Exact Velocity Research Articles

Exact solution of a ratchet with switching sawtooth potential.

We consider the flashing potential ratchet model with general asymmetric potential. Using Bloch functions, we derive equations which allow for the calculation of both the ratchet's flux and higher moments of distribution for rather general potentials. We indicate how to derive the optimal transition rates for maximal velocity of the ratchet. We calculate explicitly the exact velocity of a ratchet with simple sawtooth potential from the solution of a system of 8 linear algebraic equations. Using Bloch functions, we derive the equations for the ratchet with potentials changing periodically with time. We also consider the case of the ratchet with evolution with two different potentials acting for some random periods of time.

Limit analysis and homogenization of nanoporous materials with a general isotropic plastic matrix

In this paper, a closed-form expression of a macroscopic strength criterion for ductile nanoporous materials is established, by considering the local plastic behavior as dependent on all the three isotropic stress invariants and by referring to the case of axisymmetric strain-rate boundary conditions. The proposed criterion also predicts void-size effects on macroscopic strength properties. A homogenization procedure based on a kinematic limit-analysis is performed by addressing a hollow-sphere model comprising a rigid-ideal-plastic solid matrix. Void-size effects are accounted for by introducing an imperfect-coherent interface at the cavity boundary. Both the interface and the solid matrix are assumed to obey to a general isotropic yield function, whose parametric form allows for a significant flexibility in describing effects induced by both stress triaxiality and stress Lode angle. Taking advantage of analytical expressions recently provided by Brach et al. [Int J Plasticity 2017; 89: 1–28] for the corresponding support function and for the exact velocity field under isotropic loadings, a parametric closed-form relationship for the macroscopic strength criterion is obtained as the solution of an inequality-constrained minimization problem, the latter being faced via the Lagrangian method combined with Karush-Kuhn-Tucker conditions. Finally, several comparative illustrations are provided, showing the influence of local-yield-function parameters on the established criterion, as well as the model capability to describe the macroscopic strengthening, typical of nanoporous materials, induced by a void-size reduction for a fixed porosity level.

Specific Material Removal Rate Calculation in Five-Axis Grinding

Specific material removal rate (MRR) q′ was calculated for five-axis grinding in a virtual machining simulation environment (VMSE). The axis-symmetric tool rotational profile was arc-length parameterized. The twisted grazing curve due to the concurrent translation and rotation in every move was modeled through an exact velocity field and areal MRR density q″, positive in the front of the grazing curve on the tool surface. Variation of q′ and equivalent chip thickness h within the instantaneous engagement contour were deduced from q″. Illustrative results with a five-axis impeller blade finishing simulation are shown. The results were benchmarked against an average q′ calculated from the instantaneous MRR from the VMSE. As a function of time, maximum chip thickness hmax within the extents of contact along the tool profile in every move showed more isolated peaks than corresponding qmax′. Maximum cumulative material removed per unit length Qmax′ along the tool profile from all the moves was calculated to predict axial location of maximum risk of cutter degradation. Qmax′ and hmax are useful metrics for tool path diagnosis and tool wear analysis.

Thermal efficiency enhancement of the direct contact membrane distillation: Conductive layer integration and geometrical undulation

The roles of high conductive layer integration and geometry undulation are investigated in order to improve the performance of the direct contact membrane distillation processes. In particular, the temperature polarization coefficient, mass flux and thermal efficiency are evaluated for the baseline and undulated flow under integrated superconductive layer membrane. This work caters for experimental and numerical model development. Experimentally, a countercurrent flow module for the desalination of sea water was developed using a flat-sheet electro-spun Polyvinylidene fluoride membrane generated and characterized by the author’s group for model validation. A steady state, conjugated heat, Navier-Stokes flow model computational fluid dynamics model was developed and subjected to the exact thermal and velocity flow conditions. The setup comprises two adjacent channel flows representing the hot saline feed and the cold fresh permeate channels. The two channels are thermally coupled through the hydrophobic membrane that is equipped with superconductive feathering layers. The results show agreement between the numerical model and experimental model measurements for the surface temperature distribution and the inferred temperature polarization co-efficient. In view of these plausible results and in line with numerous works on direct contact membrane distillation, a combined Knudsen and Poiseuille flow model is integrated to estimate the permeated mass and heat flux and explore improving the Membrane Distillation system in terms of thermal efficiency. While the role of superconductive feathering showed insignificant improvement in the temperature polarization coefficient, mass flux and thermal efficiency, the effect of combined undulated channels geometry was more pronounced. The gain obtained in the mass flux reaches 5.8% at lower feed temperature (50 °C), which is associated with a 5.8% gain in thermal efficiency and a 9.5% gain in temperature polarization co-efficient. It reaches a 6.1% gain in mass flux and thermal efficiency and a 9.5% gain for temperature polarization co-efficient at a higher feed inlet temperature.

