bond destructions and rearrangements of particles. Finally, we examine the model for simple shear flows of Newtonian fluids and demonstrate that Newton's viscous law can be obtained in the framework of the devel...
Resistance coefficients for Stokes flow around a disk with a Navier slip condition
Sherwood, J. D.
2012-09-01
The Stokes drag and couple acting on a disk of zero thickness as it moves through Newtonian fluid are investigated for the case when slip can occur at the surface of the disk. It is shown that when the disk translates parallel to its axis, the well-known velocity field for a no-slip boundary condition exerts zero shear stress on the surface of the disk. The flow is therefore unchanged if the boundary condition on the disk is modified to a stress-free or to a Navier slip boundary condition. This invariance also holds for a disk that rotates about a diameter. However, flow around a disk that rotates about its axis, or that translates in its own plane (edgewise), is modified when the no-slip boundary condition is changed to a Navier slip condition. The fluid velocity can be expressed in terms of Hankel transforms, and the resulting dual integral equations are solved numerically. Results for the torque and drag on the disk are presented as functions of the slip length in the Navier boundary condition.
Chiral-aminoquinoline-based fluorescent pH probe with large stokes shift for bioimaging
Xie, Yong-Sheng; Zhang, Xin-Ling; Xie, Kun; Zhao, Yanmei; Wu, Huan; Yang, Jidong
2017-05-01
The aminoquinoline derivatives, (R)- and (S)-2-phenyl-2-(quinolin-6-ylamino)ethan-1-ol (R-PEO and S-PEO), were synthesized by a tandem one-pot three-step Csbnd N coupling method where Smiles rearrangement was the key procedure. The selected compound R-PEO showed a significant fluorescence enhancement with a turn-on ratio over 98-fold and enabled the real time determination of proton concentration in acidic solution. The fluorescence intensity of R-PEO exhibited strong pH-dependent performance with a large Stokes shift (115 nm) and responded linearly to minor pH change within the range of 3.8-6.0. With the help of 1H NMR spectrum, we also confirmed the protonation of the quinoline unit should be the proposed reaction. Compared with the conjugated acid of N-hexylquinolin-6-amine (NQA), the conjugated acid of R-PEO shows significant planar intramolecular charge transfer (PICT) character. Furthermore, biological imaging proved that R-PEO probe can be used to monitor the pH change of S. cerevisiae in vivo.
Directory of Open Access Journals (Sweden)
Masanari Okuno
Full Text Available The mechanism of surfactant-induced cell lysis has been studied with quantitative coherent anti-Stokes Raman scattering (CARS microspectroscopy. The dynamics of surfactant molecules as well as intracellular biomolecules in living Chinese Hamster Lung (CHL cells has been examined for a low surfactant concentration (0.01 w%. By using an isotope labeled surfactant having CD bonds, surfactant uptake dynamics in living cells has been traced in detail. The simultaneous CARS imaging of the cell itself and the internalized surfactant has shown that the surfactant molecules is first accumulated inside a CHL cell followed by a sudden leak of cytosolic components such as proteins to the outside of the cell. This finding indicates that surfactant uptake occurs prior to the cell lysis, contrary to what has been believed: surface adsorption of surfactant molecules has been thought to occur first with subsequent disruption of cell membranes. Quantitative CARS microspectroscopy enables us to determine the molecular concentration of the surfactant molecules accumulated in a cell. We have also investigated the effect of a drug, nocodazole, on the surfactant uptake dynamics. As a result of the inhibition of tubulin polymerization by nocodazole, the surfactant uptake rate is significantly lowered. This fact suggests that intracellular membrane trafficking contributes to the surfactant uptake mechanism.
Tu, Haohua; Boppart, Stephen A
2014-01-01
Clinical translation of coherent anti-Stokes Raman scattering microscopy is of great interest because of the advantages of noninvasive label-free imaging, high sensitivity, and chemical specificity. For this to happen, we have identified and review the technical barriers that must be overcome. Prior investigations have developed advanced techniques (features), each of which can be used to effectively overcome one particular technical barrier. However, the implementation of one or a small number of these advanced features in previous attempts for clinical translation has often introduced more tradeoffs than benefits. In this review, we outline a strategy that would integrate multiple advanced features to overcome all the technical barriers simultaneously, effectively reduce tradeoffs, and synergistically optimize CARS microscopy for clinical translation. The operation of the envisioned system incorporates coherent Raman micro-spectroscopy for identifying vibrational biomolecular markers of disease and single-frequency (or hyperspectral) Raman imaging of these specific biomarkers for real-time in vivo diagnostics and monitoring. Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Navier-Stokes-Fourier analytic solutions for non-isothermal Couette slip gas flow
Directory of Open Access Journals (Sweden)
Milićev Snežana S.
2016-01-01
Full Text Available The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented. These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls is verified and a new solution for the case of different temperature of the walls is obtained. Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number Kn≤0.1, i.e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy. [Projekat Ministarstva nauke Republike Srbije, br. 35046 i 174014
Wang, Zhiheng
2014-12-10
A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.
Masia, Francesco; Glen, Adam; Stephens, Phil; Borri, Paola; Langbein, Wolfgang
2013-11-19
In this work, we report a method to acquire and analyze hyperspectral coherent anti-Stokes Raman scattering (CARS) microscopy images of organic materials and biological samples resulting in an unbiased quantitative chemical analysis. The method employs singular value decomposition on the square root of the CARS intensity, providing an automatic determination of the components above noise, which are retained. Complex CARS susceptibility spectra, which are linear in the chemical composition, are retrieved from the CARS intensity spectra using the causality of the susceptibility by two methods, and their performance is evaluated by comparison with Raman spectra. We use non-negative matrix factorization applied to the imaginary part and the nonresonant real part of the susceptibility with an additional concentration constraint to obtain absolute susceptibility spectra of independently varying chemical components and their absolute concentration. We demonstrate the ability of the method to provide quantitative chemical analysis on known lipid mixtures. We then show the relevance of the method by imaging lipid-rich stem-cell-derived mouse adipocytes as well as differentiated embryonic stem cells with a low density of lipids. We retrieve and visualize the most significant chemical components with spectra given by water, lipid, and proteins segmenting the image into the cell surrounding, lipid droplets, cytosol, and the nucleus, and we reveal the chemical structure of the cells, with details visualized by the projection of the chemical contrast into a few relevant channels.
