Generation of dark hollow beam by use of phase-only filtering

A simple but effective scheme to generate dark hollow beams is proposed by use of phase-only filtering and optical Fourier transform. A Gaussian beam of fundamental mode is modulated by a pre-designed phase mask, which is a piecewise modification of an axicon lens, and followed by a Fourier transform to generate an ideal dark hollow beam at the focal plane. This method has an advantage that the total energy of the beam is conserved under paraxial approximation. Numerical calculations are provided to show the validity of the proposed scheme.     

A sharp first order analysis of Feynman–Kac particle models,Part II: Particle Gibbs samplers

This article provides a new theory for the analysis of the particle Gibbs (PG) sampler (Andrieu et al., 2010). Following the work of Del Moral and Jasra (2017) we provide some analysis of the particle Gibbs sampler, giving first order expansions of the kernel and minorization estimates. In addition, first order propagation of chaos estimates are derived for empirical measures of the dual particle model with a frozen path, also known as the conditional sequential Monte Carlo (SMC) update of the PG sampler. Backward and forward PG samplers are discussed, including a first comparison of the contraction estimates obtained by first order estimates. We illustrate our results with an example of fixed parameter estimation arising in hidden Markov models.     

Spread of a catalytic branching random walk on a multidimensional lattice

For a supercritical catalytic branching random walk on ${\mathbb{Z}}^d$, $d\in \mathbb{N}$, with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in ${\mathbb{R}}^d$ which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation.     

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-butbounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arithmetic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation.To further reduce the overestimation caused by the "wrapping effect" of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.     

Onset of Buoyancy-Driven Convection in Porous Media Saturated with Cold Water Cooled from Above

When porous media saturated with initially stagnant cold water around the density maximum temperature are cooled from above, convection may be induced in an unstable lower layer. In this study, the onset of buoyancy-driven convection during time-dependent cooling is investigated using the propagation theory, which transforms disturbance equations similarly, and also considering the density inversion effect. The critical Darcy–Rayleigh number Ra _D,c is found as a function of the dimensionless density maximum temperature θ _max. For Ra _D > Ra _D,c the dimensionless critical time τ _c to mark the onset of instability is presented as a function of Ra _D and θ _max. These critical conditions are compared with previous theoretical results.     

Plasmonic Newton's cradle for low-loss subwavelength energy transport: Homogeneous or heterogeneous nanoparticle chains?

Five closely spaced Au or Ag NPs are linearly arranged in analogy with Newton's cradle, forming various homogeneous and heterogeneous NP chains. Using small NPs, the Au–Ag–Ag–Ag–Au heterochain has the lowest propagation loss (17.6%) at short resonance wavelengths. When the NP diameter is increased to 80 nm, the dominant resonance is shifted to longer wavelengths. As low as 6% of the total energy dissipates in the intermediate NP component, and there seems to be little difference between the Au–Ag–Ag–Ag–Au heterochain and the Ag–Ag–Ag–Ag–Ag homochain. Besides the wavelength-dependent intrinsic loss (i.e., the imaginary part of the permittivity) in metals, the real part of the permittivity also plays a critical role in determining the propagation loss. Considering the high fabrication cost of the heterochain, the homochain composed of moderately large Ag NPs (<100 nm) may be an optimal choice for low-loss subwavelength energy transport in practice.     

Joint swing-up and stabilization of the Reaction Wheel Pendulum using Discontinuous Integral algorithm

In this paper, a third-order discontinuous integral controller is designed to jointly swing-up and robustly stabilize in finite-time the upright position of the Reaction Wheel Pendulum (RWP) system, despite some uncertainties and perturbations. To show this, a numerical estimation of the domain of attraction of the controller is used. The control algorithm produces a continuous control signal, thus reducing the usual chattering effect of the sliding-mode controllers. The theoretical results of the paper are verified by simulations and experiments in a laboratory setup.     

Rejoinder on “Likelihood-based belief function: Justification and some extensions to low-quality data”

This note is a rejoinder to comments by Dubois and Moral about my paper “Likelihood-based belief function: justification and some extensions to low-quality data” published in this issue. The main comments concern (1) the axiomatic justification for defining a consonant belief function in the parameter space from the likelihood function and (2) the Bayesian treatment of statistical inference from uncertain observations, when uncertainty is quantified by belief functions. Both issues are discussed in this note, in response to the discussants' comments.     

水下窄脉冲超宽带信号的传播特性仿真

超宽带信号具有分辨率高、截获概率低、穿透能力强等优点,将在水下目标探测、定位及通信等领域具有良好的应用前景。基于水下等离子体声源提出了窄脉冲超宽带信号产生方法,建立了以传播损失和海洋环境噪声为主要影响因素的超宽带脉冲传播信道模型;结合湖试实测数据,利用Matlab仿真软件和Welch谱分析法,仿真分析了不同频率的超宽带脉冲在水下传播不同距离后的功率谱密度以及传播特性。研究成果对水下等离子体超宽带脉冲的工程应用具有重要的参考价值,同时对水下等离子体超宽带脉冲声源的设计和研制也有一定的借鉴意义。