arXiv subjects

Quan Zhou

Publications and source records attributed to Quan Zhou.

159 records · Page 9Linked to original sources

arXiv2014

A Reduction of the Elastic Net to Support Vector Machines with an Application to GPU Computing

The past years have witnessed many dedicated open-source projects that built and maintain implementations of Support Vector Machines (SVM), parallelized for GPU, multi-core CPUs and distributed systems. Up to this point, no comparable effort has been made to parallelize the Elastic Net, despite its popularity in many high impact applications, including genetics, neuroscience and systems biology. The first contribution in this paper is of theoretical nature. We establish a tight link between two seemingly different algorithms and prove that Elastic Net regression can be reduced to SVM with squared hinge loss classification. Our second contribution is to derive a practical algorithm based on this reduction. The reduction enables us to utilize prior efforts in speeding up and parallelizing SVMs to obtain a highly optimized and parallel solver for the Elastic Net and Lasso. With a simple wrapper, consisting of only 11 lines of MATLAB code, we obtain an Elastic Net implementation that naturally utilizes GPU and multi-core CPUs. We demonstrate on twelve real world data sets, that our algorithm yields identical results as the popular (and highly optimized) glmnet implementation but is one or several orders of magnitude faster.

stat.ML↗

arXiv2013

Counter-gradient heat transport in two-dimensional turbulent Rayleigh-Bénard convection

We present high-resolution numerical investigations of heat transport by two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection over the Rayleigh number range $10^8 \leqslant Ra\leqslant 10^{10}$ and the Prandtl number range $0.7\leqslant Pr \leqslant10$. We find that there exist strong counter-gradient local heat flux with magnitude much larger than the global Nusselt number $Nu$ of the system. Two mechanisms for generating counter-gradient heat transport are identified: one is due to the bulk dynamics and the other is due to the competitions between the corner-flow rolls and the large-scale circulation (LSC). While the magnitude of the former is found to increase with increasing Prandtl number, that of the latter maximizes at medium $Pr$. We further reveal that the corner-LSC competitions lead to the anomalous $Nu$-$Pr$ relation in 2D RB convection, i.e. $Nu(Pr)$ minimizes, rather than maximizes as in three-dimensional cylindrical case, at $Pr\approx2\sim3$ for moderate $Ra$.

physics.flu-dyn↗

arXiv2013

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

We report a high-resolution numerical study of two-dimensional (2D) miscible Rayleigh-Taylor (RT) incompressible turbulence with the Boussinesq approximation. An ensemble of 100 independent realizations were performed at small Atwood number and unit Prandtl number with a spatial resolution of $2048\times8193$ grid points. Our main focus is on the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence properties. Our results show that the buoyancy force balances the inertial force at all scales below the integral length scale and thus validate the basic force-balance assumption of the Bolgiano-Obukhov scenario in 2D RT turbulence. It is further found that the Kolmogorov dissipation scale $η(t)\sim t^{1/8}$, the kinetic-energy dissipation rate $\varepsilon_u(t)\sim t^{-1/2}$, and the thermal dissipation rate $\varepsilon_θ(t)\sim t^{-1}$. All of these scaling properties are in excellent agreement with the theoretical predictions of the Chertkov model [Phys. Rev. Lett. \textbf{91}, 115001 (2003)]. We further discuss the emergence of intermittency and anomalous scaling for high order moments of velocity and temperature differences. The scaling exponents $ξ^r_p$ of the $p$th-order temperature structure functions are shown to saturate to $ξ^r_{\infty}\simeq0.78\pm0.15$ for the highest orders, $p\sim10$. The value of $ξ^r_{\infty}$ and the order at which saturation occurs are compatible with those of turbulent Rayleigh-Bénard (RB) convection [Phys. Rev. Lett. \textbf{88}, 054503 (2002)], supporting the scenario of universality of buoyancy-driven turbulence with respect to the different boundary conditions characterizing the RT and RB systems.

physics.flu-dyn↗

arXiv2012

Aspect ratio dependence of heat transport by turbulent Rayleigh-Bénard convection in rectangular cells

