Subharmonic Route to Boundary-Layer Transition - Critical Layer Nonlinearity
Mankbadi, Reda R.
1991-01-01
The linear and nonlinear dynamics of a triad of initially linear stability waves comprising a single plane wave at fundamental frequency and two symmetric oblique waves with half the frequency and streamwise wave number of the plane wave are presented. Analysis is performed for the initial nonlinear development of the waves where the order of the oblique waves' amplitude is equal to or less than that of the plane wave. Results show that the fundamental basically follows the linear theory, while the subharmonic follows an exponential-of-an-exponential growth.
NON-EQUILIBRIUM, NONLINEAR CRITICAL LAYERS IN LAMINAR-TURBULENT TRANSITION
Institute of Scientific and Technical Information of China (English)
WU Xuesong
2004-01-01
We describe some recent developments of high-Reynolds-number asymptotic theory for the nonlinear stage of laminar-turbulent transition in nearly parallel flows. The classic weakly nonlinear theory of Landau and Stuart is briefly revisited with the dual purposes of highlighting its fundamental ideas, which continue to underlie much of current theoretical thinking, as well as its difficulty in dealing with unbounded flows. We show that resolving such a difficulty requires an asymptotic approach based on the high-Reynolds-number assumption, which leads to a nonlinear critical-layer theory. Major recent results are reviewed with emphasis on the non-equilibrium effect. Future directions of investigation are indicated.
Dey, Pinkee; Suslov, Sergey A.
2016-12-01
A finite amplitude instability has been analysed to discover the exact mechanism leading to the appearance of stationary magnetoconvection patterns in a vertical layer of a non-conducting ferrofluid heated from the side and placed in an external magnetic field perpendicular to the walls. The physical results have been obtained using a version of a weakly nonlinear analysis that is based on the disturbance amplitude expansion. It enables a low-dimensional reduction of a full nonlinear problem in supercritical regimes away from a bifurcation point. The details of the reduction are given in comparison with traditional small-parameter expansions. It is also demonstrated that Squire’s transformation can be introduced for higher-order nonlinear terms thus reducing the full three-dimensional problem to its equivalent two-dimensional counterpart and enabling significant computational savings. The full three-dimensional instability patterns are subsequently recovered using the inverse transforms The analysed stationary thermomagnetic instability is shown to occur as a result of a supercritical pitchfork bifurcation.
Nonlinear Instability of Liquid Layers.
Newhouse, Lori Ann
The nonlinear instability of two superposed viscous liquid layers in planar and axisymmetric configurations is investigated. In the planar configuration, the light layer fluid is bounded below by a wall and above by a heavy semiinfinite fluid. Gravity drives the instability. In the first axisymmetric configuration, the layer is confined between a cylindrical wall and a core of another fluid. In the second, a thread is suspended in an infinite fluid. Surface tension forces drive the instability in the axisymmetric configurations. The nonlinear evolution of the fluid-fluid interface is computed for layers of arbitrary thickness when their dynamics are fully coupled to those of the second fluid. Under the assumption of creeping flow, the flow field is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind for the strength of the distribution is derived and then solved using an iterative technique. The Green's functions produce flow fields which are periodic in the direction parallel to the wall and have zero velocity on the wall. For small and moderate surface tension, planar layers evolve into a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of the plumes depends on the surface tension and the ratio of the fluid viscosities. As the viscosity of the layer increases, the plumes change from a well defined drop on top of a narrow stem to a compact column of rising fluid. The capillary instability of cylindrical interfaces and interfaces in which the core thickness varies in the axial direction are investigated. In both the unbounded and wall bounded configurations, the core evolves into a periodic array of elongated fluid drops connected by thin, almost cylindrical fluid links. The characteristics of the drop-link structure depend on the core thickness, the ratio of the core radius to the wall radius, and the ratio of the fluid viscosities. The factors controlling the
Nonlinear evolution of oblique waves on compressible shear layers
Goldstein, M. E.; Leib, S. J.
1989-01-01
The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.
Nonlinear optical properties of ultrathin metal layers
DEFF Research Database (Denmark)
Lysenko, Oleg
2016-01-01
. The optical characterization of the plasmonic waveguides is performed using femtosecond and picosecond optical pulses. Two nonlinear optical effects in the strip plasmonic waveguides are experimentally observed and reported. The first effect is the nonlinear power transmission of the plasmonic mode......-order nonlinear susceptibility of the plasmonic mode in the gold strip waveguides significantly depends on the metal layer thickness and laser pulse duration. This dependence is explained in detail in terms of the free-electron temporal dynamics in gold. The third-order nonlinear susceptibility of the gold layer...... duration dependence of the third-order nonlinear susceptibility of gold is calculated in the broad range from tens of femtoseconds to tens of picoseconds using the two-temperature model of the free-electron temporal dynamics of gold, and shows the saturation of the thirdorder nonlinear susceptibility...
Nonlinear Ekman Layer Theories and Their Applications
Institute of Scientific and Technical Information of China (English)
TAN Zhemin; FANG Juan; WU Rongsheng
2006-01-01
Based on the classical Ekman theory, a series of intermediate boundary layer models, which retain the nonlinear advective process while discard embellishments, have been proposed with the intention to understand the complex nonlinear features of the atmospheric boundary layer and its interaction with the free atmosphere. In this paper, the recent advances in the intermediate boundary-layer dynamic models are reviewed. Several intermediate models such as the boundary-layer models incorporating geostrophic momentum approximation, Ekman momentum approximation, and the weak nonlinear Ekman-layer model are a major theme.With inspection of the theoretical frameworks, the physical meaning and the limitations of each intermediate model are discussed. It is found that the qualitative descriptions of the nonlinear nature in Ekman layer made by the intermediate models are fairly consistent though the details may be different. As the application of the intermediate models is concerned, the application of the intermediate models to the study of the topographic boundary layer, frontogenesis, low-level frontal structure, and low-level jet are especially summarized in this paper. It is shown that the intermediate boundary-layer models have great potential in illustrating the low-level structures of the weather and climate systems as they are coupled with the free atmospheric models.In addition, the important remaining scientific challenges and a prospectus for future research on the intermediate model are also discussed.
The nonlinear evolution of modes on unstable stratified shear layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1993-06-01
The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber, and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by an integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear.
Critical layers and protoplanetary disk turbulence
Umurhan, Orkan M; Cuzzi, Jeffrey N
2016-01-01
A linear analysis of the zombie vortex instability is performed in a stratified shearing sheet setting for three model barotropic shear flows: the vorticity step, the shear layer and the asymmetric jet. The examination assumes that both disk-normal gravity and stratification is constant. The aim is to better understand the instability of so-called Z-modes and the subsequent nonlinear self-reproduction process discussed in the literature. We report several results: The instability is the result of a resonant interaction between a Rossby wave and a gravity wave. The associated critical layer is the location where the Doppler shifted frequency of a distant Rossby wave equals the local Brunt-Vaisala frequency. For the shear flow model we confirm the minimum required Rossby number (Ro) for instability to be 0.2. It is also found that the shear layer supports the instability in the limit where stratification vanishes. The zombie vortex instability as well as the Rossby wave instability are examined for the first ti...
Steady water waves with multiple critical layers
Ehrnström, Mats; Wahlén, Erik
2010-01-01
We construct small-amplitude periodic water waves with multiple critical layers. In addition to waves with arbitrarily many critical layers and a single crest in each period, two-dimensional sets of waves with several crests and troughs in each period are found. The setting is that of steady two-dimensional finite-depth gravity water waves with vorticity.
Nonlinear stability of non-stationary cross-flow vortices in compressible boundary layers
Gajjar, J. S. B.
1995-01-01
The nonlinear evolution of long wavelength non-stationary cross-flow vortices in a compressible boundary layer is investigated and the work extends that of Gajjar (1994) to flows involving multiple critical layers. The basic flow profile considered in this paper is that appropriate for a fully three-dimensional boundary layer with O(1) Mach number and with wall heating or cooling. The governing equations for the evolution of the cross-flow vortex are obtained and some special cases are discussed. One special case includes linear theory where exact analytic expressions for the growth rate of the vortices are obtained. Another special case is a generalization of the Bassom & Gajjar (1988) results for neutral waves to compressible flows. The viscous correction to the growth rate is derived and it is shown how the unsteady nonlinear critical layer structure merges with that for a Haberman type of viscous critical layer.
Nonlinear Biharmonic Equations with Critical Potential
Institute of Scientific and Technical Information of China (English)
Hui XIONG; Yao Tian SHEN
2005-01-01
In this paper, we study two semilinear singular biharmonic equations: one with subcritical exponent and critical potential, another with sub-critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile,we have compared the changes of the critical dimensions in singular and non-singular cases, and we get an interesting result.
Behavior of gravity waves with limited amplitude in the vicinity of critical layer
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
By using the FICE scheme, a numerical simulation of three-dimensional nonlinear propagation of gravity wave packet in a wind-stratified atmosphere is presented. The whole nonlinear propagation process of the gravity wave packet is shown; the propagation behavior of gravity waves in the vicinity of critical layer is analyzed. The results show that gravity waves encounter the critical layer when propagating in the fair winds whose velocities increase with height, and the height of critical layer propagating nonlinearly is lower than that expected by the linear gravity waves theory; the amplitudes of gravity waves increase with height as a whole before gravity waves encounter the critical layer, but the increasing extent is smaller than the result given by the linear theory of gravity waves, while the amplitudes of gravity waves reduce when gravity waves meet the critical layer; the energy of wave decreases with height, especially at the critical layer; the vertical wavelength reduces with the height increasing, but it does not become zero.
BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
彭艳
2014-01-01
In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameterαgoes to zero.
Self-guiding light in layered nonlinear media
DEFF Research Database (Denmark)
Bergé, L.; Mezentsev, V. K.; Juul Rasmussen, Jens;
2000-01-01
We study the propagation of intense optical beams in layered Kerr media. With appropriate shapes, beams with a power close to the self-focusing threshold are shown to propagate over long distances as quasistationary waveguides in cubic media supporting a periodic nonlinear refractive index. (C...
An averaging method for nonlinear laminar Ekman layers
DEFF Research Database (Denmark)
Andersen, Anders Peter; Lautrup, B.; Bohr, T.
2003-01-01
We study steady laminar Ekman boundary layers in rotating systems using,an averaging method similar to the technique of von Karman and Pohlhausen. The method allows us to explore nonlinear corrections to the standard Ekman theory even at large Rossby numbers. We consider both the standard self...
Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources
Institute of Scientific and Technical Information of China (English)
WANG LU-SHENG; WANG ZE-JIA
2011-01-01
In this paper, we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q0 and the critical Fujita exponent qc for the problem considered, and show that q0 ＝ qc for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources, which is quite different from the known results that q0 ＜ qc for the onedimensional case; moreover, the value is different from the slow case.
Energy Technology Data Exchange (ETDEWEB)
Lidorikis, E. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States); Busch, K. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)]|[Instituet fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, D-76128, Karlsruhe (Germany); Li, Q. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States); Chan, C.T. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)]|[Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong (China); Soukoulis, C.M. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)
1997-12-01
We consider the general problem of electromagnetic wave propagation through a one-dimensional system consisting of a nonlinear medium sandwiched between two linear structures. Special emphasis is given to systems where the latter comprise Bragg reflectors. We obtain an exact expression for the nonlinear response of such dielectric superlattices when the nonlinear impurity is very thin, or in the {delta}-function limit. We find that both the switching-up and switching-down intensities of the bistable response can be made very low, when the frequency of the incident wave matches that of the impurity mode of the structure. Numerical results for a nonlinear layer of finite width display qualitatively similar behavior, thus confirming the usefulness of the simpler {delta}-function model. In addition, an analytical solution for the resonance states of an infinitely extended finite-width superlattice with a finite-width nonlinear impurity is presented. {copyright} {ital 1997} {ital The American Physical Society}
The nonlinear evolution of inviscid Goertler vortices in three-dimensional boundary layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1995-09-01
The nonlinear development of inviscid Gortler vortices in a three-dimensional boundary layer is considered. We do not follow the classical approach of weakly nonlinear stability problems and consider a mode which has just become unstable. Instead we extend the method of Blackaby, Dando, and Hall (1992), which considered the closely related nonlinear development of disturbances in stratified shear flows. The Gortler modes we consider are initially fast growing and we assume, following others, that boundary-layer spreading results in them evolving in a linear fashion until they reach a stage where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. From the work of Blackaby, Dando and Hall (1993) is apparent, given the range of parameters for the Gortler problem, that there are three possible nonlinear integro-differential evolution equations for the disturbance amplitude. These are a cubic due to viscous effects, a cubic which corresponds to the novel mechanism investigated in this previous paper, and a quintic. In this paper we shall concentrate on the two cubic integro-differential equations and in particular, on the one due to the novel mechanism as this will be the first to affect a disturbance. It is found that the consideration of a spatial evolution problem as opposed to temporal (as was considered in Blackaby, Dando, and Hall, 1992) causes a number of significant changes to the evolution equations.
Strain-driven criticality underlies nonlinear mechanics of fibrous networks
Sharma, A; Rens, R; Vahabi, M; Jansen, K A; Koenderink, G H; MacKintosh, F C
2016-01-01
Networks with only central force interactions are floppy when their average connectivity is below an isostatic threshold. Although such networks are mechanically unstable, they can become rigid when strained. It was recently shown that the transition from floppy to rigid states as a function of simple shear strain is continuous, with hallmark signatures of criticality (Nat. Phys. 12, 584 (2016)). The nonlinear mechanical response of collagen networks was shown to be quantitatively described within the framework of such mechanical critical phenomenon. Here, we provide a more quantitative characterization of critical behavior in subisostatic networks. Using finite size scaling we demonstrate the divergence of strain fluctuations in the network at well-defined critical strain. We show that the characteristic strain corresponding to the onset of strain stiffening is distinct from but related to this critical strain in a way that depends on critical exponents. We confirm this prediction experimentally for collagen...
A Review on the Linear and Nonlinear Critical Speeds
DEFF Research Database (Denmark)
True, Hans
2013-01-01
values with a reasonable accuracy. In some cases the 'easier numerical methods' are really just a gamble. In this presentation the methods will be discussed. For this purpose linearisations of the nonlinear dynamical problem are made. A linearisation of the nonlinear dynamical problem simplifies......In recent years several authors have proposed 'easier numerical methods' to find multiple attractors and the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but they are not safe in the sense that you will calculate the relevant critical parameter...... the calculations and may give relevant answers to important questions such as the possibility of resonance phenomena in the designs, but a linearisation is not always allowed, and it does not help to find the critical speed of a railway vehicle. We shall also address the curious fact that the hunting motion...
ON NONLINEAR STABILITY IN NONPARALLEL BOUNDARY LAYER FLOW
Institute of Scientific and Technical Information of China (English)
TANG Deng-bin; WANG Wei-zhi
2004-01-01
The nonlinear stability problem in nonparallel boundary layer flow for two-dimensional disturbances was studied by using a newly presented method called Parabolic Stability Equations (PSE). A series of new modes generated by the nonlinear interaction of disturbance waves were tabulately analyzed, and the Mean Flow Distortion (MFD) was numerically given. The computational techniques developed, including the higher-order spectral method and the more effective algebraic mapping, increased greatly the numerical accuracy and the rate of convergence. With the predictor-corrector approach in the marching procedure, the normalization condition was satisfied, and the stability of numerical calculation could be ensured. With different initial amplitudes, the nonlinear stability of disturbance wave was studied. The results of examples show good agreement with the data given by the DNS using the full Navier-Stokes equations.
Nonlinear interaction of two waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1980-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed using the method of multiple scales. Numerical results for flow past a flat plate show that the spatial detuning wipes out resonant interactions unless the initial amplitudes are very large. Thus, a wave having a moderate amplitude has little influence on its subharmonic although it has a strong influence on its second harmonic. Moreover, two waves having moderate amplitudes have a strong influence on their difference frequency. The results show that the difference frequency can be very unstable when generated by the nonlinear interaction, even though it may be stable when introduced by itself in the boundary layer.
Energy Technology Data Exchange (ETDEWEB)
Artemyev, A. V., E-mail: ante0226@gmail.com; Vasiliev, A. A. [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS—University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2014-10-15
In this paper, we consider high-energy electron scattering and nonlinear trapping by oblique whistler waves via the Landau resonance. We use recent spacecraft observations in the radiation belts to construct the whistler wave model. The main purpose of the paper is to provide an estimate of the critical wave amplitude for which the nonlinear wave-particle resonant interaction becomes more important than particle scattering. To this aim, we derive an analytical expression describing the particle scattering by large amplitude whistler waves and compare the corresponding effect with the nonlinear particle acceleration due to trapping. The latter is much more rare but the corresponding change of energy is substantially larger than energy jumps due to scattering. We show that for reasonable wave amplitudes ∼10–100 mV/m of strong whistlers, the nonlinear effects are more important than the linear and nonlinear scattering for electrons with energies ∼10–50 keV. We test the dependencies of the critical wave amplitude on system parameters (background plasma density, wave frequency, etc.). We discuss the role of obtained results for the theoretical description of the nonlinear wave amplification in radiation belts.
Steady water waves with multiple critical layers: interior dynamics
Ehrnström, Mats; Villari, Gabriele
2010-01-01
We study small-amplitude steady water waves with multiple critical layers. Those are rotational two-dimensional gravity-waves propagating over a perfect fluid of finite depth. It is found that arbitrarily many critical layers with cat's-eye vortices are possible, with different structure at different levels within the fluid. The corresponding vorticity depends linearly on the stream function.
Nonlinear waves in stratified Taylor--Couette flow. Part 1. Layer formation
Leclercq, Colin; Augier, Pierre; Caulfield, Colm-Cille P; Dalziel, Stuart B; Linden, Paul F
2016-01-01
This paper is the first part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. Using linear analysis and direct numerical simulation, we show the critical role played by non-axisymmetric instability modes, despite the fact that the flow is centrifugally unstable in the sense of Rayleigh's criterion. Interactions between helical modes of opposite handedness leads to the formation of nonlinear coherent structures: (mixed)-ribbons and (mixed)-cross-spirals. These give birth to complex density interface patterns, seemingly appearing and disappearing periodically as the coherent structure slowly rotates around the annulus. These coherent structures seem to be responsible for the formation of layers reported in a recent experiment by Oglethorpe et al. (2013). We distinguish `dynamic layering', instantaneous, localized and caused by the vortical motions, from `static layering' corresponding to the formation of...
Collapse of nonlinear electron plasma waves in a plasma layer
Grimalsky, V.; Koshevaya, S.; Rapoport, Yu; Kotsarenko, A.
2016-10-01
The excitation of nonlinear electron plasma waves in the plasma layer is investigated theoretically. This excitation is realized by means of initial oscillatory perturbations of the volume electron concentration or by initial oscillatory distributions of the longitudinal electron velocity. The amplitudes of the initial perturbations are small and the manifestation of the volume nonlinearity is absent. When the amplitudes of the initial perturbations exceed some thresholds, the values of the electron concentration near the plasma boundary increase catastrophically. The maxima of the electron concentration reach extremely high magnitudes, and sharp peaks in the electron concentration occur, which are localized both in the longitudinal and transverse directions. This effect is interpreted as wave collapse near the plasma boundary.
Nonlinear interaction of waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1979-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed by using the method of multiple scales. For the case of two waves, a strong nonlinear interaction exists if one of the frequencies w2 is twice the other frequency w1. Numerical results for flow past a flat plate show that this interaction mechanism is strongly destabilizing even in regions where either the fundamental or its harmonic is damped in the absence of the interaction. For the case of three waves, a strong nonlinear interaction exists when w3 = w2- w1. This combination resonance causes the amplitude of the wave with the difference frequency w3 to multiply many times in magnitude in a short distance even if it is damped in the absence of the interaction. The initial amplitudes play a dominant role in determining the changes in the amplitudes of the waves in both of these mechanisms.
Critical exponent for damped wave equations with nonlinear memory
Fino, Ahmad
2010-01-01
We consider the Cauchy problem in $\\mathbb{R}^n,$ $n\\geq 1,$ for a semilinear damped wave equation with nonlinear memory. Global existence and asymptotic behavior as $t\\to\\infty$ of small data solutions have been established in the case when $1\\leq n\\leq3.$ Moreover, we derive a blow-up result under some positive data for in any dimensional space. It turns out that the critical exponent indeed coincides with the one to the corresponding semilinear heat equation.
Dynamics of parabolic problems with memory. Subcritical and critical nonlinearities
Li, Xiaojun
2016-08-01
In this paper, we study the long-time behavior of the solutions of non-autonomous parabolic equations with memory in cases when the nonlinear term satisfies subcritical and critical growth conditions. In order to do this, we show that the family of processes associated to original systems with heat source f(x, t) being translation bounded in Lloc 2 ( R ; L 2 ( Ω ) ) is dissipative in higher energy space M α , 0 < α ≤ 1, and possesses a compact uniform attractor in M 0 .
Compact way of the ionosphere layers critical frequency detection using A-map
Yusupov, Kamil; Akchurin, Adel
2016-07-01
The critical frequency of the ionosphere layer characterizes the electron density of the ionosphere layers and it is an important parameter for ionosphere observation. So, it has long been established that the critical frequencies have correlation with the solar activity, the geomagnetic activity, the neutral atmosphere and others. Based on the analysis of the critical frequency of the ionosphere the empirical models was based (e.g. IRI). Critical frequencies detection is complex due to the inhomogeneous properties of the ionosphere, which leads to the nonlinearity of reflection traces in ionogram at vertical sounding. This paper describes ionogram processing algorithm using the A-maps [Akchurin, 2011; Yusupov, 2014] for ionosphere layers critical frequency detection. For A-map construction, the reflected signal amplitude is allocated. Our ionosonde has not magnetoionic modes polarization separation; therefore, A-map has signal amplitude failures (due to interference). Also, ionosphere traces have amplitude failures associated with the signal focusing as a result of the effects of the TID and others. An important is the noise presence from the other HF radio system. To decrease the influence of these effects in critical frequency detection it is used several filtering stages that smooth A-map amplitude oscillation. Next is searching amplitude threshold, which mark the boundary of the critical frequency. The resulting F-plot easily compared with A-map, which have high precision visually noticeable critical frequency. This algorithm is well suited for the E- and F-regions critical frequency detection.
Nonlinear topographic effects in two-layer flows
Directory of Open Access Journals (Sweden)
Peter George Baines
2016-02-01
Full Text Available We consider the nature of non-linear flow of a two-layer fluid with a rigid lid over a long obstacle, such that the flow may be assumed to be hydrostatic. Such flows can generate hydraulic jumps upstream, and the model uses a new model of internal hydraulic jumps, which results in corrections to flows that have been computed using earlier models of jumps that are now known to be incorrect. The model covers the whole range of ratios of the densities of the two fluids, and is not restricted to the Boussinesq limit. The results are presented in terms of flow types in various regions of a Froude number-obstacle height (F0 – Hm diagram, in which the Froude number F0 is based on the initial flow conditions. When compared with single-layer flow, and some previous results with two layers, some surprising and novel patterns emerge on these diagrams. Specifically, in parts of the diagram where the flow may be supercritical (F0 > 1, there are regions where hysteresis may occur, implying that the flow may have two and sometimes three multiple flow states for the same conditions (i.e. values of F0 and Hm.
Noninvasive nonlinear imaging through strongly-scattering turbid layers
Katz, Ori; Guan, Yefeng; Silberberg, Yaron
2014-01-01
Diffraction-limited imaging through complex scattering media is a long sought after goal with important applications in biomedical research. In recent years, high resolution wavefront-shaping has emerged as a powerful approach to generate a sharp focus through highly scattering, visually opaque samples. However, it requires a localized feedback signal from the target point of interest, which necessitates an invasive procedure in all-optical techniques. Here, we show that by exploiting optical nonlinearities, a diffraction-limited focus can be formed inside or through a complex sample, even when the feedback signal is not localized. We prove our approach theoretically and numerically, and experimentally demonstrate it with a two-photon fluorescence signal through highly scattering biological samples. We use the formed focus to perform two-photon microscopy through highly scattering, visually opaque layers.
3D critical layers in fully-developed turbulent flows
Saxton-Fox, Theresa; McKeon, Beverley
2016-11-01
Recent work has shown that 3D critical layers drive self-sustaining behavior of exact coherent solutions of the Navier-Stokes equations (Wang et al. 2007; Hall and Sherwin 2010; Park and Graham 2015). This study investigates the role of 3D critical layers in fully-developed turbulent flows. 3D critical layer effects are identified in instantaneous snapshots of turbulent boundary layers in both experimental and DNS data (Wu et al. 2014). Additionally, a 3D critical layer effect is demonstrated to appear using only a few resolvent response modes from the resolvent analysis of McKeon and Sharma 2010, with phase relationships appropriately chosen. Connections are sought to the thin shear layers observed in turbulent boundary layers (Klewicki and Hirschi 2004; Eisma et al. 2015) and to amplitude modulation observations (Mathis et al. 2009; Duvvuri and McKeon 2014). This research is made possible by the Department of Defense through the National Defense & Engineering Graduate Fellowship (NDSEG) Program and by the Air Force Office of Scientific Research Grant # FA9550-12-1-0060. The support of the Center for Turbulence Research (CTR) summer program at Stanford is gratefully acknowledged.
Nonlinear evolution of subsonic and supersonic disturbances on a compressible free shear layer
Leib, S. J.
1991-01-01
The effects of a nonlinear-nonequilibrium-viscous critical layer on the spatial evolution of subsonic and supersonic instability modes on a compressible free shear layer is considered. It is shown that the instability wave amplitude is governed by an integrodifferential equation with cubic-type nonlinearity. Numerical and asymptotic solutions to this equation show that the amplitude either ends in a singularity at a finite downstream distance or reaches an equilibrium value, depending on the Prandtl number, viscosity law, viscous parameter and a real parameter which is determined by the linear inviscid stability theory. A necessary condition for the existence of the equilibrium solution is derived, and whether or not this condition is met is determined numerically for a wide range of physical parameters including both subsonic and supersonic disturbances. it is found that no equilibrium solution exists for the subsonic modes unless the temperature ratio of the low-to-high-speed streams exceeds a critical value, while equilibrium solutions for the most rapidly growing supersonic mode exist over most of the parameter range examined.
Critical Dispersion Distance of Silicon Nanoparticles Intercalated between Graphene Layers
Directory of Open Access Journals (Sweden)
Shuze Zhu
2012-01-01
Full Text Available Nanocomposites of silicon nanoparticles (Si NPs dispersed in between graphene layers emerge as potential anode materials of high-charge capacity for lithium-ion batteries. A key design requirement is to keep Si NPs dispersed without aggregation. Experimental design of the Si NP dispersion in graphene layers has remained largely empirical. Through extensive molecular dynamics simulations, we determine a critical NP dispersion distance as the function of NP size, below which Si NPs in between graphene layers evolve to bundle together. These results offer crucial and quantitative guidance for designing NP-graphene nanocomposite anode materials with high charge capacity.
Sahai, Aakash
2015-11-01
A parametric instability that affects the longitudinal envelope of a laser pulse interacting with a propagating critical layer is presented [Sahai, PoP 21,056707, 2014; Sahai, arXiv:1411.2401, 2014]. It is shown that non-linear mixing between the incident and reflected laser pulse from a propagating critical layer electron compression results in a beat-wave with a complete modulation of the incident wave envelope. This beat-wave modulates the velocity of the propagating critical layer, resulting in a new Doppler frequency which creates a second beat-wave, further modulating the laser envelope. The frequency spread of the laser envelope grows in time resulting in a large spectral spread of the laser pulse envelope. The velocity of the propagating critical layer acceleration structure is correspondingly modulated as is the space-charge potential. Thus, the ions that are accelerated off the potential have a large energy spread. Since, the growth rate of this instability depends upon the acceleration structure velocity, longer pulses are unfavorable for accelerating ions to higher energies with a narrow energy spread. This instability is also relevant to laser-driven fusion and laser hole-boring based fast-ignition but due to much smaller velocities, its effect is mitigated.
Institute of Scientific and Technical Information of China (English)
唐登斌; 夏浩
2002-01-01
The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition, determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier- Stokes equations.
The upper critical field in two-band layered superconductors
Institute of Scientific and Technical Information of China (English)
Liu Min-Xia; Gan Zi-Zhao
2007-01-01
The upper critical field of clean MgB2 is investigated using the two-band layered Ginzburg-Landau (GL) theory.The calculated results are fitted to the experimental data of clean MgB2 crystal very well in a broad temperature range.Based on the GL theory for clean superconductors,a phenomenOlogical theory for dirty superconductor is proposed.Selecting appropriate parameters,two-band layered GL theory is successfully applied to the crystal of Mg(B1-xCx)2 and the neutron irradiation samples of MgB2.
Scaling of the critical slip distance in granular layers
Hatano, Takahiro
2009-01-01
We investigate the nature of friction in granular layers by means of numerical simulation focusing on the critical slip distance, over which the system relaxes to a new stationary state. Analyzing a transient process in which the sliding velocity is instantaneously changed, we find that the critical slip distance is proportional to the sliding velocity. We thus define the relaxation time, which is independent of the sliding velocity. It is found that the relaxation time is proportional to the layer thickness and inversely proportional to the square root of the pressure. An evolution law for the relaxation process is proposed, which does not contain any length constants describing the surface geometry but the relaxation time of the bulk granular matter. As a result, the critical slip distance is scaled with a typical length scale of a system. It is proportional to the layer thickness in an instantaneous velocity change experiment, whereas it is scaled with the total slip distance in a spring-block system on gr...
Modeling of Nonlinear Propagation in Multi-layer Biological Tissues for Strong Focused Ultrasound
Institute of Scientific and Technical Information of China (English)
FAN Ting-Bo; LIU Zhen-Bo; ZHANG Zhe; ZHANG DONG; GONG Xiu-Fen
2009-01-01
A theoretical model of the nonlinear propagation in multi-layered tissues for strong focused ultrasound is proposed. In this model, the spheroidal beam equation (SBE) is utilized to describe the nonlinear sound propagation in each layer tissue, and generalized oblique incidence theory is used to deal with the sound transmission between two layer tissues. Computer simulation is performed on a fat-muscle-liver tissue model under the irradiation of a 1 MHz focused transducer with a large aperture angle of 35°. The results demonstrate that the tissue layer would change the amplitude of sound pressure at the focal region and cause the increase of side petals.
Existence of least energy solutions to coupled elliptic systems with critical nonlinearities
Directory of Open Access Journals (Sweden)
Gong-Ming Wei
2008-04-01
Full Text Available In this paper we study the existence of nontrivial solutions of elliptic systems with critical nonlinearities and subcritical nonlinear coupling interactions, under Dirichlet or Neumann boundary conditions. These equations are motivated from solitary waves of nonlinear Schrodinger systems in physics. Using minimax theorem and by estimates on the least energy, we prove the existence of nonstandard least energy solutions, i.e. solutions with least energy and each component is nontrivial.
Tropical cyclogenesis in a tropical wave critical layer: easterly waves
Directory of Open Access Journals (Sweden)
T. J. Dunkerton
2008-06-01
Full Text Available The development of tropical depressions within tropical waves over the Atlantic and eastern Pacific is usually preceded by a "surface low along the wave" as if to suggest a hybrid wave-vortex structure in which flow streamlines not only undulate with the waves, but form a closed circulation in the lower troposphere surrounding the low. This structure, equatorward of the easterly jet axis, resembles the familiar critical layer of waves in shear flow, a flow configuration which arguably provides the simplest conceptual framework for tropical cyclogenesis resulting from tropical waves, their interaction with the mean flow, and with diabatic processes associated with deep moist convection. The critical layer represents a sweet spot for tropical cyclogenesis in which a proto-vortex may form and grow within its parent wave. A common location for storm development within the critical layer is given by the intersection of the wave's critical latitude and trough axis, with analyzed vorticity centroid nearby. The wave and vortex live together for a time, and initially propagate at approximately the same speed. In most cases this coupled propagation continues for a few days after a tropical depression is identified. For easterly waves, as the name suggests, the propagation is westward. It is shown that in order to visualize optimally this "marsupial paradigm" one should view the flow streamlines, or stream function, in a frame of reference translating horizontally with the phase propagation of the parent wave. This translation requires an appropriate "gauge" that renders translating streamlines and isopleths of translating stream function approximately equivalent to flow trajectories. In the translating frame, the closed circulation is stationary, and a dividing streamline effectively separates air within the critical layer from air outside. The critical layer equatorward of the easterly jet axis is important to tropical cyclogenesis because it
Directory of Open Access Journals (Sweden)
Jinmyoung Seok
2015-07-01
Full Text Available In this article, we are interested in singularly perturbed nonlinear elliptic problems involving a fractional Laplacian. Under a class of nonlinearity which is believed to be almost optimal, we construct a positive solution which exhibits multiple spikes near any given local minimum components of an exterior potential of the problem.
Ground state solutions for nonlinear fractional Schrodinger equations involving critical growth
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Hua Jin
2017-03-01
Full Text Available This article concerns the ground state solutions of nonlinear fractional Schrodinger equations involving critical growth. We obtain the existence of ground state solutions when the potential is not a constant and not radial. We do not use the Ambrosetti-Rabinowitz condition, or the monotonicity condition on the nonlinearity.
Nonlinear Schrodinger elliptic systems involving exponential critical growth in R^2
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Francisco S. B. Albuquerque Albuquerque
2014-02-01
Full Text Available This article concerns the existence and multiplicity of solutions for elliptic systems with weights, and nonlinearities having exponential critical growth. Our approach is based on the Trudinger-Moser inequality and on a minimax theorem.
Double-dark-resonance-enhanced Kerr nonlinearity in a single layer of graphene nanostructure
Solookinejad, Gh.; Panahi, M.; Ahmadi Sangachin, E.; Hossein Asadpour, Seyyed
2016-08-01
In this paper, a novel scheme is proposed for the giant enhanced Kerr nonlinearity in a single layer of graphene nanostructure based on quantum optics and nonlinear optical sciences. The linear and the nonlinear susceptibility of the monolayer graphene system are presented in details by using the density matrix method and perturbation theory. After deriving the equations of motion in the steady-state regime, we analytically solve the linear and nonlinear susceptibility of the system. Our numerical results show that the giant enhanced Kerr nonlinearity can be obtained in the double-dark-resonance condition with zero linear and nonlinear absorption. Our results may have potential applications in quantum information science in infrared and terahertz regimes.
Solookinejad, G.
2016-09-01
In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.
Energy Technology Data Exchange (ETDEWEB)
Solookinejad, G., E-mail: ghsolooki@gmail.com
2016-09-15
In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.
Solving Nonlinearly Separable Classifications in a Single-Layer Neural Network.
Conaway, Nolan; Kurtz, Kenneth J
2017-03-01
Since the work of Minsky and Papert ( 1969 ), it has been understood that single-layer neural networks cannot solve nonlinearly separable classifications (i.e., XOR). We describe and test a novel divergent autoassociative architecture capable of solving nonlinearly separable classifications with a single layer of weights. The proposed network consists of class-specific linear autoassociators. The power of the model comes from treating classification problems as within-class feature prediction rather than directly optimizing a discriminant function. We show unprecedented learning capabilities for a simple, single-layer network (i.e., solving XOR) and demonstrate that the famous limitation in acquiring nonlinearly separable problems is not just about the need for a hidden layer; it is about the choice between directly predicting classes or learning to classify indirectly by predicting features.
Tropical Cyclogenesis in a Tropical Wave Critical Layer: Easterly Waves
Dunkerton, T. J.; Montgomery, M. T.; Wang, Z.
2009-01-01
The development of tropical depressions within tropical waves over the Atlantic and eastern Pacific is usually preceded by a "surface low along the wave" as if to suggest a hybrid wave-vortex structure in which flow streamlines not only undulate with the waves, but form a closed circulation in the lower troposphere surrounding the low. This structure, equatorward of the easterly jet axis, is identified herein as the familiar critical layer of waves in shear flow, a flow configuration which arguably provides the simplest conceptual framework for tropical cyclogenesis resulting from tropical waves, their interaction with the mean flow, and with diabatic processes associated with deep moist convection. The recirculating Kelvin cat's eye within the critical layer represents a sweet spot for tropical cyclogenesis in which a proto-vortex may form and grow within its parent wave. A common location for storm development is given by the intersection of the wave's critical latitude and trough axis at the center of the cat's eye, with analyzed vorticity centroid nearby. The wave and vortex live together for a time, and initially propagate at approximately the same speed. In most cases this coupled propagation continues for a few days after a tropical depression is identified. For easterly waves, as the name suggests, the propagation is westward. It is shown that in order to visualize optimally the associated Lagrangian motions, one should view the flow streamlines, or stream function, in a frame of reference translating horizontally with the phase propagation of the parent wave. In this co-moving frame, streamlines are approximately equivalent to particle trajectories. The closed circulation is quasi-stationary, and a dividing streamline separates air within the cat's eye from air outside.
Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at
Directory of Open Access Journals (Sweden)
Swati Mukhopadhyay
2013-12-01
Full Text Available The boundary layer flow of a viscous incompressible fluid toward a porous nonlinearly stretching sheet is considered in this analysis. Velocity slip is considered instead of no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equation corresponding to the momentum equation into nonlinear ordinary differential equation. Numerical solution of this equation is obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter.
Tropical cyclogenesis in a tropical wave critical layer: easterly waves
Directory of Open Access Journals (Sweden)
T. J. Dunkerton
2009-08-01
Full Text Available The development of tropical depressions within tropical waves over the Atlantic and eastern Pacific is usually preceded by a "surface low along the wave" as if to suggest a hybrid wave-vortex structure in which flow streamlines not only undulate with the waves, but form a closed circulation in the lower troposphere surrounding the low. This structure, equatorward of the easterly jet axis, is identified herein as the familiar critical layer of waves in shear flow, a flow configuration which arguably provides the simplest conceptual framework for tropical cyclogenesis resulting from tropical waves, their interaction with the mean flow, and with diabatic processes associated with deep moist convection. The recirculating Kelvin cat's eye within the critical layer represents a sweet spot for tropical cyclogenesis in which a proto-vortex may form and grow within its parent wave. A common location for storm development is given by the intersection of the wave's critical latitude and trough axis at the center of the cat's eye, with analyzed vorticity centroid nearby. The wave and vortex live together for a time, and initially propagate at approximately the same speed. In most cases this coupled propagation continues for a few days after a tropical depression is identified. For easterly waves, as the name suggests, the propagation is westward. It is shown that in order to visualize optimally the associated Lagrangian motions, one should view the flow streamlines, or stream function, in a frame of reference translating horizontally with the phase propagation of the parent wave. In this co-moving frame, streamlines are approximately equivalent to particle trajectories. The closed circulation is quasi-stationary, and a dividing streamline separates air within the cat's eye from air outside. The critical layer equatorward of the easterly jet axis is important to tropical cyclogenesis because its cat's eye provides (i a region of
On a nonlinear elliptic problem with critical potential in R2
Institute of Scientific and Technical Information of China (English)
SHEN; Yaotian; YAO; Yangxin; HEN; Zhihui
2004-01-01
Consider the existence of nontrivial solutions of homogeneous Dirichlet problem for a nonlinear elliptic equation with the critical potential in R2. By establishing a weighted inequality with the best constant, determine the critical potential in R2, and study the eigenvalues of Laplace equation with the critical potential. By the Pohozaev identity of a solution with a singular point and the Cauchy-Kovalevskaya theorem, obtain the nonexistence result of solutions with singular points to the nonlinear elliptic equation. Moreover, for the same problem, the existence results of multiple solutions are proved by the mountain pass theorem.
