Defect-controlled numerical methods and shadowing for chaotic differential equations

It is well-known that chaotic ODE's are, in the classical sense, unstable or ill-conditioned. It is not clear that variable step-size codes based on local error control can solve such problems in a useful way. In particular, it is usually difficult to show that the apparent chaos in the resulting solution is not a numerical artifact. I show here that a defect-controlled method gives useful solutions for chaotic problems. A pragmatically modified definition of what it means for a dynamical system to be chaotic is also presented.     

AutoMH: Automatically Create Evolutionary Metaheuristic Algorithms Using Reinforcement Learning

Machine learning research has been able to solve problems in multiple domains. Machine learning represents an open area of research for solving optimisation problems. The optimisation problems can be solved using a metaheuristic algorithm, which can find a solution in a reasonable amount of time. However, the time required to find an appropriate metaheuristic algorithm, that would have the convenient configurations to solve a set of optimisation problems properly presents a problem. The proposal described in this article contemplates an approach that automatically creates metaheuristic algorithms given a set of optimisation problems. These metaheuristic algorithms are created by modifying their logical structure via the execution of an evolutionary process. This process employs an extension of the reinforcement learning approach that considers multi-agents in their environment, and a learning agent composed of an analysis process and a process of modification of the algorithms. The approach succeeded in creating a metaheuristic algorithm that managed to solve different continuous domain optimisation problems from the experiments performed. The implications of this work are immediate because they describe a basis for the generation of metaheuristic algorithms in an online-evolution.     

Why Should We Interpret Quantum Mechanics?

The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this epistemic view of states appears to solve foundational problems of quantum mechanics only at the price of being essentially incomplete.     

EcoQBNs: First Application of Ecological Modeling with Quantum Bayesian Networks

A recent advancement in modeling was the development of quantum Bayesian networks (QBNs). QBNs generally differ from BNs by substituting traditional Bayes calculus in probability tables with the quantum amplification wave functions. QBNs can solve a variety of problems which are unsolvable by, or are too complex for, traditional BNs. These include problems with feedback loops and temporal expansions; problems with non-commutative dependencies in which the order of the specification of priors affects the posterior outcomes; problems with intransitive dependencies constituting the circular dominance of the outcomes; problems in which the input variables can affect each other, even if they are not causally linked (entanglement); problems in which there may be >1 dominant probability outcome dependent on small variations in inputs (superpositioning); and problems in which the outcomes are nonintuitive and defy traditional probability calculus (Parrondo’s paradox and the violation of the Sure Thing Principle). I present simple examples of these situations illustrating problems in prediction and diagnosis, and I demonstrate how BN solutions are infeasible, or at best require overly-complex latent variable structures. I then argue that many problems in ecology and evolution can be better depicted with ecological QBN (EcoQBN) modeling. The situations that fit these kinds of problems include noncommutative and intransitive ecosystems responding to suites of disturbance regimes with no specific or single climax condition, or that respond differently depending on the specific sequence of the disturbances (priors). Case examples are presented on the evaluation of habitat conditions for a bat species, representing state-transition models of a boreal forest under disturbance, and the entrainment of auditory signals among organisms. I argue that many current ecological analysis structures—such as state-and-transition models, predator–prey dynamics, the evolution of symbiotic relationships, ecological disturbance models, and much more—could greatly benefit from a QBN approach. I conclude by presenting EcoQBNs as a nascent field needing the further development of the quantum mathematical structures and, eventually, adjuncts to existing BN modeling shells or entirely new software programs to facilitate model development and application.     

A principle in dynamic coarse graining–Onsager principle and its applications

Dynamic coarse graining is a procedure to map a dynamical system with large degrees of freedom to a system with smaller degrees of freedom by properly choosing coarse grained variables. This procedure has been conducted mainly by empiricisms. In this paper, I will discuss a theoretical principle which may be useful for this procedure. I will discuss how to choose coarse grained variables (or slow variables), and how to set up their evolution equations. To this end, I will review the classical example of dynamic coarse graining, i.e., the Brownian motion theory, and show a variational principle for the evolution of the slow variables. The principle, called the Onsager principle, is useful not only to derive the evolution equations, but also to solve the problems.     

电光相位调制器谐波响应对光纤陀螺的影响

从电光相位调制器的谐波响应出发,对干涉型光纤陀螺信号零偏、零漂的产生来源进行了探讨.用干涉理论和正弦波调制解调分析从原理上指出调制器的振幅与相位两种谐波可产生陀螺信号的零偏和零漂.根据调制器典型数据所做的模拟与人为加入温漂时所得的试验结果相当吻合.从而证实调制器谐波响应是产生陀螺信号偏移和漂移的主要原因,为减小光纤陀螺零偏和零漂提供了一条新思路.     

充分发挥习题的作用培养学生独立解决问题的能力

课后习题不仅是对学生灵活应用所学知识的锻炼,也是培养学生独立分析问题、解决问题能力的有效渠道.本文通过对一道普通物理力学课程中常见习题可能得出的几种不同结果及其原因的分析,对如何通过习题帮助学生提高独立解决问题的能力进行了探讨.     

Fuzzy spaces topology change as a possible solution to the black hole information loss paradox

The black hole information loss paradox is one of the most intricate problems in modern theoretical physics. A proposal to solve this is one related with topology change. However it has found some obstacles related to unitarity and cluster decomposition (locality). In this Letter we argue that modelling the black hole's event horizon as a noncommutative manifold – the fuzzy sphere – we can solve the problems with topology change, getting a possible solution to the black hole information loss paradox.     

