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The lattice Boltzmann-immersed boundary (IB-LB) method is used to numerically simulate the sedimentation motion of a single two-dimensional, bottom-heavy squirmer in a narrow vessel. The effects of the swimming Reynolds number Re

Additional file 1. Fig. S1: Identification of CRISPR/Cas9-STK rice mutant plants. Fig. S2: Characterization of STK overexpressionplants. Fig. S3: Relative expression levels of four previously known stress-related genes up-regulated in STK-OE pants and down-regulated in STK-KO plants at 48 h under salt stress condition in rice seedlings. Fig. S4: Relative expression levels of OsSAPK10 in leaves of wild-type, STK-OE and STK-KO plants under salt stress condition.

Additional file 2. Table S1: List of primers used in this study. Table S2: Differential expression data of stress-related in the STK-OE plants.

Objective: Multi-shot interleaved echo planer imaging can obtain diffusion-weighted images (DWI) with high spatial resolution and low distortion, but suffers from ghost artifacts introduced by phase variations between shots. In this work, we aim at solving the challenging reconstructions under inter-shot motions between shots and a low signal-to-noise ratio. Methods: An explicit phase model with paired phase and magnitude priors is proposed to regularize the reconstruction (PAIR). The former prior is derived from the smoothness of the shot phase and enforced with low-rankness in the k-space domain. The latter explores similar edges among multi-b-value and multi-direction DWI with weighted total variation in the image domain. Results: Extensive simulation and in vivo results show that PAIR can remove ghost artifacts very well under a high number of shots (8 shots) and significantly suppress the noise under the ultra-high b-value (4000 s/mm2). Conclusion: The explicit phase model PAIR with complementary priors has a good performance on challenging reconstructions under inter-shot motions between shots and a low signal-to-noise ratio. Significance: PAIR has great potential in advanced clinical DWI applications and brain function research., Comment: 12 pages, 14 figures

Efficient collaboration between engineers and radiologists is important for image reconstruction algorithm development and image quality evaluation in magnetic resonance imaging (MRI). Here, we develop CloudBrain-ReconAI, an online cloud computing platform, for algorithm deployment, fast and blind reader study. This platform supports online image reconstruction using state-of-the-art artificial intelligence and compressed sensing algorithms with applications to fast imaging and high-resolution diffusion imaging. Through visiting the website, radiologists can easily score and mark the images. Then, automatic statistical analysis will be provided. CloudBrain-ReconAI is now open accessed at https://csrc.xmu.edu.cn/CloudBrain.html and will be continually improved to serve the MRI research community., Comment: 8 pages, 11 figures

Recent deep learning is superior in providing high-quality images and ultra-fast reconstructions in accelerated magnetic resonance imaging (MRI). Faithful coil sensitivity estimation is vital for MRI reconstruction. However, most deep learning methods still rely on pre-estimated sensitivity maps and ignore their inaccuracy, resulting in the significant quality degradation of reconstructed images. In this work, we propose a Joint Deep Sensitivity estimation and Image reconstruction network, called JDSI. During the image artifacts removal, it gradually provides more faithful sensitivity maps, leading to greatly improved image reconstructions. To understand the behavior of the network, the mutual promotion of sensitivity estimation and image reconstruction is revealed through the visualization of network intermediate results. Results on in vivo datasets and radiologist reader study demonstrate that, the proposed JDSI achieves the state-of-the-art performance visually and quantitatively, especially when the accelerated factor is high. Additionally, JDSI owns nice robustness to abnormal subjects and different number of autocalibration signals., Comment: 10 pages, 8 figures, 3 tables

Floral initiation is regulated by various genetic pathways in response to light, temperature, hormones and developmental status; however, the molecular mechanisms underlying the interactions between different genetic pathways are not fully understood. Here, we show that the photoresponsive gene FOF2 (F-box of flowering 2) negatively regulates flowering. FOF2 encodes a putative F-box protein that interacts specifically with ASK14, and its overexpression results in later flowering under both long-day and short-day photoperiods. Conversely, transgenic plants expressing the F-box domain deletion mutant of FOF2 (FOF2ΔF), or double loss of function mutant of FOF2 and FOL1 (FOF2-LIKE 1) present early flowering phenotypes. The late flowering phenotype of the FOF2 overexpression lines is suppressed by the flc-3 loss-of-function mutation. Furthermore, FOF2 mRNA expression is regulated by autonomous pathway gene FCA, and the repressive effect of FOF2 in flowering can be overcome by vernalization. Interestingly, FOF2 expression is regulated by light. The protein level of FOF2 accumulates in response to light, whereas it is degraded under dark conditions via the 26S proteasome pathway. Our findings suggest a possible mechanistic link between light conditions and the autonomous floral promotion pathway in Arabidopsis.