Free Carrier Front Induced Indirect Photonic Transitions: A New Paradigm for Frequency Manipulation on Chip

Nonlinear degenerate four wave mixing and cross phase modulation are established approaches for all optical frequency manipulation in a silicon chip. These approaches require exact group velocity and/or phase velocity matching of pump, signal, and idler. On the other hand, several experimental demonstrations were presented recently, where frequency of light was changed by a free carrier front propagating in a silicon waveguide. This Doppler-like effect is less known, but has important advantages for frequency manipulation on chip. It requires no phase velocity matching and is not dependent on the shape and duration of the pump pulse. It also allows packet switching and can operate in a pump power independent regime. Here, we shortly review the work on front induced indirect transitions in silicon slow light waveguides. We consider three possible interaction regimes: transmission through the front, reflection from the front, and moving with the front called surfing. We derive analytical equations for the f...

An Explicit Method for Analysis of Three-Dimensional Linear and Angular Velocity of a Joint, with Specific Application to the Knee Joint

Velocity analysis in a joint is a major area of interest in research involving the dynamics of joints and in diagnosing and monitoring the progression of some diseases such as osteoarthritis. In this study, we provide a general analytical method to determine three-dimensional linear and angular velocity of a joint. The formulations presented are explicit, having neither the limitations of numerical methods nor the necessity of simplifying the joint to a hinge or spherical (ball and socket) joint. In addition to conventional analysis of joint kinematics where only the position and orientation of the joint is considered, velocity analysis provides more information regarding the dynamics of the joint. The methodology presented is a systematic approach and can be used for various joints. As an example, a formulation to measure the velocity of the tibiofemoral component of a knee joint is presented, in terms of clinical rotations by using a joint coordinate system. The method is used to examine the in vivo velocity formulations in five ovine stifle (knee) joints by using joint kinematic data measured with an instrumented spatial linkage. The results demonstrate that the classical hinge model of the knee joint cannot predict the exact three-dimensional velocity of the knee joint through the gait cycle for all subjects.

Multiscale hybrid-mixed method for the Stokes and Brinkman equations—The method

The multiscale hybrid-mixed (MHM) method is extended to the Stokes and Brinkman equations with highly heterogeneous coefficients. The approach is constructive. We first propose an equivalent dual-hybrid formulation of the original problem using a coarse partition of the heterogeneous domain. Faces may be not aligned with jumps in the data. Then, the exact velocity and the pressure are characterized as the solution of a global face problem and the solutions of local independent Stokes (or Brinkman) problems at the continuous level. Owing to this decomposition, the one-level MHM method stems from the standard Galerkin approach for the Lagrange multiplier space. Basis functions are responsible for upscaling the unresolved scales of the medium into the global formulation. They are the exact solution of the local problems with prescribed Neumann boundary conditions on faces driven by the Lagrange multipliers. We make the MHM method effective by adopting the unusual stabilized finite element method to solve the local problems approximately. As such, equal-order interpolation turns out to be an option for the velocity, the pressure and the Lagrange multipliers. The numerical solutions share the important properties of the continuum, such as local equilibrium with respect to external forces and local mass conservation. Several academic and highly heterogeneous tests infer that the method achieves super-convergence for the velocity as well optimal convergence for the pressure and also for the stress tensor in their natural norms.