Coherent anti-stokes spectroscopy as a probe of chemical disorder in isolated carbon nanotubes
Sheps, Tatyana; Brocious, Jordan; Potma, Eric O.; Collins, Philip G.
2012-02-01
We use a third-order coherent anti-stokes (CAS) optical technique to study chemical disorder in individual carbon nanotubes. The CAS response is highly sensitive to this disorder, to the extent that a few chemical defects can appreciably decrease the overall signal. The experiments are performed on individual single- and multi-walled carbon nanotubes (SWNTs and MWNTs) connected in a transistor geometry and subjected to varying degrees of controlled, electrochemical oxidation. The overall CAS intensity can be used to probe the extent of chemical modification, and inhomogeneities along a nanotube resolve local coherent electron density fluctuations. We find that the CAS signal is also strongly affected by substrate interactions: aligned SWNTs grown on single crystal quartz are quenched compared to SWNTs on fused quartz. Finally, CAS spectroscopy on individual SWNTs and MWNTs using picosecond pulses resolves the third-order vibrational signal component at the G-band frequency. The ratio of electronic to vibrational CAS signal components is diameter dependent and in small diameter SWNTs the vibrational component is dominated by the electronic CAS signal. However, in MWNTs, this technique is a first step toward chemically sensitive CARS imaging on a single nanotube level.
On one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains
Li, Siran
2017-10-01
In this paper we consider the one-dimensional Navier-Stokes system for a heat-conducting, compressible reacting mixture which describes the dynamic combustion of fluids of mixed kinds on unbounded domains. This model has been discussed on bounded domains by Chen (SIAM J Math Anal 23:609-634, 1992) and Chen-Hoff-Trivisa (Arch Ration Mech Anal 166:321-358, 2003), among others, in which the reaction rate function is a discontinuous function obeying the Arrhenius' law of thermodynamics. We prove the global existence of weak solutions to this model on one-dimensional unbounded domains with large initial data in H^1. Moreover, the large-time behaviour of the weak solution is identified. In particular, the uniform-in-time bounds for the temperature and specific volume have been established via energy estimates. For this purpose we utilise techniques developed by Kazhikhov-Shelukhin (cf. Kazhikhov in Siber Math J 23:44-49, 1982; Solonnikov and Kazhikhov in Annu Rev Fluid Mech 13:79-95, 1981) and refined by Jiang (Commun Math Phys 200:181-193, 1999, Proc R Soc Edinb Sect A 132:627-638, 2002), as well as a crucial estimate in the recent work by Li-Liang (Arch Ration Mech Anal 220:1195-1208, 2016). Several new estimates are also established, in order to treat the unbounded domain and the reacting terms.
Imaging the intact mouse cornea using coherent anti-stokes Raman scattering (CARS).
Ammar, David A; Lei, Tim C; Kahook, Malik Y; Masihzadeh, Omid
2013-08-05
The aim of this study was to image the cellular and noncellular structures of the cornea and limbus in an intact mouse eye using the vibrational oscillation of the carbon-hydrogen bond in lipid membranes and autofluorescence as label-free contrast agents. Freshly enucleated mouse eyes were imaged using two nonlinear optical techniques: coherent anti-Stokes Raman scattering (CARS) and two-photon autofluorescence (TPAF). Sequential images were collected through the full thickness of the cornea and limbal regions. Line scans along the transverse/sagittal axes were also performed. Analysis of multiple CARS/TPAF images revealed that corneal epithelial and endothelial cells could be identified by the lipid-rich plasma membrane CARS signal. The fluorescent signal from the collagen fibers of the corneal stroma was evident in the TPAF channel. The transition from the cornea to sclera at the limbus was marked by a change in collagen pattern (TPAF channel) and thickness of surface cells (CARS channel). Regions within the corneal stroma that lack collagen autofluorescence coincided with CARS signal, indicating the presence of stromal fibroblasts or nerve fibers. The CARS technique was successful in imaging cells in the intact mouse eye, both at the surface and within corneal tissue. Multiphoton images were comparable to histologic sections. The methods described here represent a new avenue for molecular specific imaging of the mouse eye. The lack of need for tissue fixation is unique compared with traditional histology imaging techniques.
Generalized extended Navier-Stokes theory: Multiscale spin relaxation in molecular fluids
DEFF Research Database (Denmark)
Hansen, Jesper Schmidt
2013-01-01
This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia...... per unit mass. In the regime of large moment of inertia the fast relaxation is wave-vector independent and dominated by the coupling between spin and the fluid streaming velocity, whereas for small inertia the relaxation is slow and spin diffusion plays a significant role. The fast wave......-vector-independent relaxation is also observed for highly packed systems. The transverse and longitudinal spin modes have, to a good approximation, identical relaxation, indicating that the longitudinal and transverse spin viscosities have same value. The relaxation is also shown to be isomorphic invariant. Finally, the effect...... of the coupling in the zero frequency and wave-vector limit is quantified by a characteristic length scale; if the system dimension is comparable to this length the coupling must be included into the fluid dynamical description. It is found that the length scale is independent of moment of inertia but dependent...
Cheyne-stokes respiration during wakefulness in patients with chronic heart failure.