Lattice Boltzmann method is used to simulate numerically the fiber suspension flow through a parallel plate channel containing a cylinder in the dilute and concentrated regimes (nL2 = 0.125 and 2.0, here n and L are the number density and the length of fiber, respectively). The numerical results of fiber orientation distribution based on a statistical scheme are obtained and consistent qualitatively with the experimental ones. The results showed that the cylinder in the channel results in a change in the fiber orientation distribution downstream of the cylinder along the flow and transverse directions. The influences of the cylinder on the fiber orientation distribution are more significant for the concentrated suspensions than the dilute ones. The initial fiber orientations at inlet have significant and small effects on the fiber orientation distribution upstream and downstream of the cylinder, respectively.

A weakly non-linear stability analysis of two phase flow in the Blasius boundary layer has been carried out. Two mathematical models have been established based on the perturbation shape preserved assumption and linear stability model of two phase flow proposed by Stuart [On the non-linear mechanics of hydrodynamic stability, J. Fluid Mech. 4 (1958) 1–21] and Saffman [On the stability of laminar flow of dusty gas, J. Fluid Mech. 13 (1962) 120–128], respectively. The perturbation model and the perturbation energy balance equation are solved numerically with Chebyshev spectral method and artificial boundary condition. The numerical program adopted in the present study is verified by comparison with former works. The results show that the non-linear interaction between mean flow and perturbation reduces the growth rate of perturbation, while the non-linear interaction between particle phase and gas phase increases the growth rate of perturbation amplitude. The distortion of the mean flow caused by the Reynolds stress modifies the rate of transfer of energy from the mean flow to disturbance. The existence of particle alleviates the distortedness. The result also indicates that the weakly non-linear stability theory is consistent to linear stability theory, and the addition of fine and coarse particles reduces and increases the critical Reynolds number.

The collision efficiency in the Brownian coagulation is investigated. A new mechanical model of collision between two identical spherical particles is proposed, and a set of corresponding collision equations is established. The equations are solved numerically, thereby obtaining the collision efficiency for the monodisperse dioctyl phthalate spherical aerosols with diameters ranging from 100 to 760 nm in the presence of van der Waals force and the elastic deformation force. The calculated collision efficiency, in agreement with the experimental data qualitatively, decreases with the increase of particle diameter except a small peak appearing in the particles with a diameter of 510 nm. The results show that the interparticle elastic deformation force cannot be neglected in the computation of particle Brownian coagulation. Finally, a set of new expressions relating collision efficiency to particle diameter is established.

Motion of fibres in sheared fibre suspensions is simulated numerically by using the lattice Boltzmann method. The orientational distributions of the fibres are presented for different Reynolds numbers, Stokes numbers, shear rate and fibre aspect ratio. Some computational results are compared with the experimental data of pipe flow, and the qualitative agreement is achieved. The results show that the orientational distributions are greatly affected by the Reynolds numbers, while relatively insensitive to the fibre aspect ratio. The Stokes number and shear rate have obvious influence on the orientation distribution.

The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investigated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model are solved for the mean flow field and the turbulent kinetic energy. The fluctuating velocities of the fluid are assumed as a random variable with Gaussian distribution whose variance is related to the turbulent kinetic energy. The slender-body theory is used to simulate the fiber motion based on the known mean and fluctuating velocities of the fluid. The results show that at low Reynolds number, fiber concentration is high in the flow separation regions, and fiber orientation throughout the channel is widely distributed with a slight preference of aligning along the horizontal axis. With increasing of Re, the high concentration region disappears, and fiber orientation becomes homogeneous without any preferred direction. At high Reynolds number, fiber concentration increases gradually along the flow direction. The differences in the distribution of concentration and orientation between different fiber aspect ratio are evident only at low Re. Both Re and fiber aspect ratio have small effect on the variance of orientation angle.

