Relevant bibliographies by topics / Velocity autocorrelation function

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Velocity autocorrelation function'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Velocity autocorrelation function"

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Leegwater, Jan A. "Velocity autocorrelation function of Lennard‐Jones fluids." Journal of Chemical Physics 94, no. 11 (1991): 7402–10. http://dx.doi.org/10.1063/1.460171.

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Chakraborty, D. "Velocity autocorrelation function of a Brownian particle." European Physical Journal B 83, no. 3 (2011): 375–80. http://dx.doi.org/10.1140/epjb/e2011-20395-3.

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Cichocki, B., and B. U. Felderhof. "Velocity autocorrelation function of interacting Brownian particles." Physical Review E 51, no. 6 (1995): 5549–55. http://dx.doi.org/10.1103/physreve.51.5549.

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CHANG, KEH-CHIN, CHIUAN-TING LI, and HSUAN-JUNG CHEN. "EXPERIMENTAL INVESTIGATION OF VELOCITY AUTOCORRELATION FUNCTIONS IN TURBULENT PLANAR MIXING LAYER." Modern Physics Letters B 24, no. 13 (2010): 1361–64. http://dx.doi.org/10.1142/s0217984910023621.

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The velocity autocorrelation coefficient correlates the velocity in the time domain but at the same spatial position. Turbulent planar mixing layer consists of two types of turbulence, that is, shear turbulence in the central shear layer and nearly homogeneous turbulence in both the high- and low-speed free stream sides. It is interesting to know what kind of function forms can be used to represent faithfully the experimental observations of the velocity autocorrelation coefficients in the mixing layer. Various velocity autocorrelation functions are tested with the measured data. It is found that the Frenkiel function family is the most proper form to represent the measured velocity autocorrelation coefficients in both the shear layer and free stream regimes.
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Mroczek, Stefan, and Frederik Tilmann. "Joint ambient noise autocorrelation and receiver function analysis of the Moho." Geophysical Journal International 225, no. 3 (2021): 1920–34. http://dx.doi.org/10.1093/gji/ggab065.

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SUMMARY In the field of seismic interferometry, cross-correlations are used to extract Green’s function from ambient noise data. By applying a single station variation of the method, using autocorrelations, we are in principle able to retrieve zero-offset reflections in a stratified Earth. These reflections are valuable as they do not require an active seismic source and, being zero-offset, are better constrained in space than passive earthquake based measurements. However, studies that target Moho signals with ambient noise autocorrelations often give ambiguous results with unclear Moho reflections. Using a modified processing scheme and phase-weighted stacking, we determine the Moho P-wave reflection time from vertical autocorrelation traces for a test station with a known simple crustal structure (HYB in Hyderabad, India). However, in spite of the simplicity of the structure, the autocorrelation traces show several phases not related to direct reflections. Although we are able to match some of these additional phases in a qualitative way with synthetic modelling, their presence makes it hard to identify the reflection phases without prior knowledge. This prior knowledge can be provided by receiver functions. Receiver functions (arising from mode conversions) are sensitive to the same boundaries as autocorrelations, so should have a high degree of comparability and opportunity for combined analysis but in themselves are not able to independently resolve VP, VS and Moho depth. Using the timing suggested by the receiver functions as a guide, we observe the Moho S-wave reflection on the horizontal autocorrelation of the north component but not on the east component. The timing of the S reflection is consistent with the timing of the PpSs–PsPs receiver function multiple, which also depends only on the S velocity and Moho depth. Finally, we combine P receiver functions and autocorrelations from HYB in a depth–velocity stacking scheme that gives us independent estimates for VP, VS and Moho depth. These are found to be in good agreement with several studies that also supplement receiver functions to obtain unique crustal parameters. By applying the autocorrelation method to a portion of the EASI transect crossing the Bohemian Massif in central Europe, we find approximate consistency with Moho depths determined from receiver functions and spatial coherence between stations, thereby demonstrating that the method is also applicable for temporary deployments. Although application of the autocorrelation method requires great care in phase identification, it has the potential to resolve both average crustal P and S velocities alongside Moho depth in conjunction with receiver functions.
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Kumari, Shikha, and Syed Rashid Ahmad. "Velocity autocorrelation function in uniformly heated granular gas." EPJ Web of Conferences 140 (2017): 04007. http://dx.doi.org/10.1051/epjconf/201714004007.

