Search results for: nonlinear Shannon limit

Authors: Septimia Sarbu

Abstract:

The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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Authors: Mohammad A. U. Khan, Omar A. Kittaneh, M. Akbar, Tariq M. Khan, Husam A. Bayoud

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The Shannon Entropy measure has been widely used for measuring uncertainty. However, in partial settings, the histogram is used to estimate the underlying distribution. The histogram is dependent on the number of bins used. In this paper, a modification is proposed that makes the Shannon entropy based on histogram consistent. For providing the benefits, two application are picked in medical image processing applications. The simulations are carried out to show the superiority of this modified measure for image segmentation problem. The improvement may be contributed to robustness shown to uneven background in images.

Keywords: Shannon entropy, medical image processing, image segmentation, modification

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Authors: Minas Balyan

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Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Massimiliano Frezza, Sergio Bianchi, Augusto Pianese

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Introduced by Shannon in 1948 in the field of information theory as the average rate at which information is produced by a stochastic set of data, the concept of entropy has gained much attention as a measure of uncertainty and unpredictability associated with a dynamical system, eventually depicted by a stochastic process. In particular, the Shannon entropy measures the degree of order/disorder of a given signal and provides useful information about the underlying dynamical process. It has found widespread application in a variety of fields, such as, for example, cryptography, statistical physics and finance. In this regard, many contributions have employed different measures of entropy in an attempt to characterize the financial time series in terms of market efficiency, market crashes and/or financial crises. The Shannon entropy has also been considered as a measure of the risk of a portfolio or as a tool in asset pricing. This work investigates the theoretical link between the Shannon entropy and the multifractional Brownian motion (mBm), stochastic process which recently is the focus of a renewed interest in finance as a driving model of stochastic volatility. In particular, after exploring the current state of research in this area and highlighting some of the key results and open questions that remain, we show a well-defined relationship between the Shannon (log)entropy and the memory function H(t) of the mBm. In details, we allow both the length of time series and time scale to change over analysis to study how the relation modify itself. On the one hand, applications are developed after generating surrogates of mBm trajectories based on different memory functions; on the other hand, an empirical analysis of several international stock indexes, which confirms the previous results, concludes the work.

Keywords: Shannon entropy, multifractional Brownian motion, Hurst–Holder exponent, stock indexes

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Authors: Stoyan Nedeltchev, Markus Schubert

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The gas holdup fluctuations in a bubble column (0.15 m in ID) have been recorded by means of a conductivity wire-mesh sensor in order to extract information about the main transition velocities. These parameters are very important for bubble column design, operation and scale-up. For this purpose, the classical definition of the Shannon entropy was modified and used to identify both the onset (at UG=0.034 m/s) of the transition flow regime and the beginning (at UG=0.089 m/s) of the churn-turbulent flow regime. The results were compared with the Kolmogorov entropy (KE) results. A slight discrepancy was found, namely the transition velocities identified by means of the KE were shifted to somewhat higher (0.045 and 0.101 m/s) superficial gas velocities UG.

Keywords: bubble column, gas holdup fluctuations, modified Shannon entropy, Kolmogorov entropy

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Authors: M. Chen, S-Q. Zhang, X. Wang, D. Tate

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This paper presents a numerical solution, namely limit and shakedown analysis, to predict the safety state of smart structures made of heterogeneous materials under unknown cyclic loadings, for instance, the flexure hinge in the micro-positioning stage driven by piezoelectric actuator. In combination of homogenization theory and finite-element method (FEM), the safety evaluation problem is converted to a large-scale nonlinear optimization programming for an acceptable bounded loading as the design reference. Furthermore, a general numerical scheme integrated with the FEM and interior-point-algorithm based optimization tool is developed, which makes the practical application possible.

Keywords: limit state, shakedown analysis, homogenization, heterogeneous structure

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Authors: Kishor J. shinde

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We determine the values of k and p such that the Sturm-Liouville differential operator τu=-(d^2 u)/(dx^2) + kx^p u is in limit point case or limit circle case at infinity. In particular it is shown that τ is in the limit point case when (i) for p=2 and ∀k, (ii) for ∀p and k=0, (iii) for all p and k>0, (iv) for 0≤p≤2 and k<0, (v) for p<0 and k<0. τ is in the limit circle case when (i) for p>2 and k<0.

