Schrödinger's What is Life?—The 75th Anniversary of a Book that Inspired Biology

In his book What is Life?—The Physical Aspect of the Living Cell, Erwin Schrödinger gives a “naïve physicist's” answer to the question “how can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?” Although his book was met with criticism from some of his colleagues, it has had a large impact and has served as profound inspiration for pioneers of molecular biology as well as for later generations of both scientists and laymen.     

Exotic spectra, wavefunctions and transport in incommensurate lattices

We present numerical results on a range of related issues for a number of incommensurate TMB’s, each of which shows a metal-insulator type transition as a binding-to-hopping ratio is made to increase through some limiting value. These supplement a series of similar results on a couple of 1D lattices in a number of recent works (see below). A brief review pertaining to spectral properties and wavefunctions in incommensurate lattices is followed by results on the above TBM’s relating to an interesting correlation between the gross features of wavefunctions and the energies arranged in a particular sequence termed thelattice-ordered sequence, and also between the lattice-ordered energies and the on-site potentials. We present a qualitative explanation of these correlations on the basis of perturbation theory. Basic results on dynamics of wavepackets in relation to spectral characteristics of incommensurate TBM’s are also reviewed. Features of lattice-ordered energies and wavefunctions for the TBM’s under study are used in the framework of the so-called Maryland construction, leading to a qualitative prediction of criteria for recurrent and non-recurrent wavepacket dynamics in these lattices, and these predictions are checked against numerical iterations of the relevant ‘quantum maps’. Closely related to the dynamics of wavepackets are the transport properties of these lattices. Results are available to indicate that the unusual spectral characteristics of pseudorandom lattices lead to novel features in transport properties of these systems. In this context, low temperature a.c conductivity in these lattices is a good probe for the spectral characteristics and wavefunctions. However, not much is known about the a.c conductivity, excepting a set of early results pertaining to the low frequency regime, principally because of the fact that the a.c conductivity depends on global characteristics of the spectrum and the entire set of wavefunctions. We present a simple model whereby the gross structure of variation of the a.c conductivity with frequency can be obtained from a knowledge of the spectrum alone for the set of TMB’s under consideration. Numerical computations show that despite its simplicity, the model leads to results in good agreement with those from the Kubo-Greenwood formula for a.c conductivity.     

基于高阻表面和波纹槽结构的法布里-珀罗天线研究

针对尺寸有限的法布里-珀罗(Fabry-Perot,FP)天线副瓣较大、增益带宽窄的问题,提出了一种基于高阻表面和波纹槽结构的新型FP天线模型.同时使用三维全波电磁场仿真软件CST就传统FP谐振结构、周期性以及非周期性加载高阻表面阵列和波纹槽结构对天线辐射性能的影响进行数值分析.模拟和实验测试结果表明:与传统FP谐振结构相比,加载周期结构仅能在较窄频带内提高天线增益,而加载非周期结构能使该天线增益在更宽频带内得到提高且其增益稳定性更好.     

Partitions of the phase space of a measure preserving ℤ d -action into towers

Alpern proved that the phase space of an aperiodic measure preserving automorphismT can be decomposed into Rokhlin-Halmos towers of given heightsh _i and weightsm _i whenever the numbersh _i are relatively prime. In this paper an extension of the Alpern theorem to the case of free ℤ ^d -actions is given. Namely, we investigate the decomposability of the action phase space into towers of rectangular, form and present conditions on the configuration (the set of tower forms) sufficient for the existence of such a decomposition. The proof of the main result uses the technique of tilings. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 712–725, May, 1999.     

Experimental Investigation of Mixing in Aperiodic Heterogeneous Porous Media: Comparison with Stochastic Transport Theory

An electrochemical technique was used to measure concentration distributions in an aperiodic heterogeneous model for comparison with a stochastic transport theory. Four identical columns, each filled with a homogeneous distribution of glass beads, were threaded together to create a single model with aperiodic heterogeneity. The layers in the model were arranged in different ways providing 24 realizations of the permeability distribution. Comparisons between experimental moment data and moments of simulated mean concentration distributions showed that the model was not able to accurately predict experimentally observed mixing behavior.     

双稳系统中非周期随机共振的数值仿真

本文采用互相关方法研究了噪声和随机二进制信号同时激励双稳系统(施密特触发器和双势阱系统)时的输出响应，观察到非周期随机共振：利用双稳系统中的非周期随机共振效应，可以减小随机信号传输中的噪声水平，改善输出信号质量，这在数字通信领域具有十分重要的意义。     

宽波带二次谐波产生过程中误差函数的研究

在无泵浦损耗近似(undepleted pump approximation,UPA)下用模拟退火算法设计的非周期光学超晶格(aperiodi optical superlattice,AOS)中实现了1.06~1.08 μm波长范围内高转换效率的宽波带二次谐波产生(second harmonic generation,SHG),并且在该结构中研究了已有文献所提出的误差函数对宽波带SHG过程的适用性。该文献提出的误差函数可以用来很好地估计SHG过程中UPA的适用范围,并且指出误差函数只跟SHG的转换效率有关。研究结果表明:宽波带SHG过程中的误差函数曲线与该文献提出的误差函数曲线(本文中称其为标准曲线)是有偏离的,也即该文献提出的误差函数曲线并不适用于宽波带SHG过程。这是因为在实现宽波带SHG的结构中并不能达到好的准相位匹配(quasi phase matching,QPM),该文献提出的误差函数曲线只有在满足完美的QPM的情况下才完全适用。并且还发现在宽波带SHG过程中,误差函数不仅与SHG的转换效率有关,与入射的基频波波长也有关系;对于某些误差函数曲线与标准曲线偏离不大的波长,该文献提出的误差函数曲线可以近似地用来估计UPA的适用范围。     

基于差分进化算法的宽频带扫描不等间距直线阵设计

设计了宽频带波束扫描不等间距直线阵列天线。在阵列天线孔径尺寸、带宽和最大波束扫描角度给定的情况下, 采用DE 算法极小化直线阵在工作频带内扫描方向图的峰值副瓣电平,求得最优的阵元间距分布。仿真结果表明,不等 间距排布方式可在工作频带内有效地抑制直线阵方向图的栅瓣。采用Ansoft HFSS 软件对优化后的直线阵进行了建模仿 真,HFSS 仿真结果与优化计算结果基本吻合。     

Abundant periodic and aperiodic solutions of a discontinuous three-term recurrence relation

In this note, we study a discontinuous three-term recurrence relation which arises from seeking the steady states of a cellular neural network with step control function. Several collections of periodic solutions are found. A necessary and sufficient condition for a solution to be periodic is stated and aperiodic solutions are found as consequences. We also show that any periodic solution can be derived from a primary periodic solution with least period not divisible by 5. Although the periodic or aperiodic solutions we found are not exhaustive, they are quite abundant and may reflect some of the rich physical phenomena in true biological systems. Our method in this note may also provide a general approach to analyze the periodicity of solutions of similar recurrence relations.