Grimm, Wolfram; Kesper, Karl; Cassel, Werner; Timmesfeld, Nina; Hildebrandt, Olaf; Koehler, Ulrich
2017-05-01
Cheyne-Stokes respiration (CSR) during sleep has been studied extensively in patients with chronic heart failure (CHF). Prevalence and prognostic significance of CSR during wakefulness in CHF, however, are largely unknown. CSR during wakefulness with an apnea-hypopnea cut-off ≥5/h and moderate to severe CSR with an apnea-hypopnea cutoff ≥15/h were analyzed using polysomnographic recordings in 267 patients with stable CHF with reduced left ventricular (LV) ejection fraction at our institution. Primary endpoint during follow-up was heart transplant-free survival. Fifty of 267 patients (19%) had CSR during wakefulness and 73 of 267 patients (27%) had CSR during sleep. CSR during wakefulness was associated with advanced age, atrial fibrillation, decreased LV ejection fraction, increased LV end-diastolic diameter, brain natriuretic peptide, New York Heart Failure class, and CSR during sleep. During 43 months mean follow-up, 67 patients (25%) died and 4 patients (1%) underwent heart transplantation. Multivariate Cox analysis identified age, male gender, chronic kidney disease, and LV ejection fraction as predictors of reduced transplant-free survival. CSR during wakefulness with an apnea-hypopnea cutoff ≥5/h as well as moderate to severe CSR while awake using an apnea-hypopnea cutoff ≥15/h did not predict reduced transplant-free survival independently from confounding factors. CSR during wakefulness appears to be a marker of heart failure severity.
Tinoco, Adelita; Drew, Barbara J; Hu, Xiao; Mortara, David; Cooper, Bruce A; Pelter, Michele M
2017-11-01
Cheyne-Stokes respiration (CSR) has been investigated primarily in outpatients with heart failure. In this study we compare CSR and periodic breathing (PB) between healthy and cardiac groups. We compared CSR and PB, measured during 24 hr of continuous 12-lead electrocardiographic (ECG) Holter recording, in a group of 90 hospitalized patients presenting to the emergency department with symptoms suggestive of acute coronary syndrome (ACS) to a group of 100 healthy ambulatory participants. We also examined CSR and PB in the 90 patients presenting with ACS symptoms, divided into a group of 39 (43%) with confirmed ACS, and 51 (57%) with a cardiac diagnosis but non-ACS. SuperECG software was used to derive respiration and then calculate CSR and PB episodes from the ECG Holter data. Regression analyses were used to analyze the data. We hypothesized SuperECG software would differentiate between the groups by detecting less CSR and PB in the healthy group than the group of patients presenting to the emergency department with ACS symptoms. Hospitalized patients with suspected ACS had 7.3 times more CSR episodes and 1.6 times more PB episodes than healthy ambulatory participants. Patients with confirmed ACS had 6.0 times more CSR episodes and 1.3 times more PB episodes than cardiac non-ACS patients. Continuous 12-lead ECG derived CSR and PB appear to differentiate between healthy participants and hospitalized patients. © 2017 Wiley Periodicals, Inc.
A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations
Guermond, J.L.
2011-06-01
We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier-Stokes equations. The main originality of the method consists of using the operator (I-∂xx)(I-∂yy)(I-∂zz) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2×109 points. © 2011 Elsevier B.V.
Hiramatsu, Kotaro; Luo, Yizhi; Ideguchi, Takuro; Goda, Keisuke
2017-11-01
High-speed Raman spectroscopy has become increasingly important for analyzing chemical dynamics in real time. To address the need, rapid-scan Fourier-transform coherent anti-Stokes Raman scattering (FT-CARS) spectroscopy has been developed to realize broadband CARS measurements at a scan rate of more than 20,000 scans/s. However, the detection sensitivity of FT-CARS spectroscopy is inherently low due to the limited number of photons detected during each scan. In this Letter, we show our experimental demonstration of enhanced sensitivity in rapid-scan FT-CARS spectroscopy by heterodyne detection. Specifically, we implemented heterodyne detection by superposing the CARS electric field with an external local oscillator (LO) for their interference. The CARS signal was amplified by simply increasing the power of the LO without the need for increasing the incident power onto the sample. Consequently, we achieved enhancement in signal intensity and the signal-to-noise ratio by factors of 39 and 5, respectively, compared to FT-CARS spectroscopy with homodyne detection. The sensitivity-improved rapid-scan FT-CARS spectroscopy is expected to enable the sensitive real-time observation of chemical dynamics in a broad range of settings, such as combustion engines and live biological cells.
Effect of scattering on coherent anti-Stokes Raman scattering (CARS) signals.
Ranasinghesagara, Janaka C; De Vito, Giuseppe; Piazza, Vincenzo; Potma, Eric O; Venugopalan, Vasan
2017-04-17
We develop a computational framework to examine the factors responsible for scattering-induced distortions of coherent anti-Stokes Raman scattering (CARS) signals in turbid samples. We apply the Huygens-Fresnel wave-based electric field superposition (HF-WEFS) method combined with the radiating dipole approximation to compute the effects of scattering-induced distortions of focal excitation fields on the far-field CARS signal. We analyze the effect of spherical scatterers, placed in the vicinity of the focal volume, on the CARS signal emitted by different objects (2μm diameter solid sphere, 2μm diameter myelin cylinder and 2μm diameter myelin tube). We find that distortions in the CARS signals arise not only from attenuation of the focal field but also from scattering-induced changes in the spatial phase that modifies the angular distribution of the CARS emission. Our simulations further show that CARS signal attenuation can be minimized by using a high numerical aperture condenser. Moreover, unlike the CARS intensity image, CARS images formed by taking the ratio of CARS signals obtained using x- and y-polarized input fields is relatively insensitive to the effects of spherical scatterers. Our computational framework provide a mechanistic approach to characterizing scattering-induced distortions in coherent imaging of turbid media and may inspire bottom-up approaches for adaptive optical methods for image correction.
A full Stokes vector ellipsometry measurement system for in situ diagnostics in dynamic experiments
Bakshi, L.; Eliezer, S.; Appelbaum, G.; Nissim, N.; Perelmutter, L.; Mond, M.