Institute of Scientific and Technical Information of China (English)
Zhu Xiao-Feng; Zhou Lin; Zhang Dong; Gong Xiu-Fen
2005-01-01
Nonlinear propagation of focused ultrasound in layered biological tissues is theoretically studied by using the angular spectrum approach (ASA), in which an acoustic wave is decomposed into its angular spectrum, and the distribution of nonlinear acoustic fields is calculated in arbitrary planes normal to the acoustic axis. Several biological tissues are used as specimens inserted into the focusing region illuminated by a focused piston source. The second harmonic components within or beyond the biological specimens are numerically calculated. Validity of the theoretical model is examined by measurements. This approach employing the fast Fourier transformation gives a clear visualization of the focused ultrasound, which is helpful for nonlinear ultrasonic imaging.
Weakly nonlinear stability of vicsous vortices in three-dimensional boundary layers
Bassom, Andrew P.; Otto, S. R.
1993-01-01
Attention is given to the weakly nonlinear stability of essentially viscous vortices in 3D boundary layers. These modes are unstable in the absence of crossflow, but the imposition of small crossflow has a stabilizing effect. Bassom and Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wave number combinations, and the weakly nonlinear stability properties of these disturbances are described. It is shown that the effect of crossflow is to stabilize the nonlinear modes, and the present calculations allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting.
Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet
Masood Khan; Hashim
2015-01-01
This article studies the Carreau viscosity model (which is a generalized Newtonian model) and then use it to obtain a formulation for the boundary layer equations of the Carreau fluid. The boundary layer flow and heat transfer to a Carreau model over a nonlinear stretching surface is discussed. The Carreau model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical ...
Determining critical load in the multispan beams with the nonlinear model
DemÑ-r, D. Dönmez; Sinir, B. G.; Usta, L.
2017-01-01
The beams which are one of the most commonly used structural members are quite important for many researchers. Mathematical models determining the response of beams under external loads are concluded from elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. In this study, the derivation of the nonlinear model is introduced to determine the critical load in the multispan beams. Since the engineering practice of this kind of problems is very common, determining the critical load is quite important. For this purpose, the nonlinear mathematical model of the multispan Euler-Bernoulli beam is firstly obtained. To be able to obtain the independent of the material and the geometry, the present model are became dimensionless. Then, the critical axial load can be determined via the nonlinear solution of the governing equation.
Sha, Daohang
2010-01-01
Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive algorithm is presented for online learning based on matrix operation and optimization methods analytically, which can avoid the trouble to select a proper learning rate for the gradient method. The proof of weak convergence of the proposed algorithm also is given. Although this approach is proposed for three-layer, feed-forward neural networks, it could be extended to multiple layer feed-forward neural networks. The effectiveness of the proposed algorithms applied to the identification of behavior of a two-input and two-output non-linear dynamic system is demonstrated by simulation experiments.
Directory of Open Access Journals (Sweden)
anjali devi
2015-01-01
Full Text Available The effects of nonlinear radiation on hydromagnetic boundary layer flow and heat transfer over a shrinking surface is investigated in the present work. Using suitable similarity transformations, the governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. The resultant equations which are highly nonlinear are solved numerically using Nachtsheim Swigert shooting iteration scheme together with Fourth Order Runge Kutta method. Numerical solutions for velocity, skin friction coefficient and temperature are obtained for various values of physical parameters involved in the study namely Suction parameter, Magnetic parameter, Prandtl number, Radiation parameter and Temperature ratio parameter. Numerical values for dimensionless rate of heat transfer are also obtained for various physical parameters and are shown through tables. The analytical solution of the energy equation when the radiation term is taken in linear form is obtained using Confluent hypergeometric function.
Nonlinear elastic response in solid helium: critical velocity or strain?
Day, James; Syshchenko, Oleksandr; Beamish, John
2010-02-19
Torsional oscillator experiments show evidence of mass decoupling in solid 4He. This decoupling is amplitude dependent, suggesting a critical velocity for supersolidity. We observe similar behavior in the elastic shear modulus. By measuring the shear modulus over a wide frequency range, we can distinguish between an amplitude dependence which depends on velocity and one which depends on some other parameter such as displacement. In contrast with the torsional oscillator behavior, the modulus depends on the magnitude of stress, not velocity. We interpret our results in terms of the motion of dislocations which are weakly pinned by 3He impurities but which break away when large stresses are applied.
Nonlinear Bubble Dynamics And The Effects On Propagation Through Near-Surface Bubble Layers
Leighton, Timothy G.
2004-11-01
Nonlinear bubble dynamics are often viewed as the unfortunate consequence of having to use high acoustic pressure amplitudes when the void fraction in the near-surface oceanic bubble layer is great enough to cause severe attenuation (e.g. >50 dB/m). This is seen as unfortunate since existing models for acoustic propagation in bubbly liquids are based on linear bubble dynamics. However, the development of nonlinear models does more than just allow quantification of the errors associated with the use of linear models. It also offers the possibility of propagation modeling and acoustic inversions which appropriately incorporate the bubble nonlinearity. Furthermore, it allows exploration and quantification of possible nonlinear effects which may be exploited. As a result, high acoustic pressure amplitudes may be desirable even in low void fractions, because they offer opportunities to gain information about the bubble cloud from the nonlinearities, and options to exploit the nonlinearities to enhance communication and sonar in bubbly waters. This paper presents a method for calculating the nonlinear acoustic cross-sections, scatter, attenuations and sound speeds from bubble clouds which may be inhomogeneous. The method allows prediction of the time dependency of these quantities, both because the cloud may vary and because the incident acoustic pulse may have finite and arbitrary time history. The method can be readily adapted for bubbles in other environments (e.g. clouds of interacting bubbles, sediments, structures, in vivo, reverberant conditions etc.). The possible exploitation of bubble acoustics by marine mammals, and for sonar enhancement, is explored.
Approximate Critical Load of Cambered Double-Layered Grids by Shell Analogies
Directory of Open Access Journals (Sweden)
M.I. Ali
2012-08-01
Full Text Available Studies have shown that design of double-layered grids based on classical theories may lead to unsafe design. For square-on-diagonal grids, the load carrying capacity is almost the same as the buckling load. Therefore the buckling load can be used as the critical load in the design. In this study, the non-linear behavior of the grids is considered using shell analogies to determine the critical load. By applying the theorem of study and energy to a dimple, an empirical formula to predict the buckling load of thin spherical shells was derived. Then using finite element modeling, post-buckling load was identified and used to calculate the value of constant C. It is observed that the buckling load is proportional to t2.5, which gives a critical load close to what is observed in experiments and a more realistic load as compared to the Classical theory prediction. Loaddeflection curves drawn for the grids and their equivalent continuum shells correlate closely showing that the findings are valid.
Analytical study of the critical behavior of the nonlinear pendulum
Lima, F. M. S.
2010-11-01
The dynamics of a simple pendulum consisting of a small bob and a massless rigid rod has three possible regimes depending on its total energy E: Oscillatory (when E is not enough for the pendulum to reach the top position), "perpetual ascent" when E is exactly the energy needed to reach the top, and nonoscillatory for greater energies. In the latter regime, the pendulum rotates periodically without velocity inversions. In contrast to the oscillatory regime, for which an exact analytic solution is known, the other two regimes are usually studied by solving the equation of motion numerically. By applying conservation of energy, I derive exact analytical solutions to both the perpetual ascent and nonoscillatory regimes and an exact expression for the pendulum period in the nonoscillatory regime. Based on Cromer's approximation for the large-angle pendulum period, I find a simple approximate expression for the decrease of the period with the initial velocity in the nonoscillatory regime, valid near the critical velocity. This expression is used to study the critical slowing down, which is observed near the transition between the oscillatory and nonoscillatory regimes.
Directory of Open Access Journals (Sweden)
Ningning Duan
2015-01-01
Full Text Available Dimensionless nonlinear dynamical equations of a tilted support spring nonlinear packaging system with critical components were obtained under a rectangular pulse. To evaluate the damage characteristics of shocks to packaged products with critical components, a concept of the damage boundary surface was presented and applied to a titled support spring system, with the dimensionless critical acceleration of the system, the dimensionless critical velocity, and the frequency parameter ratio of the system taken as the three basic parameters. Based on the numerical results, the effects of the frequency parameter ratio, the mass ratio, the dimensionless peak pulse acceleration, the angle of the system, and the damping ratio on the damage boundary surface of critical components were discussed. It was demonstrated that with the increase of the frequency parameter ratio, the decrease of the angle, and/or the increase of the mass ratio, the safety zone of critical components can be broadened, and increasing the dimensionless peak pulse acceleration or the damping ratio may lead to a decrease of the damage zone for critical components. The results may lead to a thorough understanding of the design principles for the tilted support spring nonlinear system.
INITIAL LAYER PHENOMENA FOR A CLASS OF SINGULAR PERTURBED NONLINEAR SYSTEM WITH SLOW VARIABLES
Institute of Scientific and Technical Information of China (English)
黄蔚章; 陈育森
2004-01-01
The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different "thickness", the Norder approximate expansion of perturbed solution concerning small parameter is obtained,and the "multiple layer" phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well.
Spatial properties of entangled photon pairs generated in nonlinear layered structures
Perina, Jan
2011-01-01
A spatial quantum model of spontaneous parametric down-conversion in nonlinear layered structures is developed expanding the interacting vectorial fields into monochromatic plane waves. A two-photon spectral amplitude depending on the signal- and idler-field frequencies and propagation directions is used to derive transverse profiles of the emitted fields as well as their spatial correlations. Intensity spatial profiles and their spatial correlations are mainly determined by the positions of transmission peaks formed in these structures with photonic bands. A method for geometry optimization of the structures with respect to efficiency of the nonlinear process is suggested. Several structures composed of GaN/AlN layers are analyzed as typical examples. They allow the generation of photon pairs correlated in several emission directions. Photon-pair generation rates increasing better than the second power of the number of layers can be reached. Also structures efficiently generated photon pairs showing anti-bun...
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
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S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
Institute of Scientific and Technical Information of China (English)
Munazza Zulfiqar Ali; Tariq Abdullah
2008-01-01
We investigate the effects of introducing a defect layer in a one-dimensional photonic crystal containing single negative material layers on the transmission properties.The width of the defect layer js taken to be the same or smaller than the period of the structure.Different cases of the defect layer being linear or nonlinear and double positive or double negative are discussed.It is found that only a nonlinear double negative layer givas rises to a localized mode within the zero-φeff gap in this kind of structure.It is also shown that the important characteristics of the nonlinear defect mode such as its frequency,its FWHM and the threshold of the associated bistability can be controlled by changing the widths of the defect layer and the host layers.
Global well-posedness for nonlinear Schrodinger equations with energy-critical damping
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Binhua Feng
2015-01-01
Full Text Available We consider the Cauchy problem for the nonlinear Schrodinger equations with energy-critical damping. We prove the existence of global in-time solutions for general initial data in the energy space. Our results extend some results from [1,2].
Excitonic optical nonlinearities and transport in the layered compound semiconductor GaSe
DEFF Research Database (Denmark)
Mizeikis, V.; Vadim, Lyssenko; Østergaard, John Erland;
1995-01-01
Dephasing and transient grating experiments in the direct excitonic absorption region of GaSe at low temperatures show that a fast relaxation within the one-dimensionally disordered excitonic band results in band filling being the dominant mechanism of the optical nonlinearity. Correspondingly, we...... observe a blueshift of the nonlinear signal with excitation density. The temperature dependence of the exciton diffusion constant measured in directions parallel to the GaSe layer planes indicates that temperature-independent scattering (trapping) and scattering by acoustic phonons determine the exciton...
Fereidoon, A.; Andalib, E.; Mirafzal, A.
2016-07-01
This article studies the nonlinear vibration of viscoelastic embedded nano-sandwich structures containing of a double walled carbon nanotube (DWCNT) integrated with two piezoelectric Zinc oxide (ZnO) layers. DWCNT and ZnO layers are subjected to magnetic and electric fields, respectively. This system is conveying viscous fluid and the related force is calculated by modified Navier-Stokes relation considering slip boundary condition and Knudsen number. Visco-Pasternak model with three parameters of the Winkler modulus, shear modulus, and damp coefficient is used for simulation of viscoelastic medium. The nano-structure is simulated as an orthotropic Timoshenko beam (TB) and the effects of small scale, structural damping and surface stress are considered based on Eringen's, Kelvin-voigt and Gurtin-Murdoch theories. Energy method and Hamilton's principle are employed to derive motion equations which are then solved using differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of small scale effect, fluid velocity, thickness of piezoelectric layer, boundary condition, surface effects, van der Waals (vdW) force on the frequency and critical velocity of nano-structure. Results indicate that the frequency and critical velocity increases with assume of surface effects.
Structure of internal solitary waves in two-layer fluid at near-critical situation
Kurkina, O.; Singh, N.; Stepanyants, Y.
2015-05-01
A new model equation describing weakly nonlinear long internal waves at the interface between two thin layers of different density is derived for the specific relationships between the densities, layer thicknesses and surface tension between the layers. The equation derived and dubbed here the Gardner-Kawahara equation represents a natural generalisation of the well-known Korteweg-de Vries (KdV) equation containing the cubic nonlinear term as well as fifth-order dispersion term. Solitary wave solutions are investigated numerically and categorised in terms of two dimensionless parameters, the wave speed and fifth-order dispersion. The equation derived may be applicable to wave description in other media.
Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow
Choudhari, Meelan; Duck, Peter W.
1996-01-01
We examine the excitation of inviscid stationary crossflow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modified to a significant extent. This behavior contrasts sharply with earlier findings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the crossflow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for flow reversal to occur in the canonical solution. We also find that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to crossflow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed.
A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures
Directory of Open Access Journals (Sweden)
Liyuan Yu
2017-01-01
Full Text Available Selecting appropriate governing equations for fluid flow in fractured rock masses is of special importance for estimating the permeability of rock fracture networks. When the flow velocity is small, the flow is in the linear regime and obeys the cubic law, whereas when the flow velocity is large, the flow is in the nonlinear regime and should be simulated by solving the complex Navier-Stokes equations. The critical conditions such as critical Reynolds number and critical hydraulic gradient are commonly defined in the previous works to quantify the onset of nonlinear fluid flow. This study reviews the simplifications of governing equations from the Navier-Stokes equations, Stokes equation, and Reynold equation to the cubic law and reviews the evolutions of critical Reynolds number and critical hydraulic gradient for fluid flow in rock fractures and fracture networks, considering the influences of shear displacement, normal stress and/or confining pressure, fracture surface roughness, aperture, and number of intersections. This review provides a reference for the engineers and hydrogeologists especially the beginners to thoroughly understand the nonlinear flow regimes/mechanisms within complex fractured rock masses.
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
In safety critical systems, the control system is composed of a core control system with a fault detection and isolation scheme together with a repair or a recovery strategy. The time that it takes to detect, isolate, and recover from the fault (fault recovery time) is a critical factor in safety...... of a system. It must be guaranteed that the trajectory of a system subject to fault remains in the region of attraction (ROA) of the post-fault system during this time. This paper proposes a new algorithm to compute the critical fault recovery time for nonlinear systems with polynomial vector elds using sum...
S-polarized nonlinear surface and guided waves in an asymmetric layered structure
Energy Technology Data Exchange (ETDEWEB)
Mihalache, D.; Totia, H.
1983-08-01
An exact solution of Maxwell's equations is found, corresponding to s-polarized nonlinear surface and guided waves in an asymmetric layered structure. The system under consideration consists of a film with dielectric constant epsilon/sub 2/ bounded at the negative-z side by a linear medium with dielectric constant epsilon/sub 1/ and at the positive -z side by a nonlinear substrate characterized by the diagonal dielectric tensor epsilon/sub 11/ = epsilon/sub 22/ = epsilon/sub 33/ = epsilon/sub 0/ + ..cap alpha.. absolute value of E-vector/sup 2/, ..cap alpha.. > 0 (a selffocussing medium). We predict bistable states of s-polarized nonlinear surface and guided waves provided that the power flow in the wave is the control parameter.
Combinatorial Frequency Generation in Quasi-Periodic Stacks of Nonlinear Dielectric Layers
Directory of Open Access Journals (Sweden)
Oksana Shramkova
2014-07-01
Full Text Available Three-wave mixing in quasi-periodic structures (QPSs composed of nonlinear anisotropic dielectric layers, stacked in Fibonacci and Thue-Morse sequences, has been explored at illumination by a pair of pump waves with dissimilar frequencies and incidence angles. A new formulation of the nonlinear scattering problem has enabled the QPS analysis as a perturbed periodic structure with defects. The obtained solutions have revealed the effects of stack composition and constituent layer parameters, including losses, on the properties of combinatorial frequency generation (CFG. The CFG features illustrated by the simulation results are discussed. It is demonstrated that quasi-periodic stacks can achieve a higher efficiency of CFG than regular periodic multilayers.
Ostrovsky, Lev A; Sutin, Alexander M; Soustova, Irina A; Matveyev, Alexander L; Potapov, Andrey I; Kluzek, Zigmund
2003-02-01
The paper describes nonlinear effects due to a biharmonic acoustic signal scattering from air bubbles in the sea. The results of field experiments in a shallow sea are presented. Two waves radiated at frequencies 30 and 31-37 kHz generated backscattered signals at sum and difference frequencies in a bubble layer. A motorboat propeller was used to generate bubbles with different concentrations at different times, up to the return to the natural subsurface layer. Theoretical consideration is given for these effects. The experimental data are in a reasonably good agreement with theoretical predictions.
On the Stability of Nonlinear Viscous Vortices in Three-Dimensional Boundary Layers
1992-04-01
wave disturbances in stable and unsta- ble parallel flows , Part 2. The development of a solution for plane Poiseuille and plane Couette flow . J. Fluid...unstable parallel flows , Part 1. The basic behaviour in plane Poiseuille flow . J. Fluid Mech. 9, 353-370. Watson, J. 1960 On the nonlinear mechanics of...vortices which a particular boundary layer may support. According to a linearised theory vortices within a high G6rtler number flow can take one of
Nonlinear dynamics of bi-layered graphene sheet, double-walled carbon nanotube and nanotube bundle
Gajbhiye, Sachin O.; Singh, S. P.
2016-05-01
Due to strong van der Waals (vdW) interactions, the graphene sheets and nanotubes stick to each other and form clusters of these corresponding nanostructures, viz. bi-layered graphene sheet (BLGS), double-walled carbon nanotube (DWCNT) and nanotube bundle (NB) or ropes. This research work is concerned with the study of nonlinear dynamics of BLGS, DWCNT and NB due to nonlinear interlayer vdW forces using multiscale atomistic finite element method. The energy between two adjacent carbon atoms is represented by the multibody interatomic Tersoff-Brenner potential, whereas the nonlinear interlayer vdW forces are represented by Lennard-Jones 6-12 potential function. The equivalent nonlinear material model of carbon-carbon bond is used to model it based on its force-deflection relation. Newmark's algorithm is used to solve the nonlinear matrix equation governing the motion of the BLGS, DWCNT and NB. An impulse and harmonic excitations are used to excite these nanostructures under cantilevered, bridged and clamped boundary conditions. The frequency responses of these nanostructures are computed, and the dominant resonant frequencies are identified. Along with the forced vibration of these structures, the eigenvalue extraction problem of armchair and zigzag NB is also considered. The natural frequencies and corresponding mode shapes are extracted for the different length and boundary conditions of the nanotube bundle.
Loyer, A.; Sinou, J.-J.; Chiello, O.; Lorang, X.
2012-02-01
As noise reduction tends to be part of environmental directives, predicting squeal noise generated by disc brakes is an important industrial issue. It involves both the transient and stationary nonlinear dynamics of self-excited systems with frictional contact. Time simulation of the phenomenon is an attractive option for reducing experiment costs. However, since such computations using full finite element models of industrial disc brake systems is time-consuming, model reduction has to be performed. In this paper, both the transient and stationary nonlinear behaviors of the friction destabilized system and the effect of dynamical reduction on the nonlinear response of a simple friction destabilized system are carried out. The first part provides a description of the general modeling retained for friction destabilized systems. Then, discretization and solving processes for the stability analysis and the temporal evolution are presented. The third part presents an analysis of a sliding elastic layer for different operating conditions, in order to better understand the nonlinear behavior of such systems. Finally, spatial model reduction is performed with different kinds of reduction bases in order to analyze the different effects of modal reductions. This clearly shows the necessity of including static modes in the reduction basis and that nonlinear interactions between unstable modes are very difficult to represent with reduced bases. Finally, the proposed model and the associated studies are intended to be the benchmark cases for future comparison.
Deliktaş, Ekin; Teymür, Mevlüt
2017-07-01
In this study, the propagation of shear horizontal (SH) waves in a nonlinear elastic half space covered by a nonlinear elastic layer with a slowly varying interface is examined. The constituent materials are assumed to be homogenous, isotropic, elastic and having different mechanical properties. By employing the method of multiple scales, a nonlinear Schrödinger equation (NLS) with variable coefficients is derived for the nonlinear self-modulation of SH waves. We examine the effects of dispersion, irregularity of the interface and nonlinearity on the propagation characteristics of SH waves.
Non-linear critical taper model and determination of accretionary wedge strength
Yang, Che-Ming; Dong, Jia-Jyun; Hsieh, Yuan-Lung; Liu, Hsueh-Hua; Liu, Cheng-Lung
2016-12-01
The critical taper model has been widely used to evaluate the strength contrast between the wedge and the basal detachment of fold-and-thrust belts and accretionary wedges. However, determination of the strength parameters using the traditional critical taper model, which adopts the Mohr-Coulomb failure criterion, is difficult, if not impossible. In this study, we propose a modified critical taper model that incorporates the non-linear Hoek-Brown failure criterion. The parameters in the proposed critical Hoek-Brown wedge CHBW model can be directly evaluated via field investigations and laboratory tests. Meanwhile, the wedge strength is a function of the wedge thickness, which is oriented from stress non-linearity. The fold-and-thrust belt in western central Taiwan was used as an example to validate the proposed model. The determined wedge strength was 0.86 using a representative wedge thickness of 5.3 km; this was close to the inferred value of 0.6 from the critical taper. Interestingly, a concave topographic relief is predicted as a result of the wedge thickness dependency of the wedge strength, even if the wedge is composed of homogeneous materials and if the strength of the detachment is uniform. This study demonstrates that the influence of wedge strength on the critical taper angle can be quantified by the spatial distribution of strength variables and by the consideration of the wedge thickness dependency of wedge strength.
Stinis, Panagiotis
2010-01-01
We present numerical results for the solution of the 1D critical nonlinear Schrodinger with periodic boundary conditions and initial data that give rise to a finite time singularity. We construct, through the Mori-Zwanzig formalism, a reduced model which allows us to follow the solution after the formation of the singularity. The computed post-singularity solution exhibits the same characteristics as the post-singularity solutions constructed recently by Terence Tao.
A non-linear iterative method for multi-layer DOT sub-surface imaging system.
Hou, Hsiang-Wen; Wu, Shih-Yang; Sun, Hao-Jan; Fang, Wai-Chi
2014-01-01
Diffuse Optical Tomography (DOT) has become an emerging non-invasive technology, and has been widely used in clinical diagnosis. Functional near-infrared (FNIR) is one of the important applications of DOT. However, FNIR is used to reconstruct two-dimensional (2D) images for the sake of good spatial and temporal resolution. In this paper we propose a multiple-input and multiple-output (MIMO) based data extraction algorithm method in order to increase the spatial and temporal resolution. The non-linear iterative method is used to reconstruct better resolution images layer by layer. In terms of theory, the simulation results and original images are nearly identical. The proposed reconstruction method performs good spatial resolution, and has a depth resolutions capacity of three layers.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Temperature dependence of the magnetization M(T) of two-band superconductors is studied in the vicinity of upper critical field Hc2 by using a two-band Ginzburg-Landau (GL) theory. It is shown that magnetization M(T) has a nonlinear character due to positive curvature of upper critical field Hc2(T) and temperature dependence of effective Ginzburg-Landau parameter (n)eff(T). The results are shown to be in qualitative agreement with experimental data for the superconducting magnesium diboride, MgB2.
Sellitto, A.; Tibullo, V.; Dong, Y.
2017-03-01
By means of a nonlinear generalization of the Maxwell-Cattaneo-Vernotte equation, on theoretical grounds we investigate how nonlinear effects may influence the propagation of heat waves in isotropic thin layers which are not laterally isolated from the external environment. A comparison with the approach of the Thermomass Theory is made as well.
Fan, Ting-Bo; Liu, Zhen-Bo; Zhang, Zhe; Zhang, Dong; Gong, Xiu-Fen
2009-08-01
A theoretical model of the nonlinear propagation in multi-layered tissues for strong focused ultrasound is proposed. In this model, the spheroidal beam equation (SBE) is utilized to describe the nonlinear sound propagation in each layer tissue, and generalized oblique incidence theory is used to deal with the sound transmission between two layer tissues. Computer simulation is performed on a fat-muscle-liver tissue model under the irradiation of a 1 MHz focused transducer with a large aperture angle of 35°. The results demonstrate that the tissue layer would change the amplitude of sound pressure at the focal region and cause the increase of side petals.
Institute of Scientific and Technical Information of China (English)
Li WANG; Jixiu WANG
2014-01-01
Let B1 ⊂ RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical Sobolev exponent and singular coefficients:-div(|∇u|p-2∇u)=|x|s|u|p*(s)-2u+λ|x|t|u|p-2u, x∈B1, u|∂B1 =0, where t, s>-p, 2≤pp(p-1)t+p(p2-p+1) andλ∈(0,λ1,t), whereλ1,t is the first eigenvalue of-∆p with the Dirichlet boundary condition. Meanwhile, the nonexistence of sign-changing radial solutions is proved if the space dimension N ≤ (ps+p) min{1, p+tp+s}+p2p-(p-1) min{1, p+tp+s} andλ>0 is small.
Nonlinear analysis of pile load-settlement behavior in layered soil
Institute of Scientific and Technical Information of China (English)
吕述晖; 王奎华; 张鹏; C. J. LEO3
2015-01-01
A simplified approach is presented to analyze the single pile settlement in multilayered soil. First, a fictitious soil−pile model is employed to consider the effect of layered soil beneath pile toe on pile settlement behavior. Two approximation methods are proposed to simplify the nonlinear load transfer function and simulate the nonlinear compression of fictitious soil−pile, respectively. On this basis, an efficient program is developed. The procedures for determining the main parameters of mathematical model are discussed. Comparisons with two well-documented field experimental pile loading tests are conducted to verify the rationality of the present method. Further studies are also made to evaluate the practicability of the proposed approach when a soft substratum exists, and the results suggest that the proposed method can provide a constructive means for assessing the settlement of a single pile for use in engineering design.
Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability
Demekhin, E A; Polyanskikh, S V
2011-01-01
In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions (milliseconds); ii) 1D self-similar evolution (milliseconds-seconds); iii) The primary instability of the self-similar solution (seconds); iv) The nonlinear stage with secondary instabilities. The self-similar character of evolution at intermediately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution to over-limiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest self-similar growth of the diffusion layer and specifies its characteristic length as was first experimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). A novel principle for the characteristic wave number sele...
Surfactant and gravity dependent instability of two-layer Couette flows and its nonlinear saturation
Frenkel, Alexander L
2016-01-01
A horizontal flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant present at the interface, is investigated. The base Couette flow is driven by the horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The linear stability is determined by an eigenvalue problem for the normal modes. The growth rates and the amplitudes of disturbances of the interface, surfactant, velocities, and pressures are found analytically. For each wavenumber, there are two active normal modes. For each mode, the instability threshold conditions in terms of the system parameters are determined. In particular, it transpires that for certain parametric ranges, even arbitrarily stron...
Enhancement of optical nonlinearity of LCs with gold-nanoparticle-doped alignment layers
Lin, Hui-Chi; Fuh, Andy Y. G.; Lin, Ci-Yong; Li, Ming-Shian
2013-05-01
In this study, the optical nonlinearity of LCs with cell substrates coated with gold-nanoparticle (AuNP) -doped PVA alignment layers were examined using the Z-scan technique. The results show that the nonlinear refractive index n2 of the sample is enhanced by the gold nanoparticles doped in the alignment layers, because of the thermal effect of the absorption by the surface of the sample through the localized surface plasmon resonance (LSPR) of the gold nanoparticles. As the concentration of AuNPs in the alignment layers of the LC sample increases, the thermal effect of the LSPR increases, and |n2| observably increases. Furthermore, the self-defocusing effect (n2<0) of the sample can be modulated by the application of an external voltage, and a self-focusing effect (n2<0) can be observed when samples are illuminated by a high-intensity laser with the application of a high voltage. Therefore, the magnitude and the sign of n2 of the sample can be modulated by combining the applied electric field and the optical field.
Nonlinear optimal control of bypass transition in a boundary layer flow
Xiao, Dandan; Papadakis, George
2016-11-01
Bypass transition is observed in a flat-plate boundary-layer flow when high levels of free stream turbulence are present. This scenario is characterized by the formation of streamwise elongated streaks inside the boundary layer, their break down into turbulent spots and eventually fully turbulent flow. In the current work, we perform DNS simulations of control of bypass transition in a zero-pressure-gradient boundary layer. A non-linear optimal control algorithm is developed that employs the direct-adjoint approach to minimise a quadratic cost function based on the deviation from the Blasius velocity profile. Using the Lagrange variational approach, the distribution of the blowing/suction control velocity is found by solving iteratively the non-linear Navier-Stokes and its adjoint equations in a forward/backward loop. The optimisation is performed over a finite time horizon during which the Lagrange functional is to be minimised. Large values of optimisation horizon result in instability of the adjoint equations. The results show that the controller is able to reduce the turbulent kinetic energy of the flow in the region where the objective function is defined and the velocity profile is seen to approach the Blasius solution. Significant drag reduction is also achieved.
Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet
Directory of Open Access Journals (Sweden)
Masood Khan
2015-10-01
Full Text Available This article studies the Carreau viscosity model (which is a generalized Newtonian model and then use it to obtain a formulation for the boundary layer equations of the Carreau fluid. The boundary layer flow and heat transfer to a Carreau model over a nonlinear stretching surface is discussed. The Carreau model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical values of the power law exponent n. The modeled boundary layer conservation equations are converted to non-linear coupled ordinary differential equations by a suitable transformation. Numerical solution of the resulting equations are obtained by using the Runge-Kutta Fehlberg method along with shooting technique. This analysis reveals many important physical aspects of flow and heat transfer. Computations are performed for different values of the stretching parameter (m, the Weissenberg number (We and the Prandtl number (Pr. The obtained results show that for shear thinning fluid the fluid velocity is depressed by the Weissenberg number while opposite behavior for the shear thickening fluid is observed. A comparison with previously published data in limiting cases is performed and they are in excellent agreement.
Energy Technology Data Exchange (ETDEWEB)
Savel' ev, Sergey; Yampol' skii, V A; Rakhmanov, A L; Nori, Franco [Advanced Science Institute, Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-0198 (Japan)
2010-02-15
The recent growing interest in terahertz (THz) and sub-THz science and technology is due to its many important applications in physics, astronomy, chemistry, biology and medicine, including THz imaging, spectroscopy, tomography, medical diagnosis, health monitoring, environmental control, as well as chemical and biological identification. We review the problem of linear and nonlinear THz and sub-THz Josephson plasma waves in layered superconductors and their excitations produced by moving Josephson vortices. We start by discussing the coupled sine-Gordon equations for the gauge-invariant phase difference of the order parameter in the junctions, taking into account the effect of breaking the charge neutrality, and deriving the spectrum of Josephson plasma waves. We also review surface and waveguide Josephson plasma waves. The spectrum of these waves is presented, and their excitation is discussed. We review the propagation of weakly nonlinear Josephson plasma waves below the plasma frequency, {omega}{sub J}, which is very unusual for plasma-like excitations. In close analogy to nonlinear optics, these waves exhibit numerous remarkable features, including a self-focusing effect and the pumping of weaker waves by a stronger one. In addition, an unusual stop-light phenomenon, when {partial_derivative}{omega}/{partial_derivative}k {approx} 0, caused by both nonlinearity and dissipation, can be observed in the Josephson plasma waves. At frequencies above {omega}{sub J}, the current-phase nonlinearity can be used for transforming continuous sub-THz radiation into short, strongly amplified, pulses. We also present quantum effects in layered superconductors, specifically, the problem of quantum tunneling of fluxons through stacks of Josephson junctions. Moreover, the nonlocal sine-Gordon equation for Josephson vortices is reviewed. We discuss the Cherenkov and transition radiations of the Josephson plasma waves produced by moving Josephson vortices, either in a single
Nonlinear dynamics at the interface of two-layer stratified flows over pronounced obstacles
Cabeza, C; Bove, I; Freire, D; Marti, Arturo C; Sarasua, L G; Usera, G; Montagne, R; Araújo, M
2008-01-01
The flow of a two--layer stratified fluid over an abrupt topographic obstacle, simulating relevant situations in oceanographic problems, is investigated numerically and experimentally in a simplified two--dimensional situation. Experimental results and numerical simulations are presented at low Froude numbers in a two-layer stratified flow and for two abrupt obstacles, semi--cylindrical and prismatic. We find four different regimes of the flow immediately past the obstacles: sub-critical (I), internal hydraulic jump (II), Kelvin-Helmholtz at the interface (III) and shedding of billows (IV). The critical condition for delimiting the experiments is obtained using the hydraulic theory. Moreover, the dependence of the critical Froude number on the geometry of the obstacle are investigated. The transition from regime III to regime IV is explained with a theoretical stability analysis. The results from the stability analysis are confirmed with the DPIV measurements. In regime (IV), when the velocity upstream is lar...
Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps
Energy Technology Data Exchange (ETDEWEB)
Méndez-Bermúdez, J.A. [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570 (Mexico); Oliveira, Juliano A. de [UNESP – Univ. Estadual Paulista, Câmpus de São João da Boa Vista, Av. Professora Isette Corrêa Fontão, 505, Jardim Santa Rita das Areias, 13876-750 São João da Boa Vista, SP (Brazil); Leonel, Edson D. [Departamento de Física, UNESP – Univ. Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900 Rio Claro, SP (Brazil); Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)
2016-05-20
The critical dynamics near the transition from unlimited to limited action diffusion for two families of well known dissipative nonlinear maps, namely the dissipative standard and dissipative discontinuous maps, is characterized by the use of an analytical approach. The approach is applied to explicitly obtain the average squared action as a function of the (discrete) time and the parameters controlling nonlinearity and dissipation. This allows to obtain a set of critical exponents so far obtained numerically in the literature. The theoretical predictions are verified by extensive numerical simulations. We conclude that all possible dynamical cases, independently on the map parameter values and initial conditions, collapse into the universal exponential decay of the properly normalized average squared action as a function of a normalized time. The formalism developed here can be extended to many other different types of mappings therefore making the methodology generic and robust. - Highlights: • We analytically approach scaling properties of a family of two-dimensional dissipative nonlinear maps. • We derive universal scaling functions that were obtained before only approximately. • We predict the unexpected condition where diffusion and dissipation compensate each other exactly. • We find a new universal scaling function that embraces all possible dissipative behaviors.
Non-linear optical functions of crystalline-Si resulting from nanoscale layered systems
Energy Technology Data Exchange (ETDEWEB)
Kuznicki, Z.T. [Laboratoire PHASE, CNRS UPR 292, 23 rue du Loess, F-67037 Strasbourg cedex 2 (France)]. E-mail: kuznicki@phase.c-strasbourg.fr; Ley, M. [Laboratoire PHASE, CNRS UPR 292, 23 rue du Loess, F-67037 Strasbourg cedex 2 (France); Lezec, H.J. [ISIS, ULP, 8 allee Gaspard Monge, F-67083 Strasbourg cedex (France); Sarrabayrouse, G. [LAAS-CNRS, 7 av. du colonel Roche, 31077 Toulouse cedex 4 (France); Rousset, B. [LAAS-CNRS, 7 av. du colonel Roche, 31077 Toulouse cedex 4 (France); Rossel, F. [LAAS-CNRS, 7 av. du colonel Roche, 31077 Toulouse cedex 4 (France); Migeon, H. [LAM, Centre de Recherche Public - Gabriel Lippmann, 162a, av. de la Faiaencerie, L-1511 Luxembourg (Luxembourg); Wirtz, T. [LAM, Centre de Recherche Public - Gabriel Lippmann, 162a, av. de la Faiaencerie, L-1511 Luxembourg (Luxembourg)
2006-07-15
New non-linear optoelectronic and photovoltaic behavior of crystalline silicon (c-Si) has been obtained with a strained nanoscale Si-layered system. We have found c-Si absorptances that even exceed values of amorphous silicon (a-Si) thin films. The present investigation exploits charge carrier and photon flux transformations at the so-called carrier collection limit. A correlation between free carrier density and the absorption coefficient could be established by combining reflectivity and transmissivity measurements on samples having different surface free carrier reservoirs. In summary, Si modifications implemented on the nanoscale lead to new effects that can widen applications of conventional Si devices.
Energy Technology Data Exchange (ETDEWEB)
Mitsotakis, Dimitrios, E-mail: dmitsot@gmail.com [Victoria University of Wellington, School of Mathematics, Statistics and Operations Research, PO Box 600, Wellington 6140 (New Zealand); Dutykh, Denys, E-mail: Denys.Dutykh@univ-savoie.fr [LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex (France); Assylbekuly, Aydar, E-mail: asylbekuly@mail.ru [Khoja Akhmet Yassawi International Kazakh–Turkish University, Faculty of Natural Science, Department of Mathematics, 161200 Turkestan (Kazakhstan); Zhakebayev, Dauren, E-mail: daurjaz@mail.ru [Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics, Department of Mathematical and Computer Modelling, 050000 Almaty (Kazakhstan)
2017-05-25
In this Letter we consider long capillary–gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott–Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well. - Highlights: • A model for long capillary–gravity weakly dispersive and fully nonlinear water waves is derived. • Shallow capillary–gravity waves are classified using phase plane analysis. • Peaked travelling waves are found in the critical regime. • The dynamics of peakons in Serre–Green–Naghdi equations is studied numerically.
Optical nonlinearities in Ag/BaTiO{sub 3} multi-layer nanocomposite films
Energy Technology Data Exchange (ETDEWEB)
Yang Guang [Wuhan National Laboratory for Optoelectronics and School of Optoelectronics Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074 (China)], E-mail: gyang@hust.edu.cn; Zhou Youhua [Wuhan National Laboratory for Optoelectronics and School of Optoelectronics Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074 (China); School of Physics and Information Engineering, Jianghan University, Wuhan 430056 (China); Long Hua; Li Yuhua; Yang Yifa [Wuhan National Laboratory for Optoelectronics and School of Optoelectronics Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074 (China)
2007-07-31
The multi-layer structure of barium titanate composite thin films containing Ag nanoparticles were grown on MgO (100) substrates using pulsed laser deposition technique under the nitrogen pressure of 7.4 Pa. The X-ray photoelectron spectroscopy analysis indicated that the samples were composed of metal Ag embedded in the BaTiO{sub 3} matrices. The optical absorption properties were measured from 300 nm to 800 nm, and the absorption peaks due to the surface plasmon resonance of Ag particles were observed. With the increasing of Ag concentration in composite films, the peak absorption increased and shifted to longer wavelength (red-shift). Furthermore, the third-order optical nonlinearities of the films were determined by z-scan method and the nonlinear refractive index, n{sub 2}, and nonlinear absorption coefficient, {beta}, were determined to be about - 1.91 x 10{sup -13} m{sup 2}/W and - 5.80 x 10{sup -7} m/W, respectively.
Patterson, Shawna M.
2013-01-01
In this article, the author provides a model that juxtaposes leadership, critical theory, and learning to address the needs of educators, the organization, and students. This model provides educators with a foundational approach to nurture students' critical consciousness through self-awareness and to actualize transformational change within their…
Patterson, Shawna M.