Analysis of the Velocity and Current Measurement Method Based on B-Dot Probes for the Rail Gun

Measuring the velocity and displacement of the armature and current for a rail gun is important. The common method uses B-dot probes to acquire the discrete time points when the armature passes by them. These points can be interpolated into a curve of the armature’s displacement. Actually, the common interpolation method has some disadvantages. Some probes may break down, and the interpolation method is regardless of the process between the discrete points. So it is difficult to get the armature’s position at any time and the exact velocity at any position. Aiming at these disadvantages, this paper presents an improved method, which based on both B-dot points and the main current waveform. A B-dot probe beside the rails easily gives this waveform. The shape of the current waveform helps us to fit the curve with enough physical information. The new method can give a more precise velocity of the armature at an arbitrary position between two B-dot probes’ positions. It is also practical outside of two B-dot probes’ positions too. And it still works when some B-dot probes fail. Moreover, the current waveform with the adjusted amplitude is also calculated out. The launching experimental results and currents measured by Rogowski coils show that the improved method is highly suited for the velocity and current measurement for a rail-gun system.

Low‐dispersive FDTD on hexagon revisited

A new correctional low-dispersive finite-difference time-domain (FDTD) method based on hexagonal lattices (CH-FDTD) is introduced. The proposed method adopts scaling factor for the permittivity and permeability, which can generate nearly the exact phase velocity for a single frequency. Compared to the conventional FDTD method based on hexagonal lattices (H-FDTD) and rectangular lattices (Yee-FDTD), the numerical dispersion of the new method is significantly reduced.

Divergence Compensatory Optical Flow Method for Blood Velocimetry

Detailed blood velocity map in the vascular system can be obtained by applying the optical flow method (OFM) in processing fluoroscopic digital subtracted catheter angiographic images; however, there are still challenges with the accuracy of this method. In the present study, a divergence compensatory optical flow method (DC-OFM), in which a nonzero divergence of velocity is assumed due to the finite resolution of the image, was explored and applied to the digital subtraction angiography (DSA) images of blood flow. The objective of this study is to examine the applicability and evaluate the accuracy of DC-OFM in assessing the blood flow velocity in vessels. First, an Oseen vortex flow was simulated on the standard particle image to generate an image pair. Then, the DC-OFM was applied on the particle image pair to recover the velocity field for validation. Second, DSA images of intracranial arteries were used to examine the accuracy of the current method. For each set of images, the first image is the in vivo DSA image, and the second image is generated by superimposing a given flow field. The recovered velocity map by DC-OFM agrees well with the exact velocity for both the particle images and the angiographic images. In comparison with the traditional OFM, the present method can provide more accurate velocity estimation. The accuracy of the velocity estimation can also be improved by implementing preprocess techniques including image intensification, Gaussian filtering, and "image-shift."

Identification of Accretion as Grain Growth Mechanism in Astrophysically Relevant Water–Ice Dusty Plasma Experiment

Abstract The grain growth process in the Caltech water–ice dusty plasma experiment has been studied using a high-speed camera and a long-distance microscope lens. It is observed that (i) the ice grain number density decreases fourfold as the average grain major axis increases from 20 to 80 μm, (ii) the major axis length has a log-normal distribution rather than a power-law dependence, and (iii) no collisions between ice grains are apparent. The grains have a large negative charge resulting in strong mutual repulsion and this, combined with the fractal character of the ice grains, prevents them from agglomerating. In order for the grain kinetic energy to be sufficiently small to prevent collisions between ice grains, the volumetric packing factor (i.e., ratio of the actual volume to the volume of a circumscribing ellipsoid) of the ice grains must be less than ∼0.1 depending on the exact relative velocity of the grains in question. Thus, it is concluded that direct accretion of water molecules is very likely to dominate the observed ice grain growth.

Numerical modelling of melting and settling of an encapsulated PCM using variable viscosity

Thermal energy storage units using macro-encapsulated PCM in industrial and residential applications are contemporary due to better efficiency during charging and discharging. This article focuses on numerical modelling of the melting process in a macro-encapsulated PCM. Accounting the non-linear enthalpy–temperature relation and ramping down the velocity in solid phase is therefore fundamental. In the present article the variable viscosity method is implemented to ramp down the solid velocity and allow settling of the solid phase. This complete numerical model of melting and settling of PCM in a capsule is implemented in OpenFOAM. The numerical results for different solid viscosities are validated with experiments and show good agreement. The influence of the solid viscosity value and the pressure–velocity convergence is studied. It is observed that the pressure–velocity convergence only plays a greater role in the case where the computation of the exact solid velocity is required.