The mixing of samples in heterogeneous microchannels with a periodically stepwise surface potential was analyzed numerically using the control volume method. The equation describing the wall potential and external potential were solved first to get the distribution of wall potential and external potential, respectively, then the momentum equation was solved to get the developed flow field. Finally, the mass transport equation was solved to get the concentration field. The simulation results show that the distribution of samples at the inlet of the microchannels determines its theoretical value of concentration of solute. The heterogeneous wall potential almost has no effect on the mixing of samples in two-inlet microfluidic devices. For three-inlet mocrofluidic devices, the comprehensive ability of transportation and mixing has an optimization when the ratio of periodic length of wall potential to the height of the mocrochannel is about 4.88. The above conclusion are helpful to the optimization o...

Numerical simulation using the finite differential method was carried out to analyze the diffusion of an impulse sample in the micro-channel driven by electroosmosis. The results show that the electrical field strength applied externally and the concentration of buffer solution play a significant role in the diffusion of sample, however, hydraulic diameter and aspect ratio of height to width of channel play a small role in it. Weakening the electrical field strength applied externally and the concentration of buffer solution properly can prevent the sample band from broadening effectively, and promote the efficiency of testing and separation as well as keep a faster speed of transport. The conclusions are helpful to the optimal design for micro-channel.

The equation for the orientation probability function of slender cylindrical particles suspended in planar turbulent flows was investigated. After ensemble averaging' the equations for the mean and fluctuating probability functin were derived. The equation for the fluctuating probability function appearing in the equation of mean probability function were derived. The equation for the fluctuating probability function appearing in the equation of mean probability function was solved by using rthe method of characteristics analyisis. The orientational dispersion terms due to the random motion of cylindrical particles in the equation of mean probability function are related to the mean probability function and the Larangian fluid velocity correlations. The evolution of the mean probability function was described by amodified orientation-space-convectin equation' where the dispersion terms account for the randomizing effect of the turbulence. Supported by National Natural Science Foundation of China ...

The orientation and concentration distributions of fibres in laminar and turbulent channel flows are investigated numerically. The obtained results are in good agreement with the experimental data. In the laminar flow regime, more fibres orient to the flow direction as the Reynolds number increases. The shear rate of fluid around a fibre plays an important role in determining the orientation distribution of fibres, while the fibre density and the fibre aspect-ratio have marginal influence on the orientation distribution. In the turbulent regime, the orientation distribution of fibres becomes more homogeneous with the increase of Reynolds number and the concentration profile is flatter than that in the laminar regime. The fluctuating intensity of fibre velocity in the downstream direction is larger than that in the lateral directions.

The equation of probability distribution function for mean fibre orientation in a turbulent boundary layer is derived, in which the correlation terms of the fluctuating velocity, fluctuating angular velocity with the fluctuating probability distribution function are related to the gradient of mean probability distribution function and the dispersion coefficients in order to make the equation be solvable. The finite-difference method is used to solve the equation numerically. The results show that the fibres tend to align with the streamline, which is in agreement qualitatively with the experimental result given by visualization. The fibre aspect-ratio has a significant effect on the orientation distribution of fibres, while the effect of the distance from the wall is negligible.

The mechanism of dispersion induced by turn in the capillary electrophoresis channel flows was analyzed firstly. Then the mathematical model of electroosmotic flow is built, and the dispersion of the flow, with different distribution of charge at inner and outer wall in the turns, was simulated numerically using the finite differential method. A new approach of altering the distribution of charge at inner and outer wall in the turns was presented, based on the computational results, to minimize the dispersion induced by turn. Meanwhile, an optimization algorithm to analyze the numerical results and determine the optimal distribution of charge in the turns was also developed. It is found that the dispersion induced by turn in the capillary electrophoresis channel flows could be significantly suppressed by this approach.