2013-01-01
In this article, the author provides a model that juxtaposes leadership, critical theory, and learning to address the needs of educators, the organization, and students. This model provides educators with a foundational approach to nurture students' critical consciousness through self-awareness and to actualize transformational change within their…
Badriev, I. B.; Banderov, V. V.; Makarov, M. V.
2017-06-01
In this paper we consider the geometrically nonlinear problem of determining the equilibrium position of a sandwich plate consisting of two external carrier layers and located between transversely soft core, connected with carrier layer by means of adhesive joint. We investigate the generalized statement of the problem. For its numerical implementation we offer a two-layer iterative process and investigate the convergence of the method. Numerical experiments are carried out for the model problem.
Critical Temperature Characteristics of Layered High-Temperature Superconductor Under Pressure
Institute of Scientific and Technical Information of China (English)
LIANG Fang-Ying
2009-01-01
We consider a Ginzburg-Landau modified model of layered high-temperature superconductor under pres-sure. We have theoretically studied the relation between the pressure and the temperature of layered high-temperature superconductor. If the pressure is not a constant, we have a relation of quadratic equation between the pressure and the temperature of layered high-temperature superconductor. In a special case, we find the critical temperature decreases with further increasing pressure. In another special case, the critical temperature increases with further increasing pressure.
Mitsotakis, Dimitrios; Assylbekuly, Aydar; Zhakebaev, Dauren
2016-01-01
In this Letter we consider long capillary-gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott-Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well.
Critical properties of XY model on two-dimensional layered magnetic films
Institute of Scientific and Technical Information of China (English)
Wang Yi; Liu Xiao-Yan; Sun Lei; Zhang Xing; Han Ru-Qi
2006-01-01
Using Monte Carlo simulations, we have investigated the classical XY model on triangular lattices of ultra-thin film structures with middle ferromagnetic layers sandwiched between two antiferromagnetic layers. The internal energy,the specific heat, the chirality and the chiral susceptibility are calculated in order to clarify phase transitions and critical phenomena. From the finite-size scaling analyses, the values of critical exponents are determined. In a range of interaction parameters, we find that the chirality steeply goes up as temperature increases in a temperature range;correspondingly the value of a critical exponent for this change is estimated.
Helfrich, Karl R.
2006-08-01
The nonlinear evolution of a localized layer of buoyant, uniform potential vorticity fluid with depth H, width w and length L released adjacent to a wall in a rotating system is studied using reduced-gravity shallow-water theory and numerical modeling. In the interior, far from the two ends of the layer, the initial adjustment gives, after ignoring inertia-gravity waves, a geostrophic flow of width w and layer velocities parallel to the wall directed in the downstream direction (defined by Kelvin wave propagation). This steady geostrophic flow serves as the initial condition for a semigeostrophic solution using the method of characteristics. At the downstream end, the theory shows that the fluid intrudes along the wall as rarefaction terminating at a nose of vanishing width and depth. However, in a real fluid the presence of the lower layer leads to a blunt gravity current head. The theory is amended by introducing a gravity current head condition that has a blunt bore joined to the rarefaction by a uniform gravity current. The upstream termination of the initial layer produces a Kelvin rarefaction that propagates downstream, decreasing the layer depth along the wall, and initiating upstream flow adjacent to the wall. The theoretical solution compares favorably to numerical solutions of the reduced-gravity shallow-water equations. The agreement between theory and numerical solutions occurs regardless of whether the numerical runs are initiated with an adjusted geostrophic solution or with the release of a stagnant layer. The latter case excites inertia-gravity waves that, despite their large amplitude and breaking, do not significantly affect the evolution of the geostrophic flow. At times beyond the validity of the semigeostrophic theory, the numerical solutions evolve into a stationary array of vortices. The vortex formation can be interpreted as the finite-amplitude manifestation of a linear instability of the new flow established by the passage of the Kelvin
Inorganic bromine in the marine boundary layer: a critical review
Directory of Open Access Journals (Sweden)
R. Sander
2003-06-01
Full Text Available The cycling of inorganic bromine in the marine boundary layer (mbl has received increased attention in recent years. Bromide, a constituent of sea water, is injected into the atmosphere in association with sea-salt aerosol by breaking waves on the ocean surface. Measurements reveal that supermicrometer sea-salt aerosol is depleted in bromine by about 50% relative to conservative tracers, whereas marine submicrometer aerosol is often enriched in bromine. Model calculations, laboratory studies, and field observations strongly suggest that these depletions reflect the chemical transformation of particulate bromide to reactive inorganic gases that influence the processing of ozone and other important constituents of marine air. However, currently available techniques cannot reliably quantify many chem{Br}-containing compounds at ambient concentrations and, consequently, our understanding of inorganic Br cycling over the oceans and its global significance are uncertain. To provide a more coherent framework for future research, we have reviewed measurements in marine aerosol, the gas phase, and in rain. We also summarize sources and sinks, as well as model and laboratory studies of chemical transformations. The focus is on inorganic bromine over the open oceans, excluding the polar regions. The generation of sea-salt aerosol at the ocean surface is the major tropospheric source producing about 6.2 Tg/a of bromide. The transport of Br from continents (as mineral aerosol, and as products from biomass-burning and fossil-fuel combustion can be of local importance. Transport of degradation products of long-lived Br-containing compounds from the stratosphere and other sources contribute lesser amounts. Available evidence suggests that, following aerosol acidification, sea-salt bromide reacts to form Br_{2 } and BrCl that volatilize to the gas phase and photolyze in daylight to produce atomic Br and Cl. Subsequent transformations can destroy
Inorganic bromine in the marine boundary layer: a critical review
Directory of Open Access Journals (Sweden)
R. Sander
2003-01-01
Full Text Available The cycling of inorganic bromine in the marine boundary layer (mbl has received increased attention in recent years. Bromide, a constituent of sea water, is injected into the atmosphere in association with sea-salt aerosol by breaking waves on the ocean surface. Measurements reveal that supermicrometer sea-salt aerosol is substantially depleted in bromine (often exceeding 50% relative to conservative tracers, whereas marine submicrometer aerosol is often enriched in bromine. Model calculations, laboratory studies, and field observations strongly suggest that the supermicrometer depletions reflect the chemical transformation of particulate bromide to reactive inorganic gases that influence the processing of ozone and other important constituents of marine air. Mechanisms for the submicrometer enrichments are not well understood. Currently available techniques cannot reliably quantify many Br containing compounds at ambient concentrations and, consequently, our understanding of inorganic Br cycling over the oceans and its global significance are uncertain. To provide a more coherent framework for future research, we have reviewed measurements in marine aerosol, the gas phase, and in rain. We also summarize sources and sinks, as well as model and laboratory studies of chemical transformations. The focus is on inorganic bromine over the open oceans outside the polar regions. The generation of sea-salt aerosol at the ocean surface is the major tropospheric source producing about 6.2 Tg/a of bromide. The transport of Br from continents (as mineral aerosol, and as products from biomass-burning and fossil-fuel combustion can be of local importance. Transport of degradation products of long-lived Br containing compounds from the stratosphere and other sources contribute lesser amounts. Available evidence suggests that, following aerosol acidification, sea-salt bromide reacts to form Br2 and BrCl that volatilize to the gas phase and photolyze in daylight
Zhang, Bingbing; Shi, Guoqiang; Yang, Zhihua; Zhang, Fangfang; Pan, Shilie
2017-03-27
Deep-ultraviolet nonlinear optical (DUV NLO) crystals are the key materials to extend the output range of solid-state lasers to below 200 nm. The only practical material KBe2 BO3 F2 suffers high toxicity through beryllium and strong layered growth. Herein, we propose a beryllium-free material design and synthesis strategy for DUV NLO materials. Introducing the (BO3 F)(4-) , (BO2 F2 )(3-) , and (BOF3 )(2-) groups in borates could break through the fixed 3D B-O network that would produce a larger birefringence without layering and simultaneously keep a short cutoff edge down to DUV. The theoretical and experimental studies on a series of fluorooxoborates confirm this strategy. Li2 B6 O9 F2 is identified as a DUV NLO material with a large second harmonic generation efficiency (0.9×KDP) and a large predicted birefringence (0.07) without layering. This study provides a feasible way to break down the DUV wall for NLO materials. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Nonlinear optimal control of bypass transition in a boundary layer flow
Xiao, Dandan; Papadakis, George
2017-05-01
The central aim of the paper is to apply and assess a nonlinear optimal control strategy to suppress bypass transition, due to bimodal interactions [T. A. Zaki and P. A. Durbin, "Mode interaction and the bypass route to transition," J. Fluid Mech. 531, 85 (2005)] in a zero-pressure-gradient boundary layer. To this end, a Lagrange variational formulation is employed that results in a set of adjoint equations. The optimal wall actuation (blowing and suction from a control slot) is found by solving iteratively the nonlinear Navier-Stokes and the adjoint equations in a forward/backward loop using direct numerical simulation. The optimization is performed in a finite time horizon. Large values of optimization horizon result in the instability of the adjoint equations. The control slot is located exactly in the region of transition. The results show that the control is able to significantly reduce the objective function, which is defined as the spatial and temporal integral of the quadratic deviation from the Blasius profile plus a term that quantifies the control cost. The physical mechanism with which the actuation interacts with the flow field is investigated and analysed in relation to the objective function employed. Examination of the joint probability density function shows that the control velocity is correlated with the streamwise velocity in the near wall region but this correlation is reduced as time elapses. The spanwise averaged velocity is distorted by the control action, resulting in a significant reduction of the skin friction coefficient. Results are presented with and without zero-net mass flow constraint of the actuation velocity. The skin friction coefficient drops below the laminar value if there is no mass constraint; it remains however larger than laminar when this constraint is imposed. Results are also compared with uniform blowing using the same time-average velocity obtained from the nonlinear optimal algorithm.
Large-scale weakly nonlinear perturbations of convective magnetic dynamos in a rotating layer
Chertovskih, Roman
2015-01-01
We present a new mechanism for generation of large-scale magnetic field by thermal convection which does not involve the alpha-effect. We consider weakly nonlinear perturbations of space-periodic steady convective magnetic dynamos in a rotating layer that were identified in our previous work. The perturbations have a spatial scale in the horizontal direction that is much larger than the period of the perturbed convective magnetohydrodynamic state. Following the formalism of the multiscale stability theory, we have derived the system of amplitude equations governing the evolution of the leading terms in expansion of the perturbations in power series in the scale ratio. This asymptotic analysis is more involved than in the cases considered earlier, because the kernel of the operator of linearisation has zero-mean neutral modes whose origin lies in the spatial invariance of the perturbed regime, the operator reduced on the generalised kernel has two Jordan normal form blocks of size two, and simplifying symmetri...
Munir, Asif; Shahzad, Azeem; Khan, Masood
2014-01-01
The major focus of this article is to analyze the forced convective heat transfer in a steady boundary layer flow of Sisko fluid over a nonlinear stretching sheet. Two cases are studied, namely (i) the sheet with variable temperature (PST case) and (ii) the sheet with variable heat flux (PHF case). The heat transfer aspects are investigated for both integer and non-integer values of the power-law index. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity variables and solved numerically. The numerical results are obtained by the shooting method using adaptive Runge Kutta method with Broyden's method in the domain[Formula: see text]. The numerical results for the temperature field are found to be strongly dependent upon the power-law index, stretching parameter, wall temperature parameter, material parameter of the Sisko fluid and Prandtl number. In addition, the local Nusselt number versus wall temperature parameter is also graphed and tabulated for different values of pertaining parameters. Further, numerical results are validated by comparison with exact solutions as well as previously published results in the literature.
Munir, Asif; Shahzad, Azeem; Khan, Masood
2014-01-01
The major focus of this article is to analyze the forced convective heat transfer in a steady boundary layer flow of Sisko fluid over a nonlinear stretching sheet. Two cases are studied, namely (i) the sheet with variable temperature (PST case) and (ii) the sheet with variable heat flux (PHF case). The heat transfer aspects are investigated for both integer and non-integer values of the power-law index. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity variables and solved numerically. The numerical results are obtained by the shooting method using adaptive Runge Kutta method with Broyden’s method in the domain. The numerical results for the temperature field are found to be strongly dependent upon the power-law index, stretching parameter, wall temperature parameter, material parameter of the Sisko fluid and Prandtl number. In addition, the local Nusselt number versus wall temperature parameter is also graphed and tabulated for different values of pertaining parameters. Further, numerical results are validated by comparison with exact solutions as well as previously published results in the literature. PMID:24949738
Iizuka, S.
1998-02-01
Potential Modification Due to C60- Production * Modifications of the Floating Potential and the Plasma Potential in a C60 Plasma * Properties of Strongly Electronegative Plasma Produced at Afterglow of Electron Cyclotron Resonance Chlorine Plasma * 2.2 Particle Accelerations * Potential Structures Due to an Electron Beam-Excited Localized HF-Discharge (Invited) * Experiments and Computer Simulations of Electric Field Spikes in Electron Beam-Plasma Interaction * Magnetosonic Waves in Multi-Ion-Species Plasmas: Nonlinear Evolution and Ion Acceleration * Observation of Repetitive Electric Field Pulses Accompanying a Short Wave Train Near the Lower Hybrid Frequency in a High-Voltage Linear Plasma Discharge * Control of Potential Profile and Energy Transport to Machine Ends along Open Magnetic Field Lines in a Tandem Mirror * Observation of Ion Acceleration in Picosecond Laser Produced Plasma Expanding across a Magnetic Field * Pellet Ablation Characteristics and the Effect on the Potential in Toroidal Plasmas (Invited) * CHAPTER 3: CROSS-FIELD ELECTRIC FIELDS, VELOCITY SHEAR, AND VORTEX FORMATION * 3.1 Cross-Field Potential Structures * Laboratory Simulation of Transverse Magnetic Field Effects on Dynamics of Plasma Streams in Magnetosphere * Double-Layer-like and Sheath-like Potential Structures across Magnetic Field Lines * Relaxation of Virtual Cathode Oscillations due to Transverse Effects in a Crossed-Field Diode * Control of Radial Potential Profile and Related Low-Frequency Fluctuations in an ECR-Produced Plasma * Potential Formation in Magnetized Dusty Plasma * Potential Measurement Using Electrostatic Probe in Tokamak Boundary Plasma * Studies on Radial Electric Field and Confinement in Toroidal Plasmas (Invited) * 3.2 Velocity Shear * Space Chamber Investigations of Transverse Velocity Shear Driven Plasma Waves * Observations of the Velocity-Shear-Driven Instability in a Sodium Plasma (Invited) * The Effect of Negative Ions and Neutral Particle Collisions on the
Linear and nonlinear properties of reduced two-layer models for non-hydrostatic free-surface flow
Bai, Yefei; Cheung, Kwok Fai
2016-11-01
A two-layer model with uniform non-hydrostatic pressure in the bottom produces favorable dispersion properties for coastal wave transformation at the computational requirements of a one-layer model. We derive the nonlinear governing equations and the corresponding dispersion relation, shoaling gradient, and super- and sub-harmonics to understand the theoretical performance of this reduced model. With the layer interface near the bottom, the dispersion relation shows an extended applicable range into deeper water at the expense of a slight overestimation of the celerity in intermediate water depth. The shoaling gradient rapidly converges to the exact solution in the shallow and intermediate depth range. These complementary characteristics allow identification of an optimal interface position for both linear wave properties. The resulting model exhibits good nonlinear performance in shallow and intermediate water depth and produces super- and sub-harmonics comparable to a two-layer model. Numerical tests involving standing waves show the reduced model has smaller discretization errors in the dispersion relation comparing to a one-layer model. Case studies of regular wave transformation over a submerged bar and a uniform slope provide comparison with laboratory data and demonstrate the linear and nonlinear properties derived from the governing equations. The good shoaling and nonlinear properties give rise to accurate waveforms in both cases, while dispersion errors from the governing equations and numerical schemes accumulate over time leading to phase shifts of the modeled waves.
Improving the Critic Learning for Event-Based Nonlinear H∞ Control Design.
Wang, Ding; He, Haibo; Liu, Derong
2017-01-30
In this paper, we aim at improving the critic learning criterion to cope with the event-based nonlinear H∞ state feedback control design. First of all, the H∞ control problem is regarded as a two-player zero-sum game and the adaptive critic mechanism is used to achieve the minimax optimization under event-based environment. Then, based on an improved updating rule, the event-based optimal control law and the time-based worst-case disturbance law are obtained approximately by training a single critic neural network. The initial stabilizing control is no longer required during the implementation process of the new algorithm. Next, the closed-loop system is formulated as an impulsive model and its stability issue is handled by incorporating the improved learning criterion. The infamous Zeno behavior of the present event-based design is also avoided through theoretical analysis on the lower bound of the minimal intersample time. Finally, the applications to an aircraft dynamics and a robot arm plant are carried out to verify the efficient performance of the present novel design method.
Strain-controlled criticality governs the nonlinear mechanics of fibre networks
Sharma, A.; Licup, A. J.; Jansen, K. A.; Rens, R.; Sheinman, M.; Koenderink, G. H.; Mackintosh, F. C.
2016-06-01
Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of connections between nodes exceeds the isostatic threshold are networks stable. On increasing the connectivity through this point, such networks undergo a mechanical phase transition from a floppy to a rigid phase. However, even sub-isostatic networks become rigid when subjected to sufficiently large deformations. To study this strain-controlled transition, we perform a combination of computational modelling of fibre networks and experiments on networks of type I collagen fibres, which are crucial for the integrity of biological tissues. We show theoretically that the development of rigidity is characterized by a strain-controlled continuous phase transition with signatures of criticality. Our experiments demonstrate mechanical properties consistent with our model, including the predicted critical exponents. We show that the nonlinear mechanics of collagen networks can be quantitatively captured by the predictions of scaling theory for the strain-controlled critical behaviour over a wide range of network concentrations and strains up to failure of the material.
Cain, A. B.; Thompson, M. W.
1986-01-01
The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.
Axisymmetric finite element (FE) method was developed using a commercial computer program to simulate cone penetration process in layered granular soil. Soil was considered as a non-linear elastic plastic material which was modeled using variable elastic parameters of Young’s Modulus and Poisson’s r...
Richardson, H.; Basu, S.; Holtslag, A.A.M.
2013-01-01
For many decades, attempts have been made to find the universal value of the critical bulk Richardson number (Ri Bc ; defined over the entire stable boundary layer). By analyzing an extensive large-eddy simulation database and various published wind-tunnel data, we show that Ri Bc is not a constant,
Greenwood, D D
1991-08-01
A recent paper (Greenwood, 1990) reviewed cochlear coordinates in several species in relation to empirical frequency-position functions (Greenwood, 1961b, 1974b), one of which well fits the Békésy-Skarstein human cochlear map (Békésy, 1960; Kringlebotn et al, 1979). This increased the independence of the human function from the psychoacoustic data originally used to construct it and encouraged a second assessment of the relations of similar psychoacoustically significant bandwidths to distance and position on the cochlear map. The companion paper (Greenwood, 1991, this issue), found that, among such bandwidths, 'classical' critical bandwidth, and also 'constant interval', estimates in man correspond to equal distances to a closer extent than generally recognized, and over large parts of the frequency range they conform also to an exponential function of distance, as do most of the ERB estimates. This correspondence to almost constant and similar distances facilitates, and forms a part of, an explanation of the operational definitions of critical bandwidth in different experiments. The present account recapitulates the basic explanation of critical bandwidth and consonance offered in Greenwood (1971, 1972b, 1973b, 1974b) and Greenwood et al. (1976): by adding schematic details to the earlier account of critical bandwidth measurements in pure tone masking (the masker-notch interval), two-tone masking, narrow-band masking, and two-tone dissonance-consonance judgements and by outlining its applicability to AM and Quasi-FM detection and to two-band (nominally notched-noise) masking experiments. The measured bandwidths derive from approximately uniform dimensions of traveling wave envelopes in the peak region and from the effects of the resulting spatial pattern of nonlinear interference among primary components. In this account, critical bandwidth in man corresponds to a distance of about 1 or 1.25 mm, depending upon the direction the interval projects from the
Energy Technology Data Exchange (ETDEWEB)
Mabood, F., E-mail: mabood1971@yahoo.com [School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 (Malaysia); Khan, W.A., E-mail: wkhan_2000@yahoo.com [Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1 (Canada); Ismail, A.I.M., E-mail: izani@cs.usm.my [School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 (Malaysia)
2015-01-15
The MHD laminar boundary layer flow with heat and mass transfer of an electrically conducting water-based nanofluid over a nonlinear stretching sheet with viscous dissipation effect is investigated numerically. This is the extension of the previous study on flow and heat transfer of a nanofluid over nonlinear stretching sheet (Rana and Bhargava, Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 212–226). The governing equations are reduced to nonlinear ordinary differential equations using suitable similarity transformation. The effects of the governing parameters on dimensionless quantities like velocity, temperature, nanoparticle concentration, friction factor, local Nusselt, and Sherwood numbers are explored. It is found that the dimensionless velocity decreases and temperature increases with magnetic parameter, and the thermal boundary layer thickness increases with Brownian motion and thermophoresis parameters. - Highlights: • MHD flow of nanofluid and heat transfer over a nonlinear stretching sheet has not been studied yet. • Numerical solutions are computed with Runge–Kutta Fehlberg fourth–fifth order method. • Previous published results can be obtained from present study. • Reduced Nusselt and Sherwood numbers decrease with magnetic parameter.
Blackman, Karin; Perret, Laurent
2016-09-01
In the present work, a boundary layer developing over a rough-wall consisting of staggered cubes with a plan area packing density, λp = 25%, is studied within a wind tunnel using combined particle image velocimetry and hot-wire anemometry to investigate the non-linear interactions between large-scale momentum regions and small-scale structures induced by the presence of the roughness. Due to the highly turbulent nature of the roughness sub-layer and measurement equipment limitations, temporally resolved flow measurements are not feasible, making the conventional filtering methods used for triple decomposition unsuitable for the present work. Thus, multi-time delay linear stochastic estimation is used to decompose the flow into large-scales and small-scales. Analysis of the scale-decomposed skewness of the turbulent velocity (u') shows a significant contribution of the non-linear term uL ' uS ' 2 ¯ , which represents the influence of the large-scales ( uL ' ) onto the small-scales ( uS ' ). It is shown that this non-linear influence of the large-scale momentum regions occurs with all three components of velocity in a similar manner. Finally, through two-point spatio-temporal correlation analysis, it is shown quantitatively that large-scale momentum regions influence small-scale structures throughout the boundary layer through a non-linear top-down mechanism.
Critical CuI buffer layer surface density for organic molecular crystal orientation change
Ahn, Kwangseok; Kim, Jong Beom; Kim, Hyo Jung; Lee, Hyun Hwi; Lee, Dong Ryeol
2015-01-01
We have determined the critical surface density of the CuI buffer layer inserted to change the preferred orientation of copper phthalocyanine (CuPc) crystals grown on the buffer layer. X-ray reflectivity measurements were performed to obtain the density profiles of the buffer layers and out-of-plane and 2D grazing-incidence X-ray diffraction measurements were performed to determine the preferred orientations of the molecular crystals. Remarkably, it was found that the preferred orientation of the CuPc film is completely changed from edge-on (1 0 0) to face-on (1 1 -2) by a CuI buffer layer with a very low surface density, so low that a large proportion of the substrate surface is bare.
Clemmen, StÉphane; Solano, Eduardo; Dendooven, Jolien; Koskinen, Kalle; Kauranen, Martti; Brainis, Edouard; Detavernier, Christophe; Baets, Roel
2015-01-01
We report the fabrication of artificial unidimensional crystals exhibiting an effective bulk second-order nonlinearity. The crystals are created by cycling atomic layer deposition of three dielectric materials such that the resulting metamaterial is non-centrosymmetric in the direction of the deposition. Characterization of the structures by second-harmonic generation Maker-fringe measurements shows that the main component of their nonlinear susceptibility tensor is about 5 pm/V which is comparable to well-established materials and more than an order of magnitude greater than reported for a similar crystal [1-Alloatti et al, arXiv:1504.00101[cond-mat.mtrl- sci
Nonlinear Force-Free Magnetic Field Modeling of the Solar Corona: A Critical Assessment
De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; McTiernan, J. M.; Régnier, S.; Thalmann, J.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T.
2008-12-01
Nonlinear force-free field (NLFFF) modeling promises to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have so far failed to arrive at consistent solutions when applied to cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not been available). It is our view that the lack of robust results indicates an endemic problem with the NLFFF modeling process, and that this process will likely continue to fail until (1) more of the far-reaching, current-carrying connections are within the observational field of view, (2) the solution algorithms incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is found to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models.
Nonlinear Force-Free Magnetic Field Modeling of AR 10953: A Critical Assessment
De Rosa, Marc L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; Amari, T.; Canou, A.; McTiernan, J. M.; Régnier, S.; Thalmann, J. K.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M. C. M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T.
2009-05-01
Nonlinear force-free field (NLFFF) modeling seeks to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have failed to arrive at consistent solutions when applied to (thus far, two) cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not available). One issue is that NLFFF models require consistent, force-free vector magnetic boundary data, and vector magnetogram data sampling the photosphere do not satisfy this requirement. Consequently, several problems have arisen that are believed to affect such modeling efforts. We use AR 10953 to illustrate these problems, namely: (1) some of the far-reaching, current-carrying connections are exterior to the observational field of view, (2) the solution algorithms do not (yet) incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is needed to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models.
First-order layering and critical wetting transitions in nonadditive hard-sphere mixtures.
Hopkins, Paul; Schmidt, Matthias
2011-05-01
Using fundamental-measure density functional theory we investigate entropic wetting in an asymmetric binary mixture of hard spheres with positive nonadditivity. We consider a general planar hard wall, where preferential adsorption is induced by a difference in closest approach of the different species and the wall. Close to bulk fluid-fluid coexistence, the phase rich in the minority component adsorbs either through a series of first-order layering transitions, where an increasing number of liquid layers adsorbs sequentially, or via a critical wetting transition, where a thick film grows continuously.
Criticality in Alternating Layered Ising Models : I. Effects of connectivity and proximity
Au-Yang, Helen; Fisher, Michael E.
2013-01-01
The specific heats of exactly solvable alternating layered planar Ising models with strips of width $m_1$ lattice spacings and ``strong'' couplings $J_1$ sandwiched between strips of width $m_2$ and ``weak'' coupling $J_2$, have been studied numerically to investigate the effects of connectivity and proximity. We find that the enhancements of the specific heats of the strong layers and of the overall or `bulk' critical temperature, $T_c(J_1,J_2;m_1,m_2)$, arising from the collective effects r...
Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics.
Heydari, Ali; Balakrishnan, Sivasubramanya N
2013-01-01
To synthesize fixed-final-time control-constrained optimal controllers for discrete-time nonlinear control-affine systems, a single neural network (NN)-based controller called the Finite-horizon Single Network Adaptive Critic is developed in this paper. Inputs to the NN are the current system states and the time-to-go, and the network outputs are the costates that are used to compute optimal feedback control. Control constraints are handled through a nonquadratic cost function. Convergence proofs of: 1) the reinforcement learning-based training method to the optimal solution; 2) the training error; and 3) the network weights are provided. The resulting controller is shown to solve the associated time-varying Hamilton-Jacobi-Bellman equation and provide the fixed-final-time optimal solution. Performance of the new synthesis technique is demonstrated through different examples including an attitude control problem wherein a rigid spacecraft performs a finite-time attitude maneuver subject to control bounds. The new formulation has great potential for implementation since it consists of only one NN with single set of weights and it provides comprehensive feedback solutions online, though it is trained offline.
Clemmen, Stéphane; Hermans, Artur; Solano, Eduardo; Dendooven, Jolien; Koskinen, Kalle; Kauranen, Martti; Brainis, Edouard; Detavernier, Christophe; Baets, Roel
2015-11-15
We report the fabrication of artificial unidimensional crystals exhibiting an effective bulk second-order nonlinearity. The crystals are created by cycling atomic layer deposition of three dielectric materials such that the resulting metamaterial is noncentrosymmetric in the direction of the deposition. Characterization of the structures by second-harmonic generation Maker-fringe measurements shows that the main component of their nonlinear susceptibility tensor is about 5 pm/V, which is comparable to well-established materials and more than an order of magnitude greater than reported for a similar crystal [Appl. Phys. Lett.107, 121903 (2015)APPLAB0003-695110.1063/1.4931492]. Our demonstration opens new possibilities for second-order nonlinear effects on CMOS-compatible nanophotonic platforms.
Green, A G; Sondhi, S L
2005-12-31
Scaling arguments imply that quantum-critical points exhibit universal nonlinear responses to external probes. We investigate the origins of such nonlinearities in transport, which is especially problematic since the system is necessarily driven far from equilibrium. We argue that for a wide class of systems the new ingredient that enters is the Schwinger mechanism--the production of carriers from the vacuum by the applied field--which is then balanced against a scattering rate that is itself set by the field. We show by explicit computation how this works for the case of the symmetric superfluid-Mott insulator transition of bosons.
Hendi, S H; Panah, B Eslam
2016-01-01
In this paper, we take into account the black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. At first, we consider the cosmological constant as a dynamic pressure to study the analogy of the black hole solutions with the Van der Waals liquid--gas system in the extended phase space. We plot $P-V$, $T-V$ and $G-T$ diagrams and investigate the phase transition of adS black holes in the canonical ensemble. Moreover, we discuss about the effect of nonlinear electrodynamics on the the critical values and the universal ratio $P_{c}v_{c}/T_{c}$.
Directory of Open Access Journals (Sweden)
A. Malvandi
2014-01-01
Full Text Available Steady two-dimensional boundary layer flow of a nanofluid past a nonlinear stretching sheet is investigated analytically using the Homotopy Analysis Method (HAM. The employed model for nanofluid includes twocomponent four-equation non-homogeneous equilibrium model that incorporates the effects of Brownian motion ( Nb , thermophoresis ( Nt and Lewis number ( Le simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via the similarity variables. Analytical results are in best agreements with those existing in the literatures. The outcomes signify the decreasing trend of heat transfer rate with thermophoresis, Brownian motion and Lewis number. However, concentration rate has a sensitive behavior with parameters, especially the Brownian motion and thermophoresis parameters. Also, the weak points of numerical methods in such problems have been mentioned and the efficiency of HAM, as an alternative approach, in solving these kinds of nonlinear coupled problems has been shown.
Longitudinal instabilities affecting the moving critical layer laser-plasma ion accelerators
Sahai, Aakash Ajit
2014-01-01
In this work we analyze the longitudinal instabilities of propagating acceleration structures that are driven by a relativistically intense laser at the moving plasma critical layer [1]. These instabilities affect the energy-spectra of the accelerated ion-beams in propagating critical layer acceleration schemes [2][3]. Specifically, using analytical theory and PIC simulations we look into three fundamental physical processes and their interplay that are crucial to the understanding of energy spectral control by making the laser-plasma ion accelerators stable. The interacting processes are (i) Doppler-shifted ponderomotive bunching [1][4] (ii) potential quenching by beam-loading [2] and (iii) two-stream instabilities. These phenomenon have been observed in simulations analyzing these acceleration processes [5][6][7]. From the preliminary models and results we present in this work, we can infer measures by which these instabilities can be controlled [8] for improving the energy-spread of the beams.
Numerical Experiments on Critical Ventilation Velocity and Back-layer in Tunnel Fire
Institute of Scientific and Technical Information of China (English)
YANG Pei-zhong; JIN Hao; SHAO Gang; JIN Xian-long
2006-01-01
Full-scale numerical experiments were carried out on the vehicular fire in a long tunnel to study the critical ventilation velocity and back-layer distance with heat release rate of 5,20 and 100MW respectively. A computational fluid dynamics (CFD) model of fire-driven fluid flow FDS(Fire Dynamics Simulator) was used to solve numerically a form of the Navier-Stokes equations for fire. The results were compared with the expressions proposed in the literature. A modified equation for the critical ventilation velocity was given to better fit the experimental results. A bi-exponential model that well fitted the numerical experimental results was proposed to describe the relationship between back-layer distance and ventilation velocity.
Beneš, Michal
2010-01-01
The present paper deals with mathematical models of heat and moisture transport in layered building envelopes. The study of such processes generates a system of two doubly nonlinear evolution partial differential equations with appropriate initial and boundary conditions. The existence of the strong solution in two dimensions on a (short) time interval is proven. The proof rests on regularity results for elliptic transmission problem for composite-like materials.
Hendi, S. H.; Panahiyan, S.; Eslam Panah, B.
2016-10-01
In this paper, we take into account the black-hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. At first, we consider the cosmological constant as a dynamical pressure to study the phase transitions and analogy of the black holes with the Van der Waals liquid-gas system in the extended phase space. We make a comparison between linear and nonlinear electrodynamics and show that the lowest critical temperature belongs to Maxwell theory. Also, we make some arguments regarding how power of nonlinearity brings the system to Schwarzschild-like and Reissner-Nordström-like limitations. Next, we study the critical behavior of the system in the context of heat capacity. We show that critical behavior of system is similar to the one in phase diagrams of extended phase space. We also extend the study of phase transition points through geometrical thermodynamics (GTs). We introduce two new thermodynamical metrics for extended phase space and show that divergencies of thermodynamical Ricci scalar (TRS) of the new metrics coincide with phase transition points of the system. Then, we introduce a new method for obtaining critical pressure and horizon radius by considering denominator of the heat capacity.
Probabilistic size effect law for mode II fracture of critical lengths in snow slab weak layers
McClung, David
2016-04-01
Snow slab avalanches initiate by mode II fracture within relatively thin weak layers under stronger, cohesive slabs. For risk based avalanche prediction, it is important to understand the fracture properties of alpine snow. Alpine snow is a quasi-brittle material with a size effect on nominal shear strength meaning that strength decreases with increasing sample size. A related size effect is the critical length required for rapid propagation of a shear fracture. In that case, the probability of fracture increases with increasing crack length. In this paper, 45 sets of field measured critical lengths are presented based on 591 individual tests. From analysis, a probabilistic size effect law is derived analogous to the deterministic size effect law for nominal shear strength related to fracture mechanics. It is shown that in the limit of small crack length, the plastic limit is approached with a very low probability of failure implying very high shear strength. At the other limit, for long enough cracks, the limit of Linear Elastic Fracture Mechanics (LEFM) is approached implying high probability of failure and low nominal shear strength compatible with large sample size. It is shown that the strength size effect law and the critical length size effect law form a duality for analysis of snow avalanche weak layers. It is expected the critical length size effect law will be important in applications.
SOLUTION WITH SHOCK-BOUNDARY LAYER AND SHOCK-INTERIOR LAYER TO A CLASS OF NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,the shock behaviors of solution to a class of nonlinear singularly perturbed problems are considered.Under some appropriate conditions,the outer and interior solutions to the original problem are constructed.Using the special limit and matching theory,the expressions of solutions with the shock behavior near the boundary and some interior points are given and the domain for boundary values is obtained.
Kuehl, Joseph
2016-11-01
The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.
Sun, Yahui; Hong, Ling; Jiang, Jun; Li, Zigang
This paper proposes an efficient but simple method to determine the approximate stationary probability distribution around periodic attractors of nonautonomous nonlinear systems under multiple time-dependent parametric noises and estimate the critical noise intensity for noise-induced explosive bifurcations under a given confidence probability. After adopting a stroboscopic map constructed by a method with higher accuracy and efficiency, nonautonomous dynamical systems around periodic attractors are transformed into mapping ones. Then the mean-square analysis method of discrete systems is used to derive the stochastic sensitivity function. Based on the confidence ellipses of stochastic attractors and the global structure of deterministic nonlinear systems, the critical noise intensity of noise-induced explosive bifurcations under a given confidence probability is estimated. A Mathieu-Duffing oscillator under both multiplicative and additive noises is studied to show the validity of the proposed method.
Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin
2017-02-01
The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.
Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles
Shakra, Farah Abou
2012-01-01
Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering for a class of non star-shaped obstacles called illuminated from exterior. The main tool we use is the method of multipliers with weights that generalize the Morawetz multiplier to suit the geometry of the obstacle.
Dynamic Critical Behavior of Multi-Grid Monte Carlo for Two-Dimensional Nonlinear $\\sigma$-Models
Mana, Gustavo; Mendes, Tereza; Pelissetto, Andrea; Sokal, Alan D.
1995-01-01
We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear $\\sigma$-models: it is based on embedding an $XY$ model into the given $\\sigma$-model, and then updating the induced $XY$ model using a standard $XY$-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional $O(N)$ $\\sigma$-models with $N = 3,4,8$ and for the $SU(3)$ principal chiral model. We find that the dynamic critical exponent $z$ vari...
Gajjar, J. S. B.
1995-01-01
We consider the nonlinear stability of a fully three-dimensional boundary layer flow in an incompressible fluid and derive an equation governing the nonlinear development of a stationary cross-flow vortex. The amplitude equation is a novel integro-differential equation which has spatial derivatives of the amplitude occurring in the kernal function. It is shown that the evolution of the cross-flow vortex is strongly coupled to the properties of an unsteady wall layer which is in fact driven by an unknown slip velocity, proportional to the amplitude of the cross-flow vortex. The work is extended to obtain the corresponding equation for rotating disk flow. A number of special cases are examined and the numerical solution for one of cases, and further analysis, demonstrates the existence of finite-distance as well as focussing type singularities. The numerical solutions also indicate the presence of a new type of nonlinear wave solution for a certain set of parameter values.
Directory of Open Access Journals (Sweden)
S.K. Parida
2015-12-01
Full Text Available This work considers the two-dimensional steady MHD boundary layer flow of heat and mass transfer over a flat plate with partial slip at the surface subjected to the convective heat flux. The particular attraction lies in searching the effects of variable viscosity and variable thermal diffusivity on the behavior of the flow. In addition, non-linear thermal radiation effects and thermophoresis are taken into account. The governing nonlinear partial differential equations for the flow, heat and mass transfer are transformed into a set of coupled nonlinear ordinary differential equations by using similarity variable, which are solved numerically by applying Runge–Kutta fourth–fifth order integration scheme in association with quasilinear shooting technique. The novel results for the dimensionless velocity, temperature, concentration and ambient Prandtl number within the boundary layer are displayed graphically for various parameters that characterize the flow. The local skin friction, Nusselt number and Sherwood number are shown graphically. The numerical results obtained for the particular case are fairly in good agreement with the result of Rahman [6].
Tetreault-Friend, Melanie; Azizian, Reza; Bucci, Matteo; McKrell, Thomas; Buongiorno, Jacopo; Rubner, Michael; Cohen, Robert
2016-06-01
Porous hydrophilic surfaces have been shown to enhance the critical heat flux (CHF) in boiling heat transfer. In this work, the separate effects of pore size and porous layer thickness on the CHF of saturated water at atmospheric pressure were experimentally investigated using carefully engineered surfaces. It was shown that, for a fixed pore diameter (˜20 nm), there is an optimum layer thickness (˜2 μm), for which the CHF value is maximum, corresponding to ˜115% enhancement over the value for uncoated surfaces. Similarly, a maximum CHF value (˜100% above the uncoated surface CHF) was observed while changing the pore size at a constant layer thickness (˜1 μm). To explain these CHF maxima, we propose a mechanistic model that can capture the effect of pore size and pore thickness on CHF. The good agreement found between the model and experimental data supports the hypothesis that CHF is governed by the competition between capillary wicking, viscous pressure drop and evaporation, as well as conduction heat transfer within the porous layer. The model can be used to guide the development of engineered surfaces with superior boiling performance.
Linear Feedback Stabilization of Nonlinear Systems with an Uncontrollable Critical Mode
1992-11-17
mode that is uncontrollable. The results complement previous work on the synthesis of nonlinear stabilizing control laws. The present work addresses...analysis and stabilizing control design employ results on stability of bifurcations of parametrized systems.