We report high-precision measurements of the Nusselt number $Nu$ as a function of the Rayleigh number $Ra$ in water-filled rectangular Rayleigh-Bénard convection cells. The horizontal length $L$ and width $W$ of the cells are 50.0 cm and 15.0 cm, respectively, and the heights $H=49.9$, 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios $(Γ_x\equiv L/H,Γ_y\equiv W/H)=(1,0.3)$, $(2,0.6)$, $(4,1.2)$, $(7.3,2.2)$, $(14.3,4.3)$, and $(20.8,6.3)$. The measurements were carried out over the Rayleigh number range $6\times10^5\lesssim Ra\lesssim10^{11}$ and the Prandtl number range $5.2\lesssim Pr\lesssim7$. Our results show that for rectangular geometry turbulent heat transport is independent of the cells' aspect ratios and hence is insensitive to the nature and structures of the large-scale mean flows of the system. This is slightly different from the observations in cylindrical cells where $Nu$ is found to be in general a decreasing function of $Γ$, at least for $Γ=1$ and larger. Such a difference is probably a manifestation of the finite plate conductivity effect. Corrections for the influence of the finite conductivity of the top and bottom plates are made to obtain the estimates of $Nu_{\infty}$ for plates with perfect conductivity. The local scaling exponents $β_l$ of $Nu_{\infty}\sim Ra^{β_l}$ are calculated and found to increase from 0.243 at $Ra\simeq9\times10^5$ to 0.327 at $Ra\simeq4\times10^{10}$.

physics.flu-dyn↗

arXiv2012

Thermal boundary layer profiles in turbulent Rayleigh-Bénard convection in a cylindrical sample

We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-Bénard flow in a cylindrical sample at Rayleigh numbers Ra=10^8 to Ra=2\times10^{12} and Prandtl numbers Pr=6.4 and Pr=0.7 with the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010)] thus extending previous results for quasi-2-dimensional systems to 3D systems for the first time. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperature profile of a laminar, zero-pressure gradient boundary layer according to Pohlhausen than in the fixed reference frame. The deviation between the measured profiles in the dynamical reference frame and the laminar profiles increases with decreasing Pr, where the thermal BL is more exposed to the bulk fluctuations due to the thinner kinetic BL, and increasing Ra, where more plumes are passing the measurement location.

physics.flu-dyn↗

arXiv2011

Horizontal Structures of Velocity and Temperature Boundary Layers in 2D Numerical Turbulent Rayleigh-Bénard Convection

We investigate the structures of the near-plate velocity and temperature profiles at different horizontal positions along the conducting bottom (and top) plate of a Rayleigh-Bénard convection cell, using two-dimensional (2D) numerical data obtained at the Rayleigh number Ra=10^8 and the Prandtl number Pr=4.4 of an Oberbeck-Boussinesq flow with constant material parameters. The results show that most of the time, and for both velocity and temperature, the instantaneous profiles scaled by the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010) agree well with the classical Prandtl-Blasius laminar boundary layer (BL) profiles. Therefore, when averaging in the dynamical reference frames, which fluctuate with the respective instantaneous kinematic and thermal BL thicknesses, the obtained mean velocity and temperature profiles are also of Prandtl-Blasius type for nearly all horizontal positions. We further show that in certain situations the traditional definitions based on the time-averaged profiles can lead to unphysical BL thicknesses, while the dynamical method also in such cases can provide a well-defined BL thickness for both the kinematic and the thermal BLs.

physics.flu-dyn↗

arXiv2011

Disentangle plume-induced anisotropy in the velocity field in buoyancy-driven turbulence

We present a method of disentangling the anisotropies produced by the cliff structures in turbulent velocity field and test it in the system of turbulent Rayleigh-Bénard (RB) convection. It is found that in the RB system the cliff structures in the velocity field are generated by thermal plumes. These cliff structures induce asymmetry in the velocity increments, which leads us to consider the plus and minus velocity structure functions (VSF). The plus velocity increments exclude cliff structures, while the minus ones include them. Our results show that the scaling exponents of the plus VSFs are in excellent agreement with those predicted for homogeneous and isotropic turbulence (HIT), whereas those of the minus VSFs exhibit significant deviations from HIT expectations in places where thermal plumes abound. These results demonstrate that plus and minus VSFs can be used to quantitatively study the effect of cliff structures in the velocity field and to effectively disentangle the associated anisotropies caused by these structures.