The Navier-Stokes equation was used to describe the characteristics of electro-osmotic flow. The corresponding numerical simulations were performed for varying zeta-potential and dimension. The results indicated that a step change in zeta-potential will cause a significant variation in the velocity profile and pressure distribution of the flow. A step change both in zeta-potential and dimension will result in a more violent variation near the joint of the capillary. This variation will reduce the separation efficiency and quality of capillary electrophoresis. The conclusions are helpful to design and fabrication of microfluidic devices, the analysis of data collected from such devices and improvement of the separation efficiency of capillary electrophoresis.

The mean motion equation of turbulent fibre suspensions and the equation of probability distribution function for mean fibre orientation are derived. The successive iteration for calculating the mean orientation distribution of fibres and the mean and fluctuation-correlated quantities of suspensions is presented. The equations and their solutions are applied to a turbulent pipe flow of fibre suspensions and a corresponding experiment is performed. It is found that the theoretical and experimental results are in good agreement with each other. The obtained results for turbulent pipe flow of fibre suspensions show that the flow rate of fibre suspensions is large under the same pressure drop in comparison with the rate of Newtonian flow in the absence of fibre suspensions. Fibres play an important role in reducing the flow drag. The amount of reduction in drag augments with the increase of the concentration of the fibre mass. The relative turbulent intensity and Reynolds stress in the fibre suspensions are smaller than those in the Newtonian flow under the same condition, which illustrates that the fibres have an influence on suppressing the turbulence. The amount of suppression is directly proportional to the concentration of the fibre mass.

A collision model of two cylindrical particles is put forward. Based on the model the sedimentation of rigid cylindrical particles with mechanical contacts is simulated numerically by using the lattice Boltzmann method. Some numerical results are compared with the experimental ones given by us and others, and good agreements are found. In the sedimentation process, particles will rotate and drift at any initial orientation and terminal Reynolds number. The orientation, lateral position, drifty and sedimenting velocity of particles change periodically at small terminal Reynolds number. With the increasing terminal Reynolds number, the periodicity disappears, and an inverted T-structure forms. This structure appears more quickly and lasts for a longer time at larger terminal Reynolds number.

The motion of fibers in turbulent pipe flow was simulated by 3-D integral method based on the slender body theory and simplified model of turbulence. The orientation distribution of fibers in the computational area for different Re numbers was computed. The results which were consistent with the experimental ones show that the fluctuation velocity of turbulence cause fibers to orient randomly. The orientation distributions become broader as the Re number increases. Then the fluctuation velocity and angular velocity of fibers were obtained. Both are affected by the fluctuation velocity of turbulence. The fluctuation velocity intensity of fiber is stronger at longitudinal than at lateral, while it was opposite for the fluctuation angular velocity intensity of fibers. Finally, the spatial distribution of fiber was given. It is obvious that the fiber dispersion is strenghened with the increase of Re numbers.

A linear stability analysis of channel flow in the presence of fiber suspensions is performed. Based on slender-body theory, a modified stability equation is derived by using the natural closure approximation to determine the fiber orientation. It is found that the flow instability of fiber suspensions is governed by two parameters: H, a ratio between the axial stretching resistance of fibers and the inertial force of the fluid, and the orientational diffusivity coefficient CI that accounts for inter-fiber hydrodynamic interactions. The increment of either parameter causes an increase of critical Reynolds number, a reduction of the maximum disturbance growth rate and a shift of the peak value of velocity disturbances away from the walls. Hence, the fiber additives effectively attenuate the instability of the flow. The orientation distribution state of fibers in the flow is also examined, and the influence of parameters is determined. An investigation of different terms in the vorticity disturbance equation and an enstrophy-based energy analysis reveal the sources of disturbance energy and the mechanisms behind the instability of fiber suspensions. Finally, an experiment is performed using the visualization technique. The comparative measurements of stable lengths in every type of flow show that fiber additives have a stabilizing effect on the flow, and this effect is clearer for higher values of Re. The conclusions of experiment are in agreement with those of linear instability analysis.

