Search results for: nonlinear scattering

Authors: Madhu Aneja, Sapna Sharma

Abstract:

Thermal conductivity of ordinary heat transfer fluids is not adequate to meet today’s cooling rate requirements. Nanoparticles have been shown to increase the thermal conductivity and convective heat transfer to the base fluids. One of the possible mechanisms for anomalous increase in the thermal conductivity of nanofluids is the Brownian motions of the nanoparticles in the basefluid. In this paper, the natural convection of incompressible nanofluid over a nonlinear stretching sheet in the presence of magnetic field is studied. The flow and heat transfer induced by stretching sheets is important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. For computational purpose, Finite Element Method is used. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo – Klienstreuer – Li) correlation. In this model effect of Brownian motion on thermal conductivity is considered. The effect of important parameter i.e. nonlinear parameter, volume fraction, Hartmann number, heat source parameter is studied on velocity and temperature. Skin friction and heat transfer coefficients are also calculated for concerned parameters.

Keywords: Brownian motion, convection, finite element method, magnetic field, nanofluid, stretching sheet

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Authors: Kazuma Okada, Tomoaki Hashimoto, Hirokazu Tahara

Abstract:

Recently, the effectiveness of random dither quantization method for linear feedback control systems has been shown in several papers. However, the random dither quantization method has not yet been applied to nonlinear feedback control systems. The objective of this paper is to verify the effectiveness of random dither quantization method for nonlinear feedback control systems. For this purpose, we consider the attitude stabilization problem of satellites using discrete-level actuators. Namely, this paper provides a control method based on the random dither quantization method for stabilizing the attitude of satellites using discrete-level actuators.

Keywords: quantized control, nonlinear systems, random dither quantization

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Authors: A. Moawad, K. C. Yao, A. Mansour, R. Gautier

Abstract:

The detecting of an occupied frequency band is a major issue in cognitive radio systems. The detection process becomes difficult if the signal occupying the band of interest has faded amplitude due to multipath effects. These effects make it hard for an occupying user to be detected. This work mitigates the missed-detection problem in the context of cognitive radio in frequency-selective fading channel by proposing blind channel estimation method that is based on scattering transform. By initially applying conventional energy detection, the missed-detection probability is evaluated, and if it is greater than or equal to 50%, channel estimation is applied on the received signal followed by channel equalization to reduce the channel effects. In the proposed channel estimator, we modify the Morlet wavelet by using its first derivative for better frequency resolution. A mathematical description of the modified function and its frequency resolution is formulated in this work. The improved frequency resolution is required to follow the spectral variation of the channel. The channel estimation error is evaluated in the mean-square sense for different channel settings, and energy detection is applied to the equalized received signal. The simulation results show improvement in reducing the missed-detection probability as compared to the detection based on principal component analysis. This improvement is achieved at the expense of increased estimator complexity, which depends on the number of wavelet filters as related to the channel taps. Also, the detection performance shows an improvement in detection probability for low signal-to-noise scenarios over principal component analysis- based energy detection.

Keywords: channel estimation, cognitive radio, scattering transform, spectrum sensing

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Authors: Keita Iwai, Isao Tomita

Abstract:

To expand the optical spectrum for use in broadband optical communications, we study the properties of a semiconductor waveguide device with a tapered structure including its third-order optical nonlinearity. Spectral-broadened output by the tapered structure has the potential to create a compact, built-in device for optical communications. Here we deal with a compound semiconductor waveguide, the material of which is the same as that of laser diodes used in the communication systems, i.e., InₓGa₁₋ₓAsᵧP₁₋ᵧ, which has large optical nonlinearity. We confirm that our structure widens the output spectrum sufficiently by controlling its taper form factor while utilizing the large nonlinear refraction of InₓGa₁₋ₓAsᵧP₁₋ᵧ. We also examine the taper effect for nonlinear optical loss.