physics.flu-dyn↗

arXiv2011

Experimental Investigation of Longitudinal Space-Time Correlations of the Velocity Field in Turbulent Rayleigh-Bénard Convection

We report an experimental investigation of the longitudinal space-time cross-correlation function of the velocity field, $C(r,τ)$, in a cylindrical turbulent Rayleigh-Bénard convection cell using the particle image velocimetry (PIV) technique. We show that while the Taylor's frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows [He & Zhang, \emph{Phys. Rev. E} \textbf{73}, 055303(R) (2006)] is valid for the present velocity field for all over the cell, i.e., the isocorrelation contours of the measured $C(r,τ)$ have a shape of elliptical curves and hence $C(r,τ)$ can be related to $C(r_E,0)$ via $r_E^2=(r-βτ)^2+γ^2τ^2$ with $β$ and $γ$ being two characteristic velocities. We further show that the fitted $β$ is proportional to the mean velocity of the flow, but the values of $γ$ are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell's central region. It is found that $β$ and $γ$ are approximately the same near the sidewall, while $β\simeq0$ at cell center.

physics.flu-dyn↗

arXiv2010

Measured Instantaneous Viscous Boundary Layer in Turbulent Rayleigh-Bénard Convection

We report measurements of the instantaneous viscous boundary layer (BL) thickness $δ_v(t)$ in turbulent Rayleigh-Bénard convection. It is found that $δ_v(t)$ obtained from the measured instantaneous two-dimensional velocity field exhibits intermittent fluctuations. For small values, $δ_v(t)$ obeys a lognormal distribution, whereas for large values the distribution of $δ_v(t)$ exhibits an exponential tail. The variation of $δ_v(t)$ with time is found to be driven by the fluctuations of the large-scale mean flow velocity and the local horizontal velocities close to the plate can be used as an instant measure of this variation. It is further found that in the present parameter range of the experiment the mean velocity profile measured in the laboratory frame can be brought into coincidence with the theoretical Prandtl-Blasius laminar BL profile, if it is resampled relative to the time-dependent frame of $δ_v(t)$.

physics.flu-dyn↗

arXiv2010

Statistical and geometrical properties of thermal plumes in turbulent Rayleigh-Bénard convection

We present a systematic experimental study of geometric and statistical properties of thermal plumes in turbulent Rayleigh-Bénard convection using the thermochromic-liquid-crystal (TLC) technique. The experiments were performed in three water-filled cylindrical convection cells with aspect ratios 2, 1, and 0.5 and over the Rayleigh-number range $5\times10^7 \leq Ra \leq 10^{11}$. TLC thermal images of horizontal plane cuts at various depths below the top plate were acquired. Three-dimensional images of thermal plumes were then reconstructed from the two-dimensional slices of the temperature field. The results show that the often-called sheetlike plumes are really one-dimensional structures and may be called rodlike plumes. We find that the number densities for both sheetlike/rodlike and mushroomlike plumes have power-law dependence on $Ra$ with scaling exponents of $\sim 0.3$, which is close to that between the Nusselt number $Nu$ and $Ra$. This result suggests that it is the plume number that primarily d ermines the scaling exponent of the $Nu$-$Ra$ scaling relation. The evolution of the aspect ratio of sheetlike/rodlike plumes reveals that as $Ra$ increases the plume geometry changes from more-elongated to less-elongated. Our study of the plume area fraction (fraction of coverage over the surface of the plate) further reveals that the increased plume numbers with $Ra$ mainly comes from increased plume emission, rather than fragmentation of plumes. In addition, the area, perimeter, and the shape complexity of the two-dimensional horizontal cuts of sheetlike/rodlike plumes were studied and all are found to obey log-normal distributions.

physics.flu-dyn↗

arXiv2010

Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-Bénard convection

The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-Bénard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim Pr\lesssim5.4$. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses.

physics.flu-dyn↗

arXiv2008

Origin of the Temperature Oscillation in Turbulent Thermal Convection

We report an experimental study of the three-dimensional spatial structure of the low frequency temperature oscillations in a cylindrical Rayleigh-Bénard convection cell. It is found that thermal plumes are not emitted periodically, but randomly and continuously, from the top and bottom plates. We further found that the oscillation of the temperature field does not originate from the boundary layers, but rather is a result of the horizontal motion of the hot ascending and cold descending fluids being modulated by the twisting and sloshing motion of the bulk flow field.