Most-Critical Transient Disturbances in an Incompressible Flat-Plate Boundary Layer
Monschke, Jason; White, Edward
2015-11-01
Transient growth is a linear disturbance growth mechanism that plays a key role in roughness-induced boundary-layer transition. It occurs when superposed stable, non-orthogonal continuous spectrum modes experience algebraic disturbance growth followed by exponential decay. Algebraic disturbance growth can modify the basic state making it susceptible to secondary instabilities rapidly leading to transition. Optimal disturbance theory was developed to model the most-dangerous disturbances. However, evidence suggests roughness-induced transient growth is sub-optimal yet leads to transition earlier than optimal theory suggests. This research computes initial disturbances most unstable to secondary instabilities to further develop the applicability of transient growth theory to surface roughness. The main approach is using nonlinear adjoint optimization with solutions of the parabolized Navier-Stokes and BiGlobal stability equations. Two objective functions were considered: disturbance kinetic energy growth and sinuous instability growth rate. The first objective function was used as validation of the optimization method. Counter-rotating streamwise vortices located low in the boundary layer maximize the sinuous instability growth rate. The authors would like to acknowledge NASA and the AFOSR for funding this work through AFOSR Grant FA9550-09-1-0341.
Energy Technology Data Exchange (ETDEWEB)
Takamoto, Masahiro [Department of Applied Quantum Physics, Kyushu University, Fukuoka 812-8581 (Japan)]. E-mail: masahtap@mbox.nc.kyushu-u.ac.jp; Muraoka, Yoshinori [Department of General Education, Ariake National College of Technology, Omuta, Fukuoka 836-8585 (Japan); Idogaki, Toshihiro [Department of Applied Quantum Physics, Kyushu University, Fukuoka 812-8581 (Japan)
2007-03-15
Using Monte Carlo simulation with the Wolff algorithm and single histogram method, the critical behavior of the ferromagnetic Ising thin films with thickness ranging from n=3 to 15 layers, has been studied. With varying the ratio of surface interaction to bulk one, {kappa}=J{sub s}/J{sub B}, we found a special point {kappa}{sub sp} at which all the film have a unique critical temperature independent of film thickness n. In the region that {kappa} is less than {kappa}{sub sp}, the shift exponent {lambda} is independent of {kappa} in the limit n->{approx}, but the strength of surface coupling strongly affects the gradient of asymptotic curve {lambda} vs 1/n. When {kappa} is larger than {kappa}{sub sp}, however, the clear power law behavior is not found.
Takamoto, Masahiro; Muraoka, Yoshinori; Idogaki, Toshihiro
2007-03-01
Using Monte Carlo simulation with the Wolff algorithm and single histogram method, the critical behavior of the ferromagnetic Ising thin films with thickness ranging from n=3 to 15 layers, has been studied. With varying the ratio of surface interaction to bulk one, κ=Js/JB, we found a special point κsp at which all the film have a unique critical temperature independent of film thickness n. In the region that κ is less than κsp, the shift exponent λ is independent of κ in the limit n→∞, but the strength of surface coupling strongly affects the gradient of asymptotic curve λ vs 1/n. When κ is larger than κsp, however, the clear power law behavior is not found.
Fan, Quan-Yong; Yang, Guang-Hong
2016-01-01
This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.
Institute of Scientific and Technical Information of China (English)
张常光; 陈新栋; 范文
2016-01-01
The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.
Institute of Scientific and Technical Information of China (English)
LI Huiling; WANG Mingxin
2005-01-01
This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.
Energy Technology Data Exchange (ETDEWEB)
Son, Hong Hyun; Jeong, Ui Ju; Seo, Gwang Hyeok; Jeun, Gyoo Dong; Kim, Sung Joong [KAERI, Daejeon (Korea, Republic of)
2016-05-15
The former method is deemed challenging due to longer development period and license issue. In this regard, FeCrAl, Cr, and SiC have been received positive attention as ATF coating materials because they are highly resistant to high temperature steam reaction causing massive hydrogen generation. In this study, Cr was selected as a target deposition material on the metal substrate because we found that Cr-layered surface becomes superhydrophilic, favorable to delaying the triggering of the critical heat flux (CHF). Thus in order to investigate the effect of Cr-layered superhydrophilic surfaces (under explored coating conditions) on pool boiling heat transfer, pool boiling experiment was conducted in the saturated deionized water under atmospheric pressure. As a physical vapor deposition (PVD) method, the DC magnetron sputtering technique was introduced to develop Cr-layered nanostructure. As a control variable of DC sputtering, substrate temperature was selected. Surface wettability and nanostructure were analyzed as major surface parameters on the CHF. We believe that highly dense micro/nano structure without nucleation cavities and inner pores neutralized the wettability effect on the CHF. Moreover, superhydrophilic surface with deficient cavity density rather hinders active nucleation. This emphasizes the importance of micro/nano structure surface for enhanced boiling heat transfer.
A Nonlinear Dynamic Characterization of The Universal Scrape-off Layer Plasma Fluctuations
Mekkaoui, A
2012-01-01
A stochastic differential equation of plasma density dynamic is derived, consistent with the experimentally measured pdf and the theoretical quadratic nonlinearity. The plasma density evolves on the turbulence correlation time scale and is driven by a stochastic white noise proportional to the turbulence fluctuations amplitude, while the linear growth is quadratically damped by the fluctuation level $n_e(t)/\\bar{n}_e$.
PIV measurements of the bottom boundary layer under nonlinear surface waves
Henriquez, M.; Reniers, A. J H M; Ruessink, B. G.; Stive, M. J F
2014-01-01
Sediment in the nearshore is largely mobilized in the wave bottom boundary layer (wbbl) hereby emphasizing the importance of this relatively thin layer to nearshore morphology. This paper presents a laboratory experiment where hydrodynamic properties of the wbbl were quantified by measuring flow vel
Experimental study of nonlinear processes in a swept-wing boundary layer at the mach number M=2
Yermolaev, Yu. G.; Kosinov, A. D.; Semionov, N. V.
2014-09-01
Results of experiments aimed at studying the linear and nonlinear stages of the development of natural disturbances in the boundary layer on a swept wing at supersonic velocities are presented. The experiments are performed on a swept wing model with a lens-shaped airfoil, leading-edge sweep angle of 45°, and relative thickness of 3%. The disturbances in the flow are recorded by a constant-temperature hot-wire anemometer. For determining the nonlinear interaction of disturbances, the kurtosis and skewness are estimated for experimentally obtained distributions of the oscillating signal over the streamwise coordinate or along the normal to the surface. The disturbances are found to increase in the frequency range from 8 to 35 kHz in the region of their linear development, whereas enhancement of high-frequency disturbances is observed in the region of their nonlinear evolution. It is demonstrated that the growth of disturbances in the high-frequency spectral range ( f > 35 kHz) is caused by the secondary instability.
Khurana, Meenakshi; Rana, Puneet; Srivastava, Sangeet
2016-12-01
In the present paper, we present both linear and nonlinear analyses to investigate thermal instability on a rotating non-Newtonian viscoelastic nanofluid layer under the influence of a magnetic field. In the linear stability analysis, the stationary and oscillatory modes of convection are obtained for various controlling parameters using the normal mode technique. Both Nusselt and Sherwood numbers are calculated after employing the minimal truncated Fourier series to steady and unsteady state. The main findings conclude that rotation and strain retardation parameter increase the value of the critical Rayleigh number in the neutral stability curve which delays the onset of convection in the nanofluid layer while the stress relaxation parameter enhances the convection. The magnetic field stabilizes the system for low values of the Taylor number (rotation) but an inverse trend is observed for high Taylor number. Both Nusselt and Sherwood numbers initially oscillate with time until the steady state prevails and they decrease with both Chandrasekhar and Taylor numbers. The magnitude of the streamlines and the contours of both isotherms and iso-nanohalines concentrate near the boundaries for large values of Ra, indicating an increase in convection.
Wrinkle-to-fold transition in soft layers under equi-biaxial strain: A weakly nonlinear analysis
Ciarletta, P.
2014-12-01
Soft materials can experience a mechanical instability when subjected to a finite compression, developing wrinkles which may eventually evolve into folds or creases. The possibility to control the wrinkling network morphology has recently found several applications in many developing fields, such as scaffolds for biomaterials, stretchable electronics and surface micro-fabrication. Albeit much is known of the pattern initiation at the linear stability order, the nonlinear effects driving the pattern selection in soft materials are still unknown. This work aims at investigating the nature of the elastic bifurcation undertaken by a growing soft layer subjected to a equi-biaxial strain. Considering a skin effect at the free surface, the instability thresholds are found to be controlled by a characteristic length, defined by the ratio between capillary energy and bulk elasticity. For the first time, a weakly nonlinear analysis of the wrinkling instability is performed here using the multiple-scale perturbation method applied to the incremental theory in finite elasticity. The Ginzburg-Landau equations are derived for different superposing linear modes. This study proves that a subcritical pitchfork bifurcation drives the observed wrinkle-to-fold transition in swelling gels experiments, favoring the emergence of hexagonal creased patterns, albeit quasi-hexagonal patterns might later emerge because of an expected symmetry break. Moreover, if the surface energy is somewhat comparable to the bulk elastic energy, it has the same stabilizing effect as for fluid instabilities, driving the formation of stable wrinkles, as observed in elastic bi-layered materials.
Suess, D.; Vogler, C.; Bruckner, F.; Sepehri-Amin, H.; Abert, C.
2017-06-01
One essential feature in magnetic random access memory cells is the spin torque efficiency, which describes the ratio of the critical switching current to the energy barrier. In this paper, it is reported that the spin torque efficiency can be improved by a factor of 3.2 by the use of a dual free layer device, which consists of one layer with perpendicular crystalline anisotropy and another layer with in-plane crystalline anisotropy. Detailed simulations solving the spin transport equations simultaneously with the micromagnetics equation were performed in order to understand the origin of the switching current reduction by a factor of 4 for the dual layer structure compared to a single layer structure. The main reason could be attributed to an increased spin accumulation within the free layer due to the dynamical tilting of the magnetization within the in-plane region of the dual free layer.
Boundary layers for self-similar viscous approximations of nonlinear hyperbolic systems
Christoforou, Cleopatra
2011-01-01
We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both conservative and non conservative systems, to the analysis of the boundary Riemann problem and we show that, under appropriate assumptions, the limits of the self-similar and the classical vanishing viscosity approximation coincide. We require neither genuinely nonlinearity nor linear degeneracy of the characteristic fields.
Zhang, Chendong
2015-09-21
By using a comprehensive form of scanning tunneling spectroscopy, we have revealed detailed quasi-particle electronic structures in transition metal dichalcogenides, including the quasi-particle gaps, critical point energy locations, and their origins in the Brillouin zones. We show that single layer WSe surprisingly has an indirect quasi-particle gap with the conduction band minimum located at the Q-point (instead of K), albeit the two states are nearly degenerate. We have further observed rich quasi-particle electronic structures of transition metal dichalcogenides as a function of atomic structures and spin-orbit couplings. Such a local probe for detailed electronic structures in conduction and valence bands will be ideal to investigate how electronic structures of transition metal dichalcogenides are influenced by variations of local environment.
Zhang, Chendong; Chen, Yuxuan; Johnson, Amber; Li, Ming-Yang; Li, Lain-Jong; Mende, Patrick C; Feenstra, Randall M; Shih, Chih-Kang
2015-10-14
By using a comprehensive form of scanning tunneling spectroscopy, we have revealed detailed quasi-particle electronic structures in transition metal dichalcogenides, including the quasi-particle gaps, critical point energy locations, and their origins in the Brillouin zones. We show that single layer WSe2 surprisingly has an indirect quasi-particle gap with the conduction band minimum located at the Q-point (instead of K), albeit the two states are nearly degenerate. We have further observed rich quasi-particle electronic structures of transition metal dichalcogenides as a function of atomic structures and spin-orbit couplings. Such a local probe for detailed electronic structures in conduction and valence bands will be ideal to investigate how electronic structures of transition metal dichalcogenides are influenced by variations of local environment.
Enhancement of critical heat flux in pool boiling using atomic layer deposition of alumina
Feng, Bo; Weaver, Keith; Peterson, G. P.
2012-01-01
Alumina nano coatings on platinum (Pt) micro wires were fabricated using atomic layer deposition. During the pool boiling heat transfer, the critical heat flux (CHF) of Pt/Alumina in de-ionized water was found to have a two-fold enhancement compared to that of the same Pt bare wire. The CHF was shown to increase with coating thickness of alumina up to a thickness of 20 nm. Coating thicknesses in excess of 20 nm had no additional influence on the CHF. The enhancement of the CHF is the result of the superwetting property of the amorphous alumina coatings, which significantly increases the liquid film thickness, enhancing the rewetting of the "hot spot."
Nonlinear chemoconvection in the methylene-blue-glucose system: Two-dimensional shallow layers
Pons, A. J.; Batiste, O.; Bees, M. A.
2008-07-01
Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue-glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.
Coherent nonlinear electromagnetic response in twisted bilayer and few-layer graphene
Indian Academy of Sciences (India)
Vipin Kumar; Enamullah; Upendra Kumar; Girish S Setlur
2014-10-01
The phenomenon of Rabi oscillations far from resonance is described in bilayer and few-layer graphene. These oscillations in the population and polarization at the Dirac point in -layer graphene are seen in the nth harmonic termin the external driving frequency. The underlying reason behind these oscillations is attributable to the pseudospin degree of freedom possessed by all these systems. Conventional Rabi oscillations, which occur only near resonance, are seen in multiple harmonics in multilayer graphene. However, the experimentally measurable current density exhibits anomalous behaviour only in the first harmonic in all the graphene systems. A fully numerical solution of the optical Bloch equations is in complete agreement with the analytical results, thereby justifying the approximation schemes used in the latter. The same phenomena are also described in twisted bilayer graphene with and without an electric potential difference between the layers. It is found that the anomalous Rabi frequency is strongly dependent on twist angle for weak applied fields – a feature absent in single-layer graphene, whereas the conventional Rabi frequency is relatively independent of the twist angle.
Dey, Prasenjit
understanding the basic unexplored science as well as creating technological developments. The dephasing dynamics in semiconductors typically occur in the picosecond to femtosecond timescale, thus the use of ultrafast laser spectroscopy is a potential route to probe such excitonic responses. The focus of this dissertation is two-fold: firstly, to develop the necessary instrumentation to accurately probe the aforementioned parameters and secondly, to explore the quantum dynamics and the underlying many-body interactions in different layered semiconducting materials. A custom-built multidimensional optical non-linear spectrometer was developed in order to perform two-dimensional spectroscopic (2DFT) measurements. The advantages of this technique are multifaceted compared to regular one-dimensional and non-linear incoherent techniques. 2DFT technique is based on an enhanced version of Four wave mixing experiments. This powerful tool is capable of identifying the resonant coupling, probing the coherent pathways, unambiguously extracting the homogeneous linewidth in the presence of inhomogeneity and decomposing a complex spectra into real and imaginary parts. It is not possible to uncover such crucial features by employing one dimensional non-linear technique. Monolayers as well as bulk TMDs and group III-VI bulk layered materials are explored in this dissertation. The exciton quantum dynamics is explored with three pulse four-wave mixing whereas the phase sensitive measurements are obtained by employing two-dimensional Fourier transform spectroscopy. Temperature and excitation density dependent 2DFT experiments unfold the information associated with the many-body interactions in the layered semiconducting samples.
A Critical, Nonlinear Threshold Dictates Bacterial Invasion and Initial Kinetics During Influenza
Smith, Amber M.; Smith, Amanda P.
2016-12-01
Secondary bacterial infections increase morbidity and mortality of influenza A virus (IAV) infections. Bacteria are able to invade due to virus-induced depletion of alveolar macrophages (AMs), but this is not the only contributing factor. By analyzing a kinetic model, we uncovered a nonlinear initial dose threshold that is dependent on the amount of virus-induced AM depletion. The threshold separates the growth and clearance phenotypes such that bacteria decline for dose-AM depletion combinations below the threshold, stay constant near the threshold, and increase above the threshold. In addition, the distance from the threshold correlates to the growth rate. Because AM depletion changes throughout an IAV infection, the dose requirement for bacterial invasion also changes accordingly. Using the threshold, we found that the dose requirement drops dramatically during the first 7d of IAV infection. We then validated these analytical predictions by infecting mice with doses below or above the predicted threshold over the course of IAV infection. These results identify the nonlinear way in which two independent factors work together to support successful post-influenza bacterial invasion. They provide insight into coinfection timing, the heterogeneity in outcome, the probability of acquiring a coinfection, and the use of new therapeutic strategies to combat viral-bacterial coinfections.
Directory of Open Access Journals (Sweden)
Mohammad Sabaeian
2014-12-01
Full Text Available In this work, the effects of vertical electric field on the electronic and optical properties of strained semi-spheroid-shaped InAs/GaAs quantum dot (QD coupled to its wetting layer (WL aimed to enhance the nonlinear optical properties were investigated. The dependence of energy eigenvalues of S- and P- states and intersubband P-to-S transition energy on applied electric field was studied. A ∼∓ߙ10 meV Stark shift in the intersubband P-to-S transition energy was calculated for a semi-spheroid-shaped QD with height of 5 nm and base-length of 20 nm when bias voltage was varied from 0 V to ±0.8V. The dependence of transition dipole moment and linear and nonlinear optical properties of the system on bias voltage was also studied. It was concluded that increasing the bias voltage from -0.8V to +0.8V leads to increase in figure of merit of the system from ∼0.153 to ∼0.198.
Nonlinear thermal convection in a layer of nanofluid under G-jitter and internal heating effects
Directory of Open Access Journals (Sweden)
Bhadauria B. S.
2014-01-01
Full Text Available This paper deals with a mathematical model of controlling heat transfer in nanofluids. The time-periodic vertical vibrations of the system are considered to effect an external control of heat transport along with internal heating effects. A weakly non-linear stability analysis is based on the five-mode Lorenz model using which the Nusselt number is obtained as a function of the thermal Rayleigh number, nano-particle concentration based Rayleigh number, Prandtl number, Lewis number, modified diffusivity ratio, amplitude and frequency of modulation. It is shown that modulation can be effectively used to control convection and thereby heat transport. Further, it is found that the effect of internal Rayleigh number is to enhance the heat and nano-particles transport.
Zhang, Chendong; CHEN, YUXUAN; Johnson, Amber; Li, Ming-Yang; Li, Lain-Jong; Mende, Patrick C.; Feenstra, Randall M.; Shih, Chih-Kang
2014-01-01
Understanding quasiparticle band structures of transition metal dichalcogenides (TMDs) is critical for technological advances of these materials for atomic layer electronics and photonics. Although theoretical calculations to date have shown qualitatively similar features, there exist subtle differences which can lead to important consequences in the device characteristics. For example, most calculations have shown that all single layer (SL) TMDs have direct band gaps, while some have shown t...
Nonlinear mushy-layer convection with chimneys: stability and optimal solute fluxes
Wells, Andrew J; Orszag, Steven A
2012-01-01
We model buoyancy-driven convection with chimneys -- channels of zero solid fraction -- in a mushy layer formed during directional solidification of a binary alloy in two-dimensions. A large suite of numerical simulations is combined with scaling analysis in order to study the parametric dependence of the flow. Stability boundaries are calculated for states of finite-amplitude convection with chimneys, which for a narrow domain can be interpreted in terms of a modified Rayleigh number criterion based on the domain width and mushy-layer permeability. For solidification in a wide domain with multiple chimneys, it has previously been hypothesised that the chimney spacing will adjust to optimise the rate of removal of potential energy from the system. For a wide variety of initial liquid concentration conditions, we consider the detailed flow structure in this optimal state and derive scaling laws for how the flow evolves as the strength of convection increases. For moderate mushy-layer Rayleigh numbers these flo...
Nonlinear solid finite element analysis of mitral valves with heterogeneous leaflet layers
Prot, V.; Skallerud, B.
2009-02-01
An incompressible transversely isotropic hyperelastic material for solid finite element analysis of a porcine mitral valve response is described. The material model implementation is checked in single element tests and compared with a membrane implementation in an out-of-plane loading test to study how the layered structures modify the stress response for a simple geometry. Three different collagen layer arrangements are used in finite element analysis of the mitral valve. When the leaflets are arranged in two layers with the collagen on the ventricular side, the stress in the fibre direction through the thickness in the central part of the anterior leaflet is homogenized and the peak stress is reduced. A simulation using membrane elements is also carried out for comparison with the solid finite element results. Compared to echocardiographic measurements, the finite element models bulge too much in the left atrium. This may be due to evidence of active muscle fibres in some parts of the anterior leaflet, whereas our constitutive modelling is based on passive material.
Denison, Marie F. C.
The reduction of drag and aerodynamic heating caused by boundary layer transition is of central interest for the development of hypersonic vehicles. Receptivity to flow perturbation in the form of Tollmien-Schlichting (TS) wave growth often determines the first stage of the transition process, which can be delayed by depositing specific excitations into the boundary layer. Weakly ionized Dielectric Barrier Discharge (DBD) actuators are being investigated as possible sources of such excitations, but little is known today about their interaction with high-speed flows. In this framework, the first part of the thesis is dedicated to a receptivity study of laminar compressible boundary layers over a flat plate by linear stability analysis following an adjoint operator formulation, under DBD representative excitations assumed independent of flow conditions. The second part of the work concentrates on the development of a coupled plasma-Navier and Stokes solver targeted at the study of supersonic flow and compressibility effects on DBD forcing and non-parallel receptivity. The linear receptivity study of quasi-parallel compressible flows reveals several interesting features such as a significant shift of the region of maximum receptivity deeper into the flow at high Mach number and strong wave amplitude reduction compared to incompressible flows. The response to DBD relevant excitation distributions and to variations of the base flow conditions and system length scales follows these trends. Observed absolute amplitude changes and relative sensitivity modifications between source types are related to the evolution of the offset between forcing peak profile and relevant adjoint mode maximum. The analysis highlights the crucial importance of designing and placing the actuator in a way that matches its force field to the position of maximum boundary layer receptivity for the specific flow conditions of interest. In order to address the broad time and length scale spectrum
Global existence for an L^2 critical Nonlinear Dirac equation in one dimension
Candy, Timothy
2011-01-01
We prove global existence from $L^2$ initial data for a nonlinear Dirac equation known as the Thirring model. Local existence in $H^s$ for $s>0$, and global existence for $s>1/2$, has recently been proven by Selberg and Tesfahun by using $X^{s, b}$ spaces together with a type of null form estimate. In contrast, motivated by the recent work of Machihara, Nakanishi, and Tsugawa, we first prove local existence in $L^2$ by using null coordinates, where the time of existence depends on the profile of the initial data. To extend this to a global existence result we need to rule out concentration of $L^2$ norm, or charge, at a point. This is done by decomposing the solution into an approximately linear component and a component with improved integrability. We then prove global existence for all $s>0$.
Critical properties of XY model on two-layer Villain-ferromagnetic lattice
Institute of Scientific and Technical Information of China (English)
Wang Yi; R. Quartu; Liu Xiao-Yan; Han Ru-Qi; Horiguchi Tsuyoshi
2004-01-01
We investigate phase transitions of the XY model on a two-layer square lattice which consists of a Villain plane(J) and a ferromagnetic plane (I), using Monte Carlo simulations and a histogram method. Depending on the values of interaction parameters (I, J), the system presents three phases: namely, a Kosterlitz-Thouless (KT) phase in which the two planes are critical for I predominant over J, a chiral phase in which the two planes have a chiral order for J predominant over I and a new phase in which only the Villain plane has a chiral order and the ferromagnetic plane is paramagnetic with a small value of chirality. We clarify the nature of phase transitions by using a finite size scaling method. We find three different kinds of transitions according to the values of (I, J): the KT transition, the Ising transition and an XY-Ising transition with v = 0.849(3). It turns out that the Ising or XY-Ising transition is associated with the disappearance of the chiral order in the Villain plane.
Oscillating line source in a shear flow with a free surface: critical layer-like contributions
Ellingsen, Simen Å
2016-01-01
The linearized water-wave radiation problem for an oscillating submerged line source in an inviscid shear flow with a free surface is investigated analytically at finite, constant depth in the presence of a shear flow varying linearly with depth. The surface velocity is taken to be zero relative to the oscillating source, so that Doppler effects are absent. The radiated wave out from the source is calculated based on Euler's equation of motion with the appropriate boundary and radiation conditions, and differs substantially from the solution obtained by assuming potential flow. To wit, an additional wave is found in the downstream direction in addition to the previously known dispersive wave solutions; this wave is non-dispersive and we show how it is the surface manifestation of a critical layer-like flow generated by the combination of shear and mass flux at the source, passively advected with the flow. As seen from a system moving at the fluid velocity at the source's depth, streamlines form closed curves ...
Nonlinear electron acoustic structures generated on the high-potential side of a double layer
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R. Pottelette
2009-04-01
Full Text Available High-time resolution measurements of the electron distribution function performed in the auroral upward current region reveals a large asymmetry between the low- and high-potential sides of a double-layer. The latter side is characterized by a large enhancement of a locally trapped electron population which corresponds to a significant part (~up to 30% of the total electron density. As compared to the background hot electron population, this trapped component has a very cold temperature in the direction parallel to the static magnetic field. Accordingly, the differential drift between the trapped and background hot electron populations generates high frequency electron acoustic waves in a direction quasi-parallel to the magnetic field. The density of the trapped electron population can be deduced from the frequency where the electron acoustic spectrum maximizes. In the auroral midcavity region, the electron acoustic waves may be modulated by an additional turbulence generated in the ion acoustic range thanks to the presence of a pre-accelerated ion beam located on the high-potential side of the double layer. Electron holes characterized by bipolar pulses in the electric field are sometimes detected in correlation with these electron acoustic wave packets.
Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions
Collot, Charles; Merle, Frank; Raphaël, Pierre
2016-11-01
We consider the energy critical semilinear heat equation partial_tu = Δ u + |u|^{4/d-2}u, quad x in R^d and give a complete classification of the flow near the ground state solitary wave Q(x) = 1/(1+{|x|^2/{d(d-2)})^{d-2/2}} in dimension {d ≥ 7} , in the energy critical topology and without radial symmetry assumption. Given an initial data {Q + ɛ_0} with {|nabla ɛ_0|_{L^2} ≪ 1} , the solution either blows up in the ODE type I regime, or dissipates, and these two open sets are separated by a codimension one set of solutions asymptotically attracted by the solitary wave. In particular, non self similar type II blow up is ruled out in dimension {d ≥ 7} near the solitary wave even though it is known to occur in smaller dimensions (Schweyer, J Funct Anal 263(12):3922-3983, 2012). Our proof is based on sole energy estimates deeply connected to Martel et al. (Acta Math 212(1):59-140, 2014) and draws a route map for the classification of the flow near the solitary wave in the energy critical setting. A by-product of our method is the classification of minimal elements around Q belonging to the unstable manifold.
Energy Technology Data Exchange (ETDEWEB)
Ben Mahrsia, R.; Choubani, M., E-mail: mohsenchoubani3@yahoo.fr; Bouzaiene, L.; Maaref, H.
2016-06-25
In this paper we explore the structure parameters, hydrostatic pressure and temperature effects on Nonlinear optical rectification (NOR) in an asymmetric vertically coupled lens-shaped InAs/GaAs quantum dots. During epitaxial growth, lens-shaped quantum dots (QDs) are formed on the wetting layer (WL). Many theoretical works have neglected WL and its effect on nonlinear optical properties of QD-based systems for sake of simplicity. However, in this work the WL has been shown to be so influential in the intersubband energy and nonlinear optical rectification magnitude. Also, a detailed and comprehensive study of the nonlinear optical rectification is theoretical investigated within the framework of the compact density-matrix approach and finite difference method (FDM). It's found that nonlinear optical rectification coefficient is strongly affected not only by the WL, but also by the pressure, temperature and the coupled width between the QDs. Obtained results revealed that a red or a blue shift cane be observed. This behavior in the NOR gives a new degree of freedom in regions of interest for device applications. - Highlights: • Vertically coupled lens-shaped InAs/GaAs quantum dots is investigated. • Photon energy shifts towards the red with increasing pressure. • Photon energy shifts towards the blue with increasing temperature. • Intersubband energy decreases with increasing the wetting layer width. • Nonlinear optical rectification magnitude is controlled and adjusted.
Budroni, M. A.
2015-12-01
Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.
Fletcher, Tim; Ní Chróinín, Déirdre; O'Sullivan, Mary
2016-01-01
In this article we describe and interpret how two distinct layers of critical friendship were used to support a pedagogical innovation in pre-service teacher education. The innovation, "Learning about Meaningful Physical Education" (LAMPE), focuses on ways to teach future teachers to foster meaningful experiences for learners in physical…
Non-linear aspects of Görtler instability in boundary layers with pressure gradient
Rogenski, J. K.; de Souza, L. F.; Floryan, J. M.
2016-12-01
The laminar flow over a concave surface may undergo transition to a turbulent state driven by secondary instabilities initiated by the longitudinal vortices known as Görtler vortices. These vortices distort the boundary layer structure by modifying the streamwise velocity component in both spanwise and wall-normal directions. Numerical simulations have been conducted to identify the role of the external pressure gradients in the development and saturation of the vortices. The results show that flows with adverse pressure gradients reach saturation upstream from the saturation location for neutral and favorable pressure gradients. In the transition region, the mean spanwise shear stress is about three times larger than in the flow without the vortices.
Institute of Scientific and Technical Information of China (English)
Wenxiong Chen; Congming Li
2009-01-01
We classify all positive solutions for the following integral system……Here fi(u), 1≤i≤m, are real-valued functions of homogeneous degree n+α/n-α and aremonotone nondecreasing with respect to all the independent variables u1, u2, ..', um. In the special case n>3 and α= 2, we show that the above system is equivalent to the following elliptic PDE system………This system is closely related to the stationary Schrodinger system with critical exponents for Bose-Einstein condensate.
Strain-controlled criticality governs the nonlinear mechanics of fibre networks
Sharma, A; Rens, R; Sheinman, M; Jansen, K A; Koenderink, G H; MacKintosh, F C
2015-01-01
Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of connections between nodes exceeds the isostatic threshold are networks stable (Maxwell, J. C., Philosophical Magazine 27, 294 (1864)). Upon increasing the connectivity through this point, such networks undergo a mechanical phase transition from a floppy to a rigid phase. However, even sub-isostatic networks become rigid when subjected to sufficiently large deformations. To study this strain-controlled transition, we perform a combination of computational modeling of fibre networks and experiments on networks of type I collagen fibers, which are crucial for the integrity of biological tissues. We show theoretically that the development of rigidity is characterized by a strain-controlled continuous phase transition with signatures of criticality. Our experiments demonstrate mechanical...
Self-Organized Criticality in Astrophysics The Statistics of Nonlinear Processes in the Universe
Aschwanden, Markus
2011-01-01
The concept of ‘self-organized criticality’ (SOC) has been applied to a variety of problems, ranging from population growth and traffic jams to earthquakes, landslides and forest fires. The technique is now being applied to a wide range of phenomena in astrophysics, such as planetary magnetospheres, solar flares, cataclysmic variable stars, accretion disks, black holes and gamma-ray bursts, and also to phenomena in galactic physics and cosmology. Self-organized Criticality in Astrophysics introduces the concept of SOC and shows that, due to its universality and ubiquity, it is a law of nature. The theoretical framework and specific physical models are described, together with a range of applications in various aspects of astrophyics. The mathematical techniques, including the statistics of random processes, time series analysis, time scale and waiting time distributions, are presented and the results are applied to specific observations of astrophysical phenomena.
Scaling statistics in a critical, nonlinear physical model of tropical oceanic rainfall
Directory of Open Access Journals (Sweden)
K. M. Nordstrom
2003-01-01
Full Text Available Over the last two decades, concepts of scale invariance have come to the fore in both modeling and data analysis in hydrological precipitation research. With the advent of the use of the multiplicative random cascade model, these concepts have become increasingly more important. However, unifying this statistical view of the phenomenon with the physics of rainfall has proven to be a rather nontrivial task. In this paper, we present a simple model, developed entirely from qualitative physical arguments, without invoking any statistical assumptions, to represent tropical atmospheric convection over the ocean. The model is analyzed numerically. It shows that the data from the model rainfall look very spiky, as if generated from a random field model. They look qualitatively similar to real rainfall data sets from Global Atmospheric Research Program (GARP Atlantic Tropical Experiment (GATE. A critical point is found in a model parameter corresponding to the Convective Inhibition (CIN, at which rainfall changes abruptly from non-zero to a uniform zero value over the entire domain. Near the critical value of this parameter, the model rainfall field exhibits multifractal scaling determined from a fractional wetted area analysis and a moment scaling analysis. It therefore must exhibit long-range spatial correlations at this point, a situation qualitatively similar to that shown by multiplicative random cascade models and GATE rainfall data sets analyzed previously (Over and Gupta, 1994; Over, 1995. However, the scaling exponents associated with the model data are different from those estimated with real data. This comparison identifies a new theoretical framework for testing diverse physical hypotheses governing rainfall based in empirically observed scaling statistics.
Scaling statistics in a critical, nonlinear physical model of tropical oceanic rainfall
Nordstrom, K. M.; Gupta, V. K.
Over the last two decades, concepts of scale invariance have come to the fore in both modeling and data analysis in hydrological precipitation research. With the advent of the use of the multiplicative random cascade model, these concepts have become increasingly more important. However, unifying this statistical view of the phenomenon with the physics of rainfall has proven to be a rather nontrivial task. In this paper, we present a simple model, developed entirely from qualitative physical arguments, without invoking any statistical assumptions, to represent tropical atmospheric convection over the ocean. The model is analyzed numerically. It shows that the data from the model rainfall look very spiky, as if generated from a random field model. They look qualitatively similar to real rainfall data sets from Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE). A critical point is found in a model parameter corresponding to the Convective Inhibition (CIN), at which rainfall changes abruptly from non-zero to a uniform zero value over the entire domain. Near the critical value of this parameter, the model rainfall field exhibits multifractal scaling determined from a fractional wetted area analysis and a moment scaling analysis. It therefore must exhibit long-range spatial correlations at this point, a situation qualitatively similar to that shown by multiplicative random cascade models and GATE rainfall data sets analyzed previously (Over and Gupta, 1994; Over, 1995). However, the scaling exponents associated with the model data are different from those estimated with real data. This comparison identifies a new theoretical framework for testing diverse physical hypotheses governing rainfall based in empirically observed scaling statistics.
Directory of Open Access Journals (Sweden)
Jie Xiong
2013-01-01
Full Text Available 1 μm-thick YBa2Cu3O7-δ (YBCO films were grown on the Y2O3/yttria stabilized zirconia (YSZ/CeO2 buffer layers with different surface morphologies using direct-current sputtering. The critical current density (Jc value of YBCO was 1.1 MA/cm2 when the root mean square surface roughness (Rrms of the buffer layer was 2.5 nm. As the Rrms of the buffer layer increased to 15 nm, the Jc decreased to 0.3 MA/cm2. X-ray diffraction and scanning electron microscopy showed the strong relevance of the evolution of the structure and surface morphologies of YBCO films with the buffer layer of different Rrms. A model was proposed to explain the influence of surface morphology on the superconducting properties of YBCO films.
Wedin, Håkan; Cherubini, Stefania
2016-12-01
The asymptotic suction boundary layer (ASBL) is used for studying two permeability models, namely the Darcy and the Forchheimer model, the latter being more physically correct according to the literature. The term that defines the two apart is a function of the non-Darcian wall permeability {\\hat{K}}2 and of the wall suction {\\hat{V}}0, whereas the Darcian wall permeability {\\hat{K}}1 is common to the two models. The underlying interest of the study lies in the field of transition to turbulence where focus is put on two-dimensional nonlinear traveling waves (TWs) and their three-dimensional linear stability. Following a previous study by Wedin et al (2015 Phys. Rev. E 92 013022), where only the Darcy model was considered, the present work aims at comparing the two models, assessing where in the parameter space they cease to produce the same results. For low values of {\\hat{K}}1 both models produce almost identical TW solutions. However, when both increasing the suction {\\hat{V}}0 to sufficiently high amplitudes (i.e. lowering the Reynolds number Re, based on the displacement thickness) and using large values of the wall porosity, differences are observed. In terms of the non-dimensional Darcian wall permeability parameter, a, strong differences in the overall shape of the bifurcation curves are observed for a≳ 0.70, with the emergence of a new family of solutions at Re lower than 100. For these large values of a, a Forchheimer number {{Fo}}\\max ≳ 0.5 is found, where Fo expresses the ratio between the kinetic and viscous forces acting on the porous wall. Moreover, the minimum Reynolds number, {{Re}}g, for which the Navier-Stokes equations allow for nonlinear solutions, decreases for increasing values of a. Fixing the streamwise wavenumber to α = 0.154, as used in the study by Wedin et al referenced above, we find that {{Re}}g is lowered from Re ≈ 3000 for zero permeability, to below 50 for a = 0.80 for both permeability models. Finally, the stability of
Sturtevant, John L.; Liubich, Vlad; Gupta, Rachit
2016-04-01
Edge placement error (EPE) was a term initially introduced to describe the difference between predicted pattern contour edge and the design target for a single design layer. Strictly speaking, this quantity is not directly measurable in the fab. What is of vital importance is the relative edge placement errors between different design layers, and in the era of multipatterning, the different constituent mask sublayers for a single design layer. The critical dimensions (CD) and overlay between two layers can be measured in the fab, and there has always been a strong emphasis on control of overlay between design layers. The progress in this realm has been remarkable, accelerated in part at least by the proliferation of multipatterning, which reduces the available overlay budget by introducing a coupling of overlay and CD errors for the target layer. Computational lithography makes possible the full-chip assessment of two-layer edge to edge distances and two-layer contact overlap area. We will investigate examples of via-metal model-based analysis of CD and overlay errors. We will investigate both single patterning and double patterning. For single patterning, we show the advantage of contour-to-contour simulation over contour to target simulation, and how the addition of aberrations in the optical models can provide a more realistic CD-overlay process window (PW) for edge placement errors. For double patterning, the interaction of 4-layer CD and overlay errors is very complex, but we illustrate that not only can full-chip verification identify potential two-layer hotspots, the optical proximity correction engine can act to mitigate such hotspots and enlarge the joint CD-overlay PW.
Institute of Scientific and Technical Information of China (English)
Heinrich Hora; K. Jungwirth; B. Kralikova; J. Kraska; L. Laska; Liu Hong; G.H. Miley; P. Parys; Peng Hansheng; M. Pfeifer; K. Rohlena; Cang Yu; J. Skala; Z. Skladanowski; L. Torrisi; J. Ullschmied; J. Wolowski; Zhang Weiyan; He Xiantu; Zhang Jie; F. Osman; J. Badziak; F.P. Boody; S. Gammino; R. H(o)pfl
2004-01-01
The discovery of the essential difference of maximum ion energy for TW-ps laser plasma interaction compared with the 100 ns laser pulses [1] led to the theory of a skin layer model [2] where the control of prepulses suppressed the usual relativistic self-focusing. The subsequent generation of two nonlinear force driven blocks has been demonstrated experimentally and in extensive numerical studies where one block moves against the laser light and the other block into the irradiated target. These blocks of nearly solid state density DT plasma correspond to ion beam current densities [3] exceeding 1010 A/cm2 where the ion velocity can be chosen up to highly relativistic values. Using the results of the expected ignition of DT fuel by light ion beams, a selfsustained fusion reaction front may be generated even into uncompressed solid DT fuel similar to the Nuckolls-Wood [4] scheme where 10 kJ laser pulses produce 100 MJ fusion energy. This new and simplified scheme of laser-ICF needs and optimisation of the involved parameters.