Keywords: InₓGa₁₋ₓAsᵧP₁₋ᵧ, waveguide, nonlinear refraction, spectral spreading, taper device

Procedia PDF Downloads 126

Authors: Areeg Shermaddo

Abstract:

Solar updraft power plants (SUPP) provide a great potential for green and environmentally friendly renewable power generation. An up to 1000 m high chimney represents one of the major parts of each SUPP, which consist of the main shell structure and the stiffening rings. Including the nonlinear material behavior in a simulation of the chimney is computationally a demanding task. However, allowing the formation of cracking in concrete leads to a more economical design of the structure. In this work, an FE model of a SUPP is presented incorporating the nonlinear material behavior. The effect of wind loading intensity on the structural response is explored. Furthermore, the influence of the stiffness of the ring beams on the global behavior is as well investigated. The obtained results indicate that the minimum reinforcement is capable of carrying the tensile stresses provided that the ring beams are rather stiff.

Keywords: ABAQUS, nonlinear analysis, ring beams, SUPP

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Authors: Yousif Mohamed Y. Abdallah, Eltayeb Wagallah

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Image enhancement allows the observer to see details in images that may not be immediately observable in the original image. Image enhancement is the transformation or mapping of one image to another. The enhancement of certain features in images is accompanied by undesirable effects. To achieve maximum image quality after denoising, a new, low order, local adaptive Gaussian scale mixture model and median filter were presented, which accomplishes nonlinearities from scattering a new nonlinear approach for contrast enhancement of bones in bone scan images using both gamma correction and negative transform methods. The usual assumption of a distribution of gamma and Poisson statistics only lead to overestimation of the noise variance in regions of low intensity but to underestimation in regions of high intensity and therefore to non-optional results. The contrast enhancement results were obtained and evaluated using MatLab program in nuclear medicine images of the bones. The optimal number of bins, in particular the number of gray-levels, is chosen automatically using entropy and average distance between the histogram of the original gray-level distribution and the contrast enhancement function’s curve.

Keywords: bone scan, nuclear medicine, Matlab, image processing technique

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Authors: Khaled Sandjak, Boualem Tiliouine

Abstract:

Structural analysis of flexible pavements has been and still is currently performed using multi-layer elastic theory. However, for thinly surfaced pavements subjected to low to medium volumes of traffics, the importance of non-linear stress-strain behaviour of unbound granular materials (UGM) requires the use of more sophisticated numerical models for structural design and performance of such pavements. In the present work, nonlinear unbound aggregates constitutive model is implemented within an axisymmetric finite element code developed to simulate the nonlinear behaviour of pavement structures including two local aggregates of different mineralogical nature, typically used in Algerian pavements. The performance of the mechanical model is examined about its capability of representing adequately, under various conditions, the granular material non-linearity in pavement analysis. In addition, deflection data collected by falling weight deflectometer (FWD) are incorporated into the analysis in order to assess the sensitivity of critical pavement design criteria and pavement design life to the constitutive model. Finally, conclusions of engineering significance are formulated.

Keywords: FWD backcalculations, finite element simulations, Nonlinear resilient behaviour, pavement response and performance, RLT test results, unbound granular materials

Procedia PDF Downloads 238

Authors: R. A. Shahmiri, O. Standard, J. Hart, C. C. Sorrell

Abstract:

Yttrium stabilized tetragonal zirconium polycrystalline (Y-TZP) has been used as a dental biomaterial. The strength and toughness of zirconia can be accounted for by its toughening mechanisms, such as crack deflection, zone shielding, contact shielding, and crack bridging. Prevention of crack propagation is of critical importance in high-fatigue situations, such as those encountered in mastication and para-function. However, the poor translucency of Y-TZP means that it may not meet the aesthetic requirements due to its white/grey appearance in polycrystalline form. To improve optical property of the Zirconia, precise evaluation of its refractive index is of significance. Zirconia`s optical properties need to be studied more in depth. Number of studies assumed, scattered light is isotropically distributed over all angles from biological media when defining optical parameters. Nevertheless, optical behaviour of real biological material depends on angular scattering of light by anisotropy material. Therefore, the average cosine of the scattering angle (which represent recovery phase function in the scattering angular distribution) usually characterized by anisotropy material. It has been identified that yttrium anti-sites present in the space charge layer have no significant role in the absorption of light in the visible range. Addition of cation dopant to polycrystalline zirconia results in segregate to grain boundaries and grain growth. Intrinsic and extrinsic properties of ZrO2 and their effect on optical properties need to be investigated. Intrinsic properties such as chemical composition, defect structure (oxygen vacancy), phase configuration (porosity, second phase) and distribution of phase need to be studied to comprehend their effect on refraction index, absorption/reflection and scattering. Extrinsic properties such as surface structure, thickness, underlying tooth structure, cement layer (type, thickness), and light source (natural, curing, artificial) of ZrO2 need to be studied to understand their effect on colour and translucency of material. This research reviewed effect of stabilization of tetragonal zirconia on optical property of zirconia for dental application.

