Improved Broadband Inversion Performance for NMR in Liquids

New NMR broadband inversion pulses that compensate both for resonance offset and radiofrequency (RF) inhomogeneity are described. The approach described is a straightforward computer optimization of an initial digitized waveform generated from either a constant-amplitude frequency sweep or from an existing composite inversion pulse. Problems with convergence to local minima are alleviated by the way the optimization is carried out. For a given duration and maximum allowable RF field strength B₁ (but not necessarily given RMS power deposition), the resultant broadband inversion pulse (BIP) shows superior inversion compared to inversion pulses obtained from previous methods, including adiabatic inversion pulses. Any existing BIP can be systematically elaborated to build up longer inversion pulses that perform over larger and larger bandwidths. The resulting pulse need not be adiabatic throughout its duration or across the entire operational bandwidth.     

Approximate reconstruction of torsional potential energy surface based on voronoi tessellation

Torsional modes within a complex molecule containing various functional groups are often strongly coupled so that the harmonic approximation and one-dimensional torsional treatment are inaccurate to evaluate their partition functions. A family of multi-structural approximation methods have been proposed and applied in recent years to deal with the torsional anharmonicity. However, these methods approximate the exact “almost periodic” potential energy as a summation of local periodic functions with symmetric barrier positions and heights. In the present theoretical study, we illustrated that the approximation is inaccurate when torsional modes present non-uniformly distributed local minima. Thereby, we proposed an improved method to reconstruct approximate potential to replace the periodic potential by using information of the local minima and their Voronoi tessellation. First, we established asymmetric barrier heights by introducing two periodicity parameters and assuming that the exact barrier positions are at the boundaries of Voronoi cells. Second, we used multiplicatively weighted Voronoi tessellation to refine the barrier heights and positions by defining a structure-related distance metric. The proposed method has been tested for a few higher-dimensional cases, all of which show promising improved accuracy.     

Lens Design: Global Optimization with Escape Function

The technique of using the ‘escape function’ for global optimization in lens design is described. This includes how to identify two solutions as independent; the threshold value for this criterion can be chosen to determine how to explore local solutions—rough or fine. Choice of appropriate values for two parameters in the escape function is most important, since this will affect the efficiency of the automatic global optimization process. There are two problems, i.e. giving default values at the beginning of the design, and determining a default rule to change them when the escape is unsuccessful. The latter was solved by assuming a ‘saddle path’ as the best route to escape. An exact solution for the former was not found, but a hint for finding a second best solution is shown based on the statistical study of local minima.     

利用U-Net网络增强骨密度全波形反演

该文设计了一种使用U-Net网络解决骨密度全波形反演的初值依赖、多解、病态等问题的方法。首先使用逆时偏移成像，将其结果输入神经网络得到模型的预分布。将该分布作为全波形反演目标函数的约束，可以使反演的结果更接近最优值，还可以减小反演对初始值的依赖。该文进行了一些模拟实验，得出该文的方法可以改进全波形反演对初始值的依赖和容易陷入局部极值的问题。     

Three-dimensional electromagnetic nonlinear inversion in layered media by a hybrid diagonal tensor approximation: Stabilized biconjugate gradient fast Fourier transform method

This paper presents an efficient three-dimensional nonlinear electromagnetic inversion method in a multilayered medium for radar applications where the object size is comparable to the wavelength. In the first step of this two-step inversion algorithm, the diagonal tensor approximation is used in the Born iterative method. The solution of this approximate inversion is used as an initial guess for the second step in which further inversion is carried out using a distorted Born iterative method. Since the aim of the second step is to improve the accuracy of the inversion, a full-wave solver, the stabilized biconjugate-gradient fast Fourier transform algorithm, is used for forward modelling. The conjugate-gradient method is applied at each inversion iteration to minimize the functional cost. The usage of an iterative solver based on the FFT algorithm and the developed recursive matrix method combined with an interpolation technique to evaluate the layered medium Green's functions rapidly, makes this method highly efficient. An inversion problem with 32 768 complex unknowns can be solved with 1% relative error by using a simple personal computer. Several numerical experiments for arbitrarily located source and receiver arrays are presented to show the high efficiency and accuracy of the proposed method.     

Three-dimensional electromagnetic nonlinear inversion in layered media by a hybrid diagonal tensor approximation: Stabilized biconjugate gradient fast Fourier transform method

This paper presents an efficient three-dimensional nonlinear electromagnetic inversion method in a multilayered medium for radar applications where the object size is comparable to the wavelength. In the first step of this two-step inversion algorithm, the diagonal tensor approximation is used in the Born iterative method. The solution of this approximate inversion is used as an initial guess for the second step in which further inversion is carried out using a distorted Born iterative method. Since the aim of the second step is to improve the accuracy of the inversion, a full-wave solver, the stabilized biconjugate-gradient fast Fourier transform algorithm, is used for forward modelling. The conjugate-gradient method is applied at each inversion iteration to minimize the functional cost. The usage of an iterative solver based on the FFT algorithm and the developed recursive matrix method combined with an interpolation technique to evaluate the layered medium Green's functions rapidly, makes this method highly efficient. An inversion problem with 32 768 complex unknowns can be solved with 1% relative error by using a simple personal computer. Several numerical experiments for arbitrarily located source and receiver arrays are presented to show the high efficiency and accuracy of the proposed method.     