2012-05-01
A fast ellipsometry system with a resolution of only a few nanoseconds that can simultaneously measure all four Stokes parameters was developed for use in dynamic experiments. Due to its fine temporal resolution, the system is useful for a wide variety of dynamic setups, two of which are presented, fast foil heating and shock compression. As a test case the optical properties of nickel were measured in a fast foil heating setup. The complex index of refraction and emissivity at 532 nm and in the range of 1000-1900 K are presented. It was found that the emissivity monotonously increases below and above the melting point while an abrupt increase of about 2% was observed at the phase transition. These results are in accordance with the literature. Shock compression experiments included sample-free surface measurements. Samples of 1020 steel were shocked up to 25 GPa on the Hugoniot curve. The measured optical properties under these conditions showed a significant change; the value of the emissivity was doubled.
A spectral/B-spline method for the Navier-Stokes equations in unbounded domains
Dufresne, L
2003-01-01
The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the theta and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r-> infinity. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the lo...
Identifying time scales for violation/preservation of Stokes-Einstein relation in supercooled water.
Kawasaki, Takeshi; Kim, Kang
2017-08-01
The violation of the Stokes-Einstein (SE) relation D ~ (η/T)-1 between the shear viscosity η and the translational diffusion constant D at temperature T is of great importance for characterizing anomalous dynamics of supercooled water. Determining which time scales play key roles in the SE violation remains elusive without the measurement of η. We provide comprehensive simulation results of the dynamic properties involving η and D in the TIP4P/2005 supercooled water. This enabled the thorough identification of the appropriate time scales for the SE relation Dη/T. In particular, it is demonstrated that the temperature dependence of various time scales associated with structural relaxation, hydrogen bond breakage, stress relaxation, and dynamic heterogeneities can be definitely classified into only two classes. That is, we propose the generalized SE relations that exhibit "violation" or "preservation." The classification depends on the examined time scales that are coupled or decoupled with the diffusion. On the basis of the classification, we explain the physical origins of the violation in terms of the increase in the plateau modulus and the nonexponentiality of stress relaxation. This implies that the mechanism of SE violation is attributed to the attained solidity upon supercooling, which is in accord with the growth of non-Gaussianity and spatially heterogeneous dynamics.
mBeRFP, an improved large stokes shift red fluorescent protein.
Directory of Open Access Journals (Sweden)
Jie Yang
Full Text Available Herein, we describe the generation of a monomeric large Stokes shift (LSS red fluorescent protein, mBeRFP, with excitation and emission peaks at 446 and 615 nm, respectively. Compared with two previously reported LSS-RFPs (mKeima and LSS-mKate2, mBeRFP is approximately three times brighter. In addition, mBeRFP is characterized by improved photostability, rapid maturation, an extended lifetime, and a monomeric nature. Additionally, mBeRFP can be paired with the Alexa 647 dye as a FRET donor to detect caspase 3 activity. This FRET pair has an extremely dynamic range and a large Förster radius (approximately 6.5 nm. To demonstrate the applicability of mBeRFP for imaging in living cells, we performed dual-color imaging of mBeRFP and CFP simultaneously excited by a single excitation source, and we demonstrated that these fluorescent proteins allow the clear visualization of the dynamics of Bax during cancer cell apoptosis. Thus, mBeRFP appears to be particularly useful for cellular imaging applications.
Multitasking a three-dimensional Navier-Stokes algorithm on the Cray-2
Swisshelm, Julie M.
1989-01-01
A three-dimensional computational aerodynamics algorithm has been multitasked for efficient parallel execution on the Cray-2. It provides a means for examining the multitasking performance of a complete CFD application code. An embedded zonal multigrid scheme is used to solve the Reynolds-averaged Navier-Stokes equations for an internal flow model problem. The explicit nature of each component of the method allows a spatial partitioning of the computational domain to achieve a well-balanced task load for MIMD computers with vector-processing capability. Experiments have been conducted with both two- and three-dimensional multitasked cases. The best speedup attained by an individual task group was 3.54 on four processors of the Cray-2, while the entire solver yielded a speedup of 2.67 on four processors for the three-dimensional case. The multiprocessing efficiency of various types of computational tasks is examined, performance on two Cray-2s with different memory access speeds is compared, and extrapolation to larger problems is discussed.
A New Method of Moments for the Bimodal Particle System in the Stokes Regime
Directory of Open Access Journals (Sweden)
Yan-hua Liu
2013-01-01
Full Text Available The current paper studied the particle system in the Stokes regime with a bimodal distribution. In such a system, the particles tend to congregate around two major sizes. In order to investigate this system, the conventional method of moments (MOM should be extended to include the interaction between different particle clusters. The closure problem for MOM arises and can be solved by a multipoint Taylor-expansion technique. The exact expression is deduced to include the size effect between different particle clusters. The collision effects between different modals could also be modeled. The new model was simply tested and proved to be effective to treat the bimodal system. The results showed that, for single-modal particle system, the results from new model were the same as those from TEMOM. However, for the bimodal particle system, there was a distinct difference between the two models, especially for the zero-order moment. The current model generated fewer particles than TEMOM. The maximum deviation reached about 15% for m0 and 4% for m2. The detailed distribution of each submodal could also be investigated through current model.
Out-of-plane Stokes imaging polarimeter for early skin cancer diagnosis
Ghassemi, Pejhman; Lemaillet, Paul; Germer, Thomas A.; Shupp, Jeffrey W.; Venna, Suraj S.; Boisvert, Marc E.; Flanagan, Katherine E.; Jordan, Marion H.; Ramella-Roman, Jessica C.
2012-07-01
Optimal treatment of skin cancer before it metastasizes critically depends on early diagnosis and treatment. Imaging spectroscopy and polarized remittance have been utilized in the past for diagnostic purposes, but valuable information can be also obtained from the analysis of skin roughness. For this purpose, we have developed an out-of-plane hemispherical Stokes imaging polarimeter designed to monitor potential skin neoplasia based on a roughness assessment of the epidermis. The system was utilized to study the rough surface scattering for wax samples and human skin. The scattering by rough skin--simulating phantoms showed behavior that is reasonably described by a facet scattering model. Clinical tests were conducted on patients grouped as follows: benign nevi, melanocytic nevus, melanoma, and normal skin. Images were captured and analyzed, and polarization properties are presented in terms of the principal angle of the polarization ellipse and the degree of polarization. In the former case, there is separation between different groups of patients for some incidence azimuth angles. In the latter, separation between different skin samples for various incidence azimuth angles is observed.
