Quantum nonlocality for two-mode correlated states based on generalized pseudospin operators

In this Letter, we investigate the quantum nonlocality of two-mode correlated states. We find that the pseudospin formalism [Z.B. Chen, J.W. Pan, G. Hou, Y.D. Zhang, Phys. Rev. Lett. 88 (2002) 040406] generally fails to depict the nonlocality of the states when the photon number difference between the two modes is odd. The formalism is then generalized such that the nonlocality of a two-mode correlated state can be well revealed without regard to the difference. Later we consider the nonlocality of the two-mode intelligent SU(1,1) states in the generalized formalism and compare our results with the entanglement of the corresponding states.     

Integration of an Equilibrium System in an Enhanced Theory of Bending of Elastic Plates

The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates with transverse shear deformation and transverse normal strain is constructed by means of complex variable methods. The process helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish at infinity. An example is discussed to illustrate the theory.     

Combining the biased and unbiased sampling strategy into one convenient free energy calculation method

Constructing a free energy landscape for a large molecule is difficult. One has to use either a high temperature or a strong driving force to enhance the sampling on the free energy barriers. In this work, we propose a mixed method that combines these two kinds of acceleration strategies into one simulation. First, it applies an adaptive biasing potential to some replicas of the molecule. These replicas are particularly accelerated in a collective variable space. Second, it places some unbiased and exchangeable replicas at various temperature levels. These replicas generate unbiased sampling data in the canonical ensemble. To improve the sampling efficiency, biased replicas transfer their state variables to the unbiased replicas after equilibrium by Monte Carlo trial moves. In comparison to previous integrated methods, it is more convenient for users. It does not need an initial reference biasing potential to guide the sampling of the molecule. And it is also unnecessary to insert many replicas for the requirement of passing the free energy barriers. The free energy calculation is accomplished in a single stage. It samples the data as fast as a biased simulation and it processes the data as simple as an unbiased simulation. The method provides a minimalist approach to the construction of the free energy landscape. © 2019 Wiley Periodicals, Inc.     

Identification and treatment approach for spectral baseline distortion in processing of gas analysis online by Fourier transform infrared spectroscopy

Addressing the problem of baseline drift or distortion in Fourier transform infrared spectra when analyzing gas continuously at scene, a novel and simple method is proposed to identify and treat spectral baseline drift. Firstly, the spectral baseline was corrected with the common approach followed by standard gas analysis. Then, absorbance of analytes was reconstructed and reduced from the corrected spectrum. Finally, a Fourier transform was performed with the difference spectrum, and the first four-line strengths were used as feature variables to determine if baseline distortion occurred. In the end of this paper, this approach has been applied in the field of wellhead gas logging with Fourier transform infrared. The application results showed that all the spikes had been removed from the raw logging curves, confirming that this approach could be used to identify spectral baseline distortion accurately.     

Improving Our Knowledge on the 229mThorium Isomer: Toward a Test Bench for Time Variations of Fundamental Constants

For more than four decades, the lowest excitation in the whole landscape of atomic nuclei, the low‐lying, isomeric state of ²²⁹Th, the so‐called thorium isomer, has challenged physicists of various disciplines. Being a solitaire with its uniquely low excitation energy of <10 eV, its predicted lifetime of a few hours results in an extremely sharp relative linewidth ΔE/E as low as 10^–20. While until recently the indication of its existence was based only on indirect evidence, its unique properties inspired a multitude of potential applications, like the use of the thorium isomer as a nuclear frequency standard, potentially able to outperform even the best atomic clocks and a sensitivity‐enhanced access to potential temporal variations of fundamental constants. The various proposals to exploit the unique properties of ^229mTh are presented herein, in particular focusing on its ability to serve as a test bench for time variations of fundamental constants like the fine structure constant.     

Bayesian latent variable regression via Gibbs sampling: methodology and practical aspects

Bayesian latent variable regression (BLVR) aims to utilize all available information for empirical modeling via a Bayesian framework. Such information includes prior knowledge about the underlying variables, model parameters and measurement error distributions. This paper improves upon the existing optimization‐based BLVR (BLVR‐OPT) method [1] by developing a sampling‐based Bayesian latent variable regression (BLVR‐S) method that relies on Gibbs sampling. Use of the sampling‐based framework not only provides point estimates, but its ability to generate samples that represent the posterior distribution of the unknown variables, also readily provides error bounds. Features and advantages of this method are demonstrated via examples based on simulated data and real Near‐Infrared (NIR) spectroscopy data. Practical aspects of Bayesian modeling such as determining when the extra computation may be worth the effort are addressed by an empirical study of the effects of the amount of training data and signal to noise ratio (SNR). The benefits of BLVR seem to be most significant when the number of measurements is limited and when noise in output variables is relatively large. Copyright © 2007 John Wiley & Sons, Ltd.     

New Exact Solutions to （2＋1）-Dimensional Variable Coefficients Broer-Kaup Equations

In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.     

Localized Coherent Structures with Chaotic and Fractal Behaviors in a （2＋l）－Dimensional Modified Dispersive Water－Wave System

In this work, we reveal a novel phenomenon that the localized coherent structures of some (2 1)-dimensional physical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2 l)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach,a general variable separation solution of this system is derived. Besides the stable located coherent soliton excitations like dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractal behaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns.     

THE METHOD OF WEIGHTED DIFFERENCE FOR SINGULAR PERTURBATION PROBLEM

In this paper, we introduce a new difference approximation to the first order derivative u′and give a class of uniformly convergent difference schemes.     

Periodic solutions of singular second order differential equations: Upper and lower functions

In this paper, we continue the study of the periodic problem for the second-order equation u^′′+f(u)u^′+g(u)=h(t,u), where h is a Carathéodory function and f,g are continuous functions on (0,+∞) which may have singularities at zero. Both attractive and repulsive singularities are considered. The method relies on a novel technique of construction of lower and upper functions. As an application, we obtain new sufficient conditions for the existence of periodic solutions to the Rayleigh–Plesset equation.