Probing potential energy surfaces in confined systems: behavior of mean-square displacement in zeolites

Time evolution of mean-squared displacement based on molecular dynamics for a variety of adsorbate-zeolite systems is reported. Transition from ballistic to diffusive behavior is observed for all the systems. The transition times are found to be system dependent and show different types of dependence on temperature. Model calculations on a one-dimensional system are carried out which show that the characteristic length and transition times are dependent on the distance between the barriers, their heights, and temperature. In light of these findings, it is shown that it is possible to obtain valuable information about the average potential energy surface sampled under specific external conditions.

Identification and output tracking control of Hammerstein systems through wireless networks

his paper investigates the identification and output tracking control of a class of Hammerstein systems through a wireless network within an integrated framework and the statistic characteristics of the wireless network are modelled using the inverse Gaussian cumulative distribution function. In the proposed framework, a new networked identification algorithm is proposed to compensate for the influence of the wireless network delays so as to acquire the more precise Hammerstein system model. Then, the identified model together with the model-based approach is used to design an output tracking controller. Mean square stability conditions are given using linear matrix inequalities (LMIs) and the optimal controller gains can be obtained by solving the corresponding optimization problem expressed using LMIs. Illustrative numerical simulation examples are given to demonstrate the effectiveness of our proposed method.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Adaptive least mean square CDMA detection with Gram–Schmidt pre-processing

The Gram-Schmidt (GS) orthogonalisation procedure has been used to improve the convergence speed of least mean square (LMS) adaptive code-division multiple-access (CDMA) detectors. However, this algorithm updates two sets of parameters, namely the GS transform coefficients and the tap weights, simultaneously. Because of the additional adaptation noise introduced by the former, it is impossible to achieve the same performance as the ideal orthogonalised LMS filter, unlike the result implied in an earlier paper. The authors provide a lower bound on the minimum achievable mean squared error (MSE) as a function of the forgetting factor λ used in finding the GS transform coefficients, and propose a variable-λ algorithm to balance the conflicting requirements of good tracking and low misadjustment.

Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue

An efficient algorithm for solving the transient radiative transfer equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. The Runge–Kutta– Fehlberg method is used to solve the intensity. The discrete ordinates method is used to discretize with respect to azimuthal and zenith angles. This method offers the advantages of representing the intensity with a high accuracy using only a few Laguerre polynomials, and straightforward extension to inhomogeneous media. Also, this formulation can be easily extended for solving the 2-D and 3-D transient radiative transfer equations.

New variable step-sizes minimizing mean-square deviation for the lms-type algorithms

The least-mean-square-type (LMS-type) algorithms are known as simple and effective adaptation algorithms. However, the LMS-type algorithms have a trade-off between the convergence rate and steady-state performance. In this paper, we investigate a new variable step-size approach to achieve fast convergence rate and low steady-state misadjustment. By approximating the optimal step-size that minimizes the mean-square deviation, we derive variable step-sizes for both the time-domain normalized LMS (NLMS) algorithm and the transform-domain LMS (TDLMS) algorithm. The proposed variable step-sizes are simple quotient forms of the filtered versions of the quadratic error and very effective for the NLMS and TDLMS algorithms. The computer simulations are demonstrated in the framework of adaptive system modeling. Superior performance is obtained compared to the existing popular variable step-size approaches of the NLMS and TDLMS algorithms. © 2014 Springer Science+Business Media New York.

Simulation of dynamic pinion course using Runge-Kutta's method and impact modeling

Once defined the relationship between the Starter Motor components and their functions, it is possible to develop a mathematical model capable to predict the Starter behavior during operation. One important aspect is the engagement system behavior. The development of a mathematical tool capable of predicting it is a valuable step in order to reduce the design time, cost and engineering efforts. A mathematical model, represented by differential equations, can be developed using physics laws, evaluating force balance and energy flow through the systems degrees of freedom. Another important physical aspect to be considered in this modeling is the impact conditions (particularly on the pinion and ring-gear contact). This work is a report of those equations application on available mathematical software and the resolution of those equations by Runge-Kutta's numerical integration method, in order to build an accessible engineering tool. Copyright © 2011 SAE International.

Nuclear moments and differences in mean square charge radii of short-lived neon isotopes by collinear laser spectroscopy

Kernmomente und Kernladungsradien von kurzlebigen NeonIsotopen in der Kette 17-26,28Ne wurden mittels kollinearerLaserspektroskopie am online Massenseparator ISOLDE am CERN(Genf) vermessen. Bei kollinearer Laserspektroskopieverlangt die Bestimmung der Kernladungsradien leichterIsotope aus der Isotopeverschiebung nach einer sehr präzisenKenntnis der Ionenstrahlenergie. Zu diesem Zweck wurde eineneue, auf kollinearer Laserspektroskopie basierende Methodezur Strahlenergiemessung entwickelt und erfolgreich in denExperimenten zu Neon eingesetzt. Die experimentellenErgebnisse werden mit theoretischen Rechnungen im Rahmen desSchalenmodells und von kollektiven Kernmodellen verglichen.

Minimum Mean Square Error Approach in Images Processing for Full-field Displacements and Deformation Measurements

A vision system is applied to full-field displacements and deformation measurements in solid mechanics. A speckle like pattern is preliminary formed on the surface under investigation. To determine displacements field of one speckle image with respect to a reference speckle image, sub-images, referred to Zones Of Interest (ZOI) are considered. The field is obtained by matching a ZOI in the reference image with the respective ZOI in the moved image. Two image processing techniques are used for implementing the matching procedure: – cross correlation function and minimum mean square error (MMSE) of the ZOI intensity distribution. The two algorithms are compared and the influence of the ZOI size on the accuracy of measurements is studied.

Uma abordagem para problemas e controle ótimo via métodos de Runge-Kutta e análise de erro

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Analysis of trigonometric implicit Runge-Kutta methods

Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved.

Sobre los errores locales y globales de la integración de Ecuaciones Diferenciales Ordinarias mediante métodos de Runge-Kutta Explícitos

161 p.

Runge-Kutta starters for multistep methods /

"Supported in part by the U.S. Department of Energy under contract US ENERGY/EY-76-S-02-2383."