Investigation of porous media combustion by coherent anti-Stokes Raman spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Weikl, M.C. [Lehrstuhl fuer Technische Thermodynamik (LTT), Erlangen (Germany); Research and Development, Linde AG, Engineering Division, Pullach (Germany); Tedder, S.A. [NASA Langley Research Center, Advanced Sensing and Optical Measurement Branch, Hampton, Virginia (United States); Seeger, T.; Leipertz, A. [Lehrstuhl fuer Technische Thermodynamik (LTT), Erlangen (Germany)
2010-10-15
High efficiency, marginal pollutant emissions and low fuel consumption are desirable standards for modern combustion devices. The porous burner technology is a modern type of energy conversion with a strong potential to achieve these standards. However, due to the solid ceramic framework investigation of the thermodynamic properties of combustion, for example temperature, is difficult. The combustion process inside the ceramic structure of a porous burner was experimentally investigated by coherent anti-Stokes Raman spectroscopy (CARS). In this work, we present measurements using dual-pump dual-broadband CARS (DP-DBB-CARS) of temperature and species concentrations inside the reaction and flue gas zone of a porous media burner. Improvements to the setup and data evaluation procedure in contrast to previous measurements are discussed in detail. The results at varied thermal power and stoichiometry are presented. In addition, measurements at a range of radial positions inside a pore are conducted and correlated with the solid structure of the porous foam, which was determined by X-ray computer tomography. (orig.)
Modelling debris transport within glaciers by advection in a full-Stokes ice flow model
Wirbel, Anna; Jarosch, Alexander H.; Nicholson, Lindsey
2017-04-01
As mountain glaciers recede worldwide, an increasing proportion of the remaining glacierized area is expected to become debris covered. The spatio-temporal development of a surface debris cover has profound effects on the glacier behaviour and meltwater generation, yet little is known about how glacier dynamics influence the spatial distribution of an emerging debris cover. Motivated by this lack of understanding, we present a coupled model to simulate advection and resulting deformation of debris features within glaciers. The finite element model developed in python consists of an advection scheme coupled to a full-Stokes ice flow model, using FEniCS as the numerical framework. We show results from numerical tests that demonstrate its suitability to model advection-dominated transport of concentration in a divergence-free velocity field. The capabilities of the coupled model are demonstrated by simulating transport of debris features of different initial size, shape and location through modelled velocity fields of representative mountain glaciers. The results indicate that deformation of initial debris inputs, as a consequence of being transported through the glacier, plays an important role in determining the location and rate of debris emergence at the glacier surface. The presented work lays the foundation for comprehensive simulations of realistic patterns of debris cover, their spatial and temporal variability and the timescales over which debris covers can form.
Density and Shape Factor Terms in Stokes' Equation for Aerodynamic Behavior of Aerosols.
Hickey, Anthony J; Edwards, David A
2018-03-01
Pharmaceutical aerosols are used to treat many pulmonary diseases. The use of low-density powders has proven useful to support efficient drug delivery. Measurements must account for the low-density, spherical particle features contributing to aerodynamic behavior. Ideally, the aerodynamic particle size distribution (APSD) is measured experimentally. Without formal measurement of APSD, calculations may be performed using surrogate measures such as bulk or tapped density and dynamic shape factor in Stokes' equation. However, the particles' low density must be established independently for this approach to be valid. In addition, where particles deviate from sphericity, the dynamic shape factor must be estimated from aerodynamic measurement not from geometric imaging of morphology. Finally, geometric sizing from particle images results in number distributions that exhibit smaller median sizes than mass distributions for the same polydisperse system. Simply applying density and shape factor corrections to geometric particle sizes does not convert number distributions to mass distributions. For log-normally distributed particle size distributions, Hatch-Choate equations, employing both median size and geometric standard deviation terms, may be used to convert number to mass distributions. Assigning small APSDs from calculations based on erroneous assumptions will result in serious interpretive flaws in subsequent in vitro and in vivo data. Copyright © 2018 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Abade, Gustavo C; Cichocki, Bogdan [Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw (Poland); Ekiel-Jezewska, Maria L; Wajnryb, Eligiusz [Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw (Poland); Naegele, Gerhard, E-mail: mekiel@ippt.gov.p [Institut fuer Festkoerperforschung, Forschungszentrum Juelich, D-52425 Juelich (Germany)
2010-08-18
We study the high-frequency limiting shear viscosity, {eta}{sub {infinity}}, of colloidal suspensions of uncharged porous particles. An individual particle is modeled as a uniformly porous sphere with the internal solvent flow described by the Debye-Bueche-Brinkman equation. A precise hydrodynamic multipole method with a full account of many-particle hydrodynamic interactions encoded in the HYDROMULTIPOLE program extended to porous particles, is used to calculate {eta}{sub {infinity}}as a function of porosity and concentration. The second-order virial expansion for {eta}{sub {infinity}}is derived, and its range of applicability assessed. The simulation results are used to test the validity of generalized Stokes-Einstein relations between {eta}{sub {infinity}}and various short-time diffusion coefficients, and to quantify the accuracy of a simplifying cell model calculation of {eta}{sub {infinity}.} An easy-to-use generalized Saito formula for {eta}{sub {infinity}}is presented which provides a good description of its porosity and concentration dependence. (fast track communication)
Aithal, Abhiram; Ferrante, Antonino
2017-11-01
In order to perform direct numerical simulations (DNS) of turbulent flows over curved surfaces and axisymmetric bodies, we have developed the numerical methodology to solve the incompressible Navier-Stokes (NS) equations in curvilinear coordinates for orthogonal meshes. The orthogonal meshes are generated by solving a coupled system of non-linear Poisson equations. The NS equations in orthogonal curvilinear coordinates are discretized in space on a staggered mesh using second-order central-difference scheme and are solved with an FFT-based pressure-correction method. The momentum equation is integrated in time using the second-order Adams-Bashforth scheme. The velocity field is advanced in time by applying the pressure correction to the approximate velocity such that it satisfies the divergence free condition. The novelty of the method stands in solving the variable coefficient Poisson equation for pressure using an FFT-based Poisson solver rather than the slower multigrid methods. We present the verification and validation results of the new numerical method and the DNS results of transitional flow over a curved axisymmetric body.