Keywords: optical properties, zirconia dental biomaterial, chemical composition, phase composition

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Authors: Tsegay Giday Woldu, Haibin Zhang, Xin Zhang, Yemane Hailu Fissuh

Abstract:

It is well known that nonlinear conjugate gradient method is one of the widely used first order methods to solve large scale unconstrained smooth optimization problems. Because of the low memory requirement, attractive theoretical features, practical computational efficiency and nice convergence properties, nonlinear conjugate gradient methods have a special role for solving large scale unconstrained optimization problems. Large scale optimization problems are with important applications in practical and scientific world. However, nonlinear conjugate gradient methods have restricted information about the curvature of the objective function and they are likely less efficient and robust compared to some second order algorithms. To overcome these drawbacks, the new modified nonlinear conjugate gradient method is presented. The noticeable features of our work are that the new search direction possesses the sufficient descent property independent of any line search and it belongs to a trust region. Under mild assumptions and standard Wolfe line search technique, the global convergence property of the proposed algorithm is established. Furthermore, to test the practical computational performance of our new algorithm, numerical experiments are provided and implemented on the set of some large dimensional unconstrained problems. The numerical results show that the proposed algorithm is an efficient and robust compared with other similar algorithms.

Keywords: conjugate gradient method, global convergence, large scale optimization, sufficient descent property

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Authors: Mrinal Jana, Geetanjali Panda

Abstract:

In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example.

Keywords: fractional programming, interval valued function, interval inequalities, partial order relation

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Authors: R. Yulianingsih, S. Gohtani

Abstract:

Characteristics of pregelatinized waxy rice starch (PWR) gelatinized at different temperatures (65, 75, and 85 °C, abbreviated as PWR 65, 75 and 85 respectively) and their emulsion-stabilizing properties at different starch concentrations (3, 5, 7, and 9%) were studied. The yield stress and consistency index value of PWR solution increased with an increase in starch concentration. The pseudoplasticity of PWR 65 solution increased and that for both PWR 75 and 85 solution decreased with an increase in starch concentration. Small angle X-ray scattering (SAXS) profiles analyzed by Kratky Plot indicated that PWR 65 is natively unfolded particles while PWR 75 and 85 are the globular particles. The characteristics of emulsions stabilized with PWR were influenced by the temperature of gelatinization process and starch concentration. Elevated concentration of starch decreased the value of yield stress and increased the consistency index. PWR 65 produce stable emulsion to creaming at starch concentrations more than 5%, while PWR 85 is able to produce stable emulsion to both creaming and coalescence of droplets.

Keywords: emulsion, gelatinization temperature, rheology, small-angle X-ray scattering, waxy rice starch

Procedia PDF Downloads 139

Authors: Ju-Young Hwang, Hyo-Gyoung Kwak

Abstract:

This paper introduces a numerical analysis method for reinforced-concrete (RC) structures exposed to fire and compares the result with experimental results. The proposed analysis method for RC structure under the high temperature consists of two procedures. First step is to decide the temperature distribution across the section through the heat transfer analysis by using the time-temperature curve. After determination of the temperature distribution, the nonlinear analysis is followed. By considering material and geometrical nonlinearity with the temperature distribution, nonlinear analysis predicts the behavior of RC structure under the fire by the exposed time. The proposed method is validated by the comparison with the experimental results. Finally, prediction model to describe the status of after-cooling concrete can also be introduced based on the results of additional experiment. The product of this study is expected to be embedded for smart structure monitoring system against fire in u-City.

Keywords: RC, high temperature, after-cooling analysis, nonlinear analysis

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Authors: Somayyeh Karimiyan

Abstract:

To evaluate the seismic vulnerability of vital offshore structures with the highest possible precision, Nonlinear Time History Analyses (NLTHA), is the most reliable method. However, since it is very time-consuming, a quick procedure is greatly desired. This paper presents a quick method by combining the Push Over Analysis (POA) and the NLTHA. The POA is preformed first to recognize the more critical members, and then the NLTHA is performed to evaluate more precisely the critical members’ vulnerability. The proposed method has been applied to jacket type structure. Results show that combining POA and NLTHA is a reliable seismic evaluation method, and also that none of the earthquake characteristics alone, can be a dominant factor in vulnerability evaluation.

