Complicated Numerical Computation Research Articles

P.410 Searching for predictive validity in animal tests for mania-like behaviour

The precise and convenient calculation of bottom hole pressure can provide a guarantee for safe drilling. Most of the existing models for determining the downhole pressure or annular pressure gradient (PG) are applied only to the circular wellbore. Due to the nonuniform in situ stress and the anisotropism of formation rock, the borehole formed by rotary drilling is the closest to the ellipse, that is, the irregular circular borehole. Therefore, it is of importance to research YPL fluid flow through the eccentric elliptical annulus (EEA) for the accurate prediction of bottom hole pressure. In this paper, a numerical model for determining the PG of YPL fluid flow in the EEA is developed on the basis of fluid mechanics. Then, through parameter studies, a new regression model (RM) of the pressure ratio in the EEA is established. The commercial software ANSYS was used to research the laminar flow of yield-power-law fluids through the EEA, and the simulation results are used to verify the numerical model and new regression model. The main conclusions are as follows. (1) The PG increases quasi-linearly or linearly with the mean velocity, fluid consistency index and yield stress and hardly changes with the azimuth of the inner pipe center. The PG decreases with a/b (η) and eccentricity (ε) when the mean velocity is constant. (2) The new regression model is valid for the ranges 0.2≤Kd ≤ 0.8, 0≤ε ≤ 0.95, 0.2 ≤ n ≤ 1.0, and 1.0≤η ≤ 1.2 and shows excellent agreement with existing model and computational fluid dynamics (CFD) simulations, within ±5% error bars. (3) The maximum velocity first increases and then decreases with ε. The results of axial velocity and PG using CFD software are found to be in excellent agreement with the numerical model solutions. (4) Predicting the PG in the EEA using the new regression model has high precision and without complicated numerical computation.

Modeling of laminar flow in an eccentric elliptical annulus for YPL fluid

The precise and convenient calculation of bottom hole pressure can provide a guarantee for safe drilling. Most of the existing models for determining the downhole pressure or annular pressure gradient (PG) are applied only to the circular wellbore. Due to the nonuniform in situ stress and the anisotropism of formation rock, the borehole formed by rotary drilling is the closest to the ellipse, that is, the irregular circular borehole. Therefore, it is of importance to research YPL fluid flow through the eccentric elliptical annulus (EEA) for the accurate prediction of bottom hole pressure. In this paper, a numerical model for determining the PG of YPL fluid flow in the EEA is developed on the basis of fluid mechanics. Then, through parameter studies, a new regression model (RM) of the pressure ratio in the EEA is established. The commercial software ANSYS was used to research the laminar flow of yield-power-law fluids through the EEA, and the simulation results are used to verify the numerical model and new regression model. The main conclusions are as follows. (1) The PG increases quasi-linearly or linearly with the mean velocity, fluid consistency index and yield stress and hardly changes with the azimuth of the inner pipe center. The PG decreases with a/b (η) and eccentricity (ε) when the mean velocity is constant. (2) The new regression model is valid for the ranges 0.2≤Kd ≤ 0.8, 0≤ε ≤ 0.95, 0.2 ≤ n ≤ 1.0, and 1.0≤η ≤ 1.2 and shows excellent agreement with existing model and computational fluid dynamics (CFD) simulations, within ±5% error bars. (3) The maximum velocity first increases and then decreases with ε. The results of axial velocity and PG using CFD software are found to be in excellent agreement with the numerical model solutions. (4) Predicting the PG in the EEA using the new regression model has high precision and without complicated numerical computation.

Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

Considerations of nonlocal elasticity and surface effects in micro- and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions: hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short, explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.

Particle interactions in three-dimensional electrical field simulated by iterative dipole moment method

The dielectrophoresis (DEP) interactions of a few particles in a uniform two-dimensional (2D) electrical field have well been studied by Maxwell stress tensor (MST) method. Multiple particle interactions in three-dimensional (3D) electrical field are investigated in this work using iterative dipole moment (IDM) method which is an analytic algorithm without complicated numerical computations to solve for electrical field. The interactive DEP forces of particles calculated by IDM are found to be well agreed with those of MST method and much simple to implement. Using IDM method, a series of examples of multiple particles interactions and particle chains in a 3D uniform DC electrical field is presented. Randomly distributed similar dense particles (either all positive DEP (pDEP) or all negative DEP (nDEP) particles) in 3D uniform electrical field can generally form chains in lines parallel to the electrical field, except the case that all similar particles are in a plane perpendicular to the electrical field where the particles repel each other and move away in the plane. Randomly distributed dissimilar dense particles (mixture of pDEP and nDEP particles) can form (1) chains in lines, (2) clusters in a plane or (3) 3D groups. The chains, clusters and groups are of staggered arrangements of pDEP and nDEP particles, which are perpendicular to the electrical field.

