Statistical Approach to Dynamical Inverse Problems

Based on nonparametric estimation ideas, a statistical approach to the dynamical inverse problem for some n ^th order nonlinear differential equations is introduced. It is proved that the real-time filter type of estimators converge respectively, as the data noise tends to zero, to the unknown force function and its derivatives at an optimal rate in the minimax sense. Received: 10 October 1996 / Accepted: 20 January 1997     

Interactive Probability Models: Inverse Problems on the Sphere

We expose a class of probabilistic models withonly two outcomes that we call interactive probabilitymodels for the analysis of data that arise in situationswhere there is influence of the measurer on the measured. We reconstruct a Borel measurecorresponding to possible sets of probabilities that arerelated to outcomes of experiments. We give threeexamples: one that corresponds to the quantum mechanical case, one to a deterministic measurement, andone to a situation where the outcome of the measurementis determined by the measurement apparatusonly.     

Inverse Hyperbolic Problems and Optical Black Holes

In this paper we state a uniqueness theorem for the inverse hyperbolic problem in the case of a finite time interval. We apply this theorem to the inverse problem for the equation of the propagation of light in a moving medium (the Gordon equation). Then we study the existence of black and white holes for the general second order hyperbolic equation and for the Gordon equation and we discuss the impact of this phenomenon on the inverse problems.     

Inverse Eigenvalue Problems for Exploring the Dynamics of Systems Biology Models

This paper describes inverse eigenvalue problems that arise in studying qualitative dynamics in systems biology models. An algorithm based on lift-and-project iterations is proposed, where the lifting step entails solving a constrained matrix inverse eigenvalue problem. In particular, prior to carrying out the iterative steps, $a$-$priori$ bounds on the entries of the Jacobian matrix are computed by relying on the reaction network structure as well as the form of the rate law expressions for the model under consideration. Numerical results on a number of models show that the proposed algorithm can be used to computationally explore the possible dynamical scenarios while identifying the important mechanisms via the use of sparsity-promoting regularization.     

Meshless Collocation Method for Inverse Source Identification Problems

A novel meshless scheme is proposed for inverse source identification problems of Helmholtz-type equations. It is formulated by the non-singular general solutions of the Helmholtz-type equations augmented with radial basis functions. Under this meshless scheme, we can determine smooth source terms from partially accessible boundary measurements with accurate results. Numerical examples are presented to verify validity and accuracy of the present scheme. It is demonstrated that the present scheme is simple, accurate, stable and computationally efficient for inverse smooth source identification problems.     

Tip-Nanoparticle Near-Field Coupling in Scanning Near-Field Microscopy by Coupled Dipole Method

We use the couple dipole method to investigate the scanning near-field optical microscopy metallic tip-nanoparticle near-field interaction. Dependences of the local field intensity inside the nanoparticle on the nanosized tip shape,the tip open angle and the illumination angle are revealed. In combination with the previous results, we establish a complete model to understand the tip-nanoparticle near-field coupling mechanism.     

杆的离散系统的某些混合型振动反问题

研究杆的离散系统的混合型振动反问题,即由给定的部分频谱数据和部分模态数据构造一个杆的离散系统的刚度矩阵和质量矩阵.提出3个此类反问题,给出反问题的解法,讨论反问题的解的存在条件,给出相应的计算实例,并分析这类反问题的潜在价值.     

Optical Aharonov-Bohm Effect: An Inverse Hyperbolic Problems Approach

We describe the general setting for the optical Aharonov-Bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary measurements. We interpret the inverse problem result as a possibility in principle to detect the optical Aharonov-Bohm effect by the boundary measurements.     

近场光学显微技术

本文在介绍近场光学显微镜原理的基础上，对近场光学显微技术进行了一定深度的探讨，并着重研究了纳米级探针的制作和纳米级样品与探针间距的控制这两个近场光学显微技术中的关键问题，说明了近场光学显微探针的工作方式，阐述了近场光学成像的衬度类型，介绍了近场光学显微技术在多个领域的应用。在参考大量国内外最新研究成果的基础上，提出了一些个人的见解。     

Hermit Functional Polynomials as a Tool for Solving Inverse Problems

Russian Physics Journal - A method of writing the Fredholm or Volterra integral equation of the first kind is proposed aimed at finding the functional form of an arbitrary coefficient of the...     

Inverse Spectral-Scattering Problems on the Half-Line with the Knowledge of the Potential on a Finite Interval

The inverse spectral and scattering problems for the radial Schrödinger equation on the half-line \({[0,\infty)}\) are considered for a real-valued, integrable potential having a finite first moment. It is shown that the potential is uniquely determined in terms of the mixed spectral or scattering data which consist of the partial knowledge of the potential given on the finite interval \({[0,\varepsilon]}\) for some \({\varepsilon > 0}\) and either the amplitude or phase (being equivalent to scattering function) of the Jost function, without bound state data.     

Near-Field Fluorescence and Topography Characterization of a Single Nanometre Fluorophore by Apertureless Tip-Enhanced Scanning Near-Field Microscopy

Tip-enhanced near-field fluorescence and topography characterization of a single nanometre fluorophore is conducted by using an apertureless scanning near-field microscopy system. A fluorophore with size 80hm is mapped with a spatial resolution of 10hm. The corresponding near-field fluorescence data shows significant signal enhancement due to the apertureless tip-enhanced effect. With the nanometre spatial resolution capability and nanometre local tip-enhanced effect, the apertureless tip-enhanced scanning near-field microscopy may be further used to characterize a single molecule by realizing the local near-field spectrum assignment corresponding to topography at nanometre scale.     

细菌视紫红质近场光存储特性的研究

结合近场光学显微镜，利用菌紫质M态和基态之间的跃迁，对BR—D96N样品作了静态近场光存储特性的研究。结果表明，近场区域内细菌视紫外质在光激发前后对红光的吸收有较大差别，而且激发后无光照时会缓慢弛豫到激发前的状态，具有光致变色特性和热弛豫特性，可望作为近场光存储材料和微光学信息处理器件材料。     

近场衍射图样的抽样定理处理方法

提出近场衍射图样的抽样定理处理方法,在近场衍射中,孔径和衍射场分布为或近似为空间有界物,在其频域中可以比较精确地恢复衍射的分布。衍射场频谱带宽的近似值由频谱的幅值大于中心频谱极大幅值的１％的频率范围所确定。     

An Inverse Finite Element Method for Pure and Binary Solidification Problems

A 2D axisymmetric formulation for the solution of a directional solidification problem using an inverse finite-element method (IFEM) is presented. An algorithm developed by A. N. Alexandrou (Int. J. Numer. Methods Eng.28, 2383, 1989) has been modified and extended to include more general boundary conditions. The latter includes the explicit presence of an ampoule (with a complex shape) that contains the solid and the melt from which it is growing. Heat transfer between the ampoule and the external environment, time-dependent thermal boundary conditions, nonmonotonic temperature distributions, and species diffusion in the melt and crystal are also taken into account. Thus, our extended formulation encompasses a wider class of solidification problems than previous IFEM methods. Numerical experiments that illustrate the suitability of the extended IFEM are presented. In particular, we present a simulation of the directional solidification of zinc cadmium telluride using boundary conditions corresponding to an actual experiment scenario.