Existence and uniqueness for nonlinear boundary value problems in kinetic theory

A boundary value problem for the stationary nonlinear Boltzmann equation in a slab has been examined in a weightedL space. It has been proved that the problem possesses a unique solution for boundary data small enough. The proof is based on the implicit function theorem. It has also been shown that for the linearized problem the Fredholm alternative applies.     

The kinetic boundary layer for the Klein-Kramers equation; A new numerical approach

We explore a numerical technique for determining the structure of the kinetic boundary layer of the Klein-Kramers equation for noninteracting Brownian particles in a fluid near a wall that absorbs the Brownian particles. The equation is of interest in the theory of diffusion-controlled reactions and of the coagulation of colloidal suspensions. By numerical simulation of the Langevin equation equivalent to the Klein-Kramers equation we amass statistics of the velocities at the first return to the wall and of the return times for particles injected into the fluid at the wall with given velocities. The data can be used to construct the solutions of the standard problems at an absorbing wall, the Milne and the albedo problem. We confirm and extend earlier results by Burschka and Titulaer, obtained by a variational method vexed by the slow convergence of the underlying eigenfunction expansion. We briefly discuss some further boundary layer problems that can be attacked by exploiting the results reported here.     

On solving energy-dependent partitioned eigenvalue problem by genetic algorithm: The case of real symmetric Hamiltonian matrices

An energy-dependent partitioning scheme is explored for extracting a small number of eigenvalues of a real symmetric matrix with the help of genetic algorithm. The proposed method is tested with matrices of different sizes (30 × 30 to 1000 × 1000). Comparison is made with Löwdin’s strategy for solving the problem. The relative advantages and disadvantages of the GA-based method are analyzed     

Moment Systems Derived from Relativistic Kinetic Equations

In this paper, we are interested in the derivation of macroscopic equations from kinetic ones using a moment method in a relativistic framework. More precisely, we establish the general form of moments that are compatible with the Lorentz invariance and derive a hierarchy of relativistic moment systems from a Boltzmann kinetic equation. The proof is based on the representation theory of Lie algebras. We then extend this derivation to the classical case and general families of moments that obey the Galilean invariance are also constructed. It is remarkable that the set of formal classical limits of the so-obtained relativistic moment systems is not identical to the set of classical moments quoted in Ref. 21 and one could use a new physically relevant criterion to derive suitable moment systems in the classical case. Finally, the ultra-relativistic limit is considered.     

Remarks on scaling a model of Witten-Sander type

We try to prove rigorously that the perimeter of the large Witten-Sander cluster does not scale as the square root of its area, by making a forced comparison with the ill-posed Hele-Shaw problem of fluid dynamics. The attempt is not completely successful; nevertheless some interesting consequences of the comparison are derived.     

Inverse filtering

Inverse filtering is a noninvasive method of producing a glottogram thought to reflect the vibratory motions of the vocal fold. The flow glottogram provides information related to the type of phonation, the sound pressure level, the regularity of vocal fold vibrations, and to the presence or absence of vocal fold closure. Limited data, speech samples, filter tuning, and lack of unanimity on waveform display and interpretation have contributed to slow application of the techniques to the clinical population. The author argues the technique has utility in both diagnosis and treatment     

力梯度辛方法在圆型限制性三体问题中的应用

旋转坐标系下的圆型限制性三体问 题因含非惯性系所附加的影响部分使得动能不是动量的严格二次型, 可能导致力梯度辛积分算法的应用遇到困难. 从Lie算子运算出发, 严格论证了力梯度算子在这种情形下的物理意义 仍然像质心惯性坐标系下的圆型限制性三体问题那样是引力的梯度, 而不是引力与非惯性力所得合力的梯度, 表明了力梯度辛方法适合求解旋转坐标系下的圆型限制性三体问题. 通过应用四阶力梯度辛方法、最优化四阶力梯度辛方法和Forest-Ruth 辛方法分别求解该问题, 进行了数值对比研究, 结果显示最优化型力梯度算法能够取得最好精度. 还应用最优化型算法计算两邻近轨道的Lyapunov指数和快速Lyapunov指标, 确保高精度辛方法能够贯穿于这些混沌指标计算的全过程, 以便准确刻画此系统的动力学定性性质. 关键词： 辛积分器 圆型限制性三体问题 混沌 Lyapunov指数     

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.     

Characterization of spherical particles using high-order neural networks and scanning flow cytometry

We retrieve the radius R, real n and imaginary k parts of the refractive index of homogeneous spherical particles using angular distribution of the light-scattering intensity. To solve the inverse light-scattering problem we use a high-order neural-network technique. The effect of network parameters on optimization is examined. The technique is evaluated for noise-corrupted input data at 0.6 μm<R<10.6 μm, 1.02<n<1.38, and 0<k<0.03. The errors of retrieval for nonabsorbing particles do not exceed 0.05 μm for radius and 0.015 for refractive index. The experimental verification is fulfilled by experimental data retrieved by means of a scanning flow cytometer. The light-scattering profiles of polystyrene beads and spherized red blood cells are processed with the high-order neural networks and a non-linear regression at Mie theory. The parameters retrieved by the high-order neural networks correlate well with the parameters retrieved by the least-square method.     

Comparison of growth stress measurements with modelling in thin iron oxide films

High temperature oxidation of metals leads to residual stresses both in the metal and in the growing oxide. In this work, the evolution of this residual stresses is theoretically predicted in the growing oxide layers. The origin of these stresses is based on a microstructural model. Using experimental results providing from the oxidation kinetics, and an analysis proposed to describe the growth strain occurring in the thin layers, a set of equations is established allowing determining the stresses evolution with oxidation time. Then, the model is compared with experimental results obtained on both α-Fe and phosphated α-Fe, oxidised at different temperatures. Numerical data are extracted from experiments either with an asymptotic formulation or with an inverse method. These two methods give good agreement with experiments and allow extracting the model parameters.