Keywords: limit point case, limit circle case, Sturm-Liouville, infinity

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Authors: Abdullah Eqal Al Mazrooei

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In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: Swapan Maiti, Dipanwita Roy Chowdhury

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Nonlinear functions are essential in different cryptoprimitives as they play an important role on the security of the cipher designs. Rule 30 was identified as a powerful nonlinear function for cryptographic applications. However, an attack (MS attack) was mounted against Rule 30 Cellular Automata (CA). Nonlinear rules as well as maximum period CA increase randomness property. In this work, nonlinear rules of maximum period nonlinear hybrid CA (M-NHCA) are studied and it is shown to be a better crypto-primitive than Rule 30 CA. It has also been analysed that the M-NHCA with single nonlinearity injection proposed in the literature is vulnerable against MS attack, whereas M-NHCA with multiple nonlinearity injections provide maximum length cycle as well as better cryptographic primitives and they are also secure against MS attack.

Keywords: cellular automata, maximum period nonlinear CA, Meier and Staffelbach attack, nonlinear functions

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Authors: Amira Amamou, Mnaouar Chouchane

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This paper investigates the bifurcation and nonlinear behavior of two degrees of freedom model of a symmetrical balanced rigid rotor supported by two identical journal bearings. The fluid film hydrodynamic reactions are modeled by applying both the short and the long bearing approximation and using half Sommerfeld solution. A numerical integration of equations of the journal centre motion is presented to predict the presence and the size of stable or unstable limit cycles in the neighborhood of the stability critical speed. For their stability margins, a continuation method based on the predictor-corrector mechanism is used. The numerical results of responses show that stability and bifurcation behaviors of periodic motions depend strongly on bearing parameters and its dynamic characteristics.

Keywords: hydrodynamic journal bearing, nonlinear stability, continuation method, bifurcations

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Authors: Bououden Soraya

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This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results.

Keywords: nonlinear observer canonical form, observer, design, gene regulation, gene expression

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Authors: N. Manoj

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The aeroelastic behavior of engine nacelle strake when subjected to unsteady aerodynamic flows is investigated in this paper. Geometric nonlinear characteristics and modal parameters of nacelle strake are studied when it is under dynamic loading condition. Here, an N-S based Finite Volume solver is coupled with Finite Element (FE) based nonlinear structural solver to investigate the nonlinear characteristics of nacelle strake over a range of dynamic pressures at various phases of flight like takeoff, climb, and cruise conditions. The combination of high fidelity models for both aerodynamics and structural dynamics is used to predict the nonlinearities of strake (chine). The methodology adopted for present aeroelastic analysis is partitioned-based time domain coupled CFD and CSD solvers and it is validated by the consideration of experimental and numerical comparison of aeroelastic data for a cropped delta wing model which has a proven record. The present strake geometry is derived from theoretical formulation. The amplitude and frequency obtained from the coupled solver at various dynamic pressures is discussed, which gives a better understanding of its impact on aerodynamic design-sizing of strake.

Keywords: aeroelasticity, finite volume, geometric nonlinearity, limit cycle oscillations, strake

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Authors: Minas Balyan

Abstract:

In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. The dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well known Renninger effect takes place. In this work, the ‘third order nonlinear Renninger effect’ is considered theoretically and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity.

Keywords: third order nonlinearity, Bragg diffraction, nonlinear Renninger effect, rocking curves

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Authors: Abdullah Eqal Al Mazrooei

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Kalman filter is a famous algorithm that utilizes to estimate the state in the linear systems. It has numerous applications in technology and science. Since of the most of applications in real life can be described by nonlinear systems. So, Kalman filter does not work with the nonlinear systems because it is suitable to linear systems only. In this work, a nonlinear filtering algorithm is presented which is suitable to use with the special kinds of nonlinear systems. This filter generalizes the Kalman filter. This means that this filter also can be used for the linear systems. Our algorithm depends on a special linearization of the second degree. We introduced the nonlinear algorithm with a bilinear state-space model. A simulation example is presented to illustrate the efficiency of the algorithm.

Keywords: Kalman filter, filtering algorithm, nonlinear systems, state-space model

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Authors: Ashkan Asgari, Korous Khoshbakht, Saeid Soufizadeh

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Various factors including land lots can affect biodiversity indices in Agricultural systems. Field study conducted to evaluate factors affecting crop diversity in Sarpolzahab in 2012. Required data were collected through direct observation of farms and filling questionnaires. Total numbers of 140 questionnaires were filled, SAS Software was used to analyse data and Ecological Methodology Program was applied to calculate Shannon-Winner index, subsequently. Results of study indicated that average number of land lots for each farmer was 2.78 and various from 2.2 in Rikhak Olia Village to 4.31 in Golam Kaboud Olia Village which shows small size of land lots due to separating larger lots by children of deceased farmers. The correlation between number of land lots and species biodiversity (0.308**) was significant and Shannon-Winner index was (0.262**). Therefore, according to the mentioned results one can assume that increase in number of land lots results in improving of the target index. Multiple land lots allow farmers to cultivate various crops which results in increasing biodiversity of crops in agro ecosystem. Subsequently, this increase will facilitate economic sustainability of the farmers and distribution of work force in the region throughout the year. The correlation of seasonal workers with biodiversity of crop species (0.256**) and Shannon-Winner (0.286**) was statistically significant and increasing number of seasonal work forces had resulted in improving crop biodiversity and decreasing dominant species or single crop farming systems. Vegetable farms which have a significant diversity, require a significant number of work forces which describes correlation between number of workers and diversity of species.