Second Harmonic Generation of Lamb Wave in Numerical Perspective**Supported by the National Natural Science Foundation of China under Grant Nos 51325504, 11474093, 11622430 and 11474361, the National Key Research and Development Program of China (2016YFC0801903-02), and the Fundamental Research Funds for the Central Universities.

The influences of phase and group velocity matching on cumulative second harmonic generation of Lamb waves are investigated in numerical perspective. Finite element simulations of nonlinear Lamb wave propagation are performed for Lamb wave mode pairs with exact and approximate phase velocity matching, with and without group velocity matching, respectively. The evolution of time-domain second harmonic Lamb waves is analyzed with the propagation distance. The amplitudes of primary and second harmonic waves are calculated to characterize the acoustic nonlinearity. The results verify that phase velocity matching is necessary for generation of the cumulative second harmonic Lamb wave in numerical perspective, while group velocity matching is demonstrated to not be a necessary condition.

Modified reconstruction algorithm based on space-time adaptive processing for multichannel synthetic aperture radar systems in azimuth

A spectrum reconstruction algorithm based on space–time adaptive processing (STAP) can effectively suppress azimuth ambiguity for multichannel synthetic aperture radar (SAR) systems in azimuth. However, the traditional STAP-based reconstruction approach has to estimate the covariance matrix and calculate matrix inversion (MI) for each Doppler frequency bin, which will result in a very large computational load. In addition, the traditional STAP-based approach has to know the exact platform velocity, pulse repetition frequency, and array configuration. Errors involving these parameters will significantly degrade the performance of ambiguity suppression. A modified STAP-based approach to solve these problems is presented. The traditional array steering vectors and corresponding covariance matrices are Doppler-variant in the range-Doppler domain. After preprocessing by a proposed phase compensation method, they would be independent of Doppler bins. Therefore, the modified STAP-based approach needs to estimate the covariance matrix and calculate MI only once. The computation load could be greatly reduced. Moreover, by combining the reconstruction method and a proposed adaptive parameter estimation method, the modified method is able to successfully achieve multichannel SAR signal reconstruction and suppress azimuth ambiguity without knowing the above parameters. Theoretical analysis and experiments showed the simplicity and efficiency of the proposed methods.

Structural and vibration analysis considering the flow velocity of the heat exchanger

This study is about the heat exchanger which is serpentine type with rectangular shell. A few heat exchangers have vibration problems caused by velocity of flow, piping vibration and Karman vortex. The cracks occur on pipe wall and Heat exchanger is damaged. Vibration analysis is conducted to prevent pipe damage during the design. But the other problems are caused after analysis of vibration. It is essential to estimate exact velocity value in order to predict the effect of flow induced vibration and heat transfer characteristic. Therefore in this paper, the vibration and static analysis have been measured and analyses for pipes and curve. Also modal test is conducted for analysis of natural frequency and methodology for the velocity prediction. By comparison between the hot testing and analysis results, the 1D calculation could be verified its reliability. It is necessary to optimally designed to avoid resonance by changing the diameter of the flow velocity of the change and piping, when the resonance avoidance cannot be avoided, be advanced design in the direction of reducing the amplitude such as through reinforcement work of the high contribution part shall.

Method Comparison of Model Based Tomography and Grid Based Tomography to refine interval velocity

<span>The input data for pre stack time migration and pre stack depth migration is velocity model. <span>The exact velocity model can provide maximum result in seismic section. The best seismic <span>section can minimize possibility of errors during interpretation. Model based and grid based <span>tomography are used to refine the interval velocity model. The interval velocity will be used as <span>input in the pre stack depth migration. Initial interval velocity is obtained from RMS velocity<br /><span>using Dix formula. This velocity will be refined by global depth tomography method. The <span>global depth tomography method is divided into model based and grid based tomography. <span>Velocity analysis is performed along the horizon (depth model). Residual depth move out is <span>obtained from picking velocity. It is used as input in tomography method. The flat gather is <span>obtained at tenth iteration. The interval velocity that is obtained from tenth iteration has the <span>small errors. Tomography method can provide maximum result on velocity refinement. That is <span>shown by the result that the pre stack depth migration is much better than using initial interval <span>velocity. The pull up effect can be corrected by tomography method.</span></span></span></span></span></span></span></span></span></span></span></span><br /></span>