The influence of impurity on the critical thickness of the CeO2 buffer layer for coated conductors
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The lattice parameters, band structure, density of state and elastic constant of RE-doped CeO2 (RE=Sm, Gd, Dy), the buffer material for coated HTS conductors, are calculated using the plane-wave method with pseudopotentials based on the density functional theory (DFT) of first-principle. The rule and mechanism of the effect of rare earth impurity on the critical thickness of the CeO2 buffer layer are investigated. It is found that, in the range of the calculation, the changes of the lattice volume V and elastic constant E of CeO2 with the impurity are mainly determined by the increased electrons ne of the system. The relationship of the elastic constant E and increased electrons ne is established. It is indicated that the critical thickness of the CeO2 single buffer layer doped with Sm, Gd, and Dy may be enhanced by 22%, 43% and 33%, respectively.
Alvan, Lucie; Decressin, Thibaut
2013-01-01
Internal gravity waves (hereafter IGWs) are known as one of the candidates for explaining the angular velocity profile in the Sun and in solar-type main-sequence and evolved stars, due to their role in the transport of angular momentum. Our bringing concerns critical layers, a process poorly explored in stellar physics, defined as the location where the local relative frequency of a given wave to the rotational frequency of the fluid tends to zero (i.e that corresponds to co-rotation resonances). IGW propagate through stably-stratified radiative regions, where they extract or deposit angular momentum through two processes: radiative and viscous dampings and critical layers. Our goal is to obtain a complete picture of the effects of this latters. First, we expose a mathematical resolution of the equation of propagation for IGWs in adiabatic and non-adiabatic cases near critical layers. Then, the use of a dynamical stellar evolution code, which treats the secular transport of angular momentum, allows us to appl...
Mustafa, Meraj; Mushtaq, Ammar; Hayat, Tasawar; Ahmad, Bashir
2014-01-01
The problem of natural convective boundary layer flow of nanofluid past a vertical plate is discussed in the presence of nonlinear radiative heat flux. The effects of magnetic field, Joule heating and viscous dissipation are also taken into consideration. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations via similarity transformations and then solved numerically using the Runge-Kutta fourth-fifth order method with shooting technique. The results reveal an existence of point of inflection for the temperature distribution for sufficiently large wall to ambient temperature ratio. Temperature and thermal boundary layer thickness increase as Brownian motion and thermophoretic effects intensify. Moreover temperature increases and heat transfer from the plate decreases with an increase in the radiation parameter.
Directory of Open Access Journals (Sweden)
Meraj Mustafa
Full Text Available The problem of natural convective boundary layer flow of nanofluid past a vertical plate is discussed in the presence of nonlinear radiative heat flux. The effects of magnetic field, Joule heating and viscous dissipation are also taken into consideration. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations via similarity transformations and then solved numerically using the Runge-Kutta fourth-fifth order method with shooting technique. The results reveal an existence of point of inflection for the temperature distribution for sufficiently large wall to ambient temperature ratio. Temperature and thermal boundary layer thickness increase as Brownian motion and thermophoretic effects intensify. Moreover temperature increases and heat transfer from the plate decreases with an increase in the radiation parameter.
Dong, Ningning; Li, Yuanxin; Zhang, Saifeng; McEvoy, Niall; Zhang, Xiaoyan; Cui, Yun; Zhang, Long; Duesberg, Georg S; Wang, Jun
2016-09-01
Both the nonlinear absorption and nonlinear refraction properties of WS2 and WSe2 semiconductor films have been characterized by using Z-scan technique with femtosecond pulses at the wavelength of 1040 nm. It is found that these films have two-photon absorption response with the nonlinear absorption coefficient of ∼103 cm GW-1, and a dispersion of nonlinear refractive index in the WS2 films that translated from positive in the monolayer to negative in bulk materials.
Institute of Scientific and Technical Information of China (English)
LU Chang-gen; CAO Wei-dong; QIAN Jian-hua
2006-01-01
A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional equations. The third-order mixed explicit-implicit scheme is employed for time integration. The treatment of the three-dimensional non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Anisotropy of Critical Fields in MgB2: Two-Band Ginzburg-Landau Theory for Layered Superconductors
Institute of Scientific and Technical Information of China (English)
I.N. Askerzade; B. Tanatar
2009-01-01
The temperature dependence of the anisotropy parameter of upper critical field γHc2 (T)= Hc2(T) / Hc2(T) and London penetration depth γλ(T) = λ(T)/λ (T) are calculated using two-band Ginzburg-Landau theory for layered superconductors. It is shown that, with decreasing temperature the anisotropy parameter γHc2 (T) is increased, while the London penetration depth anisotropy γλ (T) revea/s an opposite behavior. Results of our calculations are in agreement with experimental data for single crystal MgB2 and with other calculations. Results of an analysis of magnetic field Hc1 in a single vortex between superconducting layers are also presented.
Wei, Rongfei; Tian, Xiangling; Hu, Zhongliang; Zhang, Hang; Qiao, Tian; He, Xin; Chen, Qiuqun; Chen, Zhi; Qiu, Jianrong
2016-10-31
Vertical layered MoSsub>2sub> nanosheets rooting into TiOsub>2sub> nanofibers were successfully prepared by a facile two-step method: prefabrication of porous TiOsub>2sub> nanofibers based on an electrospinning technique, and assembly of MoSsub>2sub> ultrathin nanosheets through a simple hydrothermal reaction. Significant enhancement of nonlinear optical response of the MoSsub>2sub>/TiOsub>2sub> nanocomposite was confirmed by an open-aperture z-scan measurement. The nanocomposite displayed strong optical limiting (OL) effects to ultrafast laser pulses with a low OL threshold of ~22.3 mJ/cm2, which is lower than that of pristine TiOsub>2sub> nanofibers and MoSsub>2sub> nanosheets. In addition to the contribution of the strong nonlinear absorption of MoSsub>2sub> nanosheets and TiOsub>2sub> nanofibers, such phenomenon is also attributed to the unique structure of vertically standing layered MoSsub>2sub> nanosheets on TiOsub>2sub> nanofibers with a large amount of exposed edge states, large surface areas and fast electron transfer between TiOsub>2sub> and MoSsub>2sub>. This work broadens our vision to engineering novel hierarchical MoSsub>2sub>-based nanocomposite for efficiently enhanced nonlinear light-matter interaction.
Sahai, Aakash A
2014-01-01
We analyze the motion of the plasma critical layer by two different processes in the relativistic-electron laser-plasma interaction regime ($a_0>1$). The differences are highlighted when the critical layer ions are stationary in contrast to when they move with it. Controlling the speed of the plasma critical layer in this regime is essential for creating low-$\\beta$ traveling acceleration structures of sufficient laser-excited potential for laser ion accelerators (LIA). In Relativistically Induced Transparency Acceleration (RITA) scheme the heavy plasma-ions are fixed and only trace-density light-ions are accelerated. The relativistic critical layer and the acceleration structure move longitudinally forward by laser inducing transparency through apparent relativistic increase in electron mass. In the Radiation Pressure Acceleration (RPA) scheme the whole plasma is longitudinally pushed forward under the action of the laser radiation pressure, possible only when plasma ions co-propagate with the laser front. I...
Cehelsky, Priscilla; Tung, Ka Kit
1987-01-01
Previous results based on low- and intermediate-order truncations of the two-layer model suggest the existence of multiple equilibria and/or multiple weather regimes for the extratropical large-scale flow. The importance of the transient waves in the synoptic scales in organizing the large-scale flow and in the maintenance of weather regimes was emphasized. The result shows that multiple equilibria/weather regimes that are present in lower-order models examined disappear when a sufficient number of modes are kept in the spectral expansion of the solution to the governing partial differential equations. Much of the chaotic behavior of the large-scale flow that is present in intermediate-order models is now found to be spurious. Physical reasons for the drastic modification are offered. A peculiarity in the formulation of most existing two-layer models is noted that also tends to exaggerate the importance of baroclinic processes and increase the degree of unpredictability of the large-scale flow.
Krishnamurthy, M. R.; Gireesha, B. J.; Prasannakumara, B. C.; Gorla, Rama Subba Reddy
2016-09-01
A theoretically investigation has been performed to study the effects of thermal radiation and chemical reaction on MHD velocity slip boundary layer flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet. The Brownian motion and thermophoresis effects are incorporated in the present nanofluid model. A set of proper similarity variables is used to reduce the governing equations into a system of nonlinear ordinary differential equations. An efficient numerical method like Runge-Kutta-Fehlberg-45 order is used to solve the resultant equations for velocity, temperature and volume fraction of the nanoparticle. The effects of different flow parameters on flow fields are elucidated through graphs and tables. The present results have been compared with existing one for some limiting case and found excellent validation.
The influence of impurity on the critical thickness of the CeO2 buffer layer for coated conductors
Institute of Scientific and Technical Information of China (English)
PAN Min; HUANG Zheng; MA HuanFeng; QIANG WeiRong; WEI LianFu; WANG Long; ZHAO Yong
2009-01-01
The lattice parameters, band structure, density of state and elastic constant of RE-doped CeO2 (RE=Sm, Gd, Dy), the buffer material for coated HTS conductors, are calculated using the plane-wave method with paeudopotentials based on the density functional theory (DFT) of first-principle. The rule and mechanism of the effect of rare earth impurity on the critical thickness of the CeO2 buffer layer are in-vestigated. It is found that, in the range of the calculation, the changes of the lattice volume Ⅴ and elastic constant E* of CeO2 with the impurity are mainly determined by the increased electrons △ne of the system. The relationship of the elastic constant E* and increased electrons △ne is established. It is indicated that the critical thickness of the CeO2 single buffer layer doped with Sm, Gd, and Dy may be enhanced by 22%, 43% and 33%, respectively.
Laser-written binary OMOG photomasks for high-volume non-critical 193-nm photolithographic layers
Rivière, Rémi; Gopalakrishnan, Selvi; Mazur, Martin; Öner, Nevzat; Mühle, Sven; Seltmann, Rolf
2014-10-01
Photomasks are key elements of photolithographic processes, implying that their degradation must be reliably monitored and strongly mitigated. Indeed, the photo-induced oxidation of Cr in Cr On Glass (COG) photomasks and the concomitant electrostatic-field migration present in high-volume production using 193-nm photolithographic scanners severely deteriorate the pattern transfer quality, therefore limiting the lifetime of these reticles. To moderate this effect, Opaque MoSi On Glass (OMOG) photomasks, significantly less prone to such degradation, are currently being massively used in leading-edge microfabrication flows. The type of mask fabrication process normally used involving ebeam writing is however not adapted for non-critical photolithographic layers that do not yet benefit from its inherent performances but still suffer from its high cost and its long processing time. It is therefore proposed in this work to combine the simplicity of laser writing and the resistance of MoSi to degradation by using laser-written binary OMOG photomasks for the non-critical layers (e.g. ion-implantation) of a 28-nm production flow. To evaluate one of this new reticle, its pattern transfer fidelity is compared to the one of a laser-written binary COG mask already qualified for production from a photolithographic quality perspective, both masks being treated using the same optical proximity correction (OPC) model. Dispersive and dissipative properties, critical dimension uniformity, pattern linearity and pattern proximity are directly measured on wafer level, subsequently revealing that both photomasks match in terms of OPC parameters. The utilized OPC model is moreover proven robust against the use of both types of masks, consequently making the conversion from COG to OMOG particularly simple. These experimental results therefore qualify the new mask fabrication type and pave the way for a major utilization in high-volume production.
Institute of Scientific and Technical Information of China (English)
Muhaimin; R. Kandasamy; Azme B. Khamis
2008-01-01
This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2017-03-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2016-12-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
Montgomery, M. T.; Wang, Z.; Dunkerton, T. J.
2010-11-01
Recent work has hypothesized that tropical cyclones in the deep Atlantic and eastern Pacific basins develop from within the cyclonic Kelvin cat's eye of a tropical easterly wave critical layer located equatorward of the easterly jet axis. The cyclonic critical layer is thought to be important to tropical cyclogenesis because its cat's eye provides (i) a region of cyclonic vorticity and weak deformation by the resolved flow, (ii) containment of moisture entrained by the developing flow and/or lofted by deep convection therein, (iii) confinement of mesoscale vortex aggregation, (iv) a predominantly convective type of heating profile, and (v) maintenance or enhancement of the parent wave until the developing proto-vortex becomes a self-sustaining entity and emerges from the wave as a tropical depression. This genesis sequence and the overarching framework for describing how such hybrid wave-vortex structures become tropical depressions/storms is likened to the development of a marsupial infant in its mother's pouch, and for this reason has been dubbed the "marsupial paradigm". Here we conduct the first multi-scale test of the marsupial paradigm in an idealized setting by revisiting the Kurihara and Tuleya problem examining the transformation of an easterly wave-like disturbance into a tropical storm vortex using the WRF model. An analysis of the evolving winds, equivalent potential temperature, and relative vertical vorticity is presented from coarse (28 km), intermediate (9 km) and high resolution (3.1 km) simulations. The results are found to support key elements of the marsupial paradigm by demonstrating the existence of a rotationally dominant region with minimal strain/shear deformation near the center of the critical layer pouch that contains strong cyclonic vorticity and high saturation fraction. This localized region within the pouch serves as the "attractor" for an upscale "bottom up" development process while the wave pouch and proto-vortex move together
Directory of Open Access Journals (Sweden)
M. T. Montgomery
2010-11-01
Full Text Available Recent work has hypothesized that tropical cyclones in the deep Atlantic and eastern Pacific basins develop from within the cyclonic Kelvin cat's eye of a tropical easterly wave critical layer located equatorward of the easterly jet axis. The cyclonic critical layer is thought to be important to tropical cyclogenesis because its cat's eye provides (i a region of cyclonic vorticity and weak deformation by the resolved flow, (ii containment of moisture entrained by the developing flow and/or lofted by deep convection therein, (iii confinement of mesoscale vortex aggregation, (iv a predominantly convective type of heating profile, and (v maintenance or enhancement of the parent wave until the developing proto-vortex becomes a self-sustaining entity and emerges from the wave as a tropical depression. This genesis sequence and the overarching framework for describing how such hybrid wave-vortex structures become tropical depressions/storms is likened to the development of a marsupial infant in its mother's pouch, and for this reason has been dubbed the "marsupial paradigm".
Here we conduct the first multi-scale test of the marsupial paradigm in an idealized setting by revisiting the Kurihara and Tuleya problem examining the transformation of an easterly wave-like disturbance into a tropical storm vortex using the WRF model. An analysis of the evolving winds, equivalent potential temperature, and relative vertical vorticity is presented from coarse (28 km, intermediate (9 km and high resolution (3.1 km simulations. The results are found to support key elements of the marsupial paradigm by demonstrating the existence of a rotationally dominant region with minimal strain/shear deformation near the center of the critical layer pouch that contains strong cyclonic vorticity and high saturation fraction. This localized region within the pouch serves as the "attractor" for an upscale "bottom up" development process while the wave
Directory of Open Access Journals (Sweden)
T. J. Dunkerton
2009-12-01
Full Text Available Recent work has hypothesized that tropical cyclones in the deep Atlantic and eastern Pacific basins develop from the cyclonic Kelvin cat's eye of a tropical easterly wave critical layer located equatorward of the easterly jet axis that typifies the trade wind belt. The cyclonic critical layer is thought to be important to tropical cyclogenesis because its cat's eye provides (i a region of cyclonic vorticity and weak deformation by the resolved flow, (ii containment of moisture entrained by the developing flow and/or lofted by deep convection therein, (iii confinement of mesoscale vortex aggregation, (iv a predominantly convective type of heating profile, and (v maintenance or enhancement of the parent wave until the developing proto-vortex becomes a self-sustaining entity and emerges from the wave as a tropical depression. This genesis sequence and the overarching framework for describing how such hybrid wave-vortex structures become tropical depressions/storms is likened to the development of a marsupial infant in its mother's pouch, and for this reason has been dubbed the "marsupial paradigm".
Here we conduct the first multi-scale test of the marsupial paradigm in an idealized setting by revisiting the problem of the transformation of an easterly wave-like disturbance into a tropical storm vortex using the WRF model. An analysis of the evolving winds, equivalent potential temperature, and relative vertical vorticity is presented from coarse (28 km and high resolution (3.1 km simulations. The results are found to support key elements of the marsupial paradigm by demonstrating the existence of a vorticity dominant region with minimal strain/shear deformation within the critical layer pouch that contains strong cyclonic vorticity and high saturation fraction. This localized region within the pouch serves as the "attractor" for an upscale "bottom up" development process while the wave pouch and proto-vortex move together.
Energy Technology Data Exchange (ETDEWEB)
Sahai, Aakash A., E-mail: aakash.sahai@gmail.com [Department of Electrical Engineering, Duke University, Durham, North Carolina 27708 (United States)
2014-05-15
We analyze the motion of the plasma critical layer by two different processes in the relativistic-electron laser-plasma interaction regime (a{sub 0}>1). The differences are highlighted when the critical layer ions are stationary in contrast to when they move with it. Controlling the speed of the plasma critical layer in this regime is essential for creating low-β traveling acceleration structures of sufficient laser-excited potential for laser ion accelerators. In Relativistically Induced Transparency Acceleration (RITA) scheme, the heavy plasma-ions are fixed and only trace-density light-ions are accelerated. The relativistic critical layer and the acceleration structure move longitudinally forward by laser inducing transparency through apparent relativistic increase in electron mass. In the Radiation Pressure Acceleration (RPA) scheme, the whole plasma is longitudinally pushed forward under the action of the laser radiation pressure, possible only when plasma ions co-propagate with the laser front. In RPA, the acceleration structure velocity critically depends upon plasma-ion mass in addition to the laser intensity and plasma density. In RITA, mass of the heavy immobile plasma-ions does not affect the speed of the critical layer. Inertia of the bared immobile ions in RITA excites the charge separation potential, whereas RPA is not possible when ions are stationary.
Sahai, Aakash A.
2014-05-01
We analyze the motion of the plasma critical layer by two different processes in the relativistic-electron laser-plasma interaction regime (a0>1). The differences are highlighted when the critical layer ions are stationary in contrast to when they move with it. Controlling the speed of the plasma critical layer in this regime is essential for creating low-β traveling acceleration structures of sufficient laser-excited potential for laser ion accelerators. In Relativistically Induced Transparency Acceleration (RITA) scheme, the heavy plasma-ions are fixed and only trace-density light-ions are accelerated. The relativistic critical layer and the acceleration structure move longitudinally forward by laser inducing transparency through apparent relativistic increase in electron mass. In the Radiation Pressure Acceleration (RPA) scheme, the whole plasma is longitudinally pushed forward under the action of the laser radiation pressure, possible only when plasma ions co-propagate with the laser front. In RPA, the acceleration structure velocity critically depends upon plasma-ion mass in addition to the laser intensity and plasma density. In RITA, mass of the heavy immobile plasma-ions does not affect the speed of the critical layer. Inertia of the bared immobile ions in RITA excites the charge separation potential, whereas RPA is not possible when ions are stationary.
Grachev, Andrey A; Fairall, Christopher W; Guest, Peter S; Persson, P Ola G
2012-01-01
Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin-Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on spectral analysis of wind velocity and air temperature fluctuations, it is shown that when both gradient Richardson number, Ri, and flux Richardson number, Rf, exceed a 'critical value' about 0.20-0.25, the inertial subrange associated with the Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in the supercritical regime, but this is non-Kolmogorov turbulence and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Kolmogorov...
Energy Technology Data Exchange (ETDEWEB)
Asai, M.; Aiba, K. [Tokyo Metropolitan Institute of Technology, Tokyo (Japan)
1995-09-01
Low-frequency Tollmien-Schlichting (T-S) waves may be thought generated as a result of high-frequency disturbance between two proximity frequency modes grown unstably in a separation shear layer causing secondary nonlinear interference to occur. This fact has been verified by a numerical simulation. A non-compression Navier-Stokes equation was used for the fundamental equation, a tertiary windward difference for the convection term, and a secondary central difference for other differential calculus. The Reynolds number was 200, and the disturbance was introduced by applying `v` variation continuously on the wall face. Non-introduction of the disturbance results in a steady flow. Disturbance frequencies of 0.15 and 0.20 were selected as disturbance frequencies from the relationship between the spatial amplification and the frequency dependency. The structure of the excited disturbance agreed with the intrinsic mode. The difference mode due to nonlinear interference grows as the basic mode was amplified. The basic mode decays sharply in the boundary layer after reattachment, while the difference mode decays slowly. Distribution of the difference mode is a distribution of viscous T-S waves, which may be converted into the intrinsic mode. 8 refs., 7 figs.
Energy Technology Data Exchange (ETDEWEB)
Yoon, Seok-Hyun, E-mail: seokhyun72.yoon@samsung.com; Kim, Mi-Yang [LCR Materials Group, Corporate R& D Institute, Samsung Electro-Mechanics Co., Ltd., Suwon, Gyunggi-Do 443-743 (Korea, Republic of)
2016-06-13
Temperature dependence of the dielectric nonlinearity was investigated for the BaTiO{sub 3} multilayer ceramic capacitor. The decrease in temperature caused a significant increase in the degree of dielectric nonlinearity. The Preisach analysis shows that such effect corresponds to a decrease in reversible and a significant increase in irreversible domain wall contribution to polarization. The magnitude of spontaneous polarization (P{sub S}) was increased with decreasing temperature. It can be associated with phase transition from pseudo-cubic to monoclinic and its resultant change in the polar direction, which was observed through transmission electron microscopy. These results demonstrate that the increase in P{sub S} with the decrease in temperature inhibits domain wall motion in low driving field as it is anticipated to increase the degree of intergranular constraints during domain wall motion. But it results in a more steep increase in the dielectric constants beyond the threshold field where domain wall motion can occur.
Vaithiyalingam, Sivakumar R; Sayeed, Vilayat A
2010-10-15
Advancement in the fields of material science, analytical methodologies, instrumentation, automation, continuous monitoring, feed forward/feed back control and comprehensive data collection have led to continual improvement of pharmaceutical tablet manufacturing technology, notably the multi-layer tablets. This review highlights the material attributes, formulation design, process parameters that impact the performance, and manufacturability of the multi-layer tablets. It also highlights on critical-to-quality elements that needs to be addressed in the regulatory submission.
Genesis of Pre-Hurricane Felix (2007). Part 1; The Role of the Easterly Wave Critical Layer
Wang, Zhuo; Montgomery, M. T.; Dunkerton, T. J.
2010-01-01
The formation of pre Hurricane Felix (2007) in a tropical easterly wave is examined in a two-part study using the Weather Research and Forecasting (WRF) model with a high-resolution nested grid configuration that permits the representation of cloud system processes. The simulation commences during the wave stage of the precursor African easterly-wave disturbance. Here the simulated and observed developments are compared, while in Part II of the study various large-scale analyses, physical parameterizations, and initialization times are explored to document model sensitivities. In this first part the authors focus on the wave/vortex morphology, its interaction with the adjacent intertropical convergence zone complex, and the vorticity balance in the neighborhood of the developing storm. Analysis of the model simulation points to a bottom-up development process within the wave critical layer and supports the three new hypotheses of tropical cyclone formation proposed recently by Dunkerton, Montgomery, and Wang. It is shown also that low-level convergence associated with the ITCZ helps to enhance the wave signal and extend the "wave pouch" from the jet level to the top of the atmospheric boundary layer. The region of a quasi-closed Lagrangian circulation within the wave pouch provides a focal point for diabatic merger of convective vortices and their vortical remnants. The wave pouch serves also to protect the moist air inside from dry air intrusion, providing a favorable environment for sustained deep convection. Consistent with the authors' earlier findings, the tropical storm forms near the center of the wave pouch via system-scale convergence in the lower troposphere and vorticity aggregation. Components of the vorticity balance are shown to be scale dependent, with the immediate effects of cloud processes confined more closely to the storm center than the overturning Eliassen circulation induced by diabatic heating, the influence of which extends to larger radii.
Du, Jiangfeng; Chen, Nanting; Jiang, Zhiguang; Bai, Zhiyuan; Liu, Yong; Liu, Yang; Yu, Qi
2016-01-01
DC and pulsed transfer characteristics of AlGaN/GaN high electron mobility transistors (HEMTs) have been systematically investigated. A significant difference of transconductance linearity between DC and gate-pulsed measurements is clearly observed. The acceptor-like traps in the barrier layer under the gate is the main cause of non-linear behavior of AlGaN/GaN HEMTs transconductance. A physical model has been constructed to explain the phenomenon. In the modeling, an acceptor-like trap concentration of 1.2 × 1019 cm-3 with an energy level of 0.5 eV below the conduction band minimum shows the best fit to measurement results.
Agarwal, Shilpi; Rana, Puneet
2016-04-01
In this paper, we examine a layer of Oldroyd-B nanofluid for linear and nonlinear regimes under local thermal non-equilibrium conditions for the classical Rayleigh-Bénard problem. The free-free boundary condition has been implemented with the flux for nanoparticle concentration being zero at edges. The Oberbeck-Boussinesq approximation holds good and for the rotational effect Coriolis term is included in the momentum equation. A two-temperature model explains the effect of local thermal non-equilibrium among the particle and fluid phases. The criteria for onset of stationary convection has been derived as a function of the non-dimensionalized parameters involved including the Taylor number. The assumed boundary conditions negate the possibility of overstability due to the absence of opposing forces responsible for it. The thermal Nusselt number has been obtained utilizing a weak nonlinear theory in terms of various pertinent parameters in the steady and transient mode, and has been depicted graphically. The main findings signify that the rotation has a stabilizing effect on the system. The stress relaxation parameter λ_1 inhibits whereas the strain retardation parameter λ_2 exhibits heat transfer utilizing Al2O3 nanofluids.
Energy Technology Data Exchange (ETDEWEB)
Tiginyanu, I.M.; Kravetsky, I.V.; Pavlidis, D.; Eisenbach, A.; Hildebrandt, R.; Marowsky, G.; Hartnagel, H.L.
2000-07-01
Optical second and third harmonic generation measurements were carried out on GaN layers grown by metalorganic chemical vapor deposition (MOCVD) on sapphire substrates. The measured d{sub 33} is 33 times the d{sub 11} of quartz. The angular dependence of second-harmonic intensity as well as the measured ratios d{sub 33}/d{sub 15} = {minus}2.02 and d{sub 33}/d{sub 31} = {minus}2.03 confirm the wurzite structure of the studied GaN layers with the optical c-axis oriented perpendicular to the sample surface. Fine oscillations were observed in the measured second and third harmonic angular dependencies. A simple model based on the interference of the fundamental beam in the sample was used to explain these oscillations.
Kenpankho, Prasert; Ishii, Mamoru; Supnithi, Pornchai
2016-07-01
We investigate the values of the critical frequency of the ionospheric E layer, foE, obtained at Chumphon ionospheric observatory station, Thailand. For a declining phase of the solar cycle 23 during the year 2005-2008 and an inclining phase of the solar cycle 24 during the year 2009-2013, the foE data have been used to investigate the foE variations over the equatorial geomagnetic region in Southeast Asia. A comparison between the observation data and International Reference Ionosphere (IRI) 2012 model has also been investigated and studied. The results show that the foE obtained from IRI 2012 model underestimates foE from Chumphon station especially during the period of 7-11 am and after 6 pm for each day and all seasons. As the results combining with the previous investigations, we suggest that the underestimation of ionospheric foE by IRI 2012 model is helpful for the correction and improvement of IRI model in an equatorial Asia region.
Grachev, Andrey A.; Andreas, Edgar L.; Fairall, Christopher W.; Guest, Peter S.; Persson, P. Ola G.
2013-04-01
Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin-Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity and air temperature fluctuations, it is shown that, when both the gradient Richardson number, Ri, and the flux Richardson number, Rf, exceed a `critical value' of about 0.20-0.25, the inertial subrange associated with the Richardson-Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in this supercritical regime, but this is non-Kolmogorov turbulence, and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Richardson-Kolmogorov energy cascade weakens; therefore, the applicability of local Monin-Obukhov similarity theory in stable conditions is limited by the inequalities Ri < Ri cr and Rf < Rf cr. However, it is found that Rf cr = 0.20-0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin-Obukhov local z-less predictions after the irrelevant cases (turbulence without the Richardson-Kolmogorov cascade) have been filtered out.
Energy Technology Data Exchange (ETDEWEB)
Karniadakis, George Em; Vanden-Eijnden, Eric; Lin, Guang; Wan, Xiaoliang
2013-04-03
In this project, the collective efforts of all co-PIs aim to address three current limitations in modeling stochastic systems: (1) the inputs are mostly based on ad hoc models, (2) the number of independent parameters is very high, and (3) rare and critical events are difficult to capture with existing algorithms
一类临界增长非线性椭圆方程的解%On a Class of Nonlinear Elliptic Equation at Critical Growth
Institute of Scientific and Technical Information of China (English)
章国庆; 刘三阳
2005-01-01
Using nonsmooth critical point theory, the existence of nontrivial positive solution for thefollowing nonlinear elliptic equation at critical growth is proved{-div(A(x,u) |()u|p-2()u)+1/p A′u(x,u) |()u|p=g(x,u)+|u|p*-2u,Ω;u= 0,where 1 ＜ p ＜ n2 ,g(x,0) = 0 and g(x,u) is a subcritical term, p*=np/n- p is the critical Sobolev exponent.%利用非光滑临界点理论,本文证明了一类临界增长非线性椭圆方程{-div(A(x,u) |()u|p-2()u)+1/p A′u(x,u) |()u|p=g(x,u)+|u|p*-2u,Ω;非平凡u= 0, ( )Ω正解的存在性.其中1＜p＜n2,g(x,0)=0且g(x,u)为一次临界项,p*=np/n-p是临界Sobolev指数.
2010-01-01
Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive algorithm is presented for online learning based on matrix operation and optimization methods analytically, which can avoid the trouble to select a proper learning rate for the gradient method. The proof of weak convergence of the proposed algorithm also is given...
Zhao, Hua; Xue, Tingyu; Fu, Jiayin; Zhang, Jingwen
2015-09-01
With ZnSe thin films as aligning layers in fabricating liquid crystal (LC) panel with pentylcyanobiphenyl doped with C60, the response time in writing holograms was shortened to milliseconds. When two laser beams were overlapped in an LC panel, 2D diffraction patterns were observed, along with exponential gain coefficient highly LC and ZnSe thickness dependent. In addition, energy transferring in subwavelength scale through surface grating was evident. By using a hybrid LC panel, it was found the energy transferring direction was voltage polarity and thickness dependent. Electrostatic modification based surface plasmon polariton excitation was proposed to explain all the findings
Directory of Open Access Journals (Sweden)
V. K. Karastathis
2010-11-01
Full Text Available We examine the possible non-linear behaviour of potentially liquefiable layers at selected sites located within the expansion area of the town of Nafplion, East Peloponnese, Greece. Input motion is computed for three scenario earthquakes, selected on the basis of historical seismicity data, using a stochastic strong ground motion simulation technique, which takes into account the finite dimensions of the earthquake sources. Site-specific ground acceleration synthetics and soil profiles are then used to evaluate the liquefaction potential at the sites of interest. The activation scenario of the Iria fault, which is the closest one to Nafplion (M=6.4, is found to be the most hazardous in terms of liquefaction initiation. In this scenario almost all the examined sites exhibit liquefaction features at depths of 6–12 m. For scenario earthquakes at two more distant seismic sources (Epidaurus fault – M6.3; Xylokastro fault – M6.7 strong ground motion amplification phenomena by the shallow soft soil layer are expected to be observed.
Quantum well nonlinear microcavities
Oudar, J. L.; Kuszelewicz, R.; Sfez, B.; Pellat, D.; Azoulay, R.
We report on recent progress in reducing the power threshold of all-optical bistable quantum well vertical microcavities. Significant improvements are achieved through an increase of the cavity finesse, together with a reduction of the device active layer thickness. A critical intensity of 5 μW/μm 2 has been observed on a microcavity of finesse 250, with a nonlinear medium of only 18 GaAs quantum wells of 10 nm thickness. Further improvements of the Bragg mirror quality resulted in a finesse of 700 and a power-lifetime product of 15 fJ/μm 2. Microresonator pixellation allows to obtain 2-dimensional arrays. A thermally-induced alloy-mixing technique is described, which produced a 110 meV carrier confinement energy, together with a refractive index change of -.012, averaged over the 2.6 μm nonlinear medium thickness. The resulting electrical and optical confinement is shown to improve the nonlinear characteristics, by limiting lateral carrier diffusion and light diffraction.
On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer-Wise Relevance Propagation.
Directory of Open Access Journals (Sweden)
Sebastian Bach
Full Text Available Understanding and interpreting classification decisions of automated image classification systems is of high value in many applications, as it allows to verify the reasoning of the system and provides additional information to the human expert. Although machine learning methods are solving very successfully a plethora of tasks, they have in most cases the disadvantage of acting as a black box, not providing any information about what made them arrive at a particular decision. This work proposes a general solution to the problem of understanding classification decisions by pixel-wise decomposition of nonlinear classifiers. We introduce a methodology that allows to visualize the contributions of single pixels to predictions for kernel-based classifiers over Bag of Words features and for multilayered neural networks. These pixel contributions can be visualized as heatmaps and are provided to a human expert who can intuitively not only verify the validity of the classification decision, but also focus further analysis on regions of potential interest. We evaluate our method for classifiers trained on PASCAL VOC 2009 images, synthetic image data containing geometric shapes, the MNIST handwritten digits data set and for the pre-trained ImageNet model available as part of the Caffe open source package.
Thompson, C. J.; Croke, J. C.; Grove, J. R.
2012-04-01
Non-linearity in physical systems provides a conceptual framework to explain complex patterns and form that are derived from complex internal dynamics rather than external forcings, and can be used to inform modeling and improve landscape management. One process that has been investigated previously to explore the existence of self-organised critical system (SOC) in river systems at the basin-scale is bank failure. Spatial trends in bank failure have been previously quantified to determine if the distribution of bank failures at the basin scale exhibit the necessary power law magnitude/frequency distributions. More commonly bank failures are investigated at a small-scale using several cross-sections with strong emphasis on local-scale factors such as bank height, cohesion and hydraulic properties. Advancing our understanding of non-linearity in such processes, however, requires many more studies where both the spatial and temporal measurements of the process can be used to investigate the existence or otherwise of non-linearity and self-organised criticality. This study presents measurements of bank failure throughout the Lockyer catchment in southeast Queensland, Australia, which experienced an extreme flood event in January 2011 resulting in the loss of human lives and geomorphic channel change. The most dominant form of fluvial adjustment consisted of changes in channel geometry and notably widespread bank failures, which were readily identifiable as 'scalloped' shaped failure scarps. The spatial extents of these were mapped using high-resolution LiDAR derived digital elevation model and were verified by field surveys and air photos. Pre-flood event LiDAR coverage for the catchment also existed allowing direct comparison of the magnitude and frequency of bank failures from both pre and post-flood time periods. Data were collected and analysed within a GIS framework and investigated for power-law relationships. Bank failures appeared random and occurred
NONLINEAR DYNAMICAL BIFURCATION AND CHAOTIC MOTION OF SHALLOW CONICAL LATTICE SHELL
Institute of Scientific and Technical Information of China (English)
WANG Xin-zhi; HAN Ming-jun; ZHAO Yan-ying; ZHAO Yong-gang
2006-01-01
The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.
Cao, Bing; Heale, Christopher J.; Guo, Yafang; Liu, Alan Z.; Snively, Jonathan B.
2016-11-01
A complex gravity wave event was observed from 04:30 to 08:10 UTC on 16 January 2015 by a narrow-band sodium lidar and an all-sky airglow imager located at Andes Lidar Observatory (ALO) in Cerro Pachón (30.25°S, 70.73°W), Chile. The gravity wave packet had a period of 18-35 min and a horizontal wavelength of about 40-50 km. Strong enhancements of the vertical wind perturbation, exceeding 10 m s-1, were found at ˜90 km and ˜103 km, consistent with nearly evanescent wave behavior near a reflection layer. A reduction in vertical wavelength was found as the phase speed approached the background wind speed near ˜93 km. A distinct three-layered structure was observed in the lidar data due to refraction of the wave packet. A fully nonlinear model was used to simulate this event, which successfully reproduced the amplitudes and layered structure seen in observations. The model results provide dynamical insight, suggesting that a double reflection occurring at two separate heights caused the large vertical wind amplitudes, while the three-layered structure in the temperature perturbation was a result of relatively stable regions at those altitudes. The event provides a clear perspective on the filtering processes to which short-period, small-scale gravity waves are subject in mesosphere and lower thermosphere.
Energy Technology Data Exchange (ETDEWEB)
Serletis, Apostolos [Department of Economics, University of Calgary, Calgary, Alta., T2N 1N4 (Canada)]. E-mail: Serletis@ucalgary.ca; Shahmoradi, Asghar [Faculty of Economics, University of Tehran, Tehran (Iran, Islamic Republic of)
2007-08-15
This paper uses monthly observations for the real exchange rate between Canada and the United States over the recent flexible exchange rate period (from January 1, 1973 to August 1, 2004) to test purchasing power parity between Canada and the United States using unit root and stationarity tests. Moreover, given the apparent random walk behavior in the real exchange rate, various tests from dynamical systems theory, such as for example, the Nychka et al. [Nychka DW, Ellner S, Ronald GA, McCaffrey D. Finding chaos in noisy systems. J Roy Stat Soc B 1992;54:399-426] chaos test, the Li [Li W. Absence of 1/f spectra in Dow Jones average. Int J Bifurcat Chaos 1991;1:583-97] self-organized criticality test, and the Hansen [Hansen, B.E. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 1996;64:413-30] threshold effects test are used to distinguish between stochastic and deterministic origin for the real exchange rate.
Zalian, Cyrus
2016-01-01
Context. The Blazhko effect, in RR Lyrae type stars, is a century old mystery. Dozens of theory exists, but none have been able to entirely reproduce the observational facts associated to this modulation phenomenon. Existing theory all rely on the usual continuous modelization of the star. Aims. We present a new paradigm which will not only explain the Blazhko effect, but at the same time, will give us alternative explanations to the red limit of the instability strip, the synchronization of layers, the mode selection and the existence of a limit cycle for radially pulsating stars. Methods. We describe the RR Lyrae type pulsating stars as a system of coupled nonlinear oscillators. Considering a spatial discretisation of the star, supposing a spherical symmetry, we develop the equation of motion and energy up to the third order in the radial and adiabatic case. Then, we include the influence of the ionization region as a relaxation oscillator by including elements from synchronisation theory. Results. This dis...
Huang, Like; Xu, Jie; Sun, Xiaoxiang; Du, Yangyang; Cai, Hongkun; Ni, Jian; Li, Juan; Hu, Ziyang; Zhang, Jianjun
2016-04-20
Currently, most efficient perovskite solar cells (PVKSCs) with a p-i-n structure require simultaneously electron transport layers (ETLs) and hole transport layers (HTLs) to help collecting photogenerated electrons and holes for obtaining high performance. ETL free planar PVKSC is a relatively new and simple structured solar cell that gets rid of the complex and high temperature required ETL (such as compact and mesoporous TiO2). Here, we demonstrate the critical role of high coverage of perovskite in efficient ETL free PVKSCs from an energy band and equivalent circuit model perspective. From an electrical point of view, we confirmed that the low coverage of perovskite does cause localized short circuit of the device. With coverage optimization, a planar p-i-n(++) device with a power conversion efficiency of over 11% was achieved, implying that the ETL layer may not be necessary for an efficient device as long as the perovskite coverage is approaching 100%.