Keywords: agricultural systems, biodiversity indices, Shannon-Winner index, sustainability, rural

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Authors: A. Mostafa

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This paper presents a numerical study on determination of ballistic limit velocity (V₅₀) of stainless steel 304 (SS 304) used in manufacturing security screens. The simulated ballistic impact tests were conducted on clamped sheets with different thicknesses using ABAQUS/Explicit nonlinear finite element (FE) package. The ballistic limit velocity was determined using three approaches, namely: numerical tests based on material properties, FE calculated residual velocities and FE calculated residual energies. Johnson-Cook plasticity and failure criterion were utilized to simulate the dynamic behaviour of the SS 304 under various strain rates, while the well-known Lambert-Jonas equation was used for the data regression for the residual velocity and energy model. Good agreement between the investigated numerical methods was achieved. Additionally, the dependence of the ballistic limit velocity on the sheet thickness was observed. The proposed approaches present viable and cost-effective assessment methods of the ballistic performance of SS 304, which will support the development of robust security screen systems.

Keywords: ballistic velocity, stainless steel, numerical approaches, security screen

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Authors: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita

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This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.

Keywords: dynamic response, nonlinear impact response, finite element analysis, numerical analysis

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Authors: Sheema Shuja Khattak, Gule Saman, Imran Khan, Abdus Salam

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Image segmentation plays an important role in medical imaging applications. Therefore, accurate methods are needed for the successful segmentation of medical images for diagnosis and detection of various diseases. In this paper, we have used maximum entropy to achieve image segmentation. Maximum entropy has been calculated using Shannon, Renyi, and Tsallis entropies. This work has novelty based on the detection of skin lesion caused by the bite of a parasite called Sand Fly causing the disease is called Cutaneous Leishmaniasis.

Keywords: shannon, maximum entropy, Renyi, Tsallis entropy

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Authors: Hazem M. Al-Mofleh

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In this paper, a new four-parameter univariate continuous distribution called the Normal-Generalized Hyperbolic Secant Distribution (NGHS) is defined and studied. Some general and structural distributional properties are investigated and discussed, including: central and non-central n-th moments and incomplete moments, quantile and generating functions, hazard function, Rényi and Shannon entropies, shapes: skewed right, skewed left, and symmetric, modality regions: unimodal and bimodal, maximum likelihood (MLE) estimators for the parameters. Finally, two real data sets are used to demonstrate empirically its flexibility and prove the strength of the new distribution.

Keywords: bimodality, estimation, hazard function, moments, Shannon’s entropy

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Authors: Danni Cong, Meiping Wu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokuncai, Hao Qin

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Gravity gradient instrument (GGI) is the core of the gravity gradiometer, so the structural error of the sensor has a great impact on the measurement results. In order not to affect the aimed measurement accuracy, limit error is required in the installation of the accelerometer. In this paper, based on the established measuring principle model, the radial installation limit error is calibrated, which is taken as an example to provide a method to calculate the other limit error of the installation under the premise of ensuring the accuracy of the measurement result. This method provides the idea for deriving the limit error of the geometry structure of the sensor, laying the foundation for the mechanical precision design and physical design.

Keywords: gravity gradient sensor, radial installation limit error, accelerometer, uniaxial rotational modulation

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Authors: Manouchehr Amiri

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This article introduces a general notion of physical bit information that is compatible with the basics of quantum mechanics and incorporates the Shannon entropy as a special case. This notion of physical information leads to the Binary data matrix model (BDM), which predicts the basic results of quantum mechanics, general relativity, and black hole thermodynamics. The compatibility of the model with holographic, information conservation, and Landauer’s principles are investigated. After deriving the “Bit Information principle” as a consequence of BDM, the fundamental equations of Planck, De Broglie, Beckenstein, and mass-energy equivalence are derived.