Seddik, Hakime; Greve, Ralf; Zwinger, Thomas; Sugiyama, Shin
2017-09-01
A hierarchy of approximations of the force balance for the flow of grounded ice exists, ranging from the most sophisticated full Stokes (FS) formulation to the most simplified shallow ice approximation (SIA). Both are implemented in the ice flow model Elmer/Ice, and we compare them by applying the model to the East Antarctic Shirase drainage basin. First, we apply the control inverse method to infer the distribution of basal friction with FS. We then compare FS and SIA by simulating the flow of the drainage basin under present-day conditions and for three scenarios 100 years into the future defined by the SeaRISE (Sea-level Response to Ice Sheet Evolution) project. FS reproduces the observed flow pattern of the drainage basin well, in particular the zone of fast flow near the grounding line, while SIA generally overpredicts the surface velocities. As for the transient scenarios, the ice volume change (relative to the constant-climate control run) of the surface climate experiment is nearly the same for FS and SIA, while for the basal sliding experiment (halved basal friction), the ice volume change is ˜ 30 % larger for SIA than for FS. This confirms findings of earlier studies that, in order to model ice sheet areas containing ice streams and outlet glaciers with high resolution and precision, careful consideration must be given to the choice of a suitable force balance.
Coherent anti-Stokes Raman scattering and two photon excited fluorescence for neurosurgery.
Romeike, Bernd F M; Meyer, Tobias; Reichart, Rupert; Kalff, Rolf; Petersen, Iver; Dietzek, Benjamin; Popp, Jürgen
2015-04-01
There is no established method for in vivo imaging during biopsy and surgery of the brain, which is capable to generate competitive images in terms of resolution and contrast comparable with histopathological staining. Coherent anti-Stokes Raman scattering (CARS) and two photon excited fluorescence (TPEF) microscopy are non-invasive all optical imaging techniques that are capable of high resolution, label-free, real-time, nondestructive examination of living cells and tissues. They provide image contrast based on the molecular composition of the specimen which allows the study of large tissue areas of frozen tissue sections ex vivo. Here, preliminary data on 55 lesions of the central nervous system are presented. The generated images very nicely demonstrate cytological and architectural features required for pathological tumor typing and grading. Furthermore, information on the molecular content of a probe is provided. The tool will be implemented into a biopsy needle or endoscope in the near future for in vivo studies. With this promising multimodal imaging approach the neurosurgeon might directly see blood vessels to minimize the risk for biopsy associated hemorrhages. The attending neuropathologist might directly identify the tumor and guide the selection of representative specimens for further studies. Thus, collection of non-representative material could be avoided and the risk to injure eloquent brain tissue minimized. Copyright © 2015 Elsevier B.V. All rights reserved.
Precession in Stokes flow: spin and revolution of a bacterial flagellum
Ishikawa, Takuji; Sawano, Yoichiro; Wakebe, Hiromichi; Inoue, Yuichi; Ishijima, Akihiko; Shimogonya, Yuji
2016-11-01
The bacterial flagellar motor is an ion-driven rotary machine in the cell envelope of bacteria. When we performed a bead assay, in which the cell body was affixed to a glass surface to observe the rotation of a truncated flagellum via the positioning of a 250 nm-diameter gold nanoparticle, we often observed that the filament motion consisted of two types of rotation: spin and revolution, which resulted in precession. Since the mechanism of flagella precession was unknown, we investigated it using numerical simulations. The results show that the precession occurred due to hydrodynamic interactions between the flagellum and the wall in the Stokes flow regime. We also developed a simple theory of the precession, which validity was confirmed by comparing with the simulation. The theory could be utilized to predict both the filament tilt angle and motor torque from experimental flagellar precession data. The knowledge obtained is important in understanding mechanical properties of the bacterial motor and hook. This work was supported in part by a Japan Society Promotion of Science Grants-in-Aid for Scientific Research (JSPS KAKENHI) (Grant Nos. 25000008 and 26242039).
Dual-Pump Coherent Anti-Stokes Raman Scattering Temperature and CO2 Concentration Measurements
Lucht, Robert P.; Velur-Natarajan, Viswanathan; Carter, Campbell D.; Grinstead, Keith D., Jr.; Gord, James R.; Danehy, Paul M.; Fiechtner, G. J.; Farrow, Roger L.
2003-01-01
Measurements of temperature and CO2 concentration using dual-pump coherent anti-Stokes Raman scattering, (CARS) are described. The measurements were performed in laboratory flames,in a room-temperature gas cell, and on an engine test stand at the U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base. A modeless dye laser, a single-mode Nd:YAG laser, and an unintensified back-illuminated charge-coupled device digital camera were used for these measurements. The CARS measurements were performed on a single-laser-shot basis. The standard deviations of the temperatures and CO2 mole fractions determined from single-shot dual-pump CARS spectra in steady laminar propane/air flames were approximately 2 and 10% of the mean values of approximately 2000 K and 0.10, respectively. The precision and accuracy of single-shot temperature measurements obtained from the nitrogen part of the dual-pump CARS system were investigated in detail in near-adiabatic hydrogen/air/CO2 flames. The precision of the CARS temperature measurements was found to be comparable to the best results reported in the literature for conventional two-laser, single-pump CARS. The application of dual-pump CARS for single-shot measurements in a swirl-stabilized combustor fueled with JP-8 was also demonstrated.