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Balucani, U., J. P. Brodholt, and R. Vallauri. "Analysis of the velocity autocorrelation function of water." Journal of Physics: Condensed Matter 8, no. 34 (1996): 6139–44. http://dx.doi.org/10.1088/0953-8984/8/34/004.

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Cichocki, B., and B. U. Felderhof. "Rotational velocity autocorrelation function of interacting Brownian particles." Physica A: Statistical Mechanics and its Applications 289, no. 3-4 (2001): 409–18. http://dx.doi.org/10.1016/s0378-4371(00)00532-x.

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Chtchelkatchev, N. M., and R. E. Ryltsev. "Complex singularities of the fluid velocity autocorrelation function." JETP Letters 102, no. 10 (2015): 643–49. http://dx.doi.org/10.1134/s0021364015220038.

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Lee, M. H. "Comment on 'Velocity autocorrelation function in fluctuating hydrodynamics'." Journal of Physics: Condensed Matter 4, no. 50 (1992): 10487–92. http://dx.doi.org/10.1088/0953-8984/4/50/037.

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Dissertations / Theses on the topic "Velocity autocorrelation function"

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Nava-Sedeño, Josue Manik, Haralampos Hatzikirou, Rainer Klages, and Andreas Deutsch. "Cellular automaton models for time-correlated random walks: derivation and analysis." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-231568.

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Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is “data-driven”. Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.
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Nava-Sedeño, Josue Manik, Haralampos Hatzikirou, Rainer Klages, and Andreas Deutsch. "Cellular automaton models for time-correlated random walks: derivation and analysis." Nature Publishing Group, 2017. https://tud.qucosa.de/id/qucosa%3A30690.

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Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is “data-driven”. Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.
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Khan, Salman Ahmed. "Autocorrelation function based mobile velocity estimation in correlated Rayleigh MIMO channels." Thesis, 2008. http://spectrum.library.concordia.ca/976167/1/MR45308.pdf.

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In upcoming 4 th generation mobile systems using multiple antennas, knowledge of the speed of the mobile will help allocate adaptively scarce system resources to users. Due to insufficient scattering in the propagation environment or insufficient antenna spacing on either the transmitter or receiver, Multiple Input Multiple Output (MIMO) channels are often correlated. Velocity estimation in MIMO channels has not received much attention up to now. On the other hand, a large number of schemes have been developed for velocity estimation in Single Input Single Output (SISO) systems. Some of these schemes can be categorized as Autocorrelation Function (ACF) based schemes. These ACF based schemes are easy to implement and give accurate velocity estimates. In this thesis, we focus on extending this existing class of ACF based velocity estimation schemes to correlated MIMO channels. This way, the benefits of ACF based schemes can be derived in commonly occurring correlated MIMO channels. In the first part of the thesis, we first establish a performance reference by determining the performance of ACF based schemes in uncorrelated MIMO channels. Then we analyze the performance of ACF based schemes in correlated MIMO channel using the full antenna set. Some loss in the accuracy of velocity estimates is observed compared to the case of the uncorrelated MIMO channel. To recover this loss, we then present a channel decorrelation based recovery scheme. The second part of the thesis studies the extension of ACF based schemes to the case of correlated MIMO channels with antenna selection. The performance of the ACF based schemes in this case is analyzed. In this case, a degradation of performance larger than the case of the full antenna set is noticed. Thereafter a recovery scheme based on channel decorrelation is presented. This scheme partially recovers the degradation in accuracy of velocity estimates. Thus the work performed in this thesis enables us to obtain accurate estimates of velocity in correlated MIMO channels
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Chen, Hsuan-Jung, and 陳炫蓉. "Determination of the empirical function for velocity autocorrelation coefficient in planar mixing layer." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/35610475667624142900.