Keywords: physical theory of information, binary data matrix model, Shannon information theory, bit information principle

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Authors: Boo-Sung Koh, Seung-Eock Kim

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In this paper, a direct design using a nonlinear inelastic analysis is suggested. Also, this paper compares the load carrying capacity obtained by a nonlinear inelastic analysis with experiment results to verify the accuracy of the results. The allowable stress design results of a railroad through a plate girder bridge and the safety factor of the nonlinear inelastic analysis were compared to examine the safety performance. As a result, the load safety factor for the nonlinear inelastic analysis was twice as high as the required safety factor under the allowable stress design standard specified in the civil engineering structure design standards for urban magnetic levitation railways, which further verified the advantages of the proposed direct design method.

Keywords: direct design, nonlinear inelastic analysis, residual stress, initial geometric imperfection

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi

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In this paper a real-time obstacle avoidance approach for both autonomous and non-autonomous dynamical systems (DS) is presented. In this approach the original dynamics of the controller which allow us to determine safety margin can be modulated. Different common types of DS increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle especially when robot moves very fast in changeable complex environments. The method is validated by simulation and influence of different autonomous and non-autonomous DS such as important characteristics of limit cycles and unstable DS. Furthermore, the position of different obstacles in complex environment is explained. Finally, the verification of avoidance trajectories is described through different parameters such as safety factor.

Keywords: limit cycles, nonlinear dynamical system, real time obstacle avoidance, safety margin

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Authors: Chang He, Hiroshi Tamura, Hiroshi Katsuchi, Jiaqi Wang

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In this study, the aim is to infer the slip limit (static friction limit) of contact interfaces in bolt friction joints by analyzing other bolt friction joints with the same contact surface but in a different shape. By using the Weibull distribution to deal with microelements on the contact surface statistically, the slip limit of a certain type of bolt joint was predicted from other types of bolt joint with the same contact surface. As a result, this research succeeded in predicting the slip limit of bolt joins with different numbers of contact surfaces and with different numbers of bolt rows.

Keywords: bolt joints, slip coefficient, finite element method, Weibull distribution

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: F. Boufera, F. Debbat

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This paper deals with an approach based on limit-cycles method for the problem of obstacle avoidance of mobile robots in unknown environments for any form of obstacles. The purpose of this approach is the improvement of limit-cycles method in order to obtain safe and flexible navigation. The proposed algorithm has been successfully tested in different configuration on simulation.

Keywords: mobile robot, navigation, avoidance of obstacles, limit-cycles method

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

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This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: state estimation, control systems, observer systems, nonlinear systems

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Authors: Anton V. Bourdine, Vladimir A. Burdin, Oleg R. Delmukhametov

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This work presents a fast and simple method for the design of large core silica optical fibers with differential mode delay (DMD) management. Some results are reported concerned with refractive index profile optimization for 42 µm core 16-LP-mode optical fiber for next-generation optical networks. Here special refractive index profile form provides total DMD reducing over all mode staff under desired enhanced mode effective area. Method for the simulation of 'real manufactured' few-mode optical fiber (FMF) core geometry differing from the desired optimized structure by core non-symmetrical ellipticity and refractive index profile deviation including local fluctuations is proposed. Results of the following analysis of optimized FMF with inserted geometry distortions performed by earlier on developed modification of rigorous mixed finite-element method showed strong DMD degradation that requires additional higher-order mode management. In addition, this work also presents a method for design mode division multiplexer channel precision spatial positioning scheme at FMF core end that provides one of the potentiality solutions of described DMD degradation problem concerned with 'distorted' core geometry due to features of optical fiber manufacturing techniques.

Keywords: differential mode delay, few-mode optical fibers, nonlinear Shannon limit, optical fiber non-circularity, ‘real manufactured’ optical fiber core geometry simulation, refractive index profile optimization

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Authors: Minho Kwon, Jeonghee Lim, Yeongseok Jeong, Jongyoon Moon, Donghoon Shin, Kiyoung Kim

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In the past, the criteria and procedures for the design of concrete structures were mainly based on the stresses allowed for structural components. However, although the frequency of earthquakes has increased and the risk has increased recently, it has been difficult to determine the safety factor for earthquakes in the safety assessment of structures based on allowable stresses. Recently, limit state design method has been introduced for reinforced concrete structures, and limit state-based approach has been recognized as a more effective technique for seismic design. Therefore, in this study, the limit state of the bridge, which is a structure requiring higher stability against earthquakes, was evaluated. The finite element program LS-DYNA and twenty ground motion were used for time history analysis. The fracture caused by tensile and compression of the pier were set to the limit state. In the concrete tensile fracture, the limit state arrival rate was 100% at peak ground acceleration 0.4g. In the concrete compression fracture, the limit state arrival rate was 100% at peak ground acceleration 0.2g.

Keywords: allowable stress, limit state, safety factor, peak ground acceleration

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