Procedure for retrieving the optical properties of a two-layered medium from time-resolved reflectance measurements

A procedure for retrieving the optical properties of a two-layered diffusive medium based on an exact analytical solution of the diffusion equation and on relative multidistance time-resolved reflectance measurements is presented. The method overcomes some limitations of previously developed procedures. Five parameters of the medium have been fitted: the absorption and the reduced scattering coefficients of both layers and the thickness of the first layer. The actual values of the parameters are correctly retrieved by the procedure. The inversion procedure does not require an initial guess for the unknown optical properties, but the starting value for the thickness of the first layer needs to be estimated with an error smaller than 50%.     

Exact solution and scaling theory of superradiance

The general scaling theory of transient phenomena near the instability point, which has been proposed by one of the present authors (M.S.), is applied to investigate the fluctuation and relaxation of superradiance near the complete inversion (or instability point). An exact solution for a simple model of superradiance has been obtained to study the relaxation and fluctuation of it near the complete inversion and to confirm the validity of the scaling theory. It is found that this asymptotic evaluation method yields very good results for a large system size Ω. The Ω-expansion method by van Kampen and by Kubo et al. is also discussed in this model in order to clarify the connection of it with the scaling theory.     

Ground Penetrating Radar Nondestructive Testing Based on Wavelet Sparse Representation

Now Ground penetrating radar (GPR) nondestructive testing methods have been applied to many fields of physics. But traditional electromagnetic methods (usually based on least square and local iteration) just roughly give the information of location, level and quality. In this paper we consider inverse electromagnetic problem which is concerned with the estimation of electric conductivity of Maxwell’s equations. A wavelet multilevel representation is proposed to inversion of GPR nondestructive testing. Once we decompose the objective functional onto different levels from the smallest to the largest, there are very few local minimum on the largest level component of the problem. Then local convergent Gauss-Newton method could easily find the global minimum on this level which is close to the global optimization solution on the second largest level. So, Gauss-Newton method with initial value which is solved on the largest level has serious possibility to find the global minimum of the second largest level. Repeating this step one could find the global optimization solution of the original inverse problem. On each level, the stable and fast local convergent Gauss-Newton method is carried out. Results exhibits clear advantages over damping Gauss-Newton method and testify that it is an available method, especially on aspects of wide convergence and precision.     

A Matrix-Vector Operation-Based Numerical Solution Method for Linear $m$-th Order Ordinary Differential Equations: Application to Engineering Problems

Many problems in engineering sciences can be described by linear, inhomogeneous, $m$-th order ordinary differential equations (ODEs) with variable coefficients. For this wide class of problems, we here present a new, simple, flexible, and robust solution method, based on piecewise exact integration of local approximation polynomials as well as on averaging local integrals. The method is designed for modern mathematical software providing efficient environments for numerical matrix-vector operation-based calculus. Based on cubic approximation polynomials, the presented method can be expected to perform (i) similar to the Runge-Kutta method, when applied to stiff initial value problems, and (ii) significantly better than the finite difference method, when applied to boundary value problems. Therefore, we use the presented method for the analysis of engineering problems including the oscillation of a modulated torsional spring pendulum, steady-state heat transfer through a cooling web, and the structural analysis of a slender tower based on second-order beam theory. Related convergence studies provide insight into the satisfying characteristics of the proposed solution scheme.     

Exact steady states to a nonlinear surface growth model

We report on exact stationary solutions to a nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. 80, 4221 (1998)]. Firstly, attention is focused on periodic solutions (steady states) which admit vertical points (or diverging local slopes). Such solutions, which are determined by a theoretical analysis, reveal that the nonlinear evolution equation may admit a non stationary solution with spike singularities or/and caps (dead-core solution) at maxima or/and minima. In a second part, steady states are, mathematically, generalized to a family of evolution equations. Finally, the effect of smoothening by step-edge diffusion is also revisited.     

Tunneling and energy splitting in an asymmetric double-well potential

An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency ω and the difference of the minima is close to a multiple of ?ω. A WKB wave function is constructed on both sides of the local maximum between the wells, by matching the WKB function to the exact wave functions near the classical turning points. The continuities of the wave function and its first derivative at the local maximum then give the energy-level splitting formula, which not only reproduces the instanton result for a symmetric potential, but also elucidates the appearance of resonances of tunneling in the asymmetric potential.     