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碩士<br>國立成功大學<br>航空太空工程學系碩博士班<br>94<br>The study seeks for the suitable form of the streamwise and transverse autocorrelation functions in planar mixing layer. The flow field of turbulent planar mixing layer can be divided into two parts: the free stream region and the shear layer region. The shear layer region is inherited with remarkable pressure gradient and possesses larger shear force than the free stream region. The velocity autocorrelation coefficients in shear layer region oscillate and decay faster than those in the free stream region. This study collects seven velocity autocorrelation functions from the literature, and investigates their applicability in both the free stream and shear layer regions. It is reported that there are four requirements for the velocity autocorrelation function including (1)an even function,(2)zero slope at origin(τ=0), (3)to meet the definition of integral time scale,and (4)the slope of the logarithm of the energy spectrum in the inertial subrange being -2 at high frequency. In this study, a fifth requirement that the velocity autocorrelation should have negative oscillation feature is included. The second-order autoregressive (AR) mode, which is expressed with three parameters, is widely used in atmospheric science. However, the second-order autoregressive mode does not match two of the aforementioned requirements, that is, zero slope at τ=0 and to meet the definition of integral time scale. In this study, the modified two-parameter and one-parameter AR modes, named as AR2 and AR1 functions, respectively, are proposed to remedy the drawbacks of the original AR function. It is found the functions proposed by Csanady(1973) and Altinsoy and Tugrul (2002) cannot fit the tendency of the streamwise autocorrelation coefficient, while the functions proposed by Frekiel(1953) with one parameter and AR2 with two parameters can fit the experiment data well.
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Bellissima, Stefano. "Single particle dynamics in liquid systems." Doctoral thesis, 2017. http://hdl.handle.net/2158/1088719.

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The subject of this PhD work is the microscopic dynamics in fluids, that is, a study of the behavior of these fluids at an atomic level, where the ps and nm time and length scales, respectively, are involved. The objects of the analysis are fundamental space/time autocorrelation functions of microscopic variables describing either collective or single-particle (self) properties of the system. In particular, in this thesis we exploited molecular dynamics simulation data-sets to describe the self dynamics of fluids belonging to different categories: Lennard-Jones (LJ) model fluids, semi-quantum fluids, liquid metals and hydrogen-bonded molecular liquids. A substantial step forward in the comprehension of single-particle dynamics has been possible i) by applying a new method, not attempted so far, for the description of self functions, which is based on the recently presented multi-exponential expansion theory that accounts for time autocorrelation functions in many-body Hamiltonian systems, and ii) by deepening the relationship between self and collective properties.
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Book chapters on the topic "Velocity autocorrelation function"

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Balakrishnan, V. "The Velocity Autocorrelation Function." In Elements of Nonequilibrium Statistical Mechanics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-62233-6_4.

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Frenkel, D. "Long-Time Decay of Velocity Autocorrelation Function of Two-Dimensional Lattice Gas Cellular Automata." In Springer Proceedings in Physics. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-75259-9_13.

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Asif Shakoori, Muhammad, Maogang He, Aamir Shahzad, and Misbah Khan. "Studies of Self Diffusion Coefficient in Electrorheological Complex Plasmas through Molecular Dynamics Simulations." In Plasma Science and Technology. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.98854.

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A molecular dynamics (MD) simulation method has been proposed for three-dimensional (3D) electrorheological complex (dusty) plasmas (ER-CDPs). The velocity autocorrelation function (VACF) and self-diffusion coefficient (D) have been investigated through Green-Kubo expressions by using equilibrium MD simulations. The effect of uniaxial electric field (MT) on the VACF and D of dust particles has been computed along with different combinations of plasma Coulomb coupling (Γ) and Debye screening (κ) parameters. The new simulation results reflect diffusion motion for lower-intermediate to higher plasma coupling (Γ) for the sufficient strength of 0.0 &lt; M ≥ 1.5. The simulation outcomes show that the MT significantly affects VACF and D. It is observed that the strength of MT increases with increasing the Γ and up to κ = 2. Furthermore, it is found that the increasing trend in D for the external applied MT significantly depends on the combination of plasma parameters (Γ, κ). For the lower values of Γ, the proposed method works only for the low strength of MT; at higher Γ, the simulation scheme works for lower to intermediate MT, and D increased almost 160%. The present results are in fair agreement with parts of other MD data in the literature, with our values generally overpredicting the diffusion motion in ER-CDPs. The investigations show that the present algorithm more effective for the liquids-like and solid-like state of ER-CDPs. Thus, current equilibrium MD techniques can be employed to compute the thermophysical properties and also helps to understand the microscopic mechanism in ER-CDPs.
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Shakoori, Muhammad Asif, Maogang He, Aamir Shahzad, Misbah Khan, and Ying Zhang. "Molecular Dynamics Study of Diffusion Coefficient for Low-Temperature Dusty Plasmas in the Presence of External Electric Fields." In Emerging Developments and Applications of Low Temperature Plasma. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-7998-8398-2.ch004.

