Gauge invariance and the dirac equation

The gauge invariance of the Dirac equation is reviewed and gauge-invariant operators are defined. The Hamiltonian is shown to be gauge dependent, and an energy operator is defined which is gauge invariant. Gauge-invariant operators corresponding to observables are shown to satisfy generalized Ehrenfest theorems. The time rate of change of the expectation value of the energy operator is equal to the expectation value of the power operator. The virial theorem is proved for a relativistic electron in a time-varying electromagnetic field. The conventional approach to probability amplitudes, using the eigenstates of the unperturbed Hamiltonian, is shown in general to be gauge dependent. A gaugeinvariant procedure for probability amplitudes is given, in which eigenstates of the energy operator are used. The two methods are compared by applying them to an electron in a zero electromagnetic field in an arbitrary gauge. Presented at the Dirac Symposium, Loyola University, New Orleans, May 1981.     

Controlling Surface Interactions with Grafted Polymers

The interactions between surfaces modified with grafted polymers is studied theoretically. The aim of this work is to find polymer surface modifications that will result in localized attractive interactions between the surfaces. The practical motivation of the work is to find means to control the distance between bilayers and solid supports in supported membranes. Two theoretical approaches are used, the analytical treatment of Alexander and a molecular theory. It is found that grafting each end of the polymer to each surface results in an interaction with a well defined minimum. The location of the minima is found to be very close to the thickness of the polymer layer when the chains are grafted to only one of the surfaces. The predictions of the analytical theory are in excellent agreement with the molecular approach in this case. It is found that increasing the surface coverage increases the strength of the interaction. However, increasing the polymer chain length at fixed surface coverage results in a decrease of the free energy cost associated with separating the surfaces from their optimal distance. For the cases in which grafting to both surfaces is not possible, the molecular theory is used to study the effect of functionalizing segments of the chain to achieve an attractive well. It is found that by functionalizing the free end-groups of the polymers with segments attracted to the membrane, the range of the attractive interaction is significantly larger than the thickness of the unperturbed layer. Functionlizing the middle segments of the chains results in a shorter range attraction but of the same strength as in the end-functionalized layers. The optimal polymer modification is found to be such that the functionlized groups are attracted to the bare surface but are not attracted to the grafting surface. The relevance of the results to the design of experimental surface modifiers is discussed.     

An implementation of structural change detection procedure based on experimental and numerical model correlation

A correlation of the experimental and the numerical model is implemented in order to detect structural change. The implementation of the method involves two steps: in the first the respective location is detected, and in the second the structural change is quantified. The method can detect changes in mass, stiffness or both. The numerical simulations demonstrate that the method is accurate and reliable. The method is implemented analytically and experimentally in parallel with laboratory test-cases. Improvements of the procedure are suggested and implemented in order to study the applicability to real-world cases. This study shows that model update significantly contributes to the successful structural change detection. The influence of the model reduction and model update on the detection accuracy is studied.     

INHOMOGENEOUS WAVES IN ANISOTROPIC POROUS LAYER OVERLYING SOLID BEDROCK

The problem of propagation of inhomogeneous waves in anisotropic porous layered medium is studied using transfer matrix. Firstly, transfer matrix for an anisotropic porous layer is derived. Biot's poro-elastic theory is incorporated to model the acoustics of anisotropic porous layer. The interface between porous layer and elastic half-space is considered as imperfect and modified boundary conditions are applied for this more realistic situation. The theory of transfer matrix is used to derive the analytical expression for the surface impedance. Numerical computation of results is done for different degrees of bonding in the low as well as high-frequency range. In the first case, which is relevant to geophysical studies, the surface impedance is predicted for low-frequency range and surface impedance for second model is computed in high-frequency range. It is observed that loose bondedness is accompanied by the loss of energy at the interface. The technique of transfer matrix is utilized to compute the surface impedance in both cases. The role of surface impedance in seismological studies and in the study of composites is discussed.     