Qin, Xiaofa; Sheth, Sharvil U; Sharpe, Susan M; Dong, Wei; Lu, Qi; Xu, Dazhong; Deitch, Edwin A
2011-03-01
It is well documented that the gut injury plays a critical role in the development of systemic inflammation and distant organ injury in conditions associated with splanchnic ischemia. Consequently, understanding the mechanisms leading to gut injury is important. In this context, recent work suggests a protective role for the intestinal mucus layer and an injury-inducing role for luminal pancreatic proteases. Thus, we explored the role of the mucus layer in gut barrier function by observing how the removal of the mucus layer affects ischemia-reperfusion-mediated gut injury in rats as well as the potential role of luminal pancreatic proteases in the pathogenesis of gut injury. Ischemia was induced by the ligation of blood vessels to segments of the ileum for 45 min, followed by up to 3 h of reperfusion. The ileal segments were divided into five groups. These included a nonischemic control, ischemic segments exposed to saline, the mucolytic N-acetylcysteine (NAC), pancreatic proteases, or NAC + pancreatic proteases. Changes in gut barrier function were assessed by the permeation of fluorescein isothiocyanate dextran (molecular weight, 4,000 d) in ileal everted sacs. Gut injury was measured morphologically and by the luminal content of protein, DNA, and hemoglobin. The mucus layer was assessed functionally by measuring its hydrophobicity and morphologically. Gut barrier function was promptly and effectively reestablished during reperfusion, which was accompanied by the restoration of the mucus layer. In contrast, treatment of the gut with the mucolytic NAC for 10 min during ischemia resulted in a failure of mucus restitution and further increases in gut permeability and injury. The presence of digestive proteases by themselves did not exacerbate gut injury, but in combination with NAC, they caused an even greater increase in gut injury and permeability. These results suggest that the mucus layer not only serves as a barrier between the luminal contents and gut surface
Institute of Scientific and Technical Information of China (English)
徐云滨; 郑连存
2008-01-01
A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied. Sufficient conditions for the existence and uniqueness of positive solutions to the problems are established by utilizing the monotonic approaching technique. And a theoretical estimate formula for skin friction coefficient is presented. The numerical solution is presented by using the shoot method. The reliability and efficiency of the theoretical prediction are verified by numerical results.
Eaton, D F
1991-07-19
The current state of materials development in nonlinear optics is summarized, and the promise of these materials is critically evaluated. Properties and important materials constants of current commercial materials and of new, promising, inorganic and organic molecular and polymeric materials with potential in second- and third-order nonlinear optical applications are presented.
Ceres, F.; Chirico, G. B.; Romano, N.
2009-04-01
Field water capacity and available water concepts are major agronomic parameters widely used for irrigation management, especially in Mediterranean zones facing with shortage of water. However, their definitions are still under discussion among scientists and practitioners. Field water capacity is often determined using empirical relationships (e.g. pedotransfer functions) or from water retention points obtained in the laboratory, thus underplaying or even ignoring the important role exerted by the actual evolution of water redistribution processes in a soil profile, especially if it is a layered one. An objective and replicable method for determining the field water capacity requires monitoring a water redistribution process evolving in a soil profile thoroughly wetted by a preliminary infiltration phase. Accordingly, in this study free drainage processes in soil profiles have been simulated by applying the numerical model developed by Romano et al. (1998) and verified by Brunone et al. (2003). This model solves Richards' equation by applying the Crank-Nicolson finite difference technique and uses a numerical algorithm specifically designed in case of layered soils for calculating the hydraulic conductivity between soil layers. In addition, to ensure a good correspondence between the analyses performed and actual situations, an extensive database of uniform and layered soil profiles have been employed. Outcome from the scenarios on uniform soils have shown that soil water content values under the condition of field capacity do not match water content values obtained from water retention point measured at preselected matric pressure head. Similar results have been obtained when using retention data points retrieved from the use of well-established pedotransfer functions (such as the HYPRES-PTF). In case of layered soil profiles, which actually represent the rule rather than an exception, the layer sequence and reciprocal differences in the soil hydraulic properties
Lapicque, Francois; Belhadj, Mariem; Bonnet, Caroline; Pauchet, Joël; Thomas, Yohann
2016-12-01
Formerly considered as a secondary component of fuel cell, gas diffusion layers (GDLs) have been shown to have a key role in gas transport to the catalyst layers and in water management: in particular, the microporous layer (MPL) deposited on the diffusion substrate has an active part in water distribution in the membrane electrode assembly and in its efficient removal from the cell. In addition to its perfect design for the targeted application and in combination with the macroporous substrate (MPS), the MPL structure and physicochemical properties have to contribute to the cell durability, which is still considered as insufficient for larger, massive commercialisation of this energy conversion system. The paper is aimed at reviewing the main knowledge gained on the role of the MPL on GDL operation and durability, with investigation of degradation phenomena of both MPL and MPS, together with the role played by the MPL in mitigating the occurrence of degradation phenomena that can occur in the whole fuel cell. In addition to the reviewing purpose, original data on ex-situ degradation of GDL are presented.
Matsumoto, R.; Imamura, H.
2016-12-01
Spin-torque induced magnetization dynamics in a spin-torque oscillator with an in-plane (IP) magnetized free layer and an out-of-plane (OP) magnetized polarizer under IP shape-anisotropy field (Hk) and applied IP magnetic field (Ha) was theoretically studied based on the macrospin model. The rigorous analytical expression of the critical current density (Jc1) for the OP precession was obtained. The obtained expression successfully reproduces the experimentally obtained Ha-dependence of Jc1 reported in [D. Houssameddine et al., Nat. Mater. 6, 447 (2007)].
Directory of Open Access Journals (Sweden)
R. Matsumoto
2016-12-01
Full Text Available Spin-torque induced magnetization dynamics in a spin-torque oscillator with an in-plane (IP magnetized free layer and an out-of-plane (OP magnetized polarizer under IP shape-anisotropy field (Hk and applied IP magnetic field (Ha was theoretically studied based on the macrospin model. The rigorous analytical expression of the critical current density (Jc1 for the OP precession was obtained. The obtained expression successfully reproduces the experimentally obtained Ha-dependence of Jc1 reported in [D. Houssameddine et al., Nat. Mater. 6, 447 (2007].
Qin, Xiaofa; Sheth, Sharvil U.; Sharpe, Susan M.; Dong, Wei; Lu, Qi; Xu, Dazhong; Deitch, Edwin A.
2011-01-01
It is well documented that the gut injury plays a critical role in the development of systemic inflammation and distant organ injury in conditions associated with splanchnic ischemia. Consequently understanding the mechanisms leading to gut injury is important. In this context, recent work suggests a protective role for the intestinal mucus layer and an injury-inducing role for luminal pancreatic proteases. Thus, we explored the role of the mucus layer in gut barrier function by observing how the removal of the mucus layer affects ischemia/reperfusion-mediated gut injury in rats as well as the potential role of luminal pancreatic proteases in the pathogenesis of gut injury. Ischemia was induced by the ligation of blood vessels to segments of the ileum for 45 min, followed by up to three hours of reperfusion. The ileal segments were divided into 5 groups. These included a non-ischemic control, ischemic segments exposed to saline, the mucolytic N-acetylcholine (NAC), pancreatic proteases or NAC plus pancreatic proteases. Changes in gut barrier function were assessed by the permeation of fluorescein isothiocyanate dextran (MW 4000 Da; FD4) in ileal everted sacs. Gut injury was measured morphologically and by the luminal content of protein, DNA and hemoglobin. The mucus layer was assessed functionally by measuring its hydrophobicity and morphologically. Gut barrier function was promptly and effectively re-established during reperfusion, which was accompanied by the restoration of the mucus layer. In contrast, treatment of the gut with the mucolytic NAC for 10 min during ischemia resulted in a failure of mucus restitution and further increases in gut permeability and injury. The presence of digestive proteases by themselves did not exacerbate gut injury but in combination with NAC, they caused an even greater increase in gut injury and permeability. These results suggest that the mucus layer not only serves as a barrier between the luminal contents and gut surface
Energy Technology Data Exchange (ETDEWEB)
Shiino, Tatsuya; Shiba, Shoichi; Sakai, Nami; Yamamoto, Satoshi [Department of Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Yamakura, Tetsuya [Institute of Physics, Graduate School of Pure and Applied Sciences, University of Tsukuba, Ten-nodai, Tsukuba, Ibaraki 305-8577 (Japan); Jiang, Ling [College of Information Science and Technology, Nanjing Forestry University, Nanjing 210037, Jiangsu (China); Uzawa, Yoshinori [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan); Maezawa, Hiroyuki, E-mail: shiino@taurus.phys.s.u-tokyo.ac.j [Solar-Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chigusa-ku, Nagoya 464-8602 (Japan)
2010-04-15
Thin superconducting NbTiN and NbN films with a few nm thickness are used in various device applications including in hot electron bolometer mixers. Such thin films have lower critical temperature (T{sub c}) and higher resistivity than corresponding bulk materials. In an effort to improve them, we have investigated an effect of the AlN buffer layer between the film and the substrate (quartz or soda lime glass). The AlN film is deposited by DC magnetron sputtering, and the process condition is optimized so that the x-ray diffraction intensity from the 002 surface of wurtzite AlN becomes the highest. By use of this well-characterized buffer layer, T{sub c} and the resistivity of the NbTiN film with a few nm thickness are remarkably increased and decreased, respectively, in comparison with those without the buffer layer. More importantly, the AlN buffer layer is found to be effective for NbN. With the AlN buffer layer, T{sub c} is increased from 7.3 to 10.5 K for the 8 nm NbN film. The improvement of T{sub c} and the resistivity originates from the good lattice matching between the 002 surface of AlN and the 111 surface of NbTiN or NbN, which results in better crystallization of the NbTiN or NbN film. This is further confirmed by the x-ray diffraction measurement.
Prasannakumara, B. C.; Shashikumar, N. S.; Venkatesh, P.
2017-09-01
An analysis has been carried out to study the effect of nonlinear thermal radiation on slip flow and heat transfer of fluid particle suspension with nanoparticles over a nonlinear stretching sheet immersed in a porous medium. Water is considered as a base fluid with dust particles along with suspended Aluminum Oxide (Al2O3) nanoparticles. Using appropriate similarity transformations, the coupled nonlinear partial differential equations are reduced into a set of coupled nonlinear ordinary differential equations. The reduced equations are then solved numerically using Runge-Kutta-Fehlberg45 order method with the help of shooting technique to investigate the impact of various pertinent parameters for the velocity and temperature fields. The obtained results are presented in tabular form as well as graphically and discussed in detail. Effect of different parameters on skin friction coefficient and Nusselt number are also discussed.
The linear and nonlinear stability of thread-annular flow.
Walton, Andrew G
2005-05-15
The surgical technique of thread injection of medical implants is modelled by the axial pressure-gradient-driven flow between concentric cylinders with a moving core. The linear stability of the flow to both axisymmetric and asymmetric perturbations is analysed asymptotically at large Reynolds number, and computationally at finite Reynolds number. The existence of multiple regions of instability is predicted and their dependence upon radius ratio and thread velocity is determined. A discrepancy in critical Reynolds numbers and cut-off velocity is found to exist between experimental results and the predictions of the linear theory. In order to account for this discrepancy, the high Reynolds number, nonlinear stability properties of the flow are analysed and a nonlinear, equilibrium critical layer structure is found, which leads to an enhanced correction to the basic flow. The predictions of the nonlinear theory are found to be in good agreement with the experimental data.
Directory of Open Access Journals (Sweden)
Peter Peniak
2014-03-01
Full Text Available The paper deals with creation of model for Cloud Computing with Infrastructure as a Service (IaaS. IaaS is based on a common network infrastructure with physical servers (hosts, which can be installed in various locations of the cloud. The virtualization software, called “Hypervisor”, creates a group of available virtual resources through physical infrastructure, which can be offered to customers. The main focus is paid on creation of numeric model, which would enable a proper sizing of cloud infrastructure for hardware provisioning, according to customer requirements. In addition, the model has been extended to include the requirements of mission critical systems with real time behavior and fail-safe features
Double criticality and the two-way Boussinesq equation in stratified shallow water hydrodynamics
Bridges, Thomas J.; Ratliff, Daniel J.
2016-06-01
Double criticality and its nonlinear implications are considered for stratified N-layer shallow water flows with N = 1, 2, 3. Double criticality arises when the linearization of the steady problem about a uniform flow has a double zero eigenvalue. We find that there are two types of double criticality: non-semisimple (one eigenvector and one generalized eigenvector) and semi-simple (two independent eigenvectors). Using a multiple scales argument, dictated by the type of singularity, it is shown that the weakly nonlinear problem near double criticality is governed by a two-way Boussinesq equation (non-semisimple case) and a coupled Korteweg-de Vries equation (semisimple case). Parameter values and reduced equations are constructed for the examples of two-layer and three-layer stratified shallow water hydrodynamics.
Standing waves for discrete nonlinear Schrodinger equations
Ming Jia
2016-01-01
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
Directory of Open Access Journals (Sweden)
V. S. Serov
2010-01-01
Full Text Available A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves of the Helmholtz equation describing the reflection and transmission of a plane monochromatic wave at a nonlinear lossy dielectric film situated between two lossless linear semiinfinite media. All three media are assumed to be nonmagnetic and isotropic. The permittivity of the film is modelled by a continuously differentiable function of the transverse coordinate with a saturating Kerr nonlinearity. It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation. Numerical results are presented.
Zeller, Mariana; Depine, Ricardo A
2015-01-01
A theoretical analysis of the lateral displacement (Goos-H\\"anchen shift) of spatially limited beams reflected from Attenuated Total Reflection (ATR) devices in the Otto configuration is presented when backward surface plasmon polaritons are excited at the interface between a positive refractive index slab and a semiinfinite metamaterial with negative refractive index. First, the stationary phase approximation and a phenomenological model based on the properties of the complex poles and zeroes of the reflection coefficient are used to demonstrate that: i) the excitation of backward surface waves can lead to both negative and positive (and not exclusively negative) Goos-H\\"anchen shifts, and ii) the sign of the shift depends on whether the value of the coupling layer thickness is higher or lower than a critical value characteristic of the ATR structure. Second, these findings are verified through rigorous calculations of the spatial structure of the reflected beam. For incident beams with a Gaussian profile, t...
Zhang, Qianjun; Lin, He; Yuan, Pusheng; Zhang, Xianping; Yao, Chao; Wang, Dongliang; Dong, Chiheng; Ma, Yanwei; Awaji, Satoshi; Watanabe, Kazuo
2015-10-01
A low-temperature (300-500 °C) heat treatment process under ambient pressure or uniaxial pressure was performed on Sn-added SmFeAsO1-x F x superconducting tapes fabricated by the ex situ powder-in-tube method. A highest transport critical current density (J c) of 3.95 × 104 A cm-2 (at 4.2 K and self-field) was achieved by this process. The low-temperature process allows tapes to endure much longer heat treatment without J c degradation than the high-temperature method. Microscopic analysis also revealed that this method could obtain a clear boundary without a reaction layer or interdiffusion between a superconducting core and sheath metal.
Chandiran, Aravind Kumar
2013-01-15
In this paper, a way of utilizing thin and conformal overlayer of titanium dioxide on an insulating mesoporous template as a photoanode for dye-sensitized solar cells is presented. Different thicknesses of TiO2 ranging from 1 to 15 nm are deposited on the surface of the template by atomic layer deposition. This systematic study helps unraveling the minimum critical thickness of the TiO2 overlayer required to transport the photogenerated electrons efficiently. A merely 6-nm-thick TiO2 film on a 3-μm mesoporous insulating substrate is shown to transport 8 mA/cm 2 of photocurrent density along with ≈900 mV of open-circuit potential when using our standard donor-π-acceptor sensitizer and Co(bipyridine) redox mediator. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Institute of Scientific and Technical Information of China (English)
王志仁; 吴德星; 陈大可; 吴辉碇; 宋学家; 张占海
2002-01-01
研究了气候海洋与大气的临界时间跨度及其非线性作用的大致结构.与预报的空间分辩率及系统的非线性强度相联系,气候大气和海洋的临界时间跨度可反映系统可预报的相对时间尺度.对于具有同样空间特征尺度的大气和海洋,海洋的最小临界时间跨度约是大气的9倍(可达数日至数十日).一般(外源变化缓慢的)气候海洋与大气的一阶非线性越强,其临界时间跨度越小.气候海洋与大气非线性作用的大致结构是:通常与科里奥利力对流体运动的规范作用(如地转运动)有关,非线性作用随纬度增加而减弱.距平流场的切变结构及其沿经向与纬向上强度的比较直接改变气候大气和海洋的非线性作用(比如,向东的距平环流强度与经向环流强度相当时,非线性作用最强),较强的外部驱动(风应力和压强梯度力)使非线性作用加大等等.%This paper studies the critical time span and the approximate nonlinear action structure of climatic atmosphere and ocean. The critical time span of the climatic atmosphere and ocean, which is related to the spatial resolution required, the strength of nonlinear action, and the calculation exactness, may represent the relative temporal scale of predictability. As far as the same characteristic spatial scale is concerned, the minimum critical time span of the ocean is about 9 times of that of atmosphere, several days or more. Usually,the stronger the nonlinear action, the shorter the critical time span with smooth changes of external forces.The approximate structure of nonlinear action of climatic atmosphere and ocean is: the nonlinear action decreases usually with increasing latitude, which is related to the role of the Coriolis force in fluid motion (forming geostrophic current); the nonlinear action changes with the anomalous cyclonic or anticyclonic circulation shear, for instance, when the strength of anomalous eastward zonal circulation
Directory of Open Access Journals (Sweden)
Shahriar Dastjerdi
2016-06-01
Full Text Available Nonlinear bending analysis of orthotropic annular/circular graphene sheets has been studied based on the non-local elasticity theory. The first order shear deformation theory (FSDT is applied in combination with the nonlinear Von-Karman strain field. The obtained differential equations are solved by using two methods, first the differential quadrature method (DQM and a new semi-analytical polynomial method (SAPM which is innovated by the authors. Applying the DQM or SAPM, the differential equations are transformed to nonlinear algebraic equations system. Then the Newton–Raphson iterative scheme is used. First, the obtained results from DQM and SAPM are compared and it is concluded that although the SAPM’s formulation is considerably simpler than DQM, however, the SAPM’s results are so close to DQM. The results are validated with available papers. Finally, the effects of small scale parameter on the results, the comparison between local and non-local theories, and linear to nonlinear analyses are investigated.
Magnetized Ekman Layer and Stewartson Layer in a Magnetized Taylor-Couette Flow
Liu, Wei
2007-01-01
In this paper we present axisymmetric nonlinear simulations about magnetized Ekman and Stewartson layers in a magnetized Taylor-Couette flow with a centrifugally stable angular-momemtum profile. The magnetic field is found to inhibit the Ekman suction. The width of the Ekman layer is reduced with increased magnetic field normal to the end plate. A uniformly-rotating region forms near the outer cylinder. A strong magnetic field leads to a steady Stewartson layer emanating from the junction between differentially rotating rings at the endcaps. The Stewartson layer becomes thinner with larger Reynolds number and penetrates deeper into the bulk flow with stronger magnetic field and larger Reynolds number. However, at Reynolds number larger than a critical value $\\sim 600$, axisymmetric, and perhaps also nonaxisymmetric, instabilities occur and result in a less prominent Stewartson layer that extends less far from the boundary.
Peculiar Nonlinear Depletion in Double-Layered Gated Si-δ-Doped GaAs%带门极双层Si-δ-掺杂GaAs中的奇特非线性耗尽
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The low-temperature measurement of Hall effect of the two-dimensional electron system in a double-layered gated Si-δ-doped GaAs is presented.A complex peculiar nonlinear dependence of the depletion on gate voltage is observed.The nonlinearity is also explained on the basis of the assumption that the double-capacity model consists of two δ-doped two-dimensional electron layers and a metallic gate,and the experimental result that the electron mobility is linear with the electron density on a log-log scale.%报道了带门极双层Si-δ-掺杂GaAs样品中的二维电子系统Hall效应的低温测量实验,观察到了电子耗尽过程中电子浓度与门电压的奇特、复杂的非线性关系.根据双电容器(由两个δ-掺杂二维电子层和一个金属门电极构成)模型的假设和在双对数坐标中电子迁移率与电子浓度呈线性关系的实验结果，解释了这一非线性耗尽现象.
Yankovskii, A. P.
2017-03-01
The nonlinear problem of non-stationary heat conductivity of the layered anisotropic heat-sensitive shells was formulated taking into account the linear dependence of thermal-physical characteristics of the materials of phase compositions on the temperature. The initial-boundary-value problem is formulated in the dimensionless form, and four small parameters are identified: thermal-physical, characterizing the degree of heat sensitivity of the layer material; geometric, characterizing the relative thickness of the thin-walled structure, and two small Biot numbers on the front surfaces of shells. A sequential recursion of dimensionless equations is carried out, at first, using the thermalphysical small parameter, then, small Biot numbers and, finally, geometrical small parameter. The first type of recursion allowed us to linearize the problem of heat conductivity, and on the basis of two latter types of recursion, the outer asymptotic expansion of solution to the problem of non-stationary heat conductivity of the layered anisotropic non-uniform shells and plates under boundary conditions of the II and III kind and small Biot numbers on the facial surfaces was built, taking into account heat sensitivity of the layer materials. The resulting two-dimensional boundary problems were analyzed, and asymptotic properties of solutions to the heat conductivity problem were studied. The physical explanation was given to some aspects of asymptotic temperature decomposition.
Energy Technology Data Exchange (ETDEWEB)
W Bolanos; M Segura; J Cugat; J Carvajal; X Mateos; M Pujol; R Solé; F Díaz; M Aguiló; et. al.
2011-12-31
This paper summarizes the main results we obtained in our laboratories in relation with crystalline layers obtained by liquid phase epitaxial growth of lanthanide doped KLu(WO{sub 4}){sub 2} and Nb:RbTiOPO{sub 4} grown on KLu(WO{sub 4}){sub 2} and RbTiOPO{sub 4} substrates, respectively. Macroscopic defect free epitaxial layers were grown and characterized in terms of their compositional homogeneity, structural stress in the layer/substrate interface and laser and waveguiding performances.
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
Antonella Fiacca; Nikolaos Matzakos; Nikolaos S Papageorgiou; Raffaella Servadei
2001-11-01
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
Indian Academy of Sciences (India)
G A Afrouzi; J Vahidi
2011-02-01
This paper deals with the existence and stability properties of positive weak solutions to classes of nonlinear systems involving the $(p,q)$-Laplacian of the form \\begin{equation*}\\begin{cases}-_p u= a(x)v^-c, < x\\in,\\\\ -_qv= b(x)u^-c, < x\\in,\\\\ u=0=v, < x\\in,\\end{cases}\\end{equation*} where $_p$ denotes the -Laplacian operator defined by $_pz=\\mathrm{div}(|\
Nonlinear tsunami generation mechanism
Directory of Open Access Journals (Sweden)
M. A. Nosov
2001-01-01
Full Text Available The nonlinear mechanism of long gravitational surface water wave generation by high-frequency bottom oscillations in a water layer of constant depth is investigated analytically. The connection between the surface wave amplitude and the parameters of bottom oscillations and source length is investigated.
Belokoneva, Elena L.; Stefanovich, Sergey Yu.; Volkov, Anatoly S.; Dimitrova, Olga V.
2016-10-01
Single crystals of a new silicate carbonate, K2Ca[Si2O5](CO3), have been synthesized in a multi-components hydrothermal solution with a pH value close to neutral and a high concentration of a carbonate mineralizer. The new compound has an axial structure (s.g. P6322) with unit cell parameters a = 5.04789 (15), c = 17.8668 (6) Å. Pseudosymmetry of the structure corresponds to s.g. P63/mmc which is broken only by one oxygen position. The structure consists of two layered fragments: one of the type of the mineral kalsilite (KAlSiO4) and the other of the high-temperature soda-like α-Na2CO3, Ca substituting for Na. The electro-neutral layer K2[Si2O5] (denoted K) as well as the layer Ca(CO3) (denoted S) may separately correspond to individual structures. In K2Ca[Si2O5](CO3) the S-K layers are connected together via Ca-O interactions between Ca atoms from the carbonate layer and apical O atoms from the silicate one, and also via K-O interlayer interactions. A hypothetical acentric structure, sp.gr. P-62c, is predicted on the basis of the order-disorder theory. It presents another symmetrical option for the arrangement of K-layers relative to S-layers. The K,Ca-silicate-carbonate powder produces a moderate SHG signal that is two times larger that of the α-quartz powder standard and close to other silicates with acentric structures and low electronic polarizability.
Institute of Scientific and Technical Information of China (English)
郭海兵; 李润东; 牛伟力
2013-01-01
Distant extrapolation is usually used during the start-up of the research reactor, by lifting the control rods step by step to reach the critical state. Due to the non-linearity of the integral worth of the control rods, this process was risky or conservative, especially when the rods were positioned in the non-linear region. A formula could be derived from the point reactor model, in which the reciprocal of the count rate was proportional to Δkeff. Together with the integral worth curve of the control rods, the effect of the non-linearity could be corrected. This method was valideted by critical extrapolation data.%研究堆在物理启动时一般通过棒位外推法得出临界棒位,从而逐步达到临界.但由于控制棒积分价值的非线性,使得这一外推过程不安全或过于偏保守,特别是当临界棒位处于非线性区时.根据点堆模型可导出计数率倒数与Δkeff成正比,若根据积分价值曲线将棒位对应为△keff,则可修正控制棒价值非线性的影响.通过研究堆的临界外推数据验证了这一方法的准确性.
Directory of Open Access Journals (Sweden)
N. Brisson
1998-01-01
Full Text Available In the framework of simplified water balance models devoted to irrigation scheduling or crop modelling, the relative transpiration rate (the ratio of actual to maximal transpiration is assumed to decrease linearly when the soil dries out below a critical available water value. This value is usually expressed as a fraction, F, of the maximal available soil water content. The present work aims to use the basic laws governing water transfer through the plants at a daily time step to compute F dynamically as the crop grows. It can be regarded as an expansion of Slabbers' (1980 approach to crop growing conditions. Starting from the mathematical representation given by single-root models (Gardner, 1960, an analytical expression for F is derived, using simplified hypotheses. This expression accounts for plant attributes such as the mean root radius, the critical leaf water potential for stomatal closure and the root length density profile growing with the crop. Environmental factors such as soil type and atmospheric demand also influence F. The structural influence of soil comes from the required introduction of the bulk soil hydraulic conductivity in the single-root model. The shape of the root length density profile is assumed to be sigmoidal and a new profile is calculated at each value of the rooting depth. A sensitivity analysis of F to all those factors is presented. The first general result is that F decreases as the root system grows in depth. Differences in the shape of the root profile can be responsible for differential water stress sensitivity in the early stages of growth. Yet, low critical leaf water potential can compensate partially for a poor root profile. Conversely, F is relatively insensitive to the average root radius. F sensitivity to soil type seems somewhat artificial: given the bulk soil hydraulic conductivity formula, the soil sensitivity results from F being expressed as a fraction of the maximal available soil water content
Zeller, Mariana A.; Cuevas, Mauro; Depine, Ricardo A.
2015-05-01
We present a theoretical analysis of the lateral displacement (Goos-Hänchen shift) of spatially limited beams reflected from attenuated total reflection (ATR) devices in the Otto configuration when backward surface plasmon polaritons are excited at the interface between a positive refractive index slab and a semi-infinite metamaterial with a negative refractive index. First, the stationary phase approximation and a phenomenological model based on the properties of the complex poles and zeroes of the reflection coefficient are used to demonstrate that: (i) the excitation of backward surface waves can lead to both negative and positive (and not exclusively negative) Goos-Hänchen shifts, and (ii) the sign of the shift depends on whether the value of the coupling layer thickness is higher or lower than a critical value characteristic of the ATR structure. Then, these findings are verified through rigorous calculations of the spatial structure of the reflected beam. For incident beams with a Gaussian profile, the lateral shift calculated as the first moment of the field distribution of the reflected beam agrees quite well with the predictions of approximate analysis. Near the resonant excitation of the backward surface plasmon polariton, large (negative or positive) Goos-Hänchen shifts are obtained, along with a splitting of the reflected beam.
Nonlinear dynamical behavior of shallow cylindrical reticulated shells
Institute of Scientific and Technical Information of China (English)
WANG Xin-zhi; LIANG Cong-xing; HAN Ming-jun; YEH Kai-yuan; WANG Gang
2007-01-01
By using the method of quasi-shells , the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell are founded. By using the method of the separating variable function, the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support. The tensile force is solved out from the compatible equations, a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin. The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function. The existence of the chaotic motion of the single-layer shallow cylinmapping.
Nonlinear diffusion and superconducting hysteresis
Energy Technology Data Exchange (ETDEWEB)
Mayergoyz, I.D. [Univ. of Maryland, College Park, MD (United States)
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Iwahashi, Takashi; Ishiyama, Tatsuya; Sakai, Yasunari; Morita, Akihiro; Kim, Doseok; Ouchi, Yukio
2015-10-14
IR-visible sum-frequency generation (IV-SFG) vibrational spectroscopy and a molecular dynamics (MD) simulation were used to study the local layering order at the interface of 1-butanol-d9 and 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim]PF6), a room-temperature ionic liquid (RTIL). The presence of a local non-polar layer at the interface of the two polar liquids was successfully demonstrated. In the SFG spectra of 1-butanol-d9, we observed significant reduction and enhancement in the strength of the CD3 symmetric stretching (r(+)) mode and the antisymmetric stretching (r(-)) mode peaks, respectively. The results can be well explained by the presence of an oppositely oriented quasi-bilayer structure of butanol molecules, where the bottom layer is strongly bound by hydrogen-bonding with the PF6(-) anion. MD simulations reveal that the hydrogen-bonding of butanol with the PF6(-) anion causes the preferential orientation of the butanols; the restriction on the rotational distribution of the terminal methyl group along their C3 axis enhances the r(-) mode. As for the [bmim](+) cations, the SFG spectra taken within the CH stretch region indicate that the butyl chain of [bmim](+) points away from the bulk RTIL phase to the butanol phase at the interface. Combining the SFG spectroscopy and MD simulation results, we propose an interfacial model structure of layering, in which the butyl chains of the butanol molecules form a non-polar interfacial layer with the butyl chains of the [bmim](+) cations at the interface.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Neural Networks for Non-linear Control
DEFF Research Database (Denmark)
Sørensen, O.
1994-01-01
This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process.......This paper describes how a neural network, structured as a Multi Layer Perceptron, is trained to predict, simulate and control a non-linear process....
Thompson, Lowell F
2016-01-01
In this paper we revisit the notion of the "minus logarithm of stationary probability" as a generalized potential in nonequilibrium systems and attempt to illustrate its central role in an axiomatic approach to stochastic nonequilibrium thermodynamics of complex systems. It is demonstrated that this quantity arises naturally through both monotonicity results of Markov processes and as the rate function when a stochastic process approaches a detrministic limit. We then undertake a more detailed mathematical analysis of the consequences of this quantity, culminating in a necessary and sufficient condition for the criticality of stochastic systems. This condition is then discussed in the context of recent results about criticality in biological systems.
Tunable nonlinear graphene metasurfaces
Smirnova, Daria A; Kivshar, Yuri S; Khanikaev, Alexander B
2015-01-01
We introduce the concept of nonlinear graphene metasurfaces employing the controllable interaction between a graphene layer and a planar metamaterial. Such hybrid metasurfaces support two types of subradiant resonant modes, asymmetric modes of structured metamaterial elements ("metamolecules") and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. High tunability of graphene plasmons facilitates strong interaction between the subradiant modes, modifying the spectral position and lifetime of the associated Fano resonances. We demonstrate that strong resonant interaction, combined with the subwavelength localization of plasmons, leads to the enhanced nonlinear response and high efficiency of the second-harmonic generation.
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model
Energy Technology Data Exchange (ETDEWEB)
Ghorbanpour Arani, A., E-mail: aghorban@kashanu.ac.ir [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of); Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan (Iran, Islamic Republic of); Zarei, M.Sh.; Amir, S.; Khoddami Maraghi, Z. [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of)
2013-02-01
In this work nonlinear vibration of double-walled carbon nanotube (DWCNT) embedded in an elastic medium and subjected to an axial fluid flow (incompressible and non-viscose) is investigated. The elastic medium is simulated using Pasternak foundation in which adjacent layer interactions are assumed to have been coupled by van der Waals (VdW) force. The higher-order equation of motion is derived using Hamilton's principle and nonlocal-nonlinear shell theory. Galerkin and averaging methods are adopted to solve the higher-order governing equations. Elastic medium, small scale parameter, velocity and fluid density are taken into account to calculate the effects of axial and circumferential wave numbers in this study. Results reveal that increasing circumferential wave number, leads to enhanced nonlinearity. Critical flow velocities of DWCNT are inversely related to the non-local parameter (e{sub 0}a), so that increase in the later lead to reduced critical flow velocities.
Nonlinear Metamaterials for Holography
Almeida, Euclides; Prior, Yehiam
2015-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.
Tanhaei, M. H.; Rezaei, G.
2016-10-01
In this work, effects of an on-center hydrogenic impurity, external electric and magnetic fields on the optical rectification coefficient (ORC), second and third harmonic generations (SHG and THG) of a multi-layer spherical quantum dot (MLSQD) are studied. Energy eigenvalues and eigenvectors are calculated using the direct matrix diagonalization method and optical properties are obtained using the compact density matrix approach. Our results reveal that the hydrogenic impurity and external fields have a great influence on these optical quantities. Hydrogenic impurity reduces the magnitude of the resonant peaks and shifts them to the higher energies. An increase in the magnetic (electric) field, leads to increase (decrease) the interval energies and the dipole moment matrix elements. Therefore, resonant peaks of these optical quantities find an obvious blue (red) shift and their magnitudes enhance (diminish) with increasing the external magnetic (electric) field.
Standing waves for discrete nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Ming Jia
2016-07-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Nonlinear Analysis of Buckling
Directory of Open Access Journals (Sweden)
Psotný Martin
2014-06-01
Full Text Available The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.
Institute of Scientific and Technical Information of China (English)
姜久红; 王军; 王志伟
2011-01-01
建立二自由度非线性产品包装系统模型，得到冲击动力学方程并数值求解，研究了双曲正切包装系统关键部件的矩形脉冲响应特性。运用数值求解得到关键部件破损边界曲面，并讨论了名义频率比、阻尼、脉冲激励幅值和系统参数对关键部件破损边界的影响规律，结果表明，频率比、阻尼、脉冲激励幅值和系统参数对关键部件破损边界影响显著，研究结论为产品包装设计提供科学依据。%The shock characteristic of the hyperbolic tangent nonlinear packaging system with critical component were investigated under the action of rectangular acceleration pulse. The dynamical model of the system was developed. And the numerical results of the dynamical equations were got. The damage boundary surface of critical component was obtained based on the results. And the effect of the pulse duration, the frequency ratio, the dmaping ratio, the pulse peak acceleration in additional to the defined system parameter on the DBS of critical component was discussed. It's shown that all of their effects are noticeable. The results lead to some insights into the design of cushioning packaging.
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Theoretical aspects of nonlinear echo image system
Institute of Scientific and Technical Information of China (English)
ZHANG Ruiquan; FENG Shaosong
2003-01-01
In order to develop the nonlinear echo image system to diagnose pathological changes in biological tissue , a simple physical model to analyse the character of nonlinear reflected wave in biological medium is postulated. The propagation of large amplitude plane sound wave in layered biological media is analysed for the one dimensional case by the method of successive approximation and the expression for the second order wave reflected from any interface of layered biological media is obtained. The relations between the second order reflection coefficients and the nonlinear parameters of medium below the interface are studied in three layers interfaces. Finally, the second order reflection coefficients of four layered media are calculated numerically. The results indicate that the nonlinear parameter B/A of each layer of biological media can be determined by the reflection method.
Nonlinear properties of a graded-index photonic heterostructure
Indian Academy of Sciences (India)
B Tavakkoly Moghaddam; S Roshan Entezar; H Pashei Adl
2013-05-01
The optical properties of a one-dimensional (1D) photonic heterostructure with gradedindex nonlinear materials are demonstrated theoretically. The influence of the gradation profile of the graded-index nonlinear layers on the linear and nonlinear responses of the structure are analysed. It is shown that the -factor of the defect mode and the threshold input intensity to achieve the optical bistability in the used photonic heterostructure depend on the gradation profile of the gradedindex nonlinear layers.
Nonlinear analysis of imperfect squarely-reticulated shallow spherical shells
Institute of Scientific and Technical Information of China (English)
2007-01-01
Nonlinear behavior of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections subjected to a central concentrated (joint) load has been studied in this paper. Using the asymptotic iteration method, an analytical characteristic relationship between the non-dimensional load and central deflection is obtained. The resulting asymptotic solution can be used readily to perform the analysis of parameters and predict the buckling critical load. Meanwhile, numerical examples are presented and effects of imperfection factor and boundary conditions on buckling of the structures are discussed. Comparisons with data based on the finite element method show good exactness of the resulting solution.
Nonlinear analysis of imperfect squarely- reticulated shallow spherical shells
Institute of Scientific and Technical Information of China (English)
NIE GuoHua; LI ZhiWei
2007-01-01
Nonlinear behavior of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections subjected to a central concentrated (joint) load has been studied in this paper.Using the asymptotic iteration method,an analytical characteristic relationship between the non-dimensional load and central deflection is obtained.The resulting asymptotic solution can be used readily to perform the analysis of parameters and predict the buckling critical load.Meanwhile,numerical examples are presented and effects of imperfection factor and boundary conditions on buckling of the structures are discussed.Comparisons with data based on the finite element method show good exactness of the resulting solution.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Energy Technology Data Exchange (ETDEWEB)
Itohara, Keita, E-mail: itohara@nmr.mp.es.osaka-u.ac.j [Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan); Shimizu, Sunao; Mukuda, Hidekazu; Kitaoka, Yoshio [Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan); Shirage, Parasharam M.; Kito, Hijiri; Iyo, Akira [National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568 (Japan)
2010-12-15
We report {sup 63}Cu-NMR/NQR studies on Hg-based four-layered compounds HgBa{sub 2}Ca{sub 3}Cu{sub 4} O{sub 8+y} (Hg-1234) with T{sub c}=123, 110, and 95 K. The {sup 63}Cu Knight shift measurements have revealed that the carrier density (N{sub h}) monotonously decreases with decreasing T{sub c}. Although static magnetic order was not observed at N{sub h}=0.15 for the IP with T{sub c}=95K, it was revealed that antiferromagnetic correlations critically develop, preventing from observing the NMR spectrum below {approx}200 K far above T{sub c}. Thus, we deduce that a magnetic quantum critical point, where an AFM order collapses, may exist at slightly less than N{sub h{approx}}0.15 in the Hg-based four-layered compounds, which is lower than that in Hg-based five-layered compounds, N{sub h{approx}}0.17. This result suggests that a magnetic interlayer coupling, which stabilizes an AFM order, becomes weaker in the four-layered compounds than in five-layered compounds.
Directory of Open Access Journals (Sweden)
Christophe eMagnani
2014-08-01
Full Text Available The neurons in layer II of the medial entorhinal cortex are part of the grid cell network involved in the representation of space. Many of these neurons are likely to be stellate cells with specific oscillatory and firing properties important for their function. A fundamental understanding of the nonlinear basis of these oscillatory properties is critical for the development of theories of grid cell firing. In order to evaluate the behavior of stellate neurons, measurements of their quadratic responses were used to estimate a second order Volterra kernel. This paper uses an operator theory, termed quadratic sinusoidal analysis (QSA, which quantitatively determines that the quadratic response accounts for a major part of the nonlinearity observed at membrane potential levels characteristic of normal synaptic events. Practically, neurons were probed with multi-sinusoidal stimulations to determine a Hermitian operator that captures the quadratic function in the frequency domain. We have shown that the frequency content of the stimulation plays an important role in the characteristics of the nonlinear response, which can distort the linear response as well. Stimulations with enhanced low frequency amplitudes evoked a different nonlinear response than broadband profiles. The nonlinear analysis was also applied to spike frequencies and it was shown that the nonlinear response of subthreshold membrane potential at resonance frequencies near the threshold is similar to the nonlinear response of spike trains.
