A Polydisperse Sphere Model Describing the Propagation of Light in Biological Tissue

A polydisperse sphere model with the complex refractive index is employed to describe the propagation of light in biological tissue. The scattering coefficient, absorption coefficient and scattering phase function are calculated. At the same time, the inverse problem on retrieving the particles size distribution, imaginary part of the refractive index and number density of scatterers is investigated. The result shows that the retrieval scheme together with the Chahine algorithm is effective in dealing with such an inverse problem. It is also clarified that a group of parameters including the scattering coefficient, absorption coefficient and phase function are associated with another group including the refractive index, particle size distribution and number density of scatterers, which is a problem described in two different ways and the anisotropy factor is not an independent variable, but is determined by the phase function.     

Multi-objective optimization of inverse planning for accurate radiotherapy

The multi-objective optimization of inverse planning based on the Pareto solution set, according to the multi-objective character of inverse planning in accurate radiotherapy, was studied in this paper. Firstly, the clinical requirements of a treatment plan were transformed into a multi-objective optimization problem with multiple constraints. Then, the fast and elitist multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ) was introduced to optimize the problem. A clinical example was tested using this method. The results show that an obtained set of non-dominated solutions were uniformly distributed and the corresponding dose distribution of each solution not only approached the expected dose distribution, but also met the dose-volume constraints. It was indicated that the clinical requirements were better satisfied using the method and the planner could select the optimal treatment plan from the non-dominated solution set.     

Einstein——Podolsky——Rosen entanglement in time-dependent periodic pumping non-degenerate optical parametric amplifier

The solution of the time-dependent periodic pumping non-degenerate optical parametric amplifier (NOPA) is derived when the pump depletion is considered both above and below thresholds. Based on this solution, the quantum fluctuation calculated shows that a high entanglement and a good squeezing degree of the parametric light beams are achieved near and above thresholds. We adopt two kinds of pump fields: (i) a continuously modulated pump with a sinusoidal envelope; (ii) a sequence of laser pulses with Gaussian envelopes. We analyse the time evolution of continuous variable entanglement by analytical and numerical calculations, and show that the periodic driven pumping also improves the degree of entanglement. The squeezing and Einstein-Podolsky-Rosen (EPR) entanglement by using the two pumping driven functions are investigated from below to above the threshold regions, the tendencies are nearly the same, and the Gaussian driven function is superior to that of the sine driven function, when the maximum squeezing and the minimum variance of quantum fluctuation are considered. In the meantime, the generalization of frequency degenerate OPA to frequency non-degenerated OPA problem is investigated.     

Quantum Spectra and Classical Orbits in Two-Dimensional Equilateral Triangular Billiards

We study the correspondence between quantum spectra and classical orbits in the equilateral triangular billiards. The eigenstates of such systems are not separable functions of two variables even though the problem is exactly solvable. We calculate the Fourier transform of a quantum spectral function and find that the positions of the peaks match well with the lengths of the classical orbits. This is another example showing that the quantum spectral function provides a bridge between quantum and classical mechanics.     

Lightness constancy:from haze illusion to haze removal

The human visual system processes lightness constancy to estimate reflectance under complex viewing conditions. We focus on the underlying reason the human visual system is conscious of haze, and discuss the single-image haze-removal problem based on lightness constancy from the beginning of haze illusion. Following the basic principle and model of "atmospheric transfer function", we bring about a simple dehazing paradigm by estimating two values using bilateral filtering. Practical investigation of parameters and design are analyzed in detail. Furthermore, a novel quantitative standard haziness presents itself naturally during the estimation process. Comparative study and objective evaluation demonstrate that the proposed method is fast and effective, yielding high-contrast and vivid haze-free images.     

Automatic detection of the belt-like region in an image with variational PDE model

In this paper, we propose a novel method to automatically detect the belt-like object, such as highway, river, etc., in a given image based on Mumford-Shah function and the evolution of two phase curves. The method can automatically detect two curves that are the boundaries of the belt-like object. In fact, this is a partition problem and we model it as an energy minimization of a Mumford-Shah function based minimal partition problem like active contour model. With Eulerian formulation the partial differential equations (PDEs) of curve evolution are given and the two curves will stop on the desired boundary. The stop term does not depend on the gradient of the image and the initial curves can be anywhere in the image. We also give a numerical algorithm using finite differences and present various experimental results. Compared with other methods, our method can directly detect the boundaries of belt-like object as two continuous curves, even if the image is very noisy.     