Keywords: jacket structure, seismic evaluation, push-over and nonlinear time history analyses, critical members

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Authors: Meziane Belkacem

Abstract:

We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: M. H. Korayem, Sh. Ameri, N. Yousefi Lademakhi

Abstract:

To ensure the stability of closed-loop nonlinear model predictive control (NMPC) within a finite horizon, there is a need for appropriate design terminal ingredients, which can be a time-consuming and challenging effort. Otherwise, in order to ensure the stability of the control system, it is necessary to consider an infinite predictive horizon. Increasing the prediction horizon increases computational demand and slows down the implementation of the method. In this study, a new technique has been proposed to ensure system stability without terminal ingredients. This technique has been employed in the design of the NMPC algorithm, leading to a reduction in the computational complexity of designing terminal ingredients and computational burden. The studied system is a wheeled mobile robot (WMR) subjected to non-holonomic constraints. Simulation has been investigated for two problems: trajectory tracking and adjustment mode.

Keywords: wheeled mobile robot, nonlinear model predictive control, stability, without terminal ingredients

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Authors: Esra Alveroglu Durucu, Kenan Koc

Abstract:

In this study, we synthesized and characterized nano-sized Poly- N-isopropylacrylamide (PNIPAM) hydrogels. N-isopropylacrylamide (NIPAM) micro and macro gels are known as a thermosensitive colloidal structure, and they respond to changes in the environmental conditions such as temperature and pH. Here, nano-sized gels were synthesized via precipitation copolymerization method. N,N-methylenebisacrylamide (BIS) and ammonium persulfate APS were used as crosslinker and initiator, respectively. 8-Hydroxypyrene-1,3,6- trisulfonic Acid (Pyranine, Py) molecules were used for arranging the particle size and thus physical properties of the nano-sized hydrogels. Fluorescence spectroscopy, atomic force microscopy and light scattering methods were used for characterizing the synthesized hydrogels. The results show that the gel size was decreased with increasing amount of ionic molecule from 550 to 140 nm due to the electrostatic behavior of the ionic side groups of pyranine. Light scattering experiments demonstrate that lower critical solution temperature (LCST) of the gels shifts to the lower temperature with decreasing size of gel due to the hydrophobicity–hydrophilicity balance of the polymer chains.

Keywords: hydrogels, lower critical solution temperature, nanogels, poly(n-isopropylacrylamide)

Procedia PDF Downloads 217

Authors: S. N. Derrar, M. Sekkal-Rahal

Abstract:

The Nonlinear optics (NLO) technique is widely used in the field of biological imaging. In fact, grafting biological entities with a high NLO response on tissues and cells enhances the NLO responses of these latter, and ameliorates, consequently, their biological imaging quality. In this optics, we carried out a theoretical study, in the aim of analyzing the peptide bonds created between alanine amino acid and both unnatural amino acids: L-Dopa and Azatryptophan, respectively. Ramachandran plots have been performed for these systems, and their structural parameters have been analyzed. The NLO responses of these peptides have been reported by calculating the first hyperpolarizability values of all the minima found on the plots. The use of such unnatural amino acids as endogenous probing molecules has been investigated through this study. The Density Functional Theory (DFT) has been used for structural properties, while the Second-order Møller-Plesset Perturbation Theory (MP2) has been employed for the NLO calculations.

Keywords: biological imaging, hyperpolarizability, nonlinear optics, probing molecule

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Authors: Shangerganesh Lingeshwaran

Abstract:

In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: David C. Ni

Abstract:

In the previous efforts, we constructed N-Body Systems by an extended Blaschke product (EBP), which represents a non-temporal and nonlinear extension of Lorentz transformation. In this construction, we rely only on two parameters, nonlinear degree, and relative momentum to characterize the systems. We further explored root computation via iteration with an algorithm extended from Jenkins-Traub method. The solution sets demonstrate a form of σ+ i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various canonical distributions. In this paper, we correlate the convergent sets in the original domain with solution sets, which demonstrating large-deviation distributions in the codomain. We proceed to compare our approach with the formula or principles, such as Donsker-Varadhan and Wentzell-Freidlin theories. The deterministic model based on this construction allows us to explore applications in the areas of finance and statistical mechanics.