Energy Technology Data Exchange (ETDEWEB)
Murtazaev, A. K.; Ramazanov, M. K., E-mail: sheikh77@mail.ru; Badiev, V. K. [Russian Academy of Sciences, Institute of Physics, Dagestan Scientific Center (Russian Federation)
2012-08-15
The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J{sub 1}) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = vertical bar J{sub 1}/J vertical bar = 0-0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.
Critical dynamics near QCD critical point
Minami, Yuki
2012-01-01
In this thesis, we study the critical dynamics near the QCD critical point. Near the critical point, the relevant modes for the critical dynamics are identified as the hydrodynamic modes. Thus, we first study the linear dynamics of them by the relativistic hydrodynamics. We show that the thermal diffusion mode is the most relevant mode, whereas the sound mode is suppressed around the critical point. We also find that the Landau equation, which is believed to be an acausal hydrodynamic equation, has no problem to describe slowly varying fluctuations. Moreover, we find that the Israel-Stewart equation, which is a causal one, gives the same result as the Landau equation gives in the long-wavelength region. Next, we study the nonlinear dynamics of the hydrodynamic modes by the nonlinear Langevin equation and the dynamic renormalization group (RG). In the vicinity of the critical point, the usual hydrodynamics breaks down by large fluctuations. Thus, we must consider the nonlinear Langevin equation. We construct t...
Directory of Open Access Journals (Sweden)
Amory-Mazaudier Christine
2012-11-01
Full Text Available This paper presents the statistical analysis of the diurnal variations of the F layer at the equatorial station of Ouagadougou (Lat: 12.4° N; Long: 358.5° E; dip: 5.9° from 1966 to 1998 (=> ~11 680 days. We consider three main factors of variability: (1 the season (spring, summer, autumn and winter, (2 the phase of the sunspot cycle (ascending, maximum, descending and minimum and (3 the geomagnetic activity classified by Legrand and Simon in four groups: slow solar wind, high solar wind streams, fluctuating solar wind and shock activity. We easily identify the influence of the solar wind speed and shock activity on the diurnal pattern of the F layer. Shock and recurrent activities tend to enhance or diminish the morning or afternoon maximum of the F2 layer critical frequency. The difference of the diurnal foF2 variation during the increasing and decreasing phases of the sunspot solar cycle is explained by different solar wind regimes. The slow solar wind dominates during the increasing phase of the sunspot cycle and the fluctuating solar wind dominates during the decreasing phase of the sunspot cycle. This paper demonstrates that it is possible using a large database, to bring up significant morphologies of the diurnal variation of the foF2 critical frequency as a function of (1 different solar events such as quiet solar wind, fluctuating wind, recurrent high stream wind and Coronal Mass Ejections (CMEs; (2 solar cycle phases and (3 seasons. It is an approach directly connecting the critical frequency of the F2 layer to the solar parameters.
Rayleigh reflections and nonlinear acoustics of solids
Breazeale, M. A.
1980-10-01
Schlierken studies of ultrasonic waves, and nonlinear acoustics of solids are addressed. A goniometer for use in a Schlieren system for visualization of ultrasonic waves in liquids is described. The goniometer is used to obtain Schlieren photographs of leaky Rayleigh waves excited on an Al2O3 layer on a stainless steel reflector immersed in water, showing that the Rayleigh wave velocity in this case is less than that of either a water Al203 layer or a water stainless steel layer. Also investigated are: (1) nonlinearity parameters and third order elastic constants of copper between 300 and 3 K; (2) measurement of nonlinearity parameters in small solid samples by the harmonic generation technique; (3) relationship between solid nonlinearity parameters and thermodynamic Gruneisen parameters; and (4) quantum mechanical theory of nonlinear interaction of ultrasonic waves.
CHAOTIC BELT PHENOMENA IN NONLINEAR ELASTIC BEAM
Institute of Scientific and Technical Information of China (English)
张年梅; 杨桂通
2003-01-01
The chaotic motions of axial compressed nonlinear elastic beam subjected totransverse load were studied. The damping force in the system is nonlinear. Consideringmaterial and geometric nonlinearity, nonlinear governing equation of the system wasderived. By use of nonlinear Galerkin method, differential dynamic system was set up.Melnikov method was used to analyze the characters of the system. The results showed thatchaos may occur in the system when the load parameters P0 and f satisfy some conditions.The zone of chaotic motion was belted. The route from subharmonic bifurcation to chaoswas analyzed. The critical conditions that chaos occurs were determined.
Nonlinear damping effects in spin torque dynamics of magnetic tunnel junctions
Barsukov, Igor; Chen, Yu-Jin; Lee, Han Kyu; Goncalves, Alexandre; Katine, Jordan; Arias, Rodrigo; Ivanov, Boris; Krivorotov, Ilya
2015-03-01
Performance of nanoscale spin torque devices such as memory (STT-MRAM) and auto-oscillators critically depends on magnetic relaxation. It is commonly assumed that magnetization dynamics in the presence of spin torque can be understood as simple competition between antidamping arising from spin torque and Gilbert damping of the free layer. However our experiments reveal that the situation is more complex and that nonlinear damping processes in the free layer of magnetic tunnel junction (MTJ) nanopillars can strongly alter spin torque driven dynamics. We study elliptical MTJ nanopillars with in-plane magnetizations of the free layer and SAF layers by spin torque ferromagnetic resonance. We find an excitation spectrum associated with standing spin waves of the free layer. By varying the external field, the energy of a higher-order spin wave mode becomes twice the energy of the main mode. This opens up a nonlinear, resonant relaxation channel, giving rise to a damping increase of approximately 20 percent. With increasing spin torque provided by a DC bias current, we find that this relaxation channel competes with antidamping in a nonlinear manner, increasingly contributing to and even dominating the relaxation at subcritical currents.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Santamaria, Nick; Gerdtz, Marie; Sage, Sarah; McCann, Jane; Freeman, Amy; Vassiliou, Theresa; De Vincentis, Stephanie; Ng, Ai Wei; Manias, Elizabeth; Liu, Wei; Knott, Jonathan
2015-06-01
The prevention of hospital acquired pressure ulcers in critically ill patients remains a significant clinical challenge. The aim of this trial was to investigate the effectiveness of multi-layered soft silicone foam dressings in preventing intensive care unit (ICU) pressure ulcers when applied in the emergency department to 440 trauma and critically ill patients. Intervention group patients (n = 219) had Mepilex(®) Border Sacrum and Mepilex(®) Heel dressings applied in the emergency department and maintained throughout their ICU stay. Results revealed that there were significantly fewer patients with pressure ulcers in the intervention group compared to the control group (5 versus 20, P = 0·001). This represented a 10% difference in incidence between the groups (3·1% versus 13·1%) and a number needed to treat of ten patients to prevent one pressure ulcer. Overall there were fewer sacral (2 versus 8, P = 0·05) and heel pressure ulcers (5 versus 19, P = 0·002) and pressure injuries overall (7 versus 27, P = 0·002) in interventions than in controls. The time to injury survival analysis indicated that intervention group patients had a hazard ratio of 0·19 (P = 0·002) compared to control group patients. We conclude that multi-layered soft silicone foam dressings are effective in preventing pressure ulcers in critically ill patients when applied in the emergency department prior to ICU transfer. © 2013 The Authors. International Wound Journal © 2013 Medicalhelplines.com Inc and John Wiley & Sons Ltd.
Nonlinear Acoustic Wave Interactions in Layered Media.
1980-03-06
Generated Components in Dispersive Media. . . . . . . . . . . . . 62 4.4 Dispersion in Medium II . . . . . . . . .. 68 V. CONCLUSIONS...give rise to leaky wave modes which are more thoroughly discussed 17 18 by Kapany and Burke, and by Marcuse . Leaky modes are C.C. Ghizoni, J.M...1977), 843-848. 1 7N.S. Kapany and J.J. Burke, Optical Waveeeuides, (New York: Academic Press, 1972), pp. 24-34. D. Marcuse , Theory of Dielectric Optical
Energy Technology Data Exchange (ETDEWEB)
Yan, Pengfei; Zheng, Jianming; Gu, Meng; Xiao, Jie; Zhang, Jiguang; Wang, Chongmin
2017-01-16
LiNi1/3Mn1/3Co1/3O2 (NMC333) layered cathode is often fabricated as secondary particles of consisting of densely packed primary particles, which offers advantage of high energy density and alleviation of cathode side reactions/corrosions, but introduces other drawbacks, such as intergranular cracking. Here, we report unexpected observations on the nucleation and growth of intragranular cracks in the commercial NMC333 layered cathode by using advanced S/TEM. We found that the formation of the intragranular cracks is directly associated with high voltage cycling, which is an electrochemically driven and diffusion controlled process. The intragranular cracks were noticed to be characteristically initiated from grain interior, a consequence of dislocation based crack incubation mechanism. This observation is in sharp contrast with the general theoretical models, predicting the initiation of intragranular cracks from grain boundaries or particle surface. Our study indicates that maintain a structural stability is the key step toward high voltage operation of layered cathode materials.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Theory of multiple quantum dot formation in strained-layer heteroepitaxy
Energy Technology Data Exchange (ETDEWEB)
Du, Lin; Maroudas, Dimitrios, E-mail: maroudas@ecs.umass.edu [Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003-9303 (United States)
2016-07-11
We develop a theory for the experimentally observed formation of multiple quantum dots (QDs) in strained-layer heteroepitaxy based on surface morphological stability analysis of a coherently strained epitaxial thin film on a crystalline substrate. Using a fully nonlinear model of surface morphological evolution that accounts for a wetting potential contribution to the epitaxial film's free energy as well as surface diffusional anisotropy, we demonstrate the formation of multiple QD patterns in self-consistent dynamical simulations of the evolution of the epitaxial film surface perturbed from its planar state. The simulation predictions are supported by weakly nonlinear analysis of the epitaxial film surface morphological stability. We find that, in addition to the Stranski-Krastanow instability, long-wavelength perturbations from the planar film surface morphology can trigger a nonlinear instability, resulting in the splitting of a single QD into multiple QDs of smaller sizes, and predict the critical wavelength of the film surface perturbation for the onset of the nonlinear tip-splitting instability. The theory provides a fundamental interpretation for the observations of “QD pairs” or “double QDs” and other multiple QDs reported in experimental studies of epitaxial growth of semiconductor strained layers and sets the stage for precise engineering of tunable-size nanoscale surface features in strained-layer heteroepitaxy by exploiting film surface nonlinear, pattern forming phenomena.
Stolz, A; Markey, L; Francs, G Colas des; Bouhelier, A
2013-01-01
We introduce strongly-coupled optical gap antennas to interface optical radiation with current-carrying electrons at the nanoscale. The transducer relies on the nonlinear optical and electrical properties of an optical antenna operating in the tunneling regime. We discuss the underlying physical mechanisms controlling the conversion and demonstrate that a two-wire optical antenna can provide advanced optoelectronic functionalities beyond tailoring the electromagnetic response of a single emitter. Interfacing an electronic command layer with a nanoscale optical device may thus be facilitated by the optical rectennas discussed here.
Homoclinic orbits of second-order nonlinear difference equations
Directory of Open Access Journals (Sweden)
Haiping Shi
2015-06-01
Full Text Available We establish existence criteria for homoclinic orbits of second-order nonlinear difference equations by using the critical point theory in combination with periodic approximations.
Nonlinear response and dynamical transitions in a phase-field crystal model for adsorbed overlayers
Energy Technology Data Exchange (ETDEWEB)
Ramos, J A P [Departamento de Ciencias Exatas, Universidade Estadual do Sudoeste da Bahia, 45000-000 Vitoria da Conquista, BA (Brazil); Granato, E [Laboratorio Associado de Sensores e Materiais, Instituto Nacional de Pesquisas Espaciais, 12245-970 Sao Jose dos Campos, SP (Brazil); Ying, S C; Ala-Nissila, T [Department of Physics, PO Box 1843, Brown University, Providence, RI 02912-1843 (United States); Achim, C V [Department of Applied Physics, Aalto University School of Science and Technology, PO Box 11000, FI-00076 Aalto, Espoo (Finland); Elder, K R, E-mail: Jorge@las.inpe.b [Department of Physics, Oakland University, Rochester, Michigan 48309-4487 (United States)
2010-09-01
The nonlinear response and sliding friction behavior of a phase-field crystal model for driven adsorbed atomic layers is determined numerically. The model describes the layer as a continuous density field coupled to the pinning potential of the substrate and under an external driving force. Dynamical equations which take into account both thermal fluctuations and inertial effects are used for numerical simulations of commensurate and incommensurate layers. At low temperatures, the velocity response of an initially commensurate layer shows hysteresis with dynamical melting and freezing transitions at different critical forces. The main features of the sliding friction behavior are similar to the results obtained previously from molecular dynamics simulations of particle models. However, the dynamical transitions correspond to nucleations of stripes rather than closed domains.
Yan, Pengfei; Zheng, Jianming; Gu, Meng; Xiao, Jie; Zhang, Ji-Guang; Wang, Chong-Min
2017-01-01
LiNi1/3Mn1/3Co1/3O2-layered cathode is often fabricated in the form of secondary particles, consisting of densely packed primary particles. This offers advantages for high energy density and alleviation of cathode side reactions/corrosions, but introduces drawbacks such as intergranular cracking. Here, we report unexpected observations on the nucleation and growth of intragranular cracks in a commercial LiNi1/3Mn1/3Co1/3O2 cathode by using advanced scanning transmission electron microscopy. We find the formation of the intragranular cracks is directly associated with high-voltage cycling, an electrochemically driven and diffusion-controlled process. The intragranular cracks are noticed to be characteristically initiated from the grain interior, a consequence of a dislocation-based crack incubation mechanism. This observation is in sharp contrast with general theoretical models, predicting the initiation of intragranular cracks from grain boundaries or particle surfaces. Our study emphasizes that maintaining structural stability is the key step towards high-voltage operation of layered-cathode materials.
RESEARCH ON NONLINEAR PROBLEMS IN STRUCTURAL DYNAMICS.
Research on nonlinear problems structural dynamics is briefly summarized. Panel flutter was investigated to make a critical comparison between theory...panel flutter in aerospace vehicles, plausible simplifying assumptions are examined in the light of experimental results. Structural dynamics research
Parametric resonant triad interactions in a free shear layer
Mallier, R.; Maslowe, S. A.
1993-01-01
We investigate the weakly nonlinear evolution of a triad of nearly-neutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees to the mean flow direction. Because the evolution occurs on a relatively fast time scale, the critical layer dynamics dominate the process and the amplitude evolution of the oblique waves is governed by an integro-differential equation. The long-time solution of this equation predicts very rapid (exponential of an exponential) amplification and we discuss the pertinence of this result to vortex pairing phenomena in mixing layers.
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Directory of Open Access Journals (Sweden)
DJAIRO G. DEFIGUEIREDO
2000-12-01
Full Text Available In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv, - deltav = g(x, u, v, Ñu, Ñv, in omega, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.
Ikubanni, S. O.; Adeniyi, J. O.
2017-02-01
Improved ionospheric modeling requires a better understanding of the relationship between ionospheric parameters and their influencing solar and geomagnetic sources. Published reports of the validation of the International Reference Ionosphere (IRI) for quiet-time revealed either underestimation or overestimation at a greater magnitude during high solar fluxes, especially at low latitude. With daily foF2 data from Ouagadougou (geor. 12.4°N, 1.5°W) covering a solar cycle, we have presented preliminary results from the analysis of solar dependence of six different classifications of the data: (i) daily values, (ii) monthly mean, (iii) daily quiet values (with Ap ⩽ 20), (iv) monthly-quiet-mean values, (v) monthly median, and (vi) monthly-quiet-median values. All six classifications show good nonlinear relationship with both F10.7 and F10.7P, however, the differences between the dependence of classes (i) and (iii) of foF2 on the two solar indices is more substantial than those of classes (ii), (iv), (v), and (vi). Of all the six classes, the monthly averages are best related to both solar activity indices. Further analysis shows that magnetic disturbances are non-influential in the variations of the monthly mean of both solar activity indices; this makes both good indices for quiet-time modeling. Likewise, F10.7 and F10.7P are indistinguishable for long-term modeling around the African EIA trough region. While monthly median values may be best for mid-latitude region, either the mean/median values could be used for low-latitude region. However, it could be worthwhile to examine the distribution of the data from the station under consideration.
Directory of Open Access Journals (Sweden)
Gerald B. Fuenmayor-Rivadeneira
2013-11-01
Full Text Available This article presents a synthesized review as state of the art of the study of QoS for mission-critical traffic in wireless local area networks that use the IEEE 802.11g protocol. This is to highlight previous research for their contribution will constitute a reference to guide a proposed new approach to ensuring the quality of service for this type of traffic using the above protocol. The review is based on academic and business items made during the current five years. As a result of this review it is evident that there have been many efforts to address the issue but there are still gaps in the characterization of mission-critical traffic and ensuring quality of service for the same, due the new applications and the large host of WiFi networks in business and government, which has led to increased demand for access channels and, therefore, a challenge to the progress already known, such as IEEE 802.1q.
Jayakumar, Arunkumar; Singamneni, Sarat; Ramos, Maximiano; Al-Jumaily, Ahmed M; Pethaiah, Sethu Sundar
2017-07-14
The conventional gas diffusion layer (GDL) of polymer electrolyte membrane (PEM) fuel cells incorporates a carbon-based substrate, which suffers from electrochemical oxidation as well as mechanical degradation, resulting in reduced durability and performance. In addition, it involves a complex manufacturing process to produce it. The proposed technique aims to resolve both these issues by an advanced 3D printing technique, namely selective laser sintering (SLS). In the proposed work, polyamide (PA) is used as the base powder and titanium metal powder is added at an optimised level to enhance the electrical conductivity, thermal, and mechanical properties. The application of selective laser sintering to fabricate a robust gas diffusion substrate for PEM fuel cell applications is quite novel and is attempted here for the first time.
Piłatowicz, Grzegorz; Marongiu, Andrea; Drillkens, Julia; Sinhuber, Philipp; Sauer, Dirk Uwe
2015-11-01
The internal resistance (Ri) is one of the key parameters that determine the current state of electrochemical storage systems (ESS). It is crucial for estimating cranking capability in conventional cars, available power in modern hybrid and electric vehicles and for determining commonly used factors such as state-of-health (SoH) and state-of-function (SoF). However, ESS are complex and non-linear systems. Their Ri depends on many parameters such as current rate, temperature, SoH and state-of-charge (SoC). It is also a fact that no standardized methodologies exist and many different definitions and ways of Ri determination are being used. Nevertheless, in many cases authors are not aware of the consequences that occur when different Ri definitions are being used, such as possible misinterpretations, doubtful comparisons and false figures of merit. This paper focuses on an application-oriented separation between various Ri definitions and highlights the differences between them. The investigation was based on the following technologies: lead-acid, lithium-ion and nickel metal-hydride batteries as well as electrochemical double-layer capacitors. It is not the target of this paper to provide a standardized definition of Ri but to give researchers, engineers and manufacturers a possibility to understand what the term Ri means in their own work.
Bond length variation in In0.25Ga0.75As/InP epitaxial layers thicker than the critical thickness
Tormen, M.; De Salvador, D.; Natali, M.; Drigo, A.; Romanato, F.; Rossetto, G.; Boscherini, F.; Mobilio, S.
1999-09-01
We address the issue of the local structure in an epitaxial semiconductor thin film undergoing strain relaxation due to extended defects when the critical thickness for their introduction is exceeded. The nearest neighbor environment is probed by x-ray absorption fine structure spectroscopy. The particular system studied is a set of In0.25Ga0.75As films grown on InP(001) of increasing thickness; the thicknesses were chosen so as to obtain a varying degree of relaxation, ranging from pseudomorphic growth to completely relaxed state. The samples have been thoroughly characterized with complementary structural techniques and the residual strain is measured by x-ray diffraction. We find that the Ga-As bond length exhibits a linear decrease with decreasing residual strain. By comparing these results with previous studies on bond lengths in pseudomorphic InxGa1-xAs films as a function of concentration we conclude that the bond lengths have an identical behavior as a function of the mean residual strain independently from its elastic or plastic origin. This result is reproduced by an analytical model based on the transfer of the mean macroscopic deformation at a local level. The broadening of the bond length distribution induced by extended defects is also discussed, concluding that it is not experimentally dectable.
A granular computing method for nonlinear convection-diffusion equation
Directory of Open Access Journals (Sweden)
Tian Ya Lan
2016-01-01
Full Text Available This paper introduces a method of solving nonlinear convection-diffusion equation (NCDE, based on the combination of granular computing (GrC and characteristics finite element method (CFEM. The key idea of the proposed method (denoted as GrC-CFEM is to reconstruct the solution from coarse-grained layer to fine-grained layer. It first gets the nonlinear solution on the coarse-grained layer, and then the function (Taylor expansion is applied to linearize the NCDE on the fine-grained layer. Switch to the fine-grained layer, the linear solution is directly derived from the nonlinear solution. The full nonlinear problem is solved only on the coarse-grained layer. Numerical experiments show that the GrC-CFEM can accelerate the convergence and improve the computational efficiency without sacrificing the accuracy.
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Inter-layer synchronization in multiplex networks of identical layers
Energy Technology Data Exchange (ETDEWEB)
Sevilla-Escoboza, R. [Centro Universitario de los Lagos, Universidad de Guadalajara, Jalisco 47460 (Mexico); Sendiña-Nadal, I.; Leyva, I.; Buldú, J. M. [Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid (Spain); Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid (Spain); Gutiérrez, R. [School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD (United Kingdom); Boccaletti, S. [CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence (Italy); The Italian Embassy in Israel, 25 Hamered st., 68125 Tel Aviv (Israel)
2016-06-15
Inter-layer synchronization is a distinctive process of multiplex networks whereby each node in a given layer evolves synchronously with all its replicas in other layers, irrespective of whether or not it is synchronized with the other units of the same layer. We analytically derive the necessary conditions for the existence and stability of such a state, and verify numerically the analytical predictions in several cases where such a state emerges. We further inspect its robustness against a progressive de-multiplexing of the network, and provide experimental evidence by means of multiplexes of nonlinear electronic circuits affected by intrinsic noise and parameter mismatch.
Nonlinear Dynamic Buckling of Damaged Composite Cylindrical Shells
Institute of Scientific and Technical Information of China (English)
WANG Tian-lin; TANG Wen-yong; ZHANG Sheng-kun
2007-01-01
Based on the first order shear deformation theory(FSDT), the nonlinear dynamic equations involving transverse shear deformation and initial geometric imperfections were obtained by Hamilton's philosophy. Geometric deformation of the composite cylindrical shell was treated as the initial geometric imperfection in the dynamic equations, which were solved by the semi-analytical method in this paper. Stiffness reduction was employed for the damaged sub-layer, and the equivalent stiffness matrix was obtained for the delaminated area. By circumferential Fourier series expansions for shell displacements and loads and by using Galerkin technique, the nonlinear partial differential equations were transformed to ordinary differential equations which were finally solved by the finite difference method. The buckling was judged from shell responses by B-R criteria, and critical loads were then determined. The effect of the initial geometric deformation on the dynamic response and buckling of composite cylindrical shell was also discussed, as well as the effects of concomitant delamination and sub-layer matrix damages.
Nonlinear optical model for strip plasmonic waveguides
DEFF Research Database (Denmark)
Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei
2016-01-01
This paper presents a theoretical model of nonlinear optical properties for strip plasmonic waveguides. The particular waveguides geometry that we investigate contains a gold core, adhesion layers, and silicon dioxide cladding. It is shown that the third-order susceptibility of the gold core...... significantly depends on the layer thickness and has the dominant contribution to the effective third-order susceptibility of the long-range plasmon polariton mode. This results in two nonlinear optical effects in plasmonic waveguides, which we experimentally observed and reported in [Opt. Lett. 41, 317 (2016......)]. The first effect is the nonlinear power saturation of the plasmonic mode, and the second effect is the spectral broadening of the plasmonic mode. Both nonlinear plasmonic effects can be used for practical applications and their appropriate model will be important for further developments in communication...
Multi-layer model vs. single-layer model for N and P doped poly layers in etch bias modeling
Li, Jianliang; Vidal-Russell, Ezequiel; Beale, Daniel; Wang, Chunqing; Melvin, Lawrence S., III
2010-09-01
In modern photolithography, ever smaller critical dimension (CD) budgets require tighter control over the entire process, demanding more accurate practice of optical proximity correction (OPC). In last decade, the model based OPC (MBOPC) has outpaced the rule based OPC (RBOPC) and become widely adopted in semiconductor industry. During the MBOPC process, the physical models are called to compute the signal values at the evaluation points and the design patterns are perturbed such that the final model contours are as close to the targets as possible. It has been demonstrated that in addition to simulating the optics and resist effects, the physical models must accommodate the pattern distortion due to etch process as well. While the etch process may be lumped with optics and resist processes into one model for the 65nm and above nodes, it can no longer be treated as small perturbations on photolithographic effects for more advanced nodes and it is highly desired to build a physics-based etch model formulations that differ from the conventional convolution-based process models used to simulate the optical and resist effect. Our previous studies proposed a novel non-linear etch modeling object in combination with conventional convolution kernels, which simulates the non-optics and non-resist proximity effect successfully. This study examines further the non-linear etch modeling method by checking the different behaviors of N and p doped layers which physically have different etching rates and should be represented differently in etch modeling. The experimental results indicate that the fitting accuracy is significantly improved when the data points are split into N and P groups and calibrated separately. The N and P layer etch models are used in staged MBOPCs and the results are compared with single-layer model as well.
Nonlinear graphene plasmonics (Conference Presentation)
Cox, Joel D.; Marini, Andrea; Garcia de Abajo, Javier F.
2016-09-01
The combination of graphene's intrinsically-high nonlinear optical response with its ability to support long-lived, electrically tunable plasmons that couple strongly with light has generated great expectations for application of the atomically-thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Based on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation, we show that finite-size effects produce large contributions that increase the nonlinear response associated with plasmons in nanostructured graphene to significantly higher levels than previously thought, particularly in the case of Kerr-type optical nonlinearities. Motivated by this finding, we discuss and compare saturable absorption in extended and nanostructured graphene, with or without plasmonic enhancement, within the context of passive mode-locking for ultrafast lasers. We also explore the possibility of high-harmonic generation in doped graphene nanoribbons and nanoislands, where illumination by an infrared pulse of moderate intensity, tuned to a plasmon resonance, is predicted to generate light at harmonics of order 13 or higher, extending over the visible and UV regimes. Our atomistic description of graphene's nonlinear optical response reveals its complex nature in both extended and nanostructured systems, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices.
DEFF Research Database (Denmark)
Kjellberg, Caspar Mølholt; Meredith, David
2014-01-01
The best text method is commonly applied among music scholars engaged in producing critical editions. In this method, a comment list is compiled, consisting of variant readings and editorial emendations. This list is maintained by inserting the comments into a document as the changes are made....... Since the comments are not input sequentially, with regard to position, but in arbitrary order, this list must be sorted by copy/pasting the rows into place—an error-prone and time-consuming process. Scholars who produce critical editions typically use off-the-shelf music notation software...... such as Sibelius or Finale. It was hypothesized that it would be possible to develop a Sibelius plug-in, written in Manuscript 6, that would improve the critical editing work flow, but it was found that the capabilities of this scripting language were insufficient. Instead, a 3-part system was designed and built...
Trofimov, Vyacheslav A.; Lysak, T. M.
2016-05-01
We demonstrate a new possibility of a soliton velocity control at its propagation in a nonlinear layered structure (1D photonic crystal) which is placed in a nonlinear ambient medium. Nonlinear response of the ambient medium, as well as the PhC layers, is cubic. At the initial time moment, a soliton is spread over a few layers of PhC. Then, soliton propagates across the layered structure because of the initial wave-vector direction presence for the laser beam. The soliton reaches the PhC faces and reflects from them or passes through the face. As a nonlinear medium surrounds the PhC, the laser beam obtains additional impulse after interaction with this medium and accelerates (or slows down or stops near the PhC face). Nonlinear response of the ambient medium can be additionally created by another laser beam which shines near the PhC faces.
Nonlinear Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
Nonlinear transmission sputtering
Bitensky, I. S.; Sigmund, P.
1996-05-01
General expressions have been derived for the nonlinear yield of transmission sputtering for an incident polyatomic ion under the assumption that the molecule breaks up on entering the target and that sputter yields are enhanced due to proximity of atomic trajectories. Special attention is given to the case of negligible Coulomb explosion where projectile atoms penetrate independently. For weakly overlapping trajectories, the yield enhancement factor of a polyatomic molecule can be expressed by that of a diatom, amended with a correction for triple correlations if necessary. This expression is in good agreement with recent experimental findings on phenylalanine targets. Pertinent results on multiple scattering of atomic ions are reviewed and applied to independently-moving fragment atoms. The merits of measurements at variable layer thickness in addition to variable projectile energy are mentioned.
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
Geometrically nonlinear behavior of piezoelectric laminated plates
Rabinovitch, Oded
2005-08-01
The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.
The viscous surface-internal wave problem: nonlinear Rayleigh-Taylor instability
Wang, Yanjin
2011-01-01
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface tension is either taken into account at both free boundaries or neglected at both. We are concerned with the Rayleigh-Taylor instability, so we assume that the upper fluid is heavier than the lower fluid. When the surface tension at the free internal interface is below a critical value, which we identify, we establish that the problem under consideration is nonlinearly unstable.
Interval Mathematics Applied to Critical Point Transitions
Stradi, Benito A.
2012-01-01
The determination of critical points of mixtures is important for both practical and theoretical reasons in the modeling of phase behavior, especially at high pressure. The equations that describe the behavior of complex mixtures near critical points are highly nonlinear and with multiplicity of solutions to the critical point equations. Interval arithmetic can be used to reliably locate all the critical points of a given mixture. The method also verifies the nonexistence of a critical point ...
Yang, Tianqi; Huang, Xiaoting; Zhou, Hong; Wu, Guangheng; Lai, Tianshu
2016-05-30
MoS2 films are grown on SiO2/Si substrates by chemical vapor deposition. The vibrational properties of optical phonons of mono-, bi- and multilayer MoS2 are studied by Raman scattering spectroscopy over temperature range from 90 to 540 K with 514.5 nm and 785 nm lasers. The Raman peaks of E2g1 and A1g modes are observed simultaneously for mono-, bi- and multilayer MoS2 with 514.5 nm laser, but only the Raman peak of E2g1 mode is seen for monolayer MoS2 as 785 nm laser is used, revealing electron-phonon exchange excitation mechanism of A1g mode for the first time. The Raman shifts of E2g1 and A1g modes present obvious nonlinear temperature dependence. A semi-quantitative model is used to fit the nonlinear temperature dependence of Raman shifts which matches well to experimental data. Meanwhile, the fitting results reveal that the nonlinear temperature dependence of Raman shifts of E2g1 mode mainly originates from three-phonon anharmonic effect, while one of A1g mode is contributed by stronger three- and weaker four-phonon anharmonic effects cooperatively but two contributions are comparable in intensity.
Stability and nonlinear regimes of flow over a saturated porous medium
Directory of Open Access Journals (Sweden)
T. P. Lyubimova
2013-07-01
Full Text Available The paper deals with the investigation of stability and nonlinear regimes of flow over the saturated porous medium applied to the problem of stability of water flow over the bottom covered with vegetation. It is shown that the velocity profile of steady plane-parallel flow has two inflection points, which results in instability of this flow. The neutral stability curves, the dependencies of critical Reynolds number and the wave number of most dangerous perturbations on the ratio of porous layer thickness to the total thickness are obtained. The nonlinear flow regimes are investigated numerically by finite difference method. It is found that at supercritical parameter values waves travelling in the direction of the base flow take place.
Nonlinear cumulative damage model for multiaxial fatigue
Institute of Scientific and Technical Information of China (English)
SHANG De-guang; SUN Guo-qin; DENG Jing; YAN Chu-liang
2006-01-01
On the basis of the continuum fatigue damage theory,a nonlinear uniaxial fatigue cumulative damage model is first proposed.In order to describe multiaxial fatigue damage characteristics,a nonlinear multiaxial fatigue cumulative damage model is developed based on the critical plane approach,The proposed model can consider the multiaxial fatigue limit,mean hydrostatic pressure and the unseparated characteristic for the damage variables and loading parameters.The recurrence formula of fatigue damage model was derived under multilevel loading,which is used to predict multiaxial fatigue life.The results showed that the proposed nonlinear multiaxial fatigue cumulative damage model is better than Miner's rule.
Third-order susceptibility of gold for ultrathin layers
DEFF Research Database (Denmark)
Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei
2016-01-01
This Letter presents an experimental study of nonlinear plasmonic effects in gold-stripe waveguides. The optical characterization is performed by a picosecond laser and reveals two nonlinear effects related to propagation of long-range surface plasmon polaritons: nonlinear power transmission...... of plasmonic modes and spectral broadening of plasmonic modes. The experimental values of the third-order susceptibility of the gold layers are extracted. They exhibit a clear dependence on layer thickness. (C) 2016 Optical Society of America...
The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
Pedlosky, J.; Flierl, G. R.
2006-12-01
The nonlinear dynamics of baroclinically unstable waves in a time dependent zonal shear flow is considered in the framework of the two-layer Phillips model on the beta plane. In most cases considered in this study the amplitude of the shear is well below the critical value of the steady shear version of the model. Nevertheless, the time dependent problem in which the shear oscillates periodically is unstable, and the unstable waves grow to substantial amplitudes, in some cases with strongly nonlinear and turbulent characteristics. For very small values of the shear amplitude in the presence of dissipation an analytical, asymptotic theory predicts a self-sustained wave whose amplitude undergoes a nonlinear oscillation whose period is amplitude dependent. There is a sensitive amplitude dependence of the wave on the frequency of the oscillating shear when the shear amplitude is small. This behavior is also found in a truncated model of the dynamics, and that model is used to examine larger shear amplitudes. When there is a mean value of the shear in addition to the oscillating component, but such that the total shear is still subcritical, the resulting nonlinear states exhibit a rectified horizontal buoyancy flux with a nonzero time average as a result of the instability of the oscillating shear. For higher, still subcritical, values of the shear we have detected a symmetry breaking in which a second cross-stream mode is generated through an instability of the unstable wave although this second mode would by itself be stable on the basic time dependent current. For shear values that are substantially subcritical but of order of the critical shear, calculations with a full quasi-geostrophic numerical model reveal a turbulent flow generated by the instability. If the beta effect is disregarded the inviscid, linear problem is formally stable. However, our calculations show that a small degree of nonlinearity is enough to destabilize the flow leading to large amplitude
Cross-layer design in optical networks
Brandt-Pearce, Maïté; Demeester, Piet; Saradhi, Chava
2013-01-01
Optical networks have become an integral part of the communications infrastructure needed to support society’s demand for high-speed connectivity. Cross-Layer Design in Optical Networks addresses topics in optical network design and analysis with a focus on physical-layer impairment awareness and network layer service requirements, essential for the implementation and management of robust scalable networks. The cross-layer treatment includes bottom-up impacts of the physical and lambda layers, such as dispersion, noise, nonlinearity, crosstalk, dense wavelength packing, and wavelength line rates, as well as top-down approaches to handle physical-layer impairments and service requirements.
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
PENG SHIGE
2005-01-01
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations.The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
Z-scan measurement of the nonlinear refractive index of graphene.
Zhang, Han; Virally, Stéphane; Bao, Qiaoliang; Ping, Loh Kian; Massar, Serge; Godbout, Nicolas; Kockaert, Pascal
2012-06-01
Under strong laser illumination, few-layer graphene exhibits both a transmittance increase due to saturable absorption and a nonlinear phase shift. Here, we unambiguously distinguish these two nonlinear optical effects and identify both real and imaginary parts of the complex nonlinear refractive index of graphene. We show that graphene possesses a giant nonlinear refractive index n(2)≃10(-7) cm(2) W(-1), almost 9 orders of magnitude larger than bulk dielectrics. We find that the nonlinear refractive index decreases with increasing excitation flux but slower than the absorption. This suggests that graphene may be a very promising nonlinear medium, paving the way for graphene-based nonlinear photonics.
Three-dimensional modes of a symmetric nonlinear plane waveguide
Akhmediev, N. N.; Nabiev, R. F.; Popov, Yu. M.
1989-01-01
The three-dimensional problem of a symmetric nonlinear plane waveguide, which consist of a linear medium layer surrounded by nonlinear media, is investigated. The stationary solution of this problem is a mode whose field is falling to zero at infinity in all directions perpendicular to the propagation direction. The even, odd and assymetrical solutions of the problem are obtained.
Propagation regimes of interfacial solitary waves in a three-layer fluid
Directory of Open Access Journals (Sweden)
O. E. Kurkina
2015-01-01
Full Text Available Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid immiscible layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most of near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equation (KdV-type equations with combined nonlinearity for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.
Ultrasonic nonlinear guided wave inspection of microscopic damage in a composite structure
Zhang, Li; Borigo, Cody; Owens, Steven; Lissenden, Clifford; Rose, Joseph; Hakoda, Chris
2017-02-01
Sudden structural failure is a severe safety threat to many types of military and industrial composite structures. Because sudden structural failure may occur in a composite structure shortly after macroscale damage initiates, reliable early diagnosis of microdamage formation in the composite structure is critical to ensure safe operation and to reduce maintenance costs. Ultrasonic guided waves have been widely used for long-range defect detection in various structures. When guided waves are generated under certain excitation conditions, in addition to the traditional linear wave mode (known as the fundamental harmonic wave mode), a number of nonlinear higher-order harmonic wave modes are also be generated. Research shows that the nonlinear parameters of a higher-order harmonic wave mode could have excellent sensitivity to microstructural changes in a material. In this work, we successfully employed a nonlinear guided wave structural health monitoring (SHM) method to detect microscopic impact damage in a 32-layer carbon/epoxy fiber-reinforced composite plate. Our effort has demonstrated that, utilizing appropriate transducer design, equipment, excitation signals, and signal processing techniques, nonlinear guided wave parameter measurements can be reliably used to monitor microdamage initiation and growth in composite structures.
Topological approximation of the nonlinear Anderson model
Milovanov, Alexander V.; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the
Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity
Bache, Morten; Lavrinenko, Andrei V.
2017-09-01
Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.
Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Sheet
Institute of Scientific and Technical Information of China (English)
Krishnendu Bhattacharyya
2011-01-01
An analysis is made to study boundary layer flow and heat transfer over an exponentially shrinking sheet.Using similarity transformations in exponential form,the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations,which are then solved numerically using a very effcient shooting method. The analysis reveals the conditions for the existence of steady boundary layer flow due to exponential shrinking of the sheet and it is found that when the mass suction parameter exceeds a certain critical value,steady flow is possible.The dual solutions for velocity and temperature distributions are obtained.With increasing values of the mass suction parameter,the skin friction coefficient increases for the first solution and decreases for the second solution.
On some nonlinear potential problems
Directory of Open Access Journals (Sweden)
M. A. Efendiev
1999-05-01
Full Text Available The degree theory of mappings is applied to a two-dimensional semilinear elliptic problem with the Laplacian as principal part subject to a nonlinear boundary condition of Robin type. Under some growth conditions we obtain existence. The analysis is based on an equivalent coupled system of domain--boundary variational equations whose principal parts are the Dirichlet bilinear form in the domain and the single layer potential bilinear form on the boundary, respectively. This system consists of a monotone and a compact part. Additional monotonicity implies convergence of an appropriate Richardson iteration.