Chien, Cheng-Hao; Chen, Wei-Wen; Wu, June-Tai; Chang, Ta-Chau
2012-12-01
To improve our understanding of lipid metabolism, Drosophila is used as a model animal, and its lipid homeostasis is monitored by coherent anti-Stokes Raman scattering microscopy. We are able to achieve in vivo imaging of larval fat body (analogous to adipose tissue in mammals) and oenocytes (analogous to hepatocytes) in Drosophila larvae at subcellular level without any labeling. By overexpressing two lipid regulatory proteins-Brummer lipase (Bmm) and lipid storage droplet-2 (Lsd-2)-we found different phenotypes and responses under fed and starved conditions. Comparing with the control larva, we observed more lipid droplet accumulation by ˜twofold in oenocytes of fat-body-Bmm-overexpressing (FB-Bmm-overexpressing) mutant under fed condition, and less lipid by ˜fourfold in oenocytes of fat-body-Lsd-2-overexpressing (FB-Lsd-2-overexpressing) mutant under starved condition. Moreover, together with reduced size of lipid droplets, the lipid content in the fat body of FB-Bmm-overexpressing mutant decreases much faster than that of the control and FB-Lsd-2-overexpressing mutant during starvation. From long-term starvation assay, we found FB-Bmm-overexpressing mutant has a shorter lifespan, which can be attributed to faster consumption of lipid in its fat body. Our results demonstrate in vivo observations of direct influences of Bmm and Lsd-2 on lipid homeostasis in Drosophila larvae.
Solute rotation in polar liquids: microscopic basis for the Stokes-Einstein-Debye model.
Das, Amit; Biswas, Ranjit; Chakrabarti, J
2012-01-07
Here, we develop a framework for a molecular level understanding of the celebrated Stokes-Einstein-Debye (SED) formula. In particular, we explore reasons behind the surprising success of the SED model in describing dipolar solute rotation in complex polar media. Relative importance of solvent viscosity and solute-solvent dipolar interaction is quantified via a self-consistent treatment for the total friction on a rotating solute where the hydrodynamic contribution is modified by the friction arising from the longer ranged solute-solvent dipolar interaction. Although the solute-solvent dipolar coupling is obtained via the Mori-Zwanzig formalism, the inclusion of solvent structure via the wave vector dependent viscosity in the hydrodynamic contribution incorporates solvent molecularity in the present theory. This approach satisfactorily describes the experimental rotation times measured using a dipolar solute, coumarin 153 (C153), in protic and aprotic polar liquids, and more importantly, provides microscopic explanation for insignificant contribution of electrical interactions on solute rotation, in contrast to the substantial role played by the translational dielectric friction in the context of ionic mobility. It is also discussed on how the present theory can be suitably extended to study the rotation of a realistic solute in media other than dipolar solvents.
A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics.
Hageman, Nathan S; Toga, Arthur W; Narr, Katherine L; Shattuck, David W
2009-03-01
We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.
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.
Breakdown of Stokes-Einstein relation in the supercooled liquid state of phase change materials
Energy Technology Data Exchange (ETDEWEB)
Sosso, G.C.; Bernasconi, M. [Dipartimento di Scienza dei Materiali, Universita di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano (Italy); Behler, J. [Lehrstuhl fuer Theoretische Chemie, Ruhr-Universitaet Bochum, Universitaetsstrasse 150, 44780 Bochum (Germany)
2012-10-15
The application of amorphous chalcogenide alloys as data-storage media relies on their ability to undergo an extremely fast (10-100 ns) crystallization once heated at sufficiently high temperature. However, the peculiar features that make these materials so attractive for memory devices still lack a comprehensive microscopic understanding. By means of large scale molecular dynamics simulations, we demonstrate that the supercooled liquid of the prototypical compound GeTe shows a very high atomic mobility (D {proportional_to}10{sup -6} cm{sup 2} s{sup -1}) down to temperatures close to the glass transition temperatures. This behavior leads to a breakdown of the Stokes-Einstein relation between the self-diffusion coefficient and the viscosity in the supercooled liquid. The results suggest that the fragility of the supercooled liquid is the key to understand the fast crystallization process in this class of materials. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Numerical study of the motion of a flagellated swimmer inside a tube in the Stokes regime
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.
On the quasi-unconditional stability of BDF-ADI solvers for the compressible Navier-Stokes equations
Bruno, Oscar
2015-01-01
The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating Direction Implicit) solvers of higher orders of temporal accuracy (orders $s = 2$ to $6$) for the compressible Navier-Stokes equations in two- and three-dimensional space. The proposed methodology employs the backward differentiation formulae (BDF) together with a quasilinear-like formulation, high-order extrapolation for nonlinear components, and the Douglas-Gunn splitting. A variety of numerical results presented in Part I demonstrate in practice the theoretical convergence rates enjoyed by these algorithms, as well as their excellent accuracy and stability properties for a wide range of Reynolds numbers. In particular, the proposed schemes enjoy a certain property of "quasi-unconditional stability": for small enough (problem-dependent) fixed values of the time-step $\\Delt...
DEFF Research Database (Denmark)
Yang, Yang; Kær, Søren Knudsen
2012-01-01
The flow structure of one isothermal swirling case in the Sydney swirl flame database was studied using two numerical methods. Results from the Reynolds-averaged Navier-Stokes (RANS) approach and large eddy simulation (LES) were compared with experimental measurements. The simulations were applie...... deducted from the two methods were different. The vorticity field was also studied using a velocity gradient based method. This research gained in-depth understanding of isothermal swirling flow.......The flow structure of one isothermal swirling case in the Sydney swirl flame database was studied using two numerical methods. Results from the Reynolds-averaged Navier-Stokes (RANS) approach and large eddy simulation (LES) were compared with experimental measurements. The simulations were applied...
Botet, Robert; Kuratsuji, Hiroshi
2010-03-01
We present a framework for the stochastic features of the polarization state of an electromagnetic wave propagating through the optical medium with both deterministic (controlled) and disordered birefringence. In this case, the Stokes parameters obey a Langevin-type equation on the Poincaré sphere. The functional integral method provides for a natural tool to derive the Fokker-Planck equation for the probability distribution of the Stokes parameters. We solve the Fokker-Planck equation in the case of a random anisotropic active medium submitted to a homogeneous electromagnetic field. The possible dissipation and relaxation phenomena are studied in general and in various cases, and we give hints about how to validate experimentally the corresponding phenomenological equations.