Iterative dipole moment method for the interaction of multiple dielectrophoretic particles in an AC electrical field

Dielectrophoresis (DEP) for bio-particle manipulation has been drawing much attention in recent years. The equivalent dipole moment method (EDM) has widely been used to calculate DEP forces on single particle, but this method falls short to describe the interaction between neighboring particles. The Maxwell stress tensor method (MST) is theoretically rigorous for particle interaction, but its complicated numerical computation makes it difficult to implement in practice. In this paper, an iterative dipole moment method (IDM) is presented to investigate the interaction of multiple dielectrophoretic particles in a two-dimensional AC electric field. Without cumbersome numerical computation, the inter-particle forces, the particle trajectories and chain patterns calculated by the IDM method are found to be well consistent with those by the MST method for some published results and experimental observations. Furthermore, it is found that the final stable particle chain patterns strongly depend on the initial configuration of the particle distribution. An arbitrary small disturbance to the particle locations may lead to dramatically different motion trajectories and final particle chains. By tuning the frequency of AC field, the particles can be transformed between positive DEP particles and negative DEP particles, which results in different particle chains as well.

Iterative dipole moment method for calculating dielectrophoretic forces of particle-particle electric field interactions

Dielectrophoresis (DEP) is one of the most popular techniques for bio-particle manipulation in microfluidic systems. Traditional calculation of dielectrophoretic forces of single particle based on the approximation of equivalent dipole moment (EDM) cannot be directly applied on the dense particle interactions in an electrical field. The Maxwell stress tensor (MST) method is strictly accurate in the theory for dielectrophoretic forces of particle interaction, but the cumbersome and complicated numerical computation greatly limits its practical applications. A novel iterative dipole moment (IDM) method is presented in this work for calculating the dielectrophoretic forces of particle-particle interactions. The accuracy, convergence, and simplicity of the IDM are confirmed by a series of examples of two-particle interaction in a DC/AC electrical field. The results indicate that the IDM is able to calculate the DEP particle interaction forces in good agreement with the MST method. The IDM is a purely analytical operation and does not require complicated numerical computation for solving the differential equations of an electrical field while the particle is moving.

Numerical study of particle chains of a large number of randomly distributed DEP particles using iterative dipole moment method

AbstractBACKGROUNDDielectrophoresis (DEP) has widely been used to manipulate bio‐particles in microfluidic system. The calculation of DEP interaction of a large number of dense particles has been a challenging issue. The Maxwell stress tensor (MST) method is strictly accurate in theory for DEP forces, but the complicated numerical computation is very difficult to implement. An iterative dipole moment method (IDM) is proposed in this paper to study the interaction forces and particle chains of a large number of dense particles in a uniform electrical field.RESULTSThe numerical example of ten particles interaction confirms that the IDM is able to calculate particle interaction forces in good agreement with the MST method. Particle chains of fifty randomly distributed dense particles in a uniform electrical field were simulated using the IDM method and were well consistent with experimental observations. Particle chains of different particle sizes are also investigated.CONCLUSIONThe interaction forces of DEP particles calculated by the IDM method are found to be in good agreement with those obtained using the Maxwell stress tensor (MST) method and easy to implement. The simulated particle chains show essential characteristics well consistent with experimental observations. © 2015 Society of Chemical Industry

Parallel computing 2D Voronoi diagrams using untransformed sweepcircles

Voronoi diagrams are among the most important data structures in geometric modeling. Among many efficient algorithms for computing 2D Voronoi diagrams, Fortune’s sweepline algorithm (Fortune, 1986 [5]) is popular due to its elegance and simplicity. Dehne and Klein (1987) [8] extended sweepline to sweepcircle and suggested computing a type of transformed Voronoi diagram, which is parallel in nature. However, there is no practical implementation of the sweepcircle algorithm due to the difficulty in representing the transformed edges. This paper presents a new algorithm, called untransformed sweepcircle, for constructing Voronoi diagram in R2. Starting with a degenerate circle (of zero radius) centered at an arbitrary location, as the name suggests, our algorithm sweeps the circle by increasing its radius across the plane. At any time during the sweeping process, each site inside the sweep circle defines an ellipse composing of points equidistant from that point and from the sweep circle. The union of all ellipses forms the beach curve-a star shape inside the sweep circle which divides the portion of the plane within which the Voronoi diagram can be completely determined, regardless of what other points might be outside of the sweep circle. As the sweep circle progresses, the intersection of expanding ellipses defines the Voronoi edges. We show that the sweep line algorithm is the degenerate form of the proposed sweep circle algorithm when the circle center is at infinity, and our algorithm has the same time and space complexity as the sweep line algorithm. Our untransformed sweepcircle algorithm is flexible in allowing multiple circles at arbitrary locations to sweep the domain simultaneously. The parallelized implementation is pretty easy without complicated numerical computation; the most complicated case is nothing but an arc-cosine operation. Furthermore, our algorithm supports the additively weighted Voronoi diagrams of which the Voronoi edges are hyperbolic and straight line segments. We demonstrate the efficacy of our parallel sweep circle algorithm using a GPU.