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The effects of external electric field (E) on the diffusion coefficient of dust particles in low-temperature dusty plasmas (LT-DPs) have been computed through nonequilibrium molecular dynamics (NEMD) simulations. The new simulation result was obtained by employing the integral formula of velocity autocorrelation functions (VACF) using the Green-Kubo relation. The normalized self-diffusion coefficient (D*) is investigated for different combinations of plasma coupling (Γ) and Debye screening (κ) parameters. The simulation outcome shows that the decreasing position of D* shifts toward Γ and also increased with the increase of κ. The D* linearly decreased with Γ and increased when applied external E increases. It is observed that the increasing trend of D* depends on the E strength. These investigations show that the present algorithm provides precise data with fast convergence and effects of κ, Γ, E. It is shown that the current NEMD techniques with applied external E can be employed to understand the microscopic mechanism of dusty plasmas.
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Conference papers on the topic "Velocity autocorrelation function"

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Petersen, P. M., P. Buchhave, and P. E. Andersen. "Polarization Properties of an Operational Photorefractive BSO Correlator." In Nonlinear Optics. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nlo.1992.md11.

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In this paper we report on the polarization properties of a BSO autocorrelator used for fast transparency analysis in particle image velocimetry(PIV). The autocorrelator is an optical parallel dataprocessing unit that estimate the velocity distribution of a particle flow. The correlator uses the two beam coupling configuration shown in Fig. 1(a). The input to the optical processor is the PIV-transparency that is a double exposure photograph of the particle flow. The output of the processor is the autocorrelation function which consists of two side peaks and a central spot. The distance between the peaks and their relative orientation determine the velocity and the direction of the flow. In this work we compare the exprimental results from the autocorrelator with an analytical theory from a coupled-wave theory.
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Birjandi, Amir Hossein, and Eric Bibeau. "Bubble Effects on the Acoustic Doppler Velocimeter (ADV) Measurements." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78251.

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Acoustic Doppler Velocimeter (ADV) is a useful technique for measuring flow velocities with frequency variations of up to approximately 200 Hz in laboratory settings and in field applications. Although measuring velocity with ADV has advantages over other velocity measurement methods, this technique is sensitive to operating conditions: in addition to noise, the signal can contain spikes with large amplitudes, a disadvantage of ADV. In this study, the effect of bubbles on ADV signals is experimentally assessed in a laboratory setting. Bubbles can intersect the sampling volume and the acoustic beams creating spikes. The impact and amplitude of these spikes is a function of the bubble size and position when it crosses the ADV sampling volume and the acoustic beams. Bubbles that intersect the sampling volume generate spikes in all three velocity directions simultaneously; bubbles that intersect acoustic beams, which span between the sampling volume and the ADV receivers, impact the velocity data in one or two directions, and has a negligible effect in the third direction. Bubbles that intersect the X-direction acoustic beam create spikes in velocity data in both X- and Z-directions, but have no significant impact on the Y-direction; the Y- and X-directions have spikes and the Z-direction is not significantly impacted, when bubbles intersect the Y-direction acoustic beam. In addition, spikes increase the magnitude of the power spectra at high frequencies. Without bubbles, the autocorrelation in the time domain decreases in value as the time-lag increases, approaching zero after 5 seconds. The presences of bubbles cause a large peak in the autocorrelation at a zero time-lag, and no autocorrelation thereafter. Furthermore, the autocorrelation without bubbles permit turbulence length scales to be calculated because of the positive autocorrelation value; unless spikes are removed by using an appropriate filter when bubbles are present, turbulence length scales cannot be calculated because the autocorrelation is zero.
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Nakagawa, Naofumi, Nobuo Takai, and Michiko Shigefuji. "Examination of the S-wave velocity structures by the autocorrelation function using the strong motion records in the Ishikari Plain." In The 14th SEGJ International Symposium, Online, 18–21 October 2021. Society of Exploration Geophysicists and Society of Exploration Geophysicists of Japan, 2021. http://dx.doi.org/10.1190/segj2021-081.1.

