Aggregation Processes with Catalysis-Driven Decomposition

We propose a three-species aggregation model with catalysis-driven decomposition. Based on the mean-field rate equations, we investigate the evoIution behavior of the system with the size-dependent catalysis-driven decomposition rate J（i; j; k） = Jijk^v and the constant aggregation rates. The results show that the cluster size distribution of the species without decomposition can always obey the conventional scaling law in the case of 0 ≤v ≤ 1, while the kinetic evolution of the decomposed species depends crucially on the index v. Moreover, the total size of the species without decomposition can keep a nonzero value at large times, while the total size of the decomposed species decreases exponentially with time and vanishes finally.     

Solutions of Dirac Equation for Makarov Potential with Pseudospin Symmetry

The pseudospin symmetry in the Makarov potential is investigated systematically by solving the Dirac equation. The analytical solution for the Makarov potential with pseudospin symmetry is obtained by Nikiforov-Uvarov （N-U） method. The eigenfunctions and eigenenergies are presented with equal mixture of vector and scalar potentials in opposite signs, for which is exact.     

Unconditionally convergent nonlinear solver for hyperbolic conservation laws with S-shaped flux functions

This paper addresses the convergence properties of implicit numerical solution algorithms for nonlinear hyperbolic transport problems. It is shown that the Newton–Raphson (NR) method converges for any time step size, if the flux function is convex, concave, or linear, which is, in general, the case for CFD problems. In some problems, e.g., multiphase flow in porous media, the nonlinear flux function is S-shaped (not uniformly convex or concave); as a result, a standard NR iteration can diverge for large time steps, even if an implicit discretization scheme is used to solve the nonlinear system of equations. In practice, when such convergence difficulties are encountered, the current time step is cut, previous iterations are discarded, a smaller time step size is tried, and the NR process is repeated. The criteria for time step cutting and selection are usually based on heuristics that limit the allowable change in the solution over a time step and/or NR iteration. Here, we propose a simple modification to the NR iteration scheme for conservation laws with S-shaped flux functions that converges for any time step size. The new scheme allows one to choose the time step size based on accuracy consideration only without worrying about the convergence behavior of the nonlinear solver. The proposed method can be implemented in an existing simulator, e.g., for CO₂ sequestration or reservoir flow modeling, quite easily. The numerical analysis is confirmed with simulation studies using various test cases of nonlinear multiphase transport in porous media. The analysis and numerical experiments demonstrate that the modified scheme allows for the use of arbitrarily large time steps for this class of problems.     

Denoising of quadrature ultrasound Doppler signal from bi-directional flow based on matching pursuit

Denoising of Doppler signal is a preliminary and important step in medical ultrasound imaging. To denoise quadrature Doppler signal from bi-directional flow, we propose a novel method based on matching pursuit in this paper. The proposed method is an iterative decomposition algorithm which decomposes the original Doppler signal into a linear expansion of atoms in a time-frequency dictionary. The time-frequency dictionary is similar to Fourier transform domain and the atoms are similar to orthogonal bases in Fourier transform. In each step of the iteration, the atom which gives the largest inner product with the analyzed signal is selected from the dictionary, and the contribution of this atom is subtracted from the Doppler signal. This process is repeated on the residue until the SNR reaches the maximum. The linear expansion of the selected atoms is the denoised signal. Simulations were conducted on a simulation model with a sampling rate of 12.8 kHz. When the original SNRs are 0 dB, 2 dB, 4 dB, 6 dB, 8 dB, 10 dB, the proposed method can improve the SNR for 7.9 dB, 7.8 dB, 7.5 dB, 7.3 dB, 7.05 dB, 6.8 dB respectively, reduce the root mean square error (RMSE) of the mean frequency waveform to 0.0441 kHz, 0.0303 kHz, 0.0245 kHz, 0.0215 kHz, 0.0161 kHz, 0.0125 kHz respectively, and suppress the RMSE of the spectral width waveform to 0.1774 kHz, 0.0591 kHz, 0.0486 kHz, 0.0170 kHz, 0.0145 kHz, 0.0117 kHz respectively. Preliminary in vivo evaluation was also carried out on a healthy 33-year-old male using B-K medical A/S 3535 ultrasound scanner, and the results showed that the proposed method can effectively enhance the Doppler spectrogram.     

An alternative method for plotting dispersion curves

Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.     

Reply to comment on “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models” by H.M. Zhang

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use an approach reminding of smoothed particle hydrodynamics to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the “traffic pressure”, which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others.     

Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory

A nonlocal Euler–Bernoulli elastic beam model is developed for the vibration and instability of tubular micro- and nano-beams conveying fluid using the theory of nonlocal elasticity. Based on the Newtonian method, the equation of motion is derived, in which the effect of small length scale is incorporated. With this nonlocal beam model, the natural frequencies and critical flow velocities for the case of simply supported system and for the case of cantilevered system are obtained. The effect of small length scale (i.e., the nonlocal parameter) on the properties of vibrations is discussed. It is demonstrated that the natural frequencies are generally decreased with increasing values of nonlocal parameter, both for the supported and cantilevered systems. More significantly, the effect of small length scale on the critical flow velocities is visible for fluid-conveying beams with nano-scale length; however, this effect may be neglected for micro-beams conveying fluid.     

三体系统中的Efimov态(英文)

通过求解Faddeev方程, 研究了量子三体系统中的Efimov效应。 改进了变分方法对于求解激发态的不足。 在不同的两体作用下得到了三体系统中的Efimov态。 讨论了在不同质量比的三体系统中出现Efimov态的条件。 并由三体计算的结果分析了具有两个价中子的核系统在两体存在束缚态时可能存在的Efimov效应。We studied the Efimov effect in a three body system by solving the Faddeev equations. Different models and interactions were considered. The occurrence of Efimov states was discussed. The possible Efimov state was clearly presented and its properties were investigated.     

Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.