Steelhead Critical Habitat, Coast - NOAA [ds122
California Department of Resources — This layer depicts areas designated for Steelhead Critical Habitat as well as habitat type and quality in the Coastal California Steelhead ESUs (evolutionarily...
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
The purpose of the research presented here is to investigate basic physical properties in nonlinear optical materials with delayed or nonlocal nonlinearity. Soliton propagation, spectral broadening and the influence of the nonlocality or delay of the nonlinearity are the main focusses in the work...
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind P. Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications,the Raman amplification being only one of the recent examples. In this tutorial I review the vario us nonlinear effects occurring in optical fibers from both standpoints..
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind; P.; Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications, the Raman amplification being only one of the recent examples. In this tutorial I review the various nonlinear effects occurring in optical fibers from both standpoints..
Thinking Critically about Critical Thinking
Mulnix, Jennifer Wilson
2012-01-01
As a philosophy professor, one of my central goals is to teach students to think critically. However, one difficulty with determining whether critical thinking can be taught, or even measured, is that there is widespread disagreement over what critical thinking actually is. Here, I reflect on several conceptions of critical thinking, subjecting…
Bouteraa, Mondher; Nouar, Chérif
2015-12-01
Finite-amplitude thermal convection in a shear-thinning fluid layer between two horizontal plates of finite thermal conductivity is considered. Weakly nonlinear analysis is adopted as a first approach to investigate nonlinear effects. The rheological behavior of the fluid is described by the Carreau model. As a first step, the critical conditions for the onset of convection are computed as a function of the ratio ξ of the thermal conductivity of the plates to the thermal conductivity of the fluid. In agreement with the literature, the critical Rayleigh number Ra(c) and the critical wave number k(c) decrease from 1708 to 720 and from 3.11 to 0, when ξ decreases from infinity to zero. In the second step, the critical value α(c) of the shear-thinning degree above which the bifurcation becomes subcritical is determined. It is shown that α(c) increases with decreasing ξ. The stability of rolls and squares is then investigated as a function of ξ and the rheological parameters. The limit value ξ(c), below which squares are stable, decreases with increasing shear-thinning effects. This is related to the fact that shear-thinning effects increase the nonlinear interactions between sets of rolls that constitute the square patterns [M. Bouteraa et al., J. Fluid Mech. 767, 696 (2015)]. For a significant deviation from the critical conditions, nonlinear convection terms and nonlinear viscous terms become stronger, leading to a further diminution of ξ(c). The dependency of the heat transfer on ξ and the rheological parameters is reported. It is consistent with the maximum heat transfer principle. Finally, the flow structure and the viscosity field are represented for weakly and highly conducting plates.
Holographic paramagnetism-ferromagnetism phase transition with the nonlinear electrodynamics
Zhang, Cheng-Yuan; Zhang, Ya-Nan; Wang, Huan-Yu; Wu, Meng-Meng
2016-01-01
In the probe limit, we investigate the nonlinear electrodynamical effects of the both exponential form and the logarithmic form on the holographic paramagnetism-ferromagnetism phase transition in the background of a Schwarzschild-AdS black hole spacetime. Moreover, by comparing the exponential form of nonlinear electrodynamics with the logarithmic form of nonlinear electrodynamics and the Born-Infeld nonlinear electrodynamics which has been presented in Ref.~\\cite{Wu:2016uyj}, we find that the higher nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder form in the case without external field. Furthermore, the increase of nonlinear parameter b will result in extending the period of the external magnetic field. Especially, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noticeable.
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Nonlinear reshaping of terahertz pulses with graphene metamaterials
Rapoport, Yu.; Grimalsky, V.; Iorsh, I.; Kalinich, N.; Koshevaya, S.; Castrejon-Martinez, Ch.; Kivshar, Yu. S.
2013-12-01
We study the propagation of electromagnetic waves through a slab of graphene metamaterial composed of the layers of graphene separated by dielectric slabs. Starting from the kinetic expression for two-dimensional electric current in graphene, we derive a novel equation describing the nonlinear propagation of terahertz electromagnetic pulses through the layered graphene-dielectric structure in the presence of losses and non-linearities. We demonstrate strong nonlinearity-induced reshaping of transmitted and reflected terahertz pulses through the interaction with the thin multilayer graphene metamaterial structure.
Interaction nonlinearity in asphalt binders
Motamed, Arash; Bhasin, Amit; Liechti, Kenneth M.
2012-05-01
Asphalt mixtures are complex composites that comprise aggregate, asphalt binder, and air. Several research studies have shown that the mechanical behavior of the asphalt mixture is strongly influenced by the matrix, i.e. the asphalt binder. Characterization and a thorough understanding of the binder behavior is the first and crucial step towards developing an accurate constitutive model for the composite. Accurate constitutive models for the constituent materials are critical to ensure accurate performance predictions at a material and structural level using micromechanics. This paper presents the findings from a systematic investigation into the nature of the linear and nonlinear response of asphalt binders subjected to different types of loading using the Dynamic Shear Rheometer (DSR). Laboratory test data show that a compressive normal force is generated in an axially constrained specimen subjected to torsional shear. This paper investigates the source of this normal force and demonstrates that the asphalt binder can dilate when subjected to shear loads. This paper also presents the findings from a study conducted to investigate the source of the nonlinearity in the asphalt binder. Test results demonstrate that the application of cyclic shear loads results in the development of a normal force and a concomitant reduction in the dynamic shear modulus. This form of nonlinear response is referred to as an "interaction nonlinearity". A combination of experimental and analytical tools is used to demonstrate and verify the presence of this interaction nonlinearity in asphalt binders. The findings from this study highlight the importance of modeling the mechanical behavior of asphalt binders based on the overall stress state of the material.
In situ nonlinear elastic behavior of soil observed by DAET
Energy Technology Data Exchange (ETDEWEB)
Larmat, Carene [Los Alamos National Laboratory; Renaud, Guillaume [Eramus Medical Center, Rotterdam, The Netherlands; Rutledge, James T. [EES-17: GEOPHYSICS; Lee, Richard C. [Los Alamos National Laboratory; Guyer, Robert A. [Los Alamos National Laboratory; Johnson, Paul A. [Los Alamos National Laboratory
2012-07-05
The key to safe design of critical facilities (strong ground motion in low velocity materials such as soils). Current approaches are predictions from measurements of the elastic non-linear properties of boreholes samples. Need for in-situ, local and complete determination of non-linear properties of soil, rock in response to high-strain motion.
Defocusing regimes of nonlinear waves in media with negative dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.
1996-01-01
Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...
Global Well-Posedness for Cubic NLS with Nonlinear Damping
Antonelli, Paolo
2010-11-04
We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions. © Taylor & Francis Group, LLC.
Modulational instability in nonlocal nonlinear Kerr media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Juul Rasmussen, Jens
2001-01-01
We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function....... For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media...... for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose...
Nonlinear and Non Normal Regression Models in Physiological Research
1984-01-01
Applications of nonlinear and non normal regression models are in increasing order for appropriate interpretation of complex phenomenon of biomedical sciences. This paper reviews critically some applications of these models physiological research.
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Nonlinear propagation and control of acoustic waves in phononic superlattices
Jiménez, Noé; Picó, Rubén; García-Raffi, Lluís M; Sánchez-Morcillo, Víctor J
2015-01-01
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band-gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g. cubic) nonlinearities, or extremely linear media (where distortion can be cancelled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.
Introduction to Nonlinear and Global Optimization
Hendrix, E.M.T.; Tóth, B.
2010-01-01
This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization
Critical care helps people with life-threatening injuries and illnesses. It might treat problems such as complications ... a team of specially-trained health care providers. Critical care usually takes place in an intensive care ...
DEFF Research Database (Denmark)
Tuz, Vladimir R.; Novitsky, Denis V.; Prosvirnin, Sergey L.
2014-01-01
Optical properties of one-dimensional photonic structures consisting of Kerr-type nonlinear and magnetic layers under the action of an external static magnetic field in the Faraday geometry are investigated. The structure is a periodic arrangement of alternating nonlinear and magnetic layers (a one...
Chesebro, James W.; And Others
1990-01-01
Argues that archetypal criticism is a useful way of examining universal, historical, and cross-cultural symbols in classrooms. Identifies essential features of an archetype; outlines operational and critical procedures; illustrates archetypal criticism as applied to the cross as a symbol; and provides a synoptic placement for archetypal criticism…
Plasma metamaterials as cloaking and nonlinear media
Sakai, O.; Yamaguchi, S.; Bambina, A.; Iwai, A.; Nakamura, Y.; Tamayama, Y.; Miyagi, S.
2017-01-01
Plasma metamaterials, composites of low-temperature plasmas and periodic functional microstructures, work as cloaking and nonlinear media. Due to functions of the microstructures like negative permeability, electromagnetic waves in and around plasma metamaterials propagate in a quite different manner from the case with the conventional space in which relative permeability is positive and unity. Using plasmas and plasma metamaterials, we achieve various controls of microwave propagating paths such as unidirectionality and cloaking in the two- or 3D spaces. For instance, a concentric plasma layer makes wave propagation unidirectional, and waves propagate in different routes when they start inside or outside the concentric layer. Furthermore, due to spatial permittivity gradient and anisotropic refractive index, electromagnetic waves detour in plasma metamaterial layers. Another significant point that plasma metamaterials can realize is nonlinearity. When we study high-power electromagnetic waves propagating in them, we observe several properties describable in terms of nonlinear dynamics and nonlinear photonics. Microwaves beyond threshold energy trigger bifurcations in plasma permittivity, and the second harmonic wave detected simultaneously is generated with strong emission levels. Such electromagnetic wave propagation is achieved with advantages over other materials, since plasmas and metallic microstructures work in harmony and in synergy.
Non-linear growth and condensation in multiplex networks
Nicosia, Vincenzo; Latora, Vito; Barthelemy, Marc
2013-01-01
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which a single node connects to nearly all other nodes of a layer.
How Critical Is Critical Thinking?
Shaw, Ryan D.
2014-01-01
Recent educational discourse is full of references to the value of critical thinking as a 21st-century skill. In music education, critical thinking has been discussed in relation to problem solving and music listening, and some researchers suggest that training in critical thinking can improve students' responses to music. But what exactly is…
Coherent fiber supercontinuum laser for nonlinear biomedical imaging
Tu, Haohua; Liu, Yuan; Liu, Xiaomin; Lægsgaard, Jesper; Turchinovich, Dmitry; Boppart, Stephen A.
2012-12-01
Nonlinear biomedical imaging has not benefited from the well-known techniques of fiber supercontinuum generation for reasons such as poor coherence (or high noise), insufficient controllability, low spectral power intensity, and inadequate portability. Fortunately, a few techniques involving nonlinear fiber optics and femtosecond fiber laser development have emerged to overcome these critical limitations. These techniques pave the way for conducting point-of-care nonlinear biomedical imaging by a low-maintenance cost-effective coherent fiber supercontinuum laser, which covers a broad emission wavelength of 350-1700 nm. A prototype of this laser has been demonstrated in label-free multimodal nonlinear imaging of cell and tissue samples.
Self-trapping transition in nonlinear cubic lattices
Naether, Uta; Guzmán-Silva, Diego; Molina, Mario I; Vicencio, Rodrigo A
2013-01-01
We explore the fundamental question about the critical nonlinearity value needed to dynamically localize energy in discrete nonlinear cubic (Kerr) lattices. We focus on the effective frequency and participation ratio of the profile to determine the transition into localization, performing several numerical simulations in one-, two-, and three-dimensional lattices. A simple criterium is developed - for the case of an initially localized excitation - defining the transition region in parameter space ("dynamical tongue") from a delocalized to a localized profile. A general analytical estimate of the critical nonlinearity value for which this transition occurs is obtained.
Gaillard, Pierre; Giovangigli, Vincent; Matuszewski, Lionel
2016-12-01
We investigate the impact of nonideal diffusion on the structure of supercritical cryogenic binary mixing layers. This situation is typical of liquid fuel injection in high-pressure rocket engines. Nonideal diffusion has a dramatic impact in the neighborhood of chemical thermodynamic stability limits where the components become quasi-immiscible and ultimately form a nonmixing layer. Numerical simulations are performed for mixing layers of H2 and N2 at a pressure of 100 atm and temperature around 120-150 K near chemical thermodynamic stability limits.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Ionescu, Tudor C.; Scherpen, Jacquelien M. A.
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
Directory of Open Access Journals (Sweden)
W. L. Fouché
1983-03-01
Full Text Available In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.
Nonlinear Electrodynamics and QED
2003-01-01
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topologi...
Directory of Open Access Journals (Sweden)
Pippin Barr
2016-11-01
Full Text Available Games can serve a critical function in many different ways, from serious games about real world subjects to self-reflexive commentaries on the nature of games themselves. In this essay we discuss critical possibilities stemming from the area of critical design, and more specifically Carl DiSalvo’s adversarial design and its concept of reconfiguring the remainder. To illustrate such an approach, we present the design and outcomes of two games, Jostle Bastard and Jostle Parent. We show how the games specifically engage with two previous games, Hotline Miami and Octodad: Dadliest Catch, reconfiguring elements of those games to create interactive critical experiences and extensions of the source material. Through the presentation of specific design concerns and decisions, we provide a grounded illustration of a particular critical function of videogames and hope to highlight this form as another valuable approach in the larger area of videogame criticism.
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission. (c) 2008 Optical Society of America
Organic nonlinear optical materials
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinearity-reduced interferometer
Wu, Chien-ming
2007-12-01
Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.
Energy Technology Data Exchange (ETDEWEB)
A. Alsaed
2004-09-14
The ''Disposal Criticality Analysis Methodology Topical Report'' (YMP 2003) presents the methodology for evaluating potential criticality situations in the monitored geologic repository. As stated in the referenced Topical Report, the detailed methodology for performing the disposal criticality analyses will be documented in model reports. Many of the models developed in support of the Topical Report differ from the definition of models as given in the Office of Civilian Radioactive Waste Management procedure AP-SIII.10Q, ''Models'', in that they are procedural, rather than mathematical. These model reports document the detailed methodology necessary to implement the approach presented in the Disposal Criticality Analysis Methodology Topical Report and provide calculations utilizing the methodology. Thus, the governing procedure for this type of report is AP-3.12Q, ''Design Calculations and Analyses''. The ''Criticality Model'' is of this latter type, providing a process evaluating the criticality potential of in-package and external configurations. The purpose of this analysis is to layout the process for calculating the criticality potential for various in-package and external configurations and to calculate lower-bound tolerance limit (LBTL) values and determine range of applicability (ROA) parameters. The LBTL calculations and the ROA determinations are performed using selected benchmark experiments that are applicable to various waste forms and various in-package and external configurations. The waste forms considered in this calculation are pressurized water reactor (PWR), boiling water reactor (BWR), Fast Flux Test Facility (FFTF), Training Research Isotope General Atomic (TRIGA), Enrico Fermi, Shippingport pressurized water reactor, Shippingport light water breeder reactor (LWBR), N-Reactor, Melt and Dilute, and Fort Saint Vrain Reactor spent nuclear fuel (SNF). The scope of
Nonlinear Negative Refraction by Difference Frequency Generation
Cao, Jianjun; Feng, Yaming; Wan, Wenjie
2015-01-01
Negative refraction has attracted much interest for its promising capability in imaging applications. Such an effect can be implemented by negative index meta-materials, however, which are usually accompanied by high loss and demanding fabrication processes. Recently, alternative nonlinear approaches like phase conjugation and four wave mixing have shown advantages of low-loss and easy-to-implement, but associated problems like narrow accepting angles can still halt their practical applications. Here we demonstrate theoretically and experimentally a new scheme to realize negative refraction by nonlinear difference frequency generation with wide tunability, where a thin BBO slice serves as a negative refraction layer bending the input signal beam to the idler beam at a negative angle. Furthermore, we realize optical focusing effect using such nonlinear negative refraction, which may enable many potential applications in imaging science.
Nonlinear negative refraction by difference frequency generation
Cao, Jianjun; Shen, Dongyi; Feng, Yaming; Wan, Wenjie
2016-05-01
Negative refraction has attracted much interest for its promising capability in imaging applications. Such an effect can be implemented by negative index meta-materials, however, which are usually accompanied by high loss and demanding fabrication processes. Recently, alternative nonlinear approaches like phase conjugation and four wave mixing have shown advantages of low-loss and easy-to-implement, but associated problems like narrow accepting angles can still halt their practical applications. Here, we demonstrate theoretically and experimentally a scheme to realize negative refraction by nonlinear difference frequency generation with wide tunability, where a thin Beta barium borate slice serves as a negative refraction layer bending the input signal beam to the idler beam at a negative angle. Furthermore, we realize optical focusing effect using such nonlinear negative refraction, which may enable many potential applications in imaging science.
Resolution enhancement in nonlinear photoacoustic imaging
Energy Technology Data Exchange (ETDEWEB)
Goy, Alexandre S.; Fleischer, Jason W. [Department of Electrical Engineering, Princeton University, Olden St., Princeton, New Jersey 08544 (United States)
2015-11-23
Nonlinear processes can be exploited to gain access to more information than is possible in the linear regime. Nonlinearity modifies the spectra of the excitation signals through harmonic generation, frequency mixing, and spectral shifting, so that features originally outside the detector range can be detected. Here, we present an experimental study of resolution enhancement for photoacoustic imaging of thin metal layers immersed in water. In this case, there is a threshold in the excitation below which no acoustic signal is detected. Above threshold, the nonlinearity reduces the width of the active area of the excitation beam, resulting in a narrower absorption region and thus improved spatial resolution. This gain is limited only by noise, as the active area of the excitation can be arbitrarily reduced when the fluence becomes closer to the threshold. Here, we demonstrate a two-fold improvement in resolution and quantify the image quality as the excitation fluence goes through threshold.
High resolution 3D nonlinear integrated inversion
Institute of Scientific and Technical Information of China (English)
Li Yong; Wang Xuben; Li Zhirong; Li Qiong; Li Zhengwen
2009-01-01
The high resolution 3D nonlinear integrated inversion method is based on nonlinear theory. Under layer control, the log data from several wells (or all wells) in the study area and seismic trace data adjacent to the wells are input to a network with multiple inputs and outputs and are integratedly trained to obtain an adaptive weight function of the entire study area. Integrated nonlinear mapping relationships are built and updated by the lateral and vertical geologic variations of the reservoirs. Therefore, the inversion process and its inversion results can be constrained and controlled and a stable seismic inversion section with high resolution with velocity inversion, impedance inversion, and density inversion sections, can be gained. Good geologic effects have been obtained in model computation tests and real data processing, which verified that this method has high precision, good practicality, and can be used for quantitative reservoir analysis.
Strongly nonlinear steepening of long interfacial waves
Directory of Open Access Journals (Sweden)
N. Zahibo
2007-06-01
Full Text Available The transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zero-crossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks.
Early Warning Signals for Regime Transition in the Stable Boundary Layer: A Model Study
van Hooijdonk, I. G. S.; Moene, A. F.; Scheffer, M.; Clercx, H. J. H.; van de Wiel, B. J. H.
2017-02-01
The evening transition is investigated in an idealized model for the nocturnal boundary layer. From earlier studies it is known that the nocturnal boundary layer may manifest itself in two distinct regimes, depending on the ambient synoptic conditions: strong-wind or overcast conditions typically lead to weakly stable, turbulent nights; clear-sky and weak-wind conditions, on the other hand, lead to very stable, weakly turbulent conditions. Previously, the dynamical behaviour near the transition between these regimes was investigated in an idealized setting, relying on Monin-Obukhov (MO) similarity to describe turbulent transport. Here, we investigate a similar set-up, using direct numerical simulation; in contrast to MO-based models, this type of simulation does not need to rely on turbulence closure assumptions. We show that previous predictions are verified, but now independent of turbulence parametrizations. Also, it appears that a regime shift to the very stable state is signaled in advance by specific changes in the dynamics of the turbulent boundary layer. Here, we show how these changes may be used to infer a quantitative estimate of the transition point from the weakly stable boundary layer to the very stable boundary layer. In addition, it is shown that the idealized, nocturnal boundary-layer system shares important similarities with generic non-linear dynamical systems that exhibit critical transitions. Therefore, the presence of other, generic early warning signals is tested as well. Indeed, indications are found that such signals are present in stably stratified turbulent flows.
Rosette, Arturo
2009-01-01
This study focuses on the development and practices of Critical Muralists--community-educator-artist-leader-activists--and situates these specifically in relation to the Mexican mural tradition of los Tres Grandes and in relation to the history of public art more generally. The study examines how Critical Muralists address artistic and…
Directory of Open Access Journals (Sweden)
James Sae Siew
2015-01-01
Full Text Available Rail turnouts are built to enable flexibility in the rail network as they allow for vehicles to switch between various tracks, therefore maximizing the utilisation of existing rail infrastructure. In general, railway turnouts are a safety-critical and expensive feature to a rail system as they suffer aggressive operational loads, in comparison to a plain rail track, and thus require frequent monitoring and maintenance. In practice, great consideration is given to the dynamic interaction between the turnouts components as a failed component may have adverse effects on the performance of neighbouring components. This paper presents a nonlinear 3D finite element (FE model, taking into account the nonlinearities of materials, in order to evaluate the interaction and behaviour of turnout components. Using ABAQUS, the finite element model was developed to simulate standard concrete bearers with 60 kg/m rail and with a tangential turnout radius of 250 m. The turnout structure is supported by a ballast layer, which is represented by a nonlinearly deformable tensionless solid. The numerical studies firstly demonstrate the importance of load transfer mechanisms in the failure modes of the turnout components. The outcome will lead to a better design and maintenance of railway turnouts, improving public safety and operational reliability.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Ionescu, T. C.; Scherpen, J. M. A.; Korytowski, A; Malanowski, K; Mitkowski, W; Szymkat, M
2009-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
Menon, P. K. A.; Badgett, M. E.; Walker, R. A.
1992-01-01
Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.
Leslie, Thomas M.
1993-01-01
A focused approach to development and evaluation of organic polymer films for use in optoelectronics is presented. The issues and challenges that are addressed include: (1) material synthesis, purification, and the tailoring of the material properties; (2) deposition of uniform thin films by a variety of methods; (3) characterization of material physical properties (thermal, electrical, optical, and electro-optical); and (4) device fabrication and testing. Photonic materials, devices, and systems were identified as critical technology areas by the Department of Commerce and the Department of Defense. This approach offers strong integration of basic material issues through engineering applications by the development of materials that can be exploited as the active unit in a variety of polymeric thin film devices. Improved materials were developed with unprecedented purity and stability. The absorptive properties can be tailored and controlled to provide significant improvement in propagation losses and nonlinear performance. Furthermore, the materials were incorporated into polymers that are highly compatible with fabrication and patterning processes for integrated optical devices and circuits. By simultaneously addressing the issues of materials development and characterization, keeping device design and fabrication in mind, many obstacles were overcome for implementation of these polymeric materials and devices into systems. We intend to considerably improve the upper use temperature, poling stability, and compatibility with silicon based devices. The principal device application that was targeted is a linear electro-optic modulation etalon. Organic polymers need to be properly designed and coupled with existing integrated circuit technology to create new photonic devices for optical communication, image processing, other laser applications such as harmonic generation, and eventually optical computing. The progression from microscopic sample to a suitable film
Nonlinear Giant Magnetoresistance in Dual Spin Valves
Aziz, A.; Wessely, O. P.; Ali, M.; Edwards, D. M.; Marrows, C. H.; Hickey, B. J.; Blamire, M. G.
2009-12-01
Giant magnetoresistance (GMR) arises from differential scattering of the majority and minority spin electrons by a ferromagnet (FM) so that the resistance of a heterostructure depends on the relative magnetic orientation of the FM layers within it separated by nonmagnetic spacers. Here, we show that highly nonequilibrium spin accumulation in metallic heterostructures results in a current-dependent nonlinear GMR which is not predicted within the present understanding of GMR. The behavior can be explained by allowing the scattering asymmetries in an ultrathin FM layer to be current dependent.
Nonlinear dynamic analysis of sandwich panels
Lush, A. M.
1984-01-01
Two analytical techniques applicable to large deflection dynamic response calculations for pressure loaded composite sandwich panels are demonstrated. One technique utilizes finite element modeling with a single equivalent layer representing the face sheets and core. The other technique utilizes the modal analysis computer code DEPROP which was recently modified to include transverse shear deformation in a core layer. The example problem consists of a simply supported rectangular sandwich panel. Included are comparisons of linear and nonlinear static response calculations, in addition to dynamic response calculations.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Analysis of nonlinear damping properties of carbon
Kazakova, Olga I.; Smolin, Igor Yu.; Bezmozgiy, Iosif M.
2016-11-01
This paper describes research results of nonlinear damping properties of carbon fiber reinforced plastics. The experimental and computational research is performed on flat composite specimens with the gradual structure complication (from 1 to 12 layers). Specimens are subjected to three types of testing which are modal, harmonic and transient analyses. Relationships between the amplitude response and damping ratio are obtained by means of the analysis of variance as the result of this research.
Nonlinear Dynamic Characteristics of the Railway Vehicle
Uyulan, Çağlar; Gokasan, Metin
2017-06-01
The nonlinear dynamic characteristics of a railway vehicle are checked into thoroughly by applying two different wheel-rail contact model: a heuristic nonlinear friction creepage model derived by using Kalker 's theory and Polach model including dead-zone clearance. This two models are matched with the quasi-static form of the LuGre model to obtain more realistic wheel-rail contact model. LuGre model parameters are determined using nonlinear optimization method, which it's objective is to minimize the error between the output of the Polach and Kalker model and quasi-static LuGre model for specific operating conditions. The symmetric/asymmetric bifurcation attitude and stable/unstable motion of the railway vehicle in the presence of nonlinearities which are yaw damping forces in the longitudinal suspension system are analyzed in great detail by changing the vehicle speed. Phase portraits of the lateral displacement of the leading wheelset of the railway vehicle are drawn below and on the critical speeds, where sub-critical Hopf bifurcation take place, for two wheel-rail contact model. Asymmetric periodic motions have been observed during the simulation in the lateral displacement of the wheelset under different vehicle speed range. The coexistence of multiple steady states cause bounces in the amplitude of vibrations, resulting instability problems of the railway vehicle. By using Lyapunov's indirect method, the critical hunting speeds are calculated with respect to the radius of the curved track parameter changes. Hunting, which is defined as the oscillation of the lateral displacement of wheelset with a large domain, is described by a limit cycle-type oscillation nature. The evaluated accuracy of the LuGre model adopted from Kalker's model results for prediction of critical speed is higher than the results of the LuGre model adopted from Polach's model. From the results of the analysis, the critical hunting speed must be resolved by investigating the track tests
Damage detection in initially nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Bornn, Luke [Los Alamos National Laboratory; Farrar, Charles [Los Alamos National Laboratory; Park, Gyuhae [Los Alamos National Laboratory
2009-01-01
The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits, SHM has been widely studied over the past decade. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state - a condition that often does not hold in complex 'real world' systems and systems for which monitoring begins mid-lifecycle. In this work, we highlight the inadequacy of linear-based methodology in handling initially nonlinear systems. We then show how the recently developed autoregressive support vector machine (AR-SVM) approach to time series modeling can be used for detecting damage in a system that exhibits initially nonlinear response. This process is applied to data acquired from a structure with induced nonlinearity tested in a laboratory environment.
Institute of Scientific and Technical Information of China (English)
侯祥林; 翟中海; 郑莉; 刘铁林
2012-01-01
针对非线性偏微分方程初边值问题,基于差分法和动态设计变量优化算法原理,以时间计算层上离散节点的未知函数值为设计变量,以离散节点的差分方程组构造程式化的目标函数,提出了离散节点处未知函数值的逐层高精度优化算法.编制通用程序求解具体典型算例.并通过与解析解对比,表明了求解方法的正确性和有效性,为广泛的工程应用提供条件.%For non-linear partial differential equations with initial-boundary value problems,based on the difference method and the optimization method with dynamic design variables,using unknown function values on discrete node points on time layer as design variables,the difference equations sets of all the discrete node points are constructed as stylized objective function.A layered accurate optimization algorithm about computing unknown function value on discrete node point is proposed.Universal computing program is designed,and practical examples are analyzed.Through comparing computation results with exact results,the effectiveness and the feasibility of proposed method are verified.The method can provide the condition for engineering application.
Directory of Open Access Journals (Sweden)
Simon, Jane
2010-01-01
Full Text Available This essay considers how written language frames visual objects. Drawing on Michel Foucault’s response to Raymond Roussel’s obsessive description, the essay proposes a model of criticism where description might press up against its objects. This critical closeness is then mapped across the conceptual art practice and art criticism of Ian Burn. Burn attends to the differences between seeing and reading, and considers the conditions which frame how we look at images, including how we look at, and through words. The essay goes on to consider Meaghan Morris’s writing on Lynn Silverman’s photographs. Both Morris and Burn offer an alternative to a parasitic model of criticism and enact a patient way of looking across and through visual landscapes.
Directory of Open Access Journals (Sweden)
Jane Simon
2010-09-01
Full Text Available This essay considers how written language frames visual objects. Drawing on Michel Foucault’s response to Raymond Roussel’s obsessive description, the essay proposes a model of criticism where description might press up against its objects. This critical closeness is then mapped across the conceptual art practice and art criticism of Ian Burn. Burn attends to the differences between seeing and reading, and considers the conditions which frame how we look at images, including how we look at, and through words. The essay goes on to consider Meaghan Morris’s writing on Lynn Silverman’s photographs. Both Morris and Burn offer an alternative to a parasitic model of criticism and enact a patient way of looking across and through visual landscapes.
Theoretical and Numerical Study of Nonlinear Phononic Crystals
Guerder, Pierre-Yves
This work is dedicated to the theoretical and numerical study of nonlinear phononic crystals. The studied nonlinearities are those due to the second (quadratic) and third (cubic) order elastic constants of the materials that constitute the crystals. Nonlinear effects are studied by the means of finite element methods, used to simulate the propagation of an elastic wave through the crystals. A first research project concerns the study of a bone structure, namely the dispersion of elastic waves in a structure composed of collagen and hydroxy apatite alternate constituent layers. Simulations showed that it exists a strong link between bones hydration and their ability to dissipate the energy. The second study relates to an elastic resonator. A structure composed of steel inclusions in a silica matrix shows a switch behavior when the cubic nonlinearities of steel are taken into account. This strong nonlinear effect appears when the amplitude of the incident wave reaches a threshold. A full analytical model is provided. The last study demonstrates the design of composite materials with both strong cubic nonlinearities and weak quadratic nonlinearities. The derivation of the mixing laws of the elastic parameters of a nonlinear material inside a linear one is performed up to order three. Equations show a strong amplification of the nonlinear parameters of the material for some concentrations. Numerical simulations allow to conclude that the above mentioned resonator can be produced.
Optimal constrained layer damping with partial coverage
Marcelin, J.-L.; Trompette, Ph.; Smati, A.
1992-12-01
This paper deals with the optimal damping of beams constrained by viscoelastic layers when only one or several portions of the beam are covered. An efficient finite element model for dynamic analysis of such beams is used. The design variables are the dimensions and prescribed locations of the viscoelastic layers and the objective is the maximum viscoelastic damping factor. The method for nonlinear programming in structural optimization is the so-called method of moving asymptotes.
Institute of Scientific and Technical Information of China (English)
AN Zhi-Wu; WANG Xiao-Min; LI Ming-Xuan; DENG Ming-Xi; MAO Jie
2009-01-01
Based on the exact solutions for the second-harmonic generations of the fundamental longitudinal and transverse waves propagating normally through a thin elastic layer between two solids, the approximate representations termed as 'nonlinear spring models' relating the stresses and displacements on both sides of the interface are rigorously developed by asymptotic expansions of the wave fields for an elastic layer in the limit of small thickness to wavelength ratio. The applicability for the so-called nonlinear spring models is numerically analyzed by comparison with exact solutions for the second harmonic wave reflections. The present nonlinear spring models lay a theoretical foundation to evaluate the interracial properties by nonlinear acoustic waves.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Layer-layer competition in multiplex complex networks
Gómez-Gardeñes, Jesús; Gutiérrez, Gerardo; Arenas, Alex; Gómez, Sergio
2015-01-01
The coexistence of multiple types of interactions within social, technological and biological networks has moved the focus of the physics of complex systems towards a multiplex description of the interactions between their constituents. This novel approach has unveiled that the multiplex nature of complex systems has strong influence in the emergence of collective states and their critical properties. Here we address an important issue that is intrinsic to the coexistence of multiple means of interactions within a network: their competition. To this aim, we study a two-layer multiplex in which the activity of users can be localized in each of the layer or shared between them, favoring that neighboring nodes within a layer focus their activity on the same layer. This framework mimics the coexistence and competition of multiple communication channels, in a way that the prevalence of a particular communication platform emerges as a result of the localization of users activity in one single interaction layer. Our...
Parametric localized modes in quadratic nonlinear photonic structures
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;
2001-01-01
We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....
Agrawal, Govind P
2001-01-01
The Optical Society of America (OSA) and SPIE - The International Society for Optical Engineering have awarded Govind Agrawal with an honorable mention for the Joseph W. Goodman Book Writing Award for his work on Nonlinear Fiber Optics, 3rd edition.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical
Will Nonlinear Backcalculation Help?
DEFF Research Database (Denmark)
Ullidtz, Per
2000-01-01
demonstrates, that treating the subgrade as a nonlinear elastic material, can result in more realistic moduli and a much better agreement between measured and calculated stresses and strains.The response of nonlinear elastic materials can be calculated using the Finite Element Method (FEM). A much simpler...... approach is to use the Method of Equivalent Thicknesses (MET), modified for a nonlinear subgrade. The paper includes an example where moduli backcalculated using FEM, linear elastic theory and MET are compared. Stresses and strains predicted by the three methods are also compared to measured values...
Nonlinear graphene metamaterial
Nikolaenko, Andrey E; Atmatzakis, Evangelos; Luo, Zhiqiang; Shen, Ze Xiang; De Angelis, Francesco; Boden, Stuart A; Di Fabrizio, Enzo; Zheludev, Nikolay I
2012-01-01
We demonstrate that the broadband nonlinear optical response of graphene can be resonantly enhanced by more than an order of magnitude through hybridization with a plasmonic metamaterial,while retaining an ultrafast nonlinear response time of ~1 ps. Transmission modulation close to ~1% is seen at a pump uence of ~0.03 mJ/cm^2 at the wavelength of ~1600 nm. This approach allows to engineer and enhance graphene's nonlinearity within a broad wavelength range enabling applications in optical switching, mode-locking and pulse shaping.
Nonlinear optical microscopy for imaging thin films and surfaces
Energy Technology Data Exchange (ETDEWEB)
Smilowitz, L.B.; McBranch, D.W.; Robinson, J.M.
1995-03-01
We have used the inherent surface sensitivity of second harmonic generation to develop an instrument for nonlinear optical microscopy of surfaces and interfaces. We have demonstrated the use of several nonlinear optical responses for imaging thin films. The second harmonic response of a thin film of C{sub 60} has been used to image patterned films. Two photon absorption light induced fluorescence has been used to image patterned thin films of Rhodamine 6G. Applications of nonlinear optical microscopy include the imaging of charge injection and photoinduced charge transfer between layers in semiconductor heterojunction devices as well as across membranes in biological systems.
Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
Santo, Daniele; Lannes, David
2017-01-01
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Parameters for efficient growth of second harmonic field in nonlinear photonic crystals
Energy Technology Data Exchange (ETDEWEB)
Joseph, Shereena, E-mail: sherin5462@gmail.com; Khan, Mohd. Shahid; Hafiz, Aurangzeb Khurram
2014-03-01
The ultrashort pulse propagation and nonlinear second harmonic generation under the undepleted pump approximation in a quadratic nonlinear photonic crystal (NPC) structure is theoretically investigated and the optimized parameters for high second harmonic generation conversion efficiency are extracted. The transfer matrix method is used for the numerical formulation for oblique angle of incidence. A unique set of material combination GaInP/InAlP is selected as alternating nonlinear and linear layers. The NPC parameters like incident angle and layer thickness are manipulated to obtain the exact phase matching using double resonance condition for a fixed number of layers with known experimental material parameters.
Geometrodynamics: The Nonlinear Dynamics of Curved Spacetime
Scheel, Mark A.; Thorne, Kip S.
2017-01-01
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of spacetime curvature near singularities, the instability of black strings in 5 spacetime dimensions, and the collision of four-dimensional black holes. We also discuss the prospects for further discoveries in geometrodynamics via observation of gravitational waves.
Information measures in nonlinear experimental design
Niple, E.; Shaw, J. H.
1980-01-01
Some different approaches to the problem of designing experiments which estimate the parameters of nonlinear models are discussed. The assumption in these approaches that the information in a set of data can be represented by a scalar is criticized, and the nonscalar discrimination information is proposed as the proper measure to use. The two-step decay example in Box and Lucas (1959) is used to illustrate the main points of the discussion.
Multipolar nonlinear nanophotonics
Smirnova, Daria
2016-01-01
Nonlinear nanophotonics is a rapidly developing field with many useful applications for a design of nonlinear nanoantennas, light sources, nanolasers, sensors, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. Thus, both modal and multipolar analyses are widely exploited for engineering nonlinear scattering from resonant nanoscale elements, in particular for enhancing the near-field interaction, tailoring the far-field multipolar interference, and optimization of the radiation directionality. Here, we review the recent advances in this recently emerged research field ranging from metallic structures exhibiting localized plasmonic resonances to hybrid metal-dielectric and all-dielectric...
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Directory of Open Access Journals (Sweden)
Shakeeb Bin Hasan
2014-12-01
Full Text Available Contrary to traditional optical elements, plasmonic antennas made from nanostructured metals permit the localization of electromagnetic fields on length scales much smaller than the wavelength of light. This results in huge amplitudes for the electromagnetic field close to the antenna being conducive for the observation of nonlinear effects already at moderate pump powers. Thus, these antennas exhibit a promising potential to achieve optical frequency conversion and all-optical control of light at the nano-scale. This opens unprecedented opportunities for ultrafast nonlinear spectroscopy, sensing devices, on-chip optical frequency conversion, nonlinear optical metamaterials, and novel photon sources. Here, we review some of the recent advances in exploiting the potential of plasmonic antennas to realize robust nonlinear applications.
Leburn, Christopher; Reid, Derryck
2013-01-01
The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE......) is a good solution to solve the problems associated with the use of real nonlinear sources in testing phases. However, a recent technical survey conducted during this work shows that most existing NSEs have only been concerned with simulating nonlinear systems in terrestrial applications. Furthermore......, their dynamic performance were not fast enough in order to imitate how a real nonlinear energy source would react under extreme conditions and operation modes. Particularly, a system in the sky can experience a step change of sunlight irradiation. Moreover, operation modes may include load step between nominal...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Nonlinear magnetoinductive transmission lines
Lazarides, Nikos; Tsironis, G P
2011-01-01
Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent cap...
Optimization under Nonlinear Constraints
1982-01-01
In this paper a timesaving method is proposed for maximizing likelihood functions when the parameter space is subject to nonlinear constraints, expressible as second order polynomials. The suggested approach is especially attractive when dealing with systems with many parameters.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
Daniels, Jonathan S.; Anderson, Erik P.; Lee, Thomas H.; Pourmand, Nader
2009-01-01
Impedance biosensors detect the binding of a target to an immobilized probe by quantifying changes in the impedance of the electrode-electrolyte interface. The interface's I-V relationship is inherently nonlinear, varying with DC bias, and target binding can alter the degree of nonlinearity. We propose and demonstrate a method to simultaneously measure the nonlinearity and conventional small-signal impedance using intermodulation products from a two-tone input. Intermodulation amplitudes accurately reflect the impedance's manually-measured voltage dependence. We demonstrate that changes in nonlinearity can discriminate protein binding. Our measurements suggest that target