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Afanas'ev, Alexei L., and Alexander P. Shelekhov. "The estimate of the measurement accuracy of the average Doppler frequency using the autocorrelation function method." In Coherent Laser Radar. Optica Publishing Group, 1995. http://dx.doi.org/10.1364/clr.1995.me17.

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The measurement error depends on a great deal of factors when measuring the average frequency of the Doppler Lidar. One of the main factors is the turbulent wind velocity fluctuations. The existence of these fluctuations is the cause that the particles occurring in a scattering volume have different fluctuation velocities. Moreover, the positions of the particles within the scattering volume are random. Therefore, the photocurrent statistical characteristics of the Doppler Lidar and, consequently, the measurement error depend on the state of the turbulent atmosphere and dimensions of the scattering volume. For example, the statistical characteristics of the photocurrent signal part are the non-Gaussian ones in the case of small value of the dimensions of the scattering volume and the statistical characteristics can be considered the Gaussian ones in the case of large value of the dimensions of the scattering volume. Thus the usual methods of the estimate of the measurement accuracy of the average Doppler frequency based on the assumption of the Gaussian statistics of the photocurrent signal part (see Ref. 1) have a limited application area. The behavior of the measurement error of the average frequency of the pulsed and cw- Doppler Lidar as a function of parameters of the turbulent atmosphere and the dimensions of the scattering volume is studied for the autocorrelation function method. The consideration is based on the results of Ref. 2 in which the non-Gaussian random process is analyzed.
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Byrne, Charles L., and Michael A. Fiddy. "Signal Reconstruction as a Wiener Filter Approximation." In Photon Correlation Techniques and Applications. Optica Publishing Group, 1988. http://dx.doi.org/10.1364/pcta.1988.pcmdr18.

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The problem of reconstructing a non-negative signal from a finite number of spectral data is a problem of finding an optimal approximation to one function by another. For example, for velocity measurement by crossed beam laser Doppler anemometry, a limited number of channels can provide high quality data on the autocorrelation function of the intensity of the scattered light. However, extrapolation of these data is required in order to estimate velocity distributions narrower than the point spread function determined by the number of channels, e.g. in the case of laminar flow. We describe here methods based on the theory of best approximation in weighted Hilbert spaces, (1). These methods have been under development for some time for use in a variety of 1-D and 2-D estimation problems. A new interpretation of these methods is now possible based on the close analogy between the reconstruction of a non-negative function from finitely many values of its Fourier transform, and the design of approximate Wiener filters,(2).
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Gopalan, Balaji, Edwin Malkiel, and Joseph Katz. "Diffusion of Slightly Buoyant Droplets in Isotropic Turbulence." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98530.