Long-Range Behavior of Dual-Restricted QCD Vacuum

We analyze the geometrical structure of the local non-Abelian gauge theory in terms of the magnetic symmetry, using the resemblance between the non-Abelian gauge formulations and Einstein's theory of gravitation in a higher dimensional unified space. The mathematical foundation of dual QCD in fiber bundle form is then discussed and used for the analysis of the important problem of color confinement in QCD. The associated Lagrangian formulation in magnetic gauge is shown to lead to dual dynamics due to the emergence of the topological charges of magnetic nature. The dynamical breaking of magnetic symmetry is shown to lead to the magnetic condensation of the QCD vacuum. A state of the dual superconductivity in the QCD vacuum is then shown to evolve which ultimately pushes the QCD vacuum to the confining phase. The flux tube structure of the magnetically condensed QCD vacuum is analyzed by computing the asymptotic string solutions of the field equations. The energy content of such confining structures is computed and analyzed in terms of its logarithmic and linear nature.     

Theory of zero bias anomalies due to paramagnetic impurities

The method developed by one of the authors is generalized to include paramagnetic impurities in order to explain zero bias tunneling anomalies. The self-energy of the electrons is supposed to be a local function in space; nonlocal or assisted tunneling effects are beyond the scope of the present theory. The tunneling current is expressed in terms of the local density of states at the barrier which in turn is given in terms of the life-time of the conduction electrons. The change of the local density of states depends on the positions of the impurities relative to the metal-oxide interface. This dependence is thoroughly investigated.     

Measurement of the dynamic structure function of fluorescently labeled complex fluids by fourier imaging correlation spectroscopy

The dynamics of the kicked rotor, which is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular, is studied statistically. The evolution operator of phase space densities in the chaotic component is calculated in the presence of noise, and the limit of vanishing noise is taken in the end. The relaxation rates to the equilibrium density are calculated analytically within an approximation that improves with increasing stochasticity. The results are tested numerically. A global picture is presented of relaxation to the equilibrium density in the chaotic component when the system is bounded and to diffusive behavior when it is unbounded.     

Phase order in one-dimensional piecewise linear discontinuous map

The phase order in a one-dimensional(1 D) piecewise linear discontinuous map is investigated. The striking feature is that the phase order may be ordered or disordered in multi-band chaotic regimes, in contrast to the ordered phase in continuous systems. We carried out an analysis to illuminate the underlying mechanism for the emergence of the disordered phase in multi-band chaotic regimes, and proved that the phase order is sensitive to the density distribution of the trajectories of the attractors. The scaling behavior of the net direction phase at a transition point is observed. The analytical proof of this scaling relation is obtained. Both the numerical and analytical results show that the exponent is 1, which is controlled by the feature of the map independent on whether the system is continuous or discontinuous. It extends the universality of the scaling behavior to systems with discontinuity. The result in this work is important to understanding the property of chaotic motion in discontinuous systems.     

A field theoretical approach to the anomalous hall effect in semiconductors

The anomalous Hall effect for polarized electrons in semiconductors is calculated by a field theoretical method. The results obtained are essentially equivalent to those of Luttinger except for minor generalizations (the treatment of collisions is not limited to the first term in a Born expansion and the conductivity is calculated at finite frequency). The main purpose is to set a very simple formulation that can be used to treat more complicated problems, e.g. anomalous Hall effect in the presence of a magnetic field or with a resonant precessing spin magnetization. The existence of two distinct contributions to the anomalous Hall effect is clearly shown, one of which is missed in the transport equation formulation. The order of magnitude of each contribution is discussed for two different experimental situations.     

Extension of Operational Matrix Technique for the Solution of Nonlinear System of Caputo Fractional Differential Equations Subjected to Integral Type Boundary Constrains

We extend the operational matrices technique to design a spectral solution of nonlinear fractional differential equations (FDEs). The derivative is considered in the Caputo sense. The coupled system of two FDEs is considered, subjected to more generalized integral type conditions. The basis of our approach is the most simple orthogonal polynomials. Several new matrices are derived that have strong applications in the development of computational scheme. The scheme presented in this article is able to convert nonlinear coupled system of FDEs to an equivalent S-lvester type algebraic equation. The solution of the algebraic structure is constructed by converting the system into a complex Schur form. After conversion, the solution of the resultant triangular system is obtained and transformed back to construct the solution of algebraic structure. The solution of the matrix equation is used to construct the solution of the related nonlinear system of FDEs. The convergence of the proposed method is investigated analytically and verified experimentally through a wide variety of test problems.     