The inverse Bremsstrahlung absorption in the presence of Maxwellian and non-Maxwellian electrons

Inverse Bremsstrahlung absorption(IBA) of an intense laser field in plasma containing Maxwellian and nonMaxwellian(with Kappa and q-nonextensive distribution functions) electrons is studied analytically. Our results show that IBA decreases with an increase in temperature at high intensities and a decrease in plasma density for all kinds of distribution functions. Another striking result is that IBA is independent of the laser intensity at low intensity but is dependent on it when the intensity is going to rise. Also, it could be find that the behavior of the absorption as the function of laser intensity for the Kappa distribution with κ = 10 at low intensity is close to that for the Maxwellian distribution, but at high intensity it is close to that in the presence of q-nonextensive electrons with q = 0.9. These results provide insights into the inverse Bremsstrahlung absorption in the laser–plasma interactions.     

Inverse determinations of the parameters of three-layered plate using angle probe generated Lamb waves

The study on the inverse problems in the ultrasonic nondestructive testing (NDT) has a wide application field in various industries. An error function based inversion algorithm is introduced to determine the parameters of three-layered plates from the measured velocity of multi-mode Lamb waves. A mixed-spectral estimation is proposed to combine FFT with AR model for exact determination of the ultrasonic phase velocity. Experiments are performed using two conventional angle probes as transmitter and receiver on the same surface of three-layered laminates. Inverse analyses of one parameter (thickness) and two parameters (longitudinal and transverse wave velocities in a layer, or thickness of two layers) of three-layered laminates are made. The experimental results show that the inverse approach is in good agreement with the actual value.     

Multipartite Entanglement in Heisenberg Model

The effects of anisotropy and magnetic field on multipartite entanglement of ground state in Heisenberg XY model are investigated. The multipartite entanglement increases as a function of the inverse strength of the external field when the degree of anisotropy is finite. There are two peaks when the degree of anisotropy is γ=±1. When the degree of anisotropy increases further, the multipartite entanglement will decrease and tend to a constant. The threshold of the inverse strength of the external field for generating multipartite entanglement generally decreases with the increasing of qubits.     

Lyapunov function as potential function： A dynamical equivalence

For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization: a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.     

Multi-objective optimization of inverse planning for accurate radiotherapy

The multi-objective optimization of inverse planning based on the Pareto solution set, according to the multi-objective character of inverse planning in accurate radiotherapy, was studied in this paper. Firstly,the clinical requirements of a treatment plan were transformed into a multi-objective optimization problem with multiple constraints. Then, the fast and elitist multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ)was introduced to optimize the problem. A clinical example was tested using this method. The results show that an obtained set of non-dominated solutions were uniformly distributed and the corresponding dose distribution of each solution not only approached the expected dose distribution, but also met the dosevolume constraints. It was indicated that the clinical requirements were better satisfied using the method and the planner could select the optimal treatment plan from the non-dominated solution set.     

Waveguide spectroscopy of bilayer structures

A least-squares procedure is proposed for the reconstruction of optical parameters of bilayer structures. The objective function is constructed using experimental and calculated data on the reflectance of a coupling prism. A structure consisting of two different silicon oxynitride films on a silicon substrate is studied. The effect of scattering on the solution of the inverse problem is analyzed.     

A novel algorithm for solving optimal path planning problems based on parametrization method and fuzzy aggregation

In this Letter a new approach for solving optimal path planning problems for a single rigid and free moving object in a two and three dimensional space in the presence of stationary or moving obstacles is presented. In this approach the path planning problems have some incompatible objectives such as the length of path that must be minimized, the distance between the path and obstacles that must be maximized and etc., then a multi-objective dynamic optimization problem (MODOP) is achieved. Considering the imprecise nature of decision maker's (DM) judgment, these multiple objectives are viewed as fuzzy variables. By determining intervals for the values of these fuzzy variables, flexible monotonic decreasing or increasing membership functions are determined as the degrees of satisfaction of these fuzzy variables on their intervals. Then, the optimal path planning policy is searched by maximizing the aggregated fuzzy decision values, resulting in a fuzzy multi-objective dynamic optimization problem (FMODOP). Using a suitable t-norm, the FMODOP is converted into a non-linear dynamic optimization problem (NLDOP). By using parametrization method and some calculations, the NLDOP is converted into the sequence of conventional non-linear programming problems (NLPP). It is proved that the solution of this sequence of the NLPPs tends to a Pareto optimal solution which, among other Pareto optimal solutions, has the best satisfaction of DM for the MODOP. Finally, the above procedure as a novel algorithm integrating parametrization method and fuzzy aggregation to solve the MODOP is proposed. Efficiency of our approach is confirmed by some numerical examples.     