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We study the diffusion of slightly buoyant droplets in isotropic turbulence using High Speed Digital Holographic PIV. Droplets (Specific Gravity 0.85) are injected in the central portion of an isotropic turbulence facility with weak mean flow. Perpendicular digital inline holograms are recorded in a 37 × 37 × 37 mm3 region of interest using two high speed cameras. Data are recorded at 250 frames per second (2000 frames per second is the maximum possible frame rate). An automated program is developed to obtain two dimensional tracks of the droplets from two orthogonal images and match them to get three dimensional tracks. Cross correlation of droplet images are used for measuring their velocities. The time series are low pass filtered to obtain accurate time history of droplet velocities. Data analysis determines the PDF of velocity and acceleration in three dimensions. The time history also enables us to calculate the three dimensional Lagrangian velocity autocorrelation function for different droplet radii. Integration of these functions gives us the diffusion coefficients. For shorter time scales, when the diffusion need not be Fickian we can use the three dimensional trajectories to calculate the generalized dispersion tensor and measure the time elapsed for diffusion to become Fickian.
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Uma, B., P. S. Ayyaswamy, R. Radhakrishnan, and D. M. Eckmann. "Modeling of a Nanoparticle Motion in a Newtonian Fluid: A Comparison Between Fluctuating Hydrodynamics and Generalized Langevin Procedures." In ASME 2012 Third International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/mnhmt2012-75019.

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A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed to simulate the motion of a nanocarrier in a quiescent fluid contained in a cylindrical tube. The nanocarrier is treated as a solid sphere. Thermal fluctuations are implemented using two different approaches: (1) fluctuating hydrodynamics; (2) generalized Langevin dynamics (Mittag-Leffler noise). At thermal equilibrium, the numerical predictions for temperature of the nanoparticle, velocity distribution of the particle, decay of the velocity autocorrelation function, diffusivity of the particle and particle-wall interactions are evaluated and compared with analytical results, where available. For a neutrally buoyant nanoparticle of 200 nm radius, the comparisons between the results obtained from the fluctuating hydrodynamics and the generalized Langevin dynamics approaches are provided. Results for particle diffusivity predicted by the fluctuating hydrodynamics approach compare very well with analytical predictions. Ease of computation of the thermostat is obtained with the Langevin approach although the dynamics gets altered.
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Will, S., K. Kraft, and A. Leipertz. "Determination of the Dynamic Viscosity of Selected Transparent Liquids Using Dynamic Light Scattering." In Photon Correlation and Scattering. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/pcs.1992.tub4.

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Dynamic light scattering has been used successfully for the determination of various thermophysical properties of fluids, e.g., thermal diffusivity, sound velocity and binary diffusion coefficient. The applicability to measuring dynamic viscosities has been shown, e.g., by Brunson and Byers [1]. Basis of the measurement is the Stokes-Einstein formula Here, η is the viscosity required and d is the hydrodynamic diameter of the spherical particles suspended. Viscosity measurements preferrably make use of monodisperse particles. Thus no integration over particle sizes is necessary. The particle diffusion coefficient D and the modulus q of the scattering vector of the optical arrangement form the decay constant in the autocorrelation function measured, τc = (2q2D)−1. From this value η can be determined for known temperature T.
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Gopalan, Balaji, Edwin Malkiel, Jian Sheng, and Joseph Katz. "Diesel Droplet Diffusion in Isotropic Turbulence With Digital Holographic Cinematography." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77423.

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High-speed in-line digital holographic cinematography was used to investigate the diffusion of droplets in locally isotropic turbulence. Droplets of diesel fuel (0.3–0.9mm diameter, specific gravity of 0.85) were injected into a 37×37×37mm3 sample volume located in the center of a 160-liter tank. The turbulence was generated by 4 spinning grids, located symmetrically in the corners of the tank, and was characterized prior to the experiments. The sample volume was back illuminated with two perpendicular collimated beams of coherent laser light and time series of in-line holograms were recorded with two high-speed digital cameras at 500 frames/sec. Numerical reconstruction generated a time series of high-resolution images of the droplets throughout the sample volume. We developed an algorithm for automatically detecting the droplet trajectories from each view, for matching the two views to obtain the three-dimensional tracks, and for calculating the time history of velocity. We also measured the mean fluid motion using 2-D PIV. The data enabled us to calculate the Lagrangian velocity autocorrelation function.
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Ramazanov, T. S., K. N. Dzhumagulova, T. T. Daniyarov, et al. "Velocity Autocorrelation Functions and Diffusion of Dusty Plasma." In MULTIFACETS OF DUSTRY PLASMAS: Fifth International Conference on the Physics of Dusty Plasmas. AIP, 2008. http://dx.doi.org/10.1063/1.2996845.

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