physics.flu-dyn↗

arXiv2008

Oscillations of the large-scale circulation in turbulent Rayleigh-Bénard convection: the off-center mode and its relationship with the torsional mode

We report an experimental study of the large-scale circulation (LSC) in a turbulent Rayleigh-Bénard convection cell with aspect ratio unity. The temperature-extremum-extraction (TEE) method for obtaining the dynamic information of the LSC is presented. With this method, the azimuthal angular positions of the hot ascending and cold descending flows along the sidewall are identified from the measured instantaneous azimuthal temperature profile. The motion of the LSC is then decomposed into two different modes: the azimuthal mode and the translational or off-center mode. Comparing to the previous sinusoidal-fitting (SF) method, it is found that both methods give the same information about the azimuthal motion of the LSC, but the TEE method in addition can provide information about the off-center motion of the LSC, which is found to oscillate time-periodically around the cell's central vertical axis with an amplitude being nearly independent of the turbulent intensity. It is further found that the azimuthal angular positions of the hot ascending flow near the bottom plate and the cold descending flow near the top plate oscillate periodically out of phase by $π$, leading to the torsional mode of the LSC. These oscillations are then propagated vertically along the sidewall by the hot ascending and cold descending fluids. When they reach the mid-height plane, the azimuthal positions of the hottest and coldest fluids again oscillate out of phase by $π$. It is this out-of-phase horizontal positional oscillation of the hottest and coldest fluids at the same horizontal plane that produces the off-center oscillation of the LSC. A direct velocity measurement further confirms the existence of the bulk off-center mode of the flow field near cell center.

physics.flu-dyn↗

arXiv2008

Comparative experimental study of local mixing of active and passive scalars in turbulent thermal convection

We investigate experimentally the statistical properties of active and passive scalar fields in turbulent Rayleigh-Bénard convection in water, at $Ra\sim10^{10}$. Both the local concentration of fluorescence dye and the local temperature are measured near the sidewall of a rectangular cell. It is found that, although they are advected by the same turbulent flow, the two scalars distribute differently. This difference is twofold, i.e. both the quantities themselves and their small-scale increments have different distributions. Our results show that there is a certain buoyant scale based on time domain, i.e. the Bolgiano time scale $t_B$, above which buoyancy effects are significant. Above $t_B$, temperature is active and is found to be more intermittent than concentration, which is passive. This suggests that the active scalar possesses a higher level of intermittency in turbulent thermal convection. It is further found that the mixing of both scalar fields are isotropic for scales larger than $t_B$ even though buoyancy acts on the fluid in the vertical direction. Below $t_B$, temperature is passive and is found to be more anisotropic than concentration. But this higher degree of anisotropy is attributed to the higher diffusivity of temperature over that of concentration. From the simultaneous measurements of temperature and concentration, it is shown that two scalars have similar autocorrelation functions and there is a strong and positive correlation between them.

physics.flu-dyn↗

arXiv2005

Analysis on Transmit Antenna Selection for Spatial Multiplexing Systems: A Geometrical Approach

Recently, the remarkable potential of a multiple-input multiple-output (MIMO) wireless communication system was unveiled for its ability to provide spatial diversity or multiplexing gains. For MIMO diversity schemes, it is already known that. by the optimal antenna selection maximizing the post-processing signal-to-noise ratio, the diversity order of the full system can be maintained. On the other hand, the diversity order achieved by antenna selection in spatial multiplexing systems, especially those exploiting practical coding and decoding schemes, has not been rigorously analyzed thus far. In this paper, from a geometric standpoint, we propose a new framework for theoretically analyzing the diversity order achieved by transmit antenna selection for separately encoded spatial multiplexing systems with linear and decision-feedback receivers. We rigorously show that a diversity order of (Nt-1)(Nr-1) can be achieved for an Nr by Nt SM system when L=2 antennas are selected from the transmit side; while for L>2 scenarios, we give bounds for the achievable diversity order and show that the optimal diversity order is at least (Nt-L+1)(Nr-L+1) . Furthermore, the same geometrical approach can be used to evaluate the diversity-multiplexing tradeoff curves for the considered spatial multiplexing systems with transmit antenna selection.

cs.IT↗