Method of Lines Based on Finite Element Discrete Technique to Analyze Eigenvalues of Waveguides

In this paper, a novel numerical technique to solve electromagnetic boundary value problem is described. This finite element based method of lines is developed by combining finite element method and the method of lines, so that it not only has high flexibility to treat geometrically and compositionally complex problems but also maintains high accuracy of semi-analytical technique. The geometry discretization, element mapping, element trial function and standard ordinary differential equation construction are discussed in details. Our numerical result demonstrates that this method can successfully solve the complex problems with fewer mesh lines when compared with conventional method of lines.     

Probabilistic quantum memories

Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that solves both problems. The storage capacity is exponential in the number of qbits and thus optimal. The retrieval mechanism for incomplete or noisy inputs is probabilistic, with postselection of the measurement result. The output is determined by a probability distribution on the memory which is peaked around the stored patterns closest in Hamming distance to the input.     

应用于LED灯具散热的平板热管传热特性

平板热管作为一种新型的热管技术,具有高热导率,良好的均温性等优点,成为解决大功率LED散热问题很有前途的技术之一。本文通过实验与数值模拟相结合的方法,研究了平板热管散热模组的传热性能,探讨了热源布置方式(集中式布置与分散式布置)的影响,为LED芯片的布置提供理论指导。结果表明:该平板热管散热模组的散热效果良好,能有效解决LED灯的散热问题。     

The neglected pillar of material computation

Many novel forms of computational material have been suggested, from using slime moulds to solve graph searching problems, to using packaging foam to solve differential equations. I argue that attempting to force such novel approaches into the conventional Universal Turing computational framework will provide neither insights into theoretical questions of computation, nor more powerful computational machines. Instead, we should be investigating matter from the perspective of its natural computational capabilities. I also argue that we should investigate nonbiological substrates, since these are less complex in that they have not been tuned by evolution to have their particular properties. Only then we will understand both aspects of computation (logical and physical) required to understand the computation occurring in biological systems.     

在代数多重网格法中的新插值公式

推导出代数多重网格法的一个新的插值公式。理论分析和数值计算表明这个公式很有效,且适用性强。推广了原代数多重网格法的应用范围,能够求解一些很病态的代数方程组。     

旋转矢量法在解决简谐振动相关问题中的应用

用旋转矢量法解决简谐振动问题会使解题难度降低,可以形象、直观地表示出简谐振动中各物理量之间的相互关系,有助于简化问题解决中的数学过程.在求解波动问题时,旋转矢量法同样可以有效地解决相位的问题.     

Reduction of speckles and distortion in projection system by using a rotating diffuser

A head up display (HUD) with laser backlight unit has two principle problems; one is laser speckles and the other is distortion. In this study, we propose that a rotating diffuser set at the intermediate image plane of the HUD projection system can simultaneously solve these problems. The conditions of speckle reduction and de-distortion are also estimated in this paper.     

Discrete-ordinates solution for uncoupled multi-wavelength radiative transfer problems

The discrete-ordinates method is used to solve uncoupled multi-wavelength radiative transfer problems in multi-region plane-parallel media. We present a generalized analytical discrete-ordinates formulation that includes internal sources, as well as reflecting and emitting boundaries, incident distribution of radiation on each surface and a beam incident on one surface, as boundary conditions. Four problems were selected to show the results that can be generated through this formulation.     

Creation of a soluton out of dissipation

Recent experimental observations of stimulated Raman scattering have observed an anomalous reversal of pump depletion under certain circumstances. This reversal of the pump depletion has been interpreted by Drühl, Carlsten, and Wenzel as a heavily-damped soliton whose width narrows as it propagates in the Raman-active medium. In this paper, I solve the initial value problem for such a system. Furthermore, I find that I can theoretically predict the number of such solitons which shall appear as well as give the conditions necessary for such solitons to occur. Lastly, by using the proper solution for the initial value problem, I can verify the correctness of the results given by Drühl, Carlsten, and Wenzel for the position and widths of such solitons.     

Matlab在面向“拔尖学生”的大学物理教学中的应用

介绍了在面向"拔尖学生"的大学物理教学中,融入了Matlab编程解决复杂物理问题的教学实践.以力学为例,介绍了教学实践中如何引导学生从基本的物理原理出发,借助微积分和Matlab强大的计算和画图功能解决复杂的力学问题,这项极具挑战性的学习任务不仅使学生更深入地理解了所学物理知识,更让学生体会到微积分的应用,以及计算物理的魅力,使其以后的学习和研究中能处理更加复杂的科学问题,增强了学生解决实际问题的能力和科研能力,助力拔尖学生的培养.     

Equivalent a Posteriori Error Estimator of Spectral Approximation for Control Problems with Integral Control-State Constraints in One Dimension

In this paper, we investigate the Galerkin spectral approximation for elliptic control problems with integral control and state constraints. Firstly, an a posteriori error estimator is established, which can be acted as the equivalent indicator with explicit expression. Secondly, appropriate base functions of the discrete spaces make it probable to solve the discrete system. Numerical test indicates the reliability and efficiency of the estimator, and shows the proposed method is competitive for this class of control problems. These discussions can certainly be extended to two- and three-dimensional cases.