Keywords: nonlinear Lorentz transformation, Blaschke equation, iteration solutions, root computation, large deviation distribution, deterministic model

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Authors: Abderraouf Gaaloul, Faouzi Msahli

Abstract:

The use of standard sliding mode controller, usually, leads to the appearing of an undesirable chattering phenomenon affecting the control signal. Such problem can be overcome using a higher-order sliding mode controller (HOSMC) which preserves the main properties of the standard sliding mode and deliberately increases the control smoothness. In this paper, we propose a new HOSMC for a class of uncertain multi-input multi-output nonlinear systems. Based on high gain and integral sliding mode paradigms, the established control scheme removes theoretically the chattering phenomenon and provides the stability of the control system. Numerical simulations are developed to show the effectiveness of the proposed controller when applied to solve a control problem of two water levels into a quadruple-tank process.

Keywords: nonlinear systems, sliding mode control, high gain, higher order

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Authors: Dong Sang Yoo

Abstract:

We consider nonlinear uncertain systems such that a priori information of the uncertainties is not available. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound and design a continuous robust control which renders nonlinear uncertain systems ultimately bounded.

Keywords: adaptive control, estimation, Fredholm integral, uncertain system

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Authors: Ali Murat Guler

Abstract:

A variety of experiments have been developed over the past decades, aiming at the detection of Weakly Interactive Massive Particles (WIMPs) via their scattering in an instrumented medium. The sensitivity of these experiments has improved with a tremendous speed, thanks to a constant development of detectors and analysis methods. Detectors capable of reconstructing the direction of the nuclear recoil induced by the WIMP scattering are opening a new frontier to possibly extend Dark Matter searches beyond the neutrino background. Measurement of WIMP’s direction will allow us to detect the galactic origin of dark matter and, therefore to have a clear signal-background separation. The NEWSdm experiment, based on nuclear emulsions, is intended to measure the direction of WIMP-induced nuclear coils with a solid-state detector, thus with high sensitivity. We discuss the discovery potential of a directional experiment based on the use of a solid target made of newly developed nuclear emulsions and novel read-out systems achieving nanometric resolution. We also report results of a technical test conducted in Gran Sasso.

Keywords: dark matter, direct detection, nuclear emulsion, WIMPS

Procedia PDF Downloads 247

Authors: Hocine Hammoum, Karima Bouzelha, Lounis Ziani, Lounis Hamitouche

Abstract:

In this paper, we study a complex structure which is an apartment building surmounted by a reinforced concrete water tank. The tank located on the top floor of the building is a container with capacity of 1000 m³. The building is complex in its design, its calculation and by its behavior under earthquake effect. This structure located in Algiers and aged of 53 years has been subjected to several earthquakes, but the earthquake of May 21^st, 2003 with a magnitude of 6.7 on the Richter scale that struck Boumerdes region at 40 Kms East of Algiers was fatal for it. It was downgraded after an investigation study because the central core sustained serious damage. In this paper, to estimate the degree of its damages, the seismic performance of the structure will be evaluated taking into account the hydrodynamic effect, using a static equivalent nonlinear analysis called pushover.

Keywords: performance analysis, building, reinforced concrete tank, seismic analysis, nonlinear analysis, hydrodynamic, pushover

Procedia PDF Downloads 395

Authors: A. Oukaci, R. Toufouti, D. Dib, l. Atarsia

Abstract:

This article presents a multitude of alternative techniques to control the vector control, namely the nonlinear control and sliding mode control. Moreover, the implementation of their control law applied to the high-performance to the induction motor with the objective to improve the tracking control, ensure stability robustness to parameter variations and disturbance rejection. Tests are performed numerical simulations in the Matlab/Simulink interface, the results demonstrate the efficiency and dynamic performance of the proposed strategy.