基于伴随方程法的材料热传导系数反演方法

建立利用材料内部温度场的测量结果反演材料热传导系数随时间和空间位置变化函数的伴随方程法,参考迭代正则化的思想在优化过程中给目标函数设置停止准则.对典型算例计算表明,方法在测量噪声较小情况下能得出较为合理的反演结果.但在有测量噪声的情况下,反演结果与真值在边界x=0和L处存在着一定偏差.当测量噪声较大时,反演结果与真值的偏差较为明显,且初值选取会对反演结果有相当大的影响.     

The Exact Solution of Milburn Equation Without Diffusion Approximation for the Two-Model Raman Coupled Model

By making use of the dynamical algebraic approach, we study the two-mode Raman coupled model governed by the Milburn equation and find the exact solution of the Milburn equation without diffusion approximation. The exact solution is then used to discuss the influence of intrinsic decoherence on the revivals of atomic inversion, oscillation of the photon number distribution and squeezing of radiation field in the whole ranges of the decoherence parameter γ.     

基于牛顿迭代法高温光谱温度和发射率的反演研究

针对基于光谱数据进行温度与发射率分离过程中存在的n个方程包含n+1个未知数这一欠定问题,提出利用牛顿迭代法来实现材料表面真温及发射率的反演计算,通过给定温度和发射率初值,利用泰勒级数的线性项建立迭代公式,通过迭代得到温度和发射率的近似解。分别利用理论热辐射谱和腔黑体的实验数据进行验证,结果表明,任意给定温度和发射率初值均可获得与真实温度接近的计算温度值,相对误差小于0.09。发射率反演结果与真实发射率线形一致,当温度和发射率初值越接近真实温度和发射率时,发射率反演结果越精确。该方法消除了发射率假定模型限制,有望应用于高温及超高温下各种材料真实温度和光谱发射率研究。     

Generalized source method: New possibilities for waveguide and grating problems

A new, general and exact method for resolving waveguide and grating problems is presented whereby the unknown electric field in a given dielectric distribution in the presence of an arbitrary source distribution can be obtained exactly from the known complete electric field solution in a simpler dielectric structure in the presence of the same source distribution. The method can be used in the form of an iterative scheme. The solution can also be obtained through an implicit equation which can be solved numerically without convergence problem by matrix inversion. The application of the method to the case of abnormal reflection under normal incidence from a segmented waveguide is given as an example.     

Noise induced stability in fluctuating, bistable potentials

The overdamped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is enhanced. The model works as a detector for potential fluctuations being not too fast and not too slow. This effect occurs due to the different time scales in the problem. We present a detailed analysis of this effect using the exact solution of the Fokker-Planck equation for a simple model. Further we show that for not too fast fluctuations the system can be well described by effective rate equations. The results of the rate equations agree quantitatively with the exact results.     

多原子体系与单模光场的多光子相互作用

用狄克（Ｄｉｃｋｅ）态的缀饰原子态的方法，解出了多原子体系与单模光场的多光子相互作用下总体系的量子态随时间演化的精确解。进而又研究了原子体系的粒子数反转，光场的压缩度及反聚束效应随时间的演化。通过数值计算，发出了一些新的演化规律。     

Extension of the distributed point source method for ultrasonic field modeling

The distributed point source method (DPSM) was recently proposed for ultrasonic field modeling and other applications. This method uses distributed point sources, placed slightly behind transducer surface, to model the ultrasound field. The acoustic strength of each point source is obtained through matrix inversion that requires the number of target points on the transducer surface to be equal to the number of point sources. In this work, DPSM was extended and further developed to overcome the limitations of the original method and provide a solid mathematical explanation of the physical principle behind the method. With the extension, the acoustic strength of the point sources was calculated as the solution to the least squares minimization problem instead of using direct matrix inversion. As numerical examples, the ultrasound fields of circular and rectangular transducers were calculated using the extended and original DPSMs which were then systematically compared with the results calculated using the theoretical solution and the exact spatial impulse response method. The numerical results showed the extended method can model ultrasonic fields accurately without the scaling step required by the original method. The extended method has potential applications in ultrasonic field modeling, tissue characterization, nondestructive testing, and ultrasound system optimization.     

Structure optimization by heuristic algorithm in a coarse-grained off-lattice model

A heuristic algorithm is presented for a three-dimensional off-lattice AB model consisting of hydrophobic (A) and hydrophilic (B) residues in Fibonacci sequences. By incorporating extra energy contributions into the original potential function, we convert the constrained optimization problem of AB model into an unconstrained optimization problem which can be solved by the gradient method. After the gradient minimization leads to the basins of the local energy minima, the heuristic off-trap strategy and subsequent neighborhood search mechanism are then proposed to get out of local minima and search for the lower-energy configurations. Furthermore, in order to improve the efficiency of the proposed algorithm, we apply the improved version called the new PERM with importance sampling (nPERMis) of the chain-growth algorithm, pruned-enriched-Rosenbluth method (PERM), to face-centered-cubic (FCC)-lattice to produce the initial configurations. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. In several cases, we found the ground state energies are lower than the best values reported in the present literature.