A peculiar Maxwell’s Demon observed in a time-dependent stadium-like billiard

The dynamics of a driven stadium-like billiard is considered using the formalism of discrete mappings. The model presents a resonant velocity that depends on the rotation number around fixed points and external boundary perturbation which plays an important separation rule in the model. We show that particles exhibiting Fermi acceleration (initial velocity is above the resonant one) are scaling invariant with respect to the initial velocity and external perturbation. However, initial velocities below the resonant one lead the particles to decelerate therefore unlimited energy growth is not observed. This phenomenon may be interpreted as a specific Maxwell’s Demon which may separate fast and slow billiard particles.     

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.     

Studies on the growth,structural, optical,SHG and thermal properties of γ-glycine single crystal: An organic nonlinear optical crystal

Single crystals of the organic nonlinear optical material γ-glycine have been grown in the presence of Zinc sulphate by slow evaporation technique at ambient temperature for the first time. Bulk growth of γ-glycine single crystals was grown by Top-seeded solution growth method. The γ-phase of glycine was confirmed by powder X-ray diffraction and the FTIR analysis. Elemental analysis CHN was performed to confirm the non-inclusion of zinc sulphate species into the solution. Inductively coupled plasma optical emission spectrometry study (ICP-OES) was employed to quantify the concentration of Zinc element in the grown γ-glycine single crystals. The optical transmission was ascertained from UV–Vis–NIR spectrum. The optical band gap was estimated for γ-glycine single crystal using UV–Vis–NIR study. Differential scanning calorimetry analysis was employed to explore information about thermal stability, phase transition and melting point of the grown crystal. The second harmonic generation relative efficiency was measured by Kurtz and Perry powder technique.     

On symmetries,reductions, conservation laws and conserved quantities of optical solitons with inter-modal dispersion

This paper studies the compressional dispersive Alfvén (CDA) waves where Noether symmetries will be calculated from which the corresponding conservation laws will be obtained via Noether's theorem. Furthermore, one case of double reduction is performed via the association of a conserved vector with a Noether symmetry (with zero gauge). The conserved quantities of optical solitons in the presence of intermodal dispersion that is governed by the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. The invariance-multiplier method is adopted to carry out the analysis, from which the conserved densities are then retrieved. Finally, the conserved quantities are obtained using the 1-soliton solution of the governing equation.     

The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread

The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency.     

有分压电阻和e偏振非相干背景光辐照的光折变晶体中非相干耦合空间孤子对

为了得到光折变晶体中非相干耦合空间孤子对统一理论的结果,基于单光子光折变空间光孤子的基本理论模型,建立了稳态条件下有分压电阻和e偏振非相干均匀背景光辐照的单光子光伏光折变晶体中非相干耦合空间孤子对理论. 研究表明:这种孤子对是由两束偏振方向和波长都相同的互不相干光束耦合形成的, 孤子对两光束都能在晶体中稳定传播;当分压电阻、e偏振背景光、外加电场和光伏场取不同值时, 可获得14种光折变非相干耦合空间孤子对. 本文的结果对完善和充实光折变空间孤子理论体系有重要意义.     

基于增益调制的激光成像准确度研究

微通道板电压与增益对数理论上呈线性关系,为了更接近实际情况,根据已知的微通道板电压与增益对数的函数关系选取一组线性数据点,并在其基础上加一组随机数作为波动,得到新的电压与增益对数的关系,获得指数拟合公式,用于还原目标的距离信息.对成像准确度进行理论分析,结果表明成像准确度与系统信噪比和增益调制函数有关,且信噪比越高,距离准确度越高.测量了微通道板增益与电压的关系曲线,在不同电压条件下照射同一距离同一目标得到回波图像,利用不同电压下回波图像灰度值之比得到相对增益之比.分别在恒定增益和调制增益下,对距离成像系统60m的目标进行成像,利用增益曲线对所得的图像进行处理,准确还原出目标的距离信息,准确度达到分米量级.     

Construction of minimal mass blow-up solutions to rough nonlinear Schrödinger equations

We study the focusing mass-critical rough nonlinear Schrödinger equations, where the stochastic integration is taken in the sense of controlled rough path. In both dimensions one and two, the minimal mass blow-up solutions are constructed, which behave asymptotically like the pseudo-conformal blow-up solutions near the blow-up time. Furthermore, the global well-posedness is obtained if the mass of initial data is below that of the ground state. These results yield that the mass of ground state is exactly the threshold of global well-posedness and blow-up in the stochastic focusing mass-critical case. Similar results are also obtained for a class of nonlinear Schrödinger equations with lower order perturbations, particularly in the absence of the standard pseudo-conformal symmetry and the conservation law of energy.     

Solving nonlinear equations with the convex combination of two positive spectral coefficients

We present a spectral algorithm based on the convex combination of two modified spectral coefficients for solving systems of nonlinear equations. The proposed algorithm does not require the exact or approximated directional derivative for its implementation. By employing a derivative-free line search, the global convergence of the sequence generated by the algorithm is supported. Numerical experiments are given to demonstrate the performance of the algorithm compared with a similar algorithm in the literature for solving nonlinear equations problems.     

Input-to-state stability and stabilization for switched nonlinear positive systems

Input-to-state stability (ISS) analysis and stabilization are concerned in this paper for switched nonlinear positive systems (SNPS), where the deterministic and random switching are both included. For general SNPS, switched affine nonlinear positive systems (SANPS) and switched linear positive systems (SLPS) with deterministic and some kinds of random ”slow” switching, some criterions on ISS are provided. From the criterions for SANPS and SLPS, the ISS properties can be judged just by the differential, algebraic and switching characteristics of the systems. Further, based on the criterions for SANPS and SLPS, some state feedback controllers are designed such that the closed-loop systems be positive, ISS or ISS in some stochastic senses. Four simulation examples verify the validity of our results.