The spatial and orientational distributions of fibers in laminar and turbulent pipe flows are simulated numerically. The simulated results are consistent with the experimental data available in the literature. In the laminar flow regime, more fibers are aligned with the flow direction with increasing Reynolds number. The shear rate of fluid around a fiber is the key factor for determining the orientation distribution of fibers. The fibers aspect ratio and fiber density have insignificant influence, while the fiber velocity and the fiber Stokes number have marginal influence, on the orientation distribution of fibers. In the turbulent regime, the spatial and orientational distributions become more homogeneous with increasing Reynolds number, and the fluctuation intensity of fiber velocity in the streamwise direction is larger than that in the other two directions, in contrast to the fluctuation intensity of the fiber angular velocity, which is weaker in the streamwise direction.

Lattice Boltzmann method is used to investigate sedimentation of a single fiber in a Newtonian fluid. The effects of the aspect ratio of a fiber are carefully examined. The computational results show that the stable orientation of a single fiber is the horizontal direction. The terminal Reynolds number increases as the aspect ratio increases, and basically remains invariable when the aspect ratio is high enough. The lateral drift of the fiber is more apparent at higher aspect ratios and the orientation of the fiber at which the lateral drifting velocity reaches the maximal is not sensitive to the value of the aspect ratio. When the aspect ratio is around 2.8, the fiber rotates fastest from the vertical location to the horizontal. Some of the results are compared with the experimental data and good agreements are found.

Based on the momentum and constitutive equations, the modified Orr-Sommerfeld equation describing the flow stability in a cylindrical particle two-phase flow was derived. For a cylindrical particle two-phase boundary layer, the neutral stability curves and critical Reynolds number were given with numerical simulation. The results show that the cylindrical particles have a suppression effect on the flow instability, the larger the particle volume fraction and the particle aspect-ratio are, the more obvious the suppression effect is.

The computed orientation distribution of fibers immersed in laminar pipe flows showed that the longitudinal distributions are wide for small Reynolds numbers and become narrower with increasingRe. For lowRe number, the axial orientation distributions are broad with almost no preferred orientations. For highRe number, the axial distribution becomes narrow, with sharp maxima. The mean values of the longitudinal orientation depend strongly on theRe number. The computed results are in qualitative agreement with relevant experimental results.

The orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated, and an application was taken in a wedge-shaped flow field. The relationship between the orientation distribution function and particle orientation angles was obtained. The results show that comparing with the most probable angle distribution which comes to being in short time, the distribution of the steady state doesn't vary much in range; the main difference is the anti-clockwise rotation in the right and upper field, that is, particles rotate more at the points where the velocity gradients are larger. The most probable orientations are close to the direction of local streamlines. In the direction of streamlines, with poleradius decreasing, the most probable angles increase, but the angles between their orientations and the local streamlines decrease.

The fluid fluctuating velocity equations which include the term of cylinder particles were established. The turbulent intensity and Reynolds stress of fluid were obtained by averaging fluctuating velocity based on the solution of the fluctuating velocity equations. Above approach was used to solve the channel turbulent flows, and computational results were compared with the experimental ones for the case of single phase flow. The effects of volume fraction of particles, the ratio of particle length to diameter and the particle relaxation time on turbulent properties were illustrated by changing cylinder particle parameters. It is shown that particles play a restraining role to turbulent properties in the flows. The degree of restraint is directly proportional to the volume fraction of particle, the ratio of particle length to diameter and inversely proportional to particle relaxation time.

In order to investigate the effects of injection position to drag reduction as well at further the effects of polymer additives on turbulent structures, LDA messurements of turbulent pipe flows were conducted. The amount of drag reduction grows with the increase of the Reynolds number, and injecting the polymer at the centre of pipe is more effective than at the wall. Due to the addition of polymer solution, the axial, radial r.m.s. velocity fluctuations and Reynolds stress decrease over the entire pipe cross-section, the time auto-correlation coefficients of axial and radial velocity fluctuation at the centre of pipe decay more slowly, the number of spectrum peaks is decreased, and the peak shifts towards lower wave numbers

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists.

The evolution of the coherent structures in a two-dimensional time-developing mixing layer of the FENE-P fluids is examined numerically. By the means of an appropriate filtering for the polymer stress, some characteristics of the coherent structures at high b were obtained, which Azaiez and Homsy did not address. The results indicate that adding polymer to the Newtonian fluids will cause stronger vorticity diffusion, accompanied with weaker fundamental and subharmonical perturbations and slower rotational motion of neighboring vortices during pairing. This effect decreases with the Weissenberg number, but increases with b. In addition, the time when the consecutive rollers are completely coalesced into one delays in the viscoelastic mixing layer compared with the Newtonian one of the same total viscosity.

