Electronic Polarizability and Optical Basicity of BaO-B2O3-TeO2 Glass System

[(TeO2)0.7(B2O3)0.3]1-x (BaO)x, x = 0.00, 0.05, 0.10, 0.20, 0.25, 0.30 and 0.35 mol fraction glass series were successfully synthesized by conventional melt quenching method. Amorphous phase of all samples was confirmed through X-ray diffraction while optical properties were determined using UV-VIS spectrophotometer. Fourier Transform Infrared (FTIR) analysis showed that the glass structure consisted of TeO3, TeO4, TeO6, BO3 and BO4 structural units. The optical band gap energy, Eopt which was calculated from Tauc’ plots decreased as the amount of BaO increases, whereas, the Urbach energy value increased. The increase in Urbach energy value was attributed to the increase of defects in glass structure. The refractive indices of glass were found to increase along with the increased amount of BaO, due to the high polarization and high density of host material and glass modifier. The molar polarizability, αm, oxide ion polarizability, αo2- and optical basicity, Λ of the glasses are calculated by Lorentz-Lorenz equation. The glasses were found to possess αm values between 8.106 – 8.489 Å3, and αo2- values between 3.303 to 4.772. Meanwhile, optical basicity increases from 0.115 to 0.893.

Polymer Characterization

As discussed in section 10.1007/978-3-658-35926-3_2, the characterization of cross-linking and especially its spatial distribution is crucial for the fabrication of micro optics, MEMS, and semiconductors. Some studies have found that the measurement of the refractive index over the cross-linking process can be used as an indicator for the degree of cross-linking of a sample. According to Kudo et al., [130], the cross-linking of a polymeric material leads to a densification which can be directly related to an increase in refractive index using the Lorentz-Lorenz equation.

Reconstruction of Nonlinear Flows from Noisy Time Series

Nonlinear dynamics is a rapidly developing subject across all disciplines involving spatial or temporal evolution. The reconstruction of the equations of motion for a nonlinear system from observed time series has been a hot topic for a long time. Nevertheless, in practice only partial information is available for many systems which are very likely contaminated with noise. Here, based on the invariance of the evolution equation during time translation, a globally valid local approximation of the trajectory is determined, which could be reliably used for the reconstruction of the vector fields with unknown parameters or functional forms, even with partial information of the state evolution. The global consideration very effectively alleviates noise interference and bestows exceptional robustness to the technique, which asks only for solution of linear equations and thus is very efficient. The new scheme is nicely demonstrated in the Lorenz equation in different conditions, while an FHN neural network model is used to show its strength in high-dimensions.

Practical Feasibility of Arago-Biot and Lorentz-Lorenz Theory Through Variation of Refractive Index of Typical Binary Liquid Mixtures Employing Low-Cost Experimental Setup

Optical properties of the solutions comprising of two or more miscible liquids have been of immense interest both in the area of chemical and physical sciences. To date, there are reports on studies regarding different combinations of binary liquid mixtures. However, the experiments involved are either high-ended or using sophisticated instrumentation. Our prime objective is to set up a simple laboratory arrangement to estimate the refractive index of typical binary-liquid mixtures obtained by proportionate variations in combinations selecting from benzene, ethyl acetate, tetrahydrofuran, and water; without involving high-standard instrumentation or expensive laboratory setups. In the present study, we adopted a basic method to determine the refractive index of pure liquids of low polarity, like, benzene (C6H6) and tetrahydrofuran or THF (C4H8O) and of high polarities, such as ethyl acetate or EtOAc or EA (C4H8O2), and water (H2O) and also their binary homogeneous mixture with high accuracy. Our experimental data involving variation of refractive index with molar volume fraction matched very well with theoretical interpretations by Arago-Biot and Lorentz-Lorenz equation. In our results, density corrections have been neglected as we have chosen non-volatile solvents.

Abrupt Change Detection Method Based on Features of Lorenz Trajectories

This paper presents a definition of bifurcation-type abrupt changes based on the bifurcation features of Lorenz trajectories. These abrupt changes are the result of the transition behavior of dynamical system trajectories among different equilibrium regions. We demonstrate that these bifurcation-type jumps can better reflect the nature of abrupt change. In analyzing the features of Lorenz equation trajectories, a dynamical method for detecting bifurcation-type abrupt changes is presented. A numerical solution of the Lorenz equation is adopted, using a curve integral or vector product to construct a time series of positive and negative values. Changes in the sign of this time series accurately determine whether the trajectory is in the right or left equilibrium region, and the points at which the time series is equal to zero are the times at which the trajectory jumps between different equilibrium regions, that is, the occurrence times of bifurcation-type abrupt changes. This method is completely dependent on the dynamical characteristics of the system. A theoretical approach for detecting abrupt climate changes based on the dynamical characteristics of the atmospheric model is described. Compared with the original method of identifying abrupt climate changes, this method has dynamic significance and can detect abrupt changes in multi-dimensional time series. Although this method can be applied theoretically, applications to real atmospheric data first require the data to be smoothed.