The Tsallis entropy of natural information

Estimating the information contained in natural data, such as electroencephalography data, is unusually difficult because the relationship between the physical data and the information that it encodes is unknown. This unknown relationship is often called the encoding problem. The present work provides a solution to this problem by deriving a method to estimate the Tsallis entropy in natural data. The method is based on two findings. The first finding is that the physical instantiation of any information event, that is, the physical occurrence of a symbol of information, must begin and end at a discontinuity or critical point (maximum, minimum, or saddle point) in the data. The second finding is that, in certain data types such as the encephalogram (EEG), the variance within of an EEG waveform event is directly proportional to its probability of occurrence.These two outcomes yield two results. The first is the easy binning of data into separate information events. The second is the ability to estimate probabilities in two ways: frequency counting and computing the variance within of an EEG waveform. These results are used to derive a linear estimator of the Tsallis entropy functional, allowing it to be estimated without deducing the encoding.This method for estimating the Tsallis entropy is first used to estimate the information in simple signals. The amount of information estimated is highly accurate. The method is then applied to two problems in electroencephalography. The first is distinguishing normal aging from very early Alzheimer's disease (mild cognitive impairment), and the second is medication monitoring of Alzheimer's disease treatment. The former is done with an accuracy of 92% and the latter with an accuracy of 91%. This detection accuracy is the highest published accuracy in the literature, which suggests that this method for Tsallis entropy estimation is both accurate and useful.     

SU-8光刻胶应变分布光学全场检测方法

由于SU-8光刻胶的内应力将会影响高深宽比结构的全金属光栅的制作质量,本文针对近年来SU-8光刻胶应力测量困难的情况,提出了一种基于激光剪切散斑干涉技术的SU-8光刻胶应变分布测量的新方法。该方法通过对被测胶体加载前后两幅干涉图像的处理,直接得到被测胶体结构的全场应变分布情况,由胶体的应变变形数据即可反映出内应力的变化和分布趋势。同时使用ANSYS有限元分析软件对同一被测胶体进行应变仿真模拟研究,获得胶体结构的变形场仿真数据。组建了实验系统,进行了实验验证,结果表明:实际测量变形量约为1.189μm,仿真的最大变形量为1.088μm,测量误差在允许范围内,且测量的形变趋势与仿真模拟结果相一致,表明激光剪切散斑干涉技术可应用于SU-8光刻胶的应变分布全场无损检测。     

Polarization modulation in single-frequency He-Ne laser with an anisotropy feedback cavity

The polarization state is modulated by tilting birefringence component placed in the feedback external cavity.The variation of the polarization state in one period of modulation is found to be similar to sine wave.The periods become increasingly smaller.The maximum of variation in one period decreases against the rotated angle.The experimental phenomenon is subjected to the change of optical path and secondary reflection.The phenomenon is analyzed theoretically based on geometrical optics and crystal optics.High-accuracy measurements of absolute and relative angles can be realized based on the experimental phenomenon.The angle resolution is 0.1 arcsec in theory.     

Clausius-Mossotti-Type relation for planar monolayers

The dielectric properties of a quasi-two-dimensional molecular monolayer are analyzed. The dielectric function of the monolayer is expressed in terms of molecular polarizability and monolayer characteristics. The expression is analogous to the well-known Clausius-Mossotti equation for three-dimensional systems. The response of the monolayer to an external field is calculated. The case of a planar array of nanoparticles is also considered. The solution is obtained in the framework of a local-field theory.     