The two-way coupling model was adopted to study the two-dimensional gas-solid mixing layer. The flow was simulated by pseudo-spectral method and particles were traced with Lagrangian method. It is found that the concentration and the Stokes number of the particles have distinct effect on the flow not only accounting for the influence of the flow on the particles, but also the particles' counteraction on the flow. The particles accelerate the dispersion of the vorticity and inhibit the variance of the flow and diminish the intensity of the coherent structure. The lifetime of the vortex is shortened. The pattern of particles' distribution is similar to the results from one-way coupling model.

The stability equation of interface of two-phase jet and the corresponding particle gas disturbance velocity ratio equation are derived by means of the phase-coupled model. The stability curves of interface of two-phase jet far different particle properties and the corresponding particle-gas disturbance velocity ratio curves are given out through numerical computation. Further, several important conclusions on effect of particle property on growth and propagation of disturbance of interface of two-phase jet and particle disturbance property are presented on the basis of analyses of the obtained stability curves and particle-gas disturbance velocity ratio curves. These important conclusions can play a guiding role in studying development of two-phase jet and executing artificial controls over it in project practice.

The Galerkin method is used to solve the diffusion equation of the distribution function for rigid rod-like polymers and the pseudo-spectral method is used to solve the momentum equation that includes the stress tensor determined by distribution function of polymers. The properties of the coherent structure in a two-dimensional time-developing viscoelastic mixing layer are given and the most probable orientations of the multibead rods as well as the stresses of polymers are obtained. The results indicate that adding polymers to the Newtonian fluid will result in a stronger vorticity diffusion, accompanied by weaker fundamental and subharmonic perturbations, less intense vortex roll-up of the mixing layer, lower oscillation frequency of fundamental energy, slower rotational motion of neighboring vortices and shorter life times of eddies. The results also show that the stretching of large eddies will have a great effect on the behavior of rod-like molecules, since the most probable orientations of rods seem to coincide with the local fluid stretching directions.

In this paper, the three-dimensional vortex filament method was used to simulate the evolution of vortex structures in the axisymmetric round jet. The results agree well with the ones given by Chung and Troutt. Then one-coupling model was employed to calculate the particle motion based on the computed flows. The results show that the particle motion is affected by flows obviously at the case of particle number St≪1 and negligibly at St≫1, particles distribute around the vortex structures uniformly at St ∼ 1. When perturbations with wavenumber 5 are introduced to vortex rings, particles disperse wider along radial direction, which conforms to the experimental results. The degree of particle dispersion is in the direct ratio to the amplitude of perturbation. The conclusions given in the paper are useful to the practice usage.

The evolution of the three-dimensional time-developing mixing layer is simulated numerically using the pseudo-spectral method. The initial perturbations used in this study consisted of the two-dimensional fundamental wave and the streamwise-invariant three-dimensional disturbance. A comparison of the formations of the streamwise vortices with different amplitude functions for three-dimensional disturbances is made. In one case the results are similar to that of Rogers & Moser[1], whereas a different way in which the quadrupole forms and sudden expansion of the rib are observed in another case. The simulation also confirms that the stretching by the forming roller rather than Rayleigh centrifugal instability is responsible for the formation of the rib. Finally, numerical flow visualization results are presented.

Self-similarity of power law velocity profile of a simulated atmospheric boundary layer is studied experimentally. The results demonstrate that the self-similarity maintains very well along the streamwise direction for the same rough surface but changes significantly with the surface roughness at the same position. The self-similarity of the vertical velocity profiles is affected by enhancement of the free stream velocity when the roughness concentration is relatively denser.

Numerical simulations have been performed in time-developing plane mixing layers of the viscoelastic second-order fluids with pseudo-spectral method. Roll-up, pairing and merging of large eldies were examined at high Reynolds numbers and low Deborah numbers. The effect of viscoelastics on the evolution of the large coherent structure was shown by making a comparison between the second-order and Newtonian fluids at the same Reynolds numbers.