Directory of Open Access Journals (Sweden)
I. Yu. Popov
2014-06-01
Full Text Available Geodynamic modeling is often related with challenging computations involving solution of the Stokes and continuity equations under the condition of highly variable viscosity. Based on a new analytical approach we have developed particular analytical solutions for 2-D and 3-D incompressible Stokes flows with both linearly and exponentially variable viscosity. We demonstrate how these particular solutions can be converted into 2-D and 3-D test problems suitable for benchmarking numerical codes aimed at modeling various mantle convection and lithospheric dynamics problems. The Main advantage of this new generalized approach is that a large variety of benchmark solutions can be generated, including relatively complex cases with open model boundaries, non-vertical gravity and variable gradients of the viscosity and density fields, which are not parallel to the Cartesian axes. Examples of respective 2-D and 3-D MatLab codes are provided with this paper.
Wang, Ya-Guang; Yin, Jierong; Zhu, Shiyong
2017-10-01
In this paper, we will analyze the vanishing viscosity limit of the incompressible Navier-Stokes equations with the Navier slip boundary conditions in a bounded domain of R2. When the slip length is smaller than or equal to the order of viscosity, by using an energy method and developing Kato's approach given in the work of Kato [Math. Sci. Res. Inst. Publ. 2, 85-98 (1984)], we obtain several conditions to guarantee that the solution of the Navier-Stokes equations with the Navier slip boundary conditions goes to the solution of the associated problem of the Euler equations in the energy space L2 uniformly in time, as the viscosity goes to zero.
Gottschall, Thomas; Meyer, Tobias; Baumgartl, Martin; Dietzek, Benjamin; Popp, Jürgen; Limpert, Jens; Tünnermann, Andreas
2014-09-08
Imaging based on coherent anti-Stokes Raman scattering (CARS) relies on the interaction of high peak-power, synchronized picosecond pulses with narrow bandwidths and a well-defined frequency difference. Recently a new type of fiber-based CARS laser source based on four-wave-mixing (FWM) has been developed. In order to enhance its spectral resolution and efficiency, a FWM based fiber optical parametric oscillator (FOPO) is proposed in this work. The source delivers 180 mW with 5.6 kW peak power for the CARS pump and 130 mW with 2.9 kW peak power for the Stokes signal. CARS resonances around 2850 and 2930 cm(-1) can be resolved with a resolution of 1 cm(-1) enabling high-contrast, spectrally resolved CARS imaging of biological tissue.
Wolf, Jacek; Świerblewska, Ewa; Jasiel-Wojculewicz, Hanna; Gockowski, Krzysztof; Wyrzykowski, Bogdan; Somers, Virend K; Narkiewicz, Krzysztof
2014-07-01
We report a case of a 41-year-old man who was noted to have position-dependent Cheyne-Stokes respiration with central sleep apnea (CSA) during sleep. The patient had multiple cardiovascular risk factors and target organ damages, including a history of two myocardial infarctions, transient ischemic attack, and chronic kidney disease. His hypertension was refractory to a number of antihypertensive medicines, however, a complete elimination of sleep-disordered breathing with oral theophylline treatment was paralleled by a significant BP fall with a subsequent need for reduction of antihypertensive drugs. Following these surprising observations we decided to withdraw theophylline from treatment (in-clinic). Theophylline discontinuation resulted in a gradual increase in BP and an urgent call for antihypertensive treatment modification. These observations suggest a potent hypotensive action of oral theophylline via Cheyne-Stokes respiration with CSA elimination. Our data suggest that CSA may be a mechanism that raises BP even during the daytime.
Reynolds-averaged Navier-Stokes based ice accretion for aircraft wings
Lashkajani, Kazem Hasanzadeh
This thesis addresses one of the current issues in flight safety towards increasing icing simulation capabilities for prediction of complex 2D and 3D glaze ice shapes over aircraft surfaces. During the 1980's and 1990's, the field of aero-icing was established to support design and certification of aircraft flying in icing conditions. The multidisciplinary technologies used in such codes were: aerodynamics (panel method), droplet trajectory calculations (Lagrangian framework), thermodynamic module (Messinger model) and geometry module (ice accretion). These are embedded in a quasi-steady module to simulate the time-dependent ice accretion process (multi-step procedure). The objectives of the present research are to upgrade the aerodynamic module from Laplace to Reynolds-Average Navier-Stokes equations solver. The advantages are many. First, the physical model allows accounting for viscous effects in the aerodynamic module. Second, the solution of the aero-icing module directly provides the means for characterizing the aerodynamic effects of icing, such as loss of lift and increased drag. Third, the use of a finite volume approach to solving the Partial Differential Equations allows rigorous mesh and time convergence analysis. Finally, the approaches developed in 2D can be easily transposed to 3D problems. The research was performed in three major steps, each providing insights into the overall numerical approaches. The most important realization comes from the need to develop specific mesh generation algorithms to ensure feasible solutions in very complex multi-step aero-icing calculations. The contributions are presented in chronological order of their realization. First, a new framework for RANS based two-dimensional ice accretion code, CANICE2D-NS, is developed. A multi-block RANS code from U. of Liverpool (named PMB) is providing the aerodynamic field using the Spalart-Allmaras turbulence model. The ICEM-CFD commercial tool is used for the iced airfoil
Weeks, Tyler; Schie, Iwan; den Hartigh, Laura J.; Rutledge, John C.; Huser, Thomas
2011-01-01
We demonstrate that doubly-resonant coherent anti-Stokes Raman scattering can provide enhanced and highly specific contrast for molecules containing unique Raman-active small molecular groups. This combination provides contrast for molecules that can otherwise be difficult to discriminate by Raman spectroscopy. Here, human monocytes were incubated with either deuterated oleic acid or 17-octadecynoic acid (a fatty acid with an end terminal acetylene group). The carbon-deuterium stretching vibr...