SPH simulation of fuel drop impact on heated surfaces

The interaction of liquid drops and heated surfaces is of great importance in many applications. This paper describes a numerical method, based on smoothed particle hydrodynamics (SPH), for simulating n-heptane drop impact on a heated surface. The SPH method uses numerical Lagrangian particles, which obey the laws of fluid dynamics, to describe the fluid flows. By incorporating the Peng–Robinson equation of state, the present SPH method can directly simulate both the liquid and vapor phases and the phase change process between them. The numerical method was validated by two experiments on drop impact on heated surfaces at low impact velocities. The numerical method was then used to predict drop-wall interactions at various temperatures and velocities. The model was able to predict the different outcomes, such as rebound, spread, splash, breakup, and the Leidenfrost phenomenon, consistent with the physical understanding.     

Time-resolved imaging of mode-conversion process of terahertz transients in subwavelength waveguides

We studied the mode-conversion process of terahertz pulses from a planar subwavelength waveguide to a tilted rectangular subwavelength waveguide. An unusual wavefront rotation, which led to an extra conversion time, was observed using a time-resolved imaging technique. We simulated the mode conversion process by a finite-difference time-domain method, and the results agreed well with the experiments. According to the simulations, the conversion time was demonstrated to become longer as the tilt angle or width of the rectangular waveguide increased. This work provides the possibility to optimize the future high-speed communications and terahertz integrated platforms.     

The spike timing precision of FitzHugh--Nagumo neuron network coupled by gap junctions

It has been proved recently that the spike timing can play an important role in information transmission, so in this paper we develop a network with N-unit FitzHugh--Nagumo neurons coupled by gap junctions and discuss the dependence of the spike timing precision on synaptic coupling strength, the noise intensity and the size of the neuron ensemble. The calculated results show that the spike timing precision decreases as the noise intensity increases; and the ensemble spike timing precision increases with coupling strength increasing. The electric synapse coupling has a more important effect on the spike timing precision than the chemical synapse coupling.     

System Size Resonance Associated with Canard Phenomenon in a Biological Cell System

The influence of internal noise on the calcium oscillations is studied. It is found that stochastic calcium oscillations occur when the internal noise is considered, while the corresponding deterministic dynamics only yields a steady state. Also, the performance of such oscillations shows two maxima with the variation of the system size, indicating the occurrence of system size resonance. This behavior is found to be intimately connected with the canard phenomenon. Interestingly, it is also found that one of the optimal system sizes matches well with the real cell size, and such a match is robust to the variation of the control parameters.     

利用多维模态理论分析圆柱贮箱液体非线性晃动

将多维模态理论应用到求解作横向运动圆柱贮箱中液体的非线性晃动问题. 首先通过压力积分变分原理推导出描述液体作非线性晃动的一般形式无穷维模态系统,然后根据Narimanov-Moiseev三阶渐近假设关系,通过选取二阶主模态和三阶次模态,将无穷维模态系统降为五维渐近模态系统. 通过对这个模态系统的数值积分可以看出一些典型的非线性特征(如波峰大于波谷、节径移动等).      

Magnetic Fingerprints on the Spectra of One Electron and Two Electrons Interacting in Parabolic Quantum Dots

Magnetic fingerprints on the spectra of an electron interacting with a negatively charged ion in a parabolic quantum dot, and of two interacting electrons in such a dot, are investigated via a new pseudoperturbative methodical proposal. The effects of ion-electron and electron-electron interactions on the spectra are studied. The effect of the central spike (m ² – 1/4)/q ² on the spectral properties of the above problems is emphasized. Compared with those obtained by Zhu et al. [J. Phys.: Condens. Matter., Vol. 11 (1999) 229], via a series solution, the results are found in excellent accord. Higher excited states are also reported.     

Mathematical modeling of methane flow in a borehole coal mining system

Safety in coal mining is greatly increased by the drainage of the methane content of coal seams through boreholes, simultaneously producing significant energy. The design of suitable drainage technology is based on the mathematical modeling of methane flow in coal seams. In the calculation of the methane pressure, the new mathematical model presented in this paper considers both the sorption phenomenon of methane depending upon the methane pressure and the fact that the variation in methane pressure can create a change in the stress condition of the rock and, as a consequence of this, a change in the permeability of the coal. The new mathematical model can be used for the numerical simulation of the flow processes in coal seams and methane drainage technology can be designed more accurately.     

Bott's vanishing theorem for regular Lie algebroids

Differential geometry has discovered many objects which determine Lie algebroids playing a role analogous to that of Lie algebras for Lie groups. For example:

--- differential groupoids,

--- principal bundles,

--- vector bundles,

--- actions of Lie groups on manifolds,

--- transversally complete foliations,

--- nonclosed Lie subgroups,

--- Poisson manifolds,

--- some complete closed pseudogroups.

We carry over the idea of Bott's Vanishing Theorem to regular Lie algebroids (using the Chern-Weil homomorphism of transitive Lie algebroids investigated by the author) and, next, apply it to new situations which are not described by the classical version, for example, to the theory of transversally complete foliations and nonclosed Lie subgroups in order to obtain some topological obstructions for the existence of involutive distributions and Lie subalgebras of some types (respectively).

     

On a Liouville-type theorem and the Fujita blow-up phenomenon

The main purpose of this paper is to obtain the well-known results of H.Fujita and K.Hayakawa on the nonexistence of nontrivial nonnegative global solutions for the Cauchy problem for the equation

with on the half-space as a consequence of a new Liouville theorem of elliptic type for solutions of () on . This new result is in turn a consequence of other new phenomena established for nonlinear evolution problems. In particular, we prove that the inequality

has no nontrivial solutions on when We also show that the inequality

has no nontrivial nonnegative solutions for , and it has no solutions on bounded below by a positive constant for 1.$">

     

Extrapolation Algorithms for Filtering Series of Functions,and Treating the Gibbs Phenomenon

In this paper, we study the application of some convergence acceleration methods to Fourier series, to orthogonal series, and, more generally, to series of functions. Sometimes, the convergence of these series is slow and, moreover, they exhibit a Gibbs phenomenon, in particular when the solution or its first derivative has discontinuities. It is possible to circumvent, at least partially, these drawbacks by applying a convergence acceleration method (in particular, the -algorithm) or by approximating the series by a rational function (in particular, a Padé approximant). These issues are discussed and some numerical results are presented. We will see that adding its conjugate series as an imaginary part to a Fourier series greatly improves the efficiency of the algorithms for accelerating the convergence of the series and reducing the Gibbs phenomenon. Conjugacy for series of functions will also be considered.