样条混合元法解板壳问题

应用三次B样条插值函数与二类变量广义变分原理建立一种样条混合元法来求解板壳结构的弯曲问题。应用样条函数来构造壳体的二类场函数:一类为位移场函数,另一类为广义力场函数,由二类变量广义变分原理导出样条混合元法的系统方程组。给出若干数值算例,其计算结果与其它方法作了比较。     

Separation of continuous lines mutually overlapping and smoothed by the instrumental function

Direct and inverse spectroscopy problems concerning superposition of overlapping continuous spectral lines, as well as smoothing of the total spectrum by the instrumental function, are considered. The direct problem is formulated in two stages: initially, the total spectrum is formed by lines with a given intensity distribution, and, then, a smoothed by the spectrometer instrumental function and noisy spectrum is obtained. The inverse problem is also formulated in two stages: initially, the Fredholm integral equation of the first kind is solved by the Tikhonov regularization method (an ill-posed problem), and, then, the problem of reconstruction of separate line-component shapes from the total spectrum is solved, which is the problem of line separation (division). The individual line components are modeled by Gaussians and Lorentzians. Numerical illustrations are shown. Gaussian and dispersion (Lorentz) instrumental functions are considered.     

Reconstruction of dynamic displacement and velocity from measured accelerations using the variational statement of an inverse problem

This paper presents two types of finite impulse response (FIR) filters to reconstruct dynamic displacement induced by structural vibration from measured acceleration. The governing equation for the reconstruction is derived by taking the variation of a minimization problem, which defines an inverse problem on displacement. A regularization function for overcoming the ill-posedness of the inverse problem is included in the minimization problem. The governing equation of the inverse problem becomes the same type of differential equation as that of a beam on an elastic foundation. The conventional FIR (CFIR) filter directly approximates the transfer function of the governing equation, while the FEM-based FIR (FFIR) filter is formulated by the discretization of the minimization problem with the finite element method. For the finite element discretization, the Hermitian shape function is utilized. The proposed FFIR filter is capable of reconstructing displacement and velocity simultaneously. The fundamental characteristics of the proposed filters are investigated in the frequency domain using the transfer and accuracy functions. It is shown that the proposed FIR filters suppress low frequency noise components in measured accelerations effectively, and reconstruct physically meaningful displacement accurately. The validity of the proposed filters is demonstrated through a numerical simulation study, a field experiment and an evaluation of flutter derivatives using measurements taken from a wind tunnel test.     

Recovering doping profiles in semiconductor devices with the Boltzmann–Poisson model

We investigate numerically an inverse problem related to the Boltzmann–Poisson system of equations for transport of electrons in semiconductor devices. The objective of the (ill-posed) inverse problem is to recover the doping profile of a device, presented as a source function in the mathematical model, from its current–voltage characteristics. To reduce the degree of ill-posedness of the inverse problem, we proposed to parameterize the unknown doping profile function to limit the number of unknowns in the inverse problem. We showed by numerical examples that the reconstruction of a few low moments of the doping profile is possible when relatively accurate time-dependent or time-independent measurements are available, even though the later reconstruction is less accurate than the former. We also compare reconstructions from the Boltzmann–Poisson (BP) model to those from the classical drift–diffusion-Poisson (DDP) model, assuming that measurements are generated with the BP model. We show that the two type of reconstructions can be significantly different in regimes where drift–diffusion-Poisson equation fails to model the physics accurately. However, when noise presented in measured data is high, no difference in the reconstructions can be observed.     

Dynamical symmetries and conservation laws for Korteweg-de Vries equation

The KdV-equation in two space time dimensions with the set of rapidly decreasing test functions as initial conditions is treated in the setting of nonlinear group and Lie algebra representations. The topological properties of the direct and inverse scattering mappings are discussed in detail.The algebra of continuous constants of motion turns out to be generated as in the linear case by three constants of motion and an extension of a representation of the e₂ Lie algebra on space-time symmetries to its enveloping algebra. The integrability of these representations is studied.It is further proved that the “moment problem” does not have a unique solution in this setting.The existence of noncommutative algebras of smooth time independent constants of motion is pointed out.     

Inverse radiation problem of temperature distribution in one-dimensional isotropically scattering participating slab with variable refractive index

In this paper, an inverse analysis is performed for estimation of source term distribution from the measured exit radiation intensities at the boundary surfaces in a one-dimensional absorbing, emitting and isotropically scattering medium between two parallel plates with variable refractive index. The variation of refractive index is assumed to be linear. The radiative transfer equation is solved by the constant quadrature discrete ordinate method. The inverse problem is formulated as an optimization problem for minimizing an objective function which is expressed as the sum of square deviations between measured and estimated exit radiation intensities at boundary surfaces. The conjugate gradient method is used to solve the inverse problem through an iterative procedure. The effects of various variables on source estimation are investigated such as type of source function, errors in the measured data and system parameters, gradient of refractive index across the medium, optical thickness, single scattering albedo and boundary emissivities. The results show that in the case of noisy input data, variation of system parameters may affect the inverse solution, especially at high error values in the measured data. The error in measured data plays more important role than the error in radiative system parameters except the refractive index distribution; however the accuracy of source estimation is very sensitive toward error in refractive index distribution. Therefore, refractive index distribution and measured exit intensities should be measured accurately with a limited error bound, in order to have an accurate estimation of source term in a graded index medium.