By considering the effect of suspended solid particles in the ordinary equations for two-dimension inviscid incompressible mixing layer, the Rayleigh equation and the modified Rayleigh equation are obtained. And then, by solving the corresponding eigen-value equations with numerical computational method, the relation curves between perturbation frequency and spacial growth rate of the mixing layer for the varying particle loading, ratio of particle velocity to fluid velocity and Stokes number are got. Several important conclusions on the effect of suspended solid particles on unstability of the mixing layer are presented in the end by analyzing all the relation curves.

A necessary maximum principle is proved for optimal controls of stochastic systems driven by multidimensional Teugel's martingales. The multidimensional Teugel's martingales are constructed by orthogonalizing the multidimensional L\'{e}vy processes. The control domain need not be convex, and the control is allowed to enter into the terms of Teugel's martingales.

In this paper we show the existence and form uniqueness of a solution for multidimensional backward stochastic differential equations driven by a multidimensional L��vy process with moments of all orders. The results are important from a pure mathematical point of view as well as in the world of finance: an application to Clark-Ocone and Feynman-Kac formulas for multidimensional L��vy processes is presented. Moreover, the Feynman-Kac formula and the related partial differential integral equations provide an analogue of the famous Black-Scholes partial differential equation and thus can be used for the purpose of option pricing in a multidimensional L��vy market.

For a general Multidimensional L��vy process (satisfying some moment conditions), we introduce the Multidimensional power jump processes and the related Multidimensional Teugels martingales. Furthermore, we orthogonalize the Multidimensional Teugels martingales by applying Gram-Schmidt process. We give a chaotic representation for every square integral random variable in terms of these orthogonalized Multidimensional Teugels martingales. The predictable representation with respect to the same set of Multidimensional orthogonalized martingales of square integrable random variables and of square integrable martingales is an easy consequence of the chaotic representation.

The results of plane turbulent wake given by Chou Peiyuan[1] are considered as the first order approximation and put into the equations of turbulent fluctuation. The equations are solved numerically within the range of micro-scale by means of spectrum method. The double, triple and quadruple fluctuating velocity correlations are obtained by computation. They are in good agreement with experimental results.

The collision efficiency of nanoparticles with diameters from 100 nm to 750 nm in the Brownian coagulation is studied by building and solving numerically the equations of particle collision in the presence of the van der Waals force, the elastic deformation force, the Stokes resistance, the lubrication force and the electrostatic force. The results show that the collision efficiency decreases overall with the increasing particle diameter. It is found that there exists an abrupt increase in the collision efficiency when the particle diameter is equals to 550 nm. Finally a new expression for the collision efficiency is presented.

We present a study on the vortex structures and behavior of a flow past two rotating circular cylinders arranged side-by-side at a range of absolute rotational speeds (|α| ≤ 2) for two different gap spacings g* = 1.5 and 0.7 at Reynolds numbers Re = 160 and 200. The results show that the flow becomes stabilized and finally steady beyond the critical rotational speed as | α | increases, regardless of the variation in Re and g*. The value of critical rotational speed increases with increasing Re. The wake patterns change in the unsteady regimes for g* = 1.5 and 0.7. With increasing |α|, the time-averaged drag coefficient D decreases and the lift coefficient L increases, respectively. D at Re = 160 and g* = 0.7 decreases rapidly, resulting in the smallest value at the same |α| for 1 ≤ |α| ≤ 2. D augments with increasing g* at the same |α|. For g* = 1.5, D has a little disparity between the cases of Re = 160 and 200. For the flow past two still cylinders, L is inversely proportional to g* of two cylinders for a fixed |α|, and is not dependent on Re.

The flow properties in microtubes, such as velocity profiles and pressure distributions, are different from those in macrotubes. We attribute this phenomenon to the molecular interactions between the solid wall and inner liquid. The apparent viscosity, which takes into consideration the molecular interactions, is introduced in the present study and the Navier–Stokes equations are solved. Water is adopted in the calculation. For the hydrophilic material wall, the water is more like to adhere to the wall. The velocity near the wall is smaller than that of conventional theory, while the centerline velocity and pressure gradients are much larger. Such a phenomenon becomes much more obvious with the decrease in tube diameter.