Regularized image system for Stokes flow outside a solid sphere

The image system for a three-dimensional flow generated by regularized forces outside a solid sphere is formulated and implemented as an extension of the method of regularized Stokeslets. The method is based on replacing a point force given by a delta distribution with a smooth localized function and deriving the exact velocity field produced by the forcing. In order to satisfy zero-flow boundary conditions at a solid sphere, the image system for singular Stokeslets is generalized to give exact cancellation of the regularized flow at the surface of the sphere. The regularized image system contains the same elements as the singular counterpart but with coefficients that depend on a regularization parameter. As this parameter vanishes, the expressions reduce to the image system of the singular Stokeslet. The expression relating force and velocity can be inverted to compute the forces that generate a given velocity boundary condition elsewhere in the flow. We present several examples within the context of biological flows at the microscale in order to validate and highlight the usefulness of the image system in computations.

Velocity calibration for microseismic event location using surface data

Because surface-based monitoring of hydraulic fracturing is not restricted by borehole geometry or the difficulties in maintaining subsurface equipment, it is becoming an increasingly common part of microseismic monitoring. The ability to determine an accurate velocity model for the monitored area directly affects the accuracy of microseismic event locations. However, velocity model calibration for location with surface instruments is difficult for several reasons: well log measurements are often inaccurate or incomplete, yielding intractable models; origin times of perforation shots are not always accurate; and the non-uniqueness of velocity models obtained by inversion becomes especially problematic when only perforation shots are used. In this paper, we propose a new approach to overcome these limitations. We establish an initial velocity model from well logging data, and then use the root mean square (RMS) error of double-difference arrival times as a proxy measure for the misfit between the well log velocity model and the true velocity structure of the medium. Double-difference RMS errors are reduced by using a very fast simulated annealing for model perturbance, and a sample set of double-difference RMS errors is then selected to determine an empirical threshold. This threshold value is set near the minimum RMS of the selected samples, and an appropriate number of travel times within the threshold range are chosen. The corresponding velocity models are then used to relocate the perforation-shot. We use the velocity model with the smallest relative location errors as the basis for microseismic location. Numerical analysis with exact input velocity models shows that although large differences exist between the calculated and true velocity models, perforation shots can still be located to their actual positions with the proposed technique; the location inaccuracy of the perforation is <2 m. Further tests on field data demonstrate the validity of this technique.

An Exact Rescaling Velocity Method for some Kinetic Flocking Models

In this work, we discuss kinetic descriptions of flocking models, of the so-called Cucker-Smale and Motsch-Tadmor types. These models are given by Vlasov-type equations where the interactions taken into account are only given long-range bi-particles interaction potential. We introduce a new exact rescaling velocity method, inspired by a recent work of Filbet and Rey, allowing to observe numerically the flocking behavior of the solutions to these equations, without a need of remeshing or taking a very fine grid in the velocity space. To stabilize the exact method, we also introduce a modification of the classical upwind finite volume scheme which preserves the physical properties of the solution, such as momentum conservation.

Eddy current sensor based velocity and distance estimation in rail vehicles

The precise localisation of rail vehicles is fundamental to the development and employment of more efficient train control systems in security, logistics and disposition applications. A key element of this is the exact and reliable velocity and distance estimation. The popular satellite navigation (global navigation satellite systems) and visual odometry, based on optical systems, tend to fail in the rough environment of rail application scenarios. This study describes an approach to making a precise distance estimate using an innovative eddy current sensor system. This is achieved through the combination of an augmented cross-correlation approach to highly accurate velocity estimation. That is subsequently employed to determine the travelled distance based on counting rail clamps in a spatial transformed space. This approach relies on recursive state estimation of the dynamic states and a statistical assessment of the counted rail clamps for the purpose of outlier rejection. The proposed methods are compared and evaluated in a quantitative way on the basis of experimental data. The results prove that the proposed approach can improve the accuracy and reliability of velocity measurement and relative position detection.