Performances of PMMA-Based Optical Fiber Bragg Grating Sensor in Extended Temperature Range

PMMA based optical fiber Bragg grating (POFBG) sensors are investigated in an environmental chamber with controlled temperature and relative humidity at temperature extended to 70 °C. At below a critical temperature of 50 °C the POFBG sensor exhibits good linearity and sensitivity for both temperature and humidity sensing. Nonlinear responses are observed at higher temperature, giving rise to varying, reduced magnitudes of sensitivities. An important feature of POFBG humidity sensing is observed at above critical temperature where the POFBG humidity sensitivity turns from positive to negative. A theoretical model based on Lorentz–Lorenz equation is presented to estimate the dependence of POFBG refractive index on temperature and relative humidity. The experimental results qualitatively agree with the theoretical analyses.

Bayesian Identification of Dynamical Systems

Many inference problems relate to a dynamical system, as represented by dx/dt = f (x), where x ∈ ℝn is the state vector and f is the (in general nonlinear) system function or model. Since the time of Newton, researchers have pondered the problem of system identification: how should the user accurately and efficiently identify the model f – including its functional family or parameter values – from discrete time-series data? For linear models, many methods are available including linear regression, the Kalman filter and autoregressive moving averages. For nonlinear models, an assortment of machine learning tools have been developed in recent years, usually based on neural network methods, or various classification or order reduction schemes. The first group, while very useful, provide “black box" solutions which are not readily adaptable to new situations, while the second group necessarily involve the sacrificing of resolution to achieve order reduction. To address this problem, we propose the use of an inverse Bayesian method for system identification from time-series data. For a system represented by a set of basis functions, this is shown to be mathematically identical to Tikhonov regularization, albeit with a clear theoretical justification for the residual and regularization terms, respectively as the negative logarithms of the likelihood and prior functions. This insight justifies the choice of regularization method, and can also be extended to access the full apparatus of the Bayesian inverse solution. Two Bayesian methods, based on the joint maximum a posteriori (JMAP) and variational Bayesian approximation (VBA), are demonstrated for the Lorenz equation system with added Gaussian noise, in comparison to the regularization method of least squares regression with thresholding (the SINDy algorithm). The Bayesian methods are also used to estimate the variances of the inferred parameters, thereby giving the estimated model error, providing an important advantage of the Bayesian approach over traditional regularization methods.

Persamaan Lorenz untuk Keamanan Nomor Serial Sistem Operasi Window7

Serial number of operating system windows 7 needs to be safeguarded, so can’t be used by the others. Security of the data can use by modern cryptography such as Vernam Cipher methods and classic cryptography such as Caesar Cipher methods. The security level both of this method depends on the keywords used and it will difficult to crack if the random key is used more and more. To get a random key, we can take from chaos of Lorenz equations as key-generator for encryption and description. Before utilizing chaos in the Lorenz equations, we have to find the maximum t (time) for the inverse problem solution to fit with the forward problem solution. We can use Runge-Kutta method in the Lorenz equations for forward problem solution and inverse problem solution. The solution of integral that obtained by the Runge-Kutta method can be searched by Trapezoidal method. The result of Runge-Kutta solution and Trapezoidal will be used as key-generator for encryption and description. In the simulations performed, the best orde in Runge-Kutta method is 4 and t max is 2. The encryption key is used as the initial condition of Lorenz equation, then the result is integrable by the Trapezoidal method. The result of orde 4 from Runge-Kutta method and Trapezoidal method used as a key-generator. Application of Lorenz equation as key-generator for encryption and decryption, may change the cryptography algorithms of symmetric to be asymmetric.

Benchmarking DFT Approaches for the Calculation of Polarizability Inputs for Refractive Index Predictions in Organic Polymers

<pre>In a previous study, we introduced a new computational protocol to accurately predict the index of refraction (RI) of organic polymers using a combination of <i>first-principles</i> and data modeling. This protocol is based on the Lorentz-Lorenz equation and involves the calculation of static polarizabilities and number densities of oligomer sequences, which are extrapolated to the polymer limit. We chose to compute the polarizabilities within the density functional theory (DFT) framework using the PBE0/def2-TZVP-D3 model chemistry. While this <i>ad hoc</i> choice proved remarkably successful, it is also relatively expensive from a computational perspective. It represents the bottleneck step in the overall RI modeling protocol, thus limiting its utility for virtual high-throughput screening studies, in which efficiency is essential. For polymers that exhibit late-onset extensivity, the employed linear extrapolation scheme can require demanding calculations on long-oligomer sequences, thus becoming another bottleneck.</pre> <pre>In the work presented here, we benchmark DFT model chemistries to identify approaches that optimize the balance between accuracy and efficiency for this application domain. We compare results for conjugated and non-conjugated polymers, augment our original extrapolation approach with a non-linear option, analyze how the polarizability errors propagate into the RI predictions, and offer guidance for method selection. </pre>