工作在亚毫米波段的付里叶变换谱仪

本文介绍了我们研制成功的工作在亚毫米波段的付里叶变换谱仪。工作波长为33μm至500μm,分弁率为1cm^-1。本仪器的主要特点是:1,采用微型机控制的数据采集和数据处理;2,动镜采用液压驱动,激光控制取样;3,整个干涉仪置于真空之中,以防水蒸汽的吸收。     

Troubles with Quantum Anisotropic Cosmological Models: Loss of Unitarity

The anisotropic Bianchi I cosmological model coupled with perfect fluid is quantized in the minisuperspace. The perfect fluid is described by using the Schutz formalism which allows to attribute dynamical degrees of freedom to matter. A Schrödinger-type equation is obtained where the matter variables play the role of time. However, the signature of the kinetic term is hyperbolic. This Schrödinger-like equation is solved and a wave packet is constructed. The norm of the resulting wave function comes out to be time dependent, indicating the loss of unitarity in this model. The loss of unitarity is due to the fact that the effective Hamiltonian is hermitian but not self-adjoint. The expectation value and the bohmian trajectories are evaluated leading to different cosmological scenarios, what is a consequence of the absence of a unitary quantum structure. The consistency of this quantum model is discussed as well as the generality of the absence of unitarity in anisotropic quantum models.     

The nonreciprocal effect under low- and high-frequency collinear acousto-optic interactions

The nonreciprocal effect under collinear acousto-optic interaction in the low- and high-frequency regimes is studied theoretically. The magnitudes of nonreciprocity determined from the ultrasonic frequency and from the wavelength of light are shown to be quantitatively identical. An expression that governs the magnitude of the nonreciprocity and that is valid for both low- and high-frequency regimes of the collinear acousto-optic interaction is obtained. The shape and width of the frequency characteristic of the collinear acousto-optic interaction calculated in the low diffraction efficiency approximation are shown to be the same in the low- and high-frequency regimes. The dependence of the frequency bandwidth of the collinear acousto-optic interaction on the ultrasonic-wave attenuation and diffraction efficiency is obtained. The magnitude of the nonreciprocal effect in some of the crystals used in acousto-optics is estimated numerically. The nonreciprocity of the collinear interaction is shown to be substantially stronger in the high-frequency regime relative to the low-frequency regime. Sapphire is proved to be an optimal material for experimental realization of the nonreciprocal effect in the high-frequency regime.     

The onset of convection of a poorly conducting fluid in a modulated thermal field

The stability of a poorly conducting fluid in a constant electric field of a horizontal capacitor is investigated under a variable temperature gradient. It is assumed that free charge in the fluid is generated only due to the nonhomogeneous conductivity of the fluid. The Floquet theory is used to determine the convection thresholds. The instability boundaries and the characteristics of critical perturbations are determined. In addition to the synchronous and subharmonic responses to an external action, the instability can be attributed to quasiperiodic perturbations. The low-frequency limit of modulation is considered by an asymptotic method. The critical electric Rayleigh number is represented as a function of inverse frequency and heating level.     

双光折变晶体半线性相位共轭器的自脉动

在由两块光折变BaTiO3晶体(其中一块晶体为全内反射式自抽运相位共轭镜工作方式,起外反射镜作用)构成的半线性自抽运相位共轭器中观察到了相位共轭光的自脉动现象。自脉动的平均频率f与入射光功率I0的关系为f∝I01.43;相位共轭光的平均维持时间ΔT与入射光功率I0近似成反比。观察到光折变BaTiO3晶体中扇形散射光具有动态的空间结构,扇形散射光的这种特性是引起上述半线性自抽运相位共轭器中相位共轭光脉动的原因     

用频域法实现圆环形目标物的计数

研究了用频域法实现圆环形目标物计数的方法。对空域中含有圆环形目标物的二值图像，经傅里叶变换后在频域内进行滤波，再经傅里叶反变换后取一阈值进行处理，则对应于圆环形目标物即变为一个实心体，然后对实心体进行计数即可实现对圆环形目标物的计数。对该方法进行了数学描述，并分别用模拟图像和实际图像进行了实验。结果表明，该方法消除噪声的效果好，对部分封闭圆的检测同样有效，且可用于目标物有粘连的情况。该方法对圆环形目标物的尺寸相差不大的情况更为有效。