Keywords: Induction Motor (IM), Non-linear Control (NLC), Sliding Mode Control (SMC), nonlinear sliding surface

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Authors: Yosra Baaziz, Moez Labidi

Abstract:

Given limited research on monetary policy rules in revolutionary countries, this paper challenges the suitability of the Taylor rule in characterizing the monetary policy behavior of the Tunisian Central Bank (BCT), especially in turbulent times. More specifically, we investigate the possibility that the Taylor rule should be formulated as a threshold process and examine the validity of such nonlinear Taylor rule as a robust rule for conducting monetary policy in Tunisia. Using quarterly data from 1998:Q4 to 2013:Q4 to analyze the movement of nominal short-term interest rate of the BCT, we find that the nonlinear Taylor rule improves its performance with the advent of special events providing thus a better description of the Tunisian interest rate setting. In particular, our results show that the adoption of an appropriate nonlinear approach leads to a reduction in the errors of 150 basis points in 1999 and 2009, and 60 basis points in 2011, relative to the linear approach.

Keywords: policy rule, central bank, exchange rate, taylor rule, nonlinearity

Procedia PDF Downloads 276

Authors: Ju-young Hwang, Hyo-Gyoung Kwak, Hong Jae Yim

Abstract:

This paper introduces a numerical analysis method for reinforced-concrete (RC) structures exposed to fire and compares the result with experimental results. The proposed analysis method for RC structure under the high temperature consists of two procedures. First step is to decide the temperature distribution across the section through the heat transfer analysis by using the time-temperature curve. After determination of the temperature distribution, the nonlinear analysis is followed. By considering material and geometrical non-linearity with the temperature distribution, nonlinear analysis predicts the behavior of RC structure under the fire by the exposed time. The proposed method is validated by the comparison with the experimental results. Finally, Prediction model to describe the status of after-cooling concrete can also be introduced based on the results of additional experiment. The product of this study is expected to be embedded for smart structure monitoring system against fire in u-City.

Keywords: RC structures, heat transfer analysis, nonlinear analysis, after-cooling concrete model

Procedia PDF Downloads 339

Authors: Haowen Xi

Abstract:

We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: L. A. Ostrovsky, Yu. A. Stepanyants

Abstract:

Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described.

Keywords: Earth rotation, internal waves, nonlinear waves, solitons

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

Abstract:

Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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Authors: Xiaojie Jiang, Wei Cai, Yinxiao Xiang, Ni Zhang, Mengxin Ren, Xinzheng Zhang, Jingjun Xu

Abstract:

Reflection phase of graphene plasmons (GPs) at an abrupt interface is very important, which determines the plasmon resonance of graphene structures of deep sub-wavelength scales. However, at an abrupt graphene edge, the reflection phase is always a constant, ΦR ≈ π/4. In this work, we show that the reflection phase of GPs can be efficiently changed through substrate design. Reflection phase of graphene plasmons (GPs) at an abrupt interface is very important, which determines the plasmon resonance of graphene structures of deep sub-wavelength scales. However, at an abrupt graphene edge, the reflection phase is always a constant, ΦR ≈ π/4. In this work, we show that the reflection phase of GPs can be efficiently changed through substrate design. Specifically, the reflection phase is no longer π/4 at the interface formed by placing a graphene sheet on different substrates. Moreover, tailorable reflection phase of GPs up to 2π variation can be further achieved by scattering GPs at a junction consisting of two such dielectric interfaces with various gap width acting as a Fabry-Perot cavity. Besides, the evolution of plasmon mode in graphene ribbons based on the interface reflection phase tuning is predicted, which is expected to be observed in near-field experiments with scattering-type scanning near-field optical microscopy (s-SNOM). Our work provides another way for in-plane plasmon control, which should find applications for integrated plasmon devices design using graphene.Specifically, the reflection phase is no longer π/4 at the interface formed by placing a graphene sheet on different substrates. Moreover, tailorable reflection phase of GPs up to 2π variation can be further achieved by scattering GPs at a junction consisting of two such dielectric interfaces with various gap width acting as a Fabry-Perot cavity. Besides, the evolution of plasmon mode in graphene ribbons based on the interface reflection phase tuning is predicted, which is expected to be observed in near-field experiments with scattering-type scanning near-field optical microscopy (s-SNOM). Our work provides a new way for in-plane plasmon control, which should find applications for integrated plasmon devices design using graphene.

Keywords: graphene plasmons, reflection phase tuning, plasmon mode tuning, Fabry-Perot cavity

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