Exact spectral functions of a non-Fermi liquid in one dimension

We study the exact one-electron propagator and spectral function of a solvable model of interacting electrons due to Schulz and Shastry. The solution previously found for the energies and wave functions is extended to give spectral functions that turn out to be computable, interesting, and nontrivial. They provide one of the few examples of cases where the spectral functions are known asymptotically as well as exactly.

Quadratic Lyapunov functions for linear systems Journal

The paper deals with the existence of a quadratic Lyapunov function V = x′P(t)x for an exponentially stable linear system with varying coefficients described by the vector differential equation S0305004100044777_inline1 The derivative dV/dt is allowed to be strictly semi-(F) and the locus dV/dt = 0 does not contain any arc of the system trajectory. It is then shown that the coefficient matrix A(t) of the exponentially stable sy

Acquisition time improvement of PLLs using some aiding functions

Analytical studies are carried out to minimize acquisition time in phase-lock loop (PLL) applications using aiding functions. A second order aided PLL is realized with the help of the quasi-stationary approach to verify the acquisition behavior in the absence of noise. Time acquisition is measured both from the study of the LPF output transient and by employing a lock detecting and indicating circuit to crosscheck experimental and analytical results. A closed form solution is obtained for the evaluation of the time acquisition using different aiding functions. The aiding signal is simple and economical and can be used with state of the art hardware.

The advection-condensation model and water-vapour probability density functions

The statistically steady humidity distribution resulting from an interaction of advection, modelled as an uncorrelated random walk of moist parcels on an isentropic surface, and a vapour sink, modelled as immediate condensation whenever the specific humidity exceeds a specified saturation humidity, is explored with theory and simulation. A source supplies moisture at the deep-tropical southern boundary of the domain and the saturation humidity is specified as a monotonically decreasing function of distance from the boundary. The boundary source balances the interior condensation sink, so that a stationary spatially inhomogeneous humidity distribution emerges. An exact solution of the Fokker-Planck equation delivers a simple expression for the resulting probability density function (PDF) of the wate-rvapour field and also the relative humidity. This solution agrees completely with a numerical simulation of the process, and the humidity PDF exhibits several features of interest, such as bimodality close to the source and unimodality further from the source. The PDFs of specific and relative humidity are broad and non-Gaussian. The domain-averaged relative humidity PDF is bimodal with distinct moist and dry peaks, a feature which we show agrees with middleworld isentropic PDFs derived from the ERA interim dataset. Copyright (C) 2011 Royal Meteorological Society

Thermal Weight Functions and Stress Intensity Factors for Bonded Dissimilar Media Using Body Analogy

In this study, an analytical method is presented for the computation of thermal weight functions in two dimensional bi-material elastic bodies containing a crack at the interface and subjected to thermal loads using body analogy method. The thermal weight functions are derived for two problems of infinite bonded dissimilar media, one with a semi-infinite crack and the other with a finite crack along the interface. The derived thermal weight functions are shown to reduce to the already known expressions of thermal weight functions available in the literature for the respective homogeneous elastic body. Using these thermal weight functions, the stress intensity factors are computed for the above interface crack problems when subjected to an instantaneous heat source.

An interior penalty method for a sixth-order elliptic equation

We derive and study a C(0) interior penalty method for a sixth-order elliptic equation on polygonal domains. The method uses the cubic Lagrange finite-element space, which is simple to implement and is readily available in commercial software. After introducing some notation and preliminary results, we provide a detailed derivation of the method. We then prove the well-posedness of the method as well as derive quasi-optimal error estimates in the energy norm. The proof is based on replacing Galerkin orthogonality with a posteriori analysis techniques. Using this approach, we are able to obtain a Cea-like lemma with minimal regularity assumptions on the solution. Numerical experiments are presented that support the theoretical findings.

Detection of a periodic structure embedded in surface roughness, for various correlation functions

This paper deals with surface profilometry, where we try to detect a periodic structure, hidden in randomness using the matched filter method of analysing the intensity of light, scattered from the surface. From the direct problem of light scattering from a composite rough surface of the above type, we find that the detectability of the periodic structure can be hindered by the randomness, being dependent on the correlation function of the random part. In our earlier works, we had concentrated mainly on the Cauchy-type correlation function for the rough part. In the present work, we show that this technique can determine the periodic structure of different kinds of correlation functions of the roughness, including Cauchy, Gaussian etc. We study the detection by the matched filter method as the nature of the correlation function is varied.

Fracture analysis of concrete using singular fractal functions with lattice beam network and confirmation with acoustic emission study

In the present study singular fractal functions (SFF) were used to generate stress-strain plots for quasibrittle material like concrete and cement mortar and subsequently stress-strain plot of cement mortar obtained using SFF was used for modeling fracture process in concrete. The fracture surface of concrete is rough and irregular. The fracture surface of concrete is affected by the concrete's microstructure that is influenced by water cement ratio, grade of cement and type of aggregate 11-41. Also the macrostructural properties such as the size and shape of the specimen, the initial notch length and the rate of loading contribute to the shape of the fracture surface of concrete. It is known that concrete is a heterogeneous and quasi-brittle material containing micro-defects and its mechanical properties strongly relate to the presence of micro-pores and micro-cracks in concrete 11-41. The damage in concrete is believed to be mainly due to initiation and development of micro-defects with irregularity and fractal characteristics. However, repeated observations at various magnifications also reveal a variety of additional structures that fall between the `micro' and the `macro' and have not yet been described satisfactorily in a systematic manner [1-11,15-17]. The concept of singular fractal functions by Mosolov was used to generate stress-strain plot of cement concrete, cement mortar and subsequently the stress-strain plot of cement mortar was used in two-dimensional lattice model [28]. A two-dimensional lattice model was used to study concrete fracture by considering softening of matrix (cement mortar). The results obtained from simulations with lattice model show softening behavior of concrete and fairly agrees with the experimental results. The number of fractured elements are compared with the acoustic emission (AE) hits. The trend in the cumulative fractured beam elements in the lattice fracture simulation reasonably reflected the trend in the recorded AE measurements. In other words, the pattern in which AE hits were distributed around the notch has the same trend as that of the fractured elements around the notch which is in support of lattice model. (C) 2011 Elsevier Ltd. All rights reserved.

Analysis of a linear one-dimensional active noise control system by means of block diagrams and transfer functions

In arriving at the ideal filter transfer function for an active noise control system in a duct, the effect of the auxiliary sources (generally loudspeakers) on the waves generated by the primary source has invariably been neglected in the existing literature, implying a rigid wall or infinite impedance. The present paper presents a fairly general analysis of a linear one-dimensional noise control system by means of block diagrams and transfer functions. It takes into account the passive as well as active role of a terminal primary source, wall-mounted auxiliary source, open duct radiation impedance, and the effects of mean flow and damping. It is proved that the pressure generated by a source against a load impedance can be looked upon as a sum of two pressure waves, one generated by the source against an anechoic termination and the other by reflecting the rearward wave (incident on the source) off the passive source impedance. Application of this concept is illustrated for both the types of sources. A concise closed-form expression for the ideal filter transfer function is thus derived and discussed. Finally, the dynamics of an adaptive noise control system is discussed briefly, relating its standing-wave variables and transfer functions with those of the progressive-wave model presented here.

On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.