CORRELATION ENERGIES CALCULATIONS FOR POLY (p-PHENYLENEVINYLENE) (PPV) CHAINS

The present study calculates correlation energies of the different length poly(p-phenylenevinylene) (PPV) units using the formula recently developed for π conjugated polymers, and analyzes the correlation energies from the phenylene unit and the vinylene unit in single and three PPV unit cells as well as the effect of the correlation energies on the band energy gap of the PPV. The present method avoids the complicated numerical computations about the correlation effects for the π electronic conjugated molecule systems with large unit cells.

Efficient spectral watermarking of large meshes with orthogonal basis functions

Allowing for copyright protection and ownership assertion, digital watermarking techniques, which have been successfully applied to classical media types like audio, images, and video, have recently been adapted for the newly emerged multimedia data type of 3D geometry models. In particular, the widely used spread-spectrum methods can be generalized for 3D datasets by transforming the original model to a frequency domain and perturbing the coefficients of the most dominant basis functions. Previous approaches employing this kind of spectral watermarking are mainly based on multiresolution mesh analysis, wavelet domain transformation, or spectral mesh analysis. Though they already exhibit good resistance to many types of real-world attacks, they are often far too slow to cope with very large meshes due to their complicated numerical computations. In this paper, we present a novel spectral watermarking scheme using new orthogonal basis functions based on radial basis functions. With our proposed fast basis function orthogonalization, while observing a persistence with respect to various attacks that is similar to that of other related approaches, our scheme runs faster by two orders of magnitude and thus can efficiently watermark very large models.

Effects of along- and cross-radar-beam winds on Doppler radar spectrum

Abstract. Beam broadening effects on the Doppler radar spectrum induced by along- and cross-radar-beam winds are theoretically investigated in this article. Analytical expression of beam broadening spectrum for a vertical beam subject to a constant vertical wind in the absence of horizontal wind is derived first. We find that the resultant beam broadening spectral shape is in an exponential form, rather than a Gaussian shape. The peak of the exponential spectrum corresponds to the true vertical wind velocity, and the spectral width σ is a function of vertical wind velocity w and the half-power beam width θ1/2 of the radar beam, in accordance with the expression σ=0.09wθ1/22. The beam broadening spectrum for a vertical radar beam subject to both vertical and horizontal winds is numerically studied, and the result shows that the spectral shape is distorted from the Gaussian form. The estimated vertical wind velocity of the distorted spectrum is very close to the true vertical wind velocity with a difference of less than 0.6% for a typical case. However, its spectral width is substantially greater than that of the conventional Gaussian spectrum broadened by horizontal wind only. The difference of the spectral widths Δσ (in unit of percentage) in the two, as a function of the half-power beam width and the ratio of vertical to horizontal wind velocities, can be well approximated by a parabolic equation. With this equation and the conventional Gaussian beam broadening spectral width caused by horizontal wind, the true width of the distorted beam broadening spectrum induced by vertical and horizontal winds can be inferred without complicated numerical computation. Through a transformation of wind velocity from vertical and horizontal winds into along- and cross-radar-beam winds defined on the cross section of an oblique radar beam, the results obtained from the case of vertical radar beam can be directly applied to the case of the oblique beam. We show that in some special cases the beam broadening spectral widths of an oblique beam subject to both vertical and horizontal winds will be exceedingly narrower than those estimated by the existing formula, irrespective of the presence of strong horizontal wind velocity.

FPGA implementation of a near computation free image compression scheme based on adaptive decimation

Adaptive decimation is a technique that can be applied to compress images with good visual quality at low bit-rate. Despite the low complexity of the method, the encoding process involves floating point computation that requires the use of medium speed processors in order to achieve real time operation. In this paper, a new approach has been taken to restructure the adaptive decimation algorithm to a form that includes only small amount of arithmetic operations. The revised algorithm can be implemented with simple logic circuits. The encoder is practically free from complicated numerical computation. A FPGA implementation of the proposed algorithm was realized. The architecture of the encoder is simple and suitable for valuable applications in the development of low cost non-processor based multimedia products.

On the theory of leaky waves in crystals

The problem of finding the velocity of the leaky wave given rise to by the Rayleigh wave on the mechanically free surface of anisotropic media is investigated. Approximate expressions for the real and imaginary parts of the velocity of the leaky wave are derived without any assumptions about the symmetry of the crystal. Employing obtained formulae allows one to avoid complicated numerical computations for most of the practically interesting situations. Specific features of the resonance reflection of elastic waves in the vicinity of the leaky wave branch are briefly discussed.

Upper bound to a single-domain behavior of a ferromagnetic cylinder

For a right circular, finite ferromagnetic cylinder with a radius R, a parameter, Rc1, is calculated so that for R>Rc1 there is always a nonuniform magnetization state whose free energy is smaller than that of the uniform magnetization state. Numerical computations for the cases of permalloy and of magnetite give Rc1, which is quite close to the recently calculated Rc0 in a cylinder of these materials. The latter is defined, as in the fundamental theorem of Brown on spherical particles, so that the lowest free-energy state is that of a uniform magnetization, if R<Rc0. The closeness of Rc0 and Rc1 makes them a sufficiently good estimate for the critical size at which the particle changes from uniform to nonuniform magnetization state, without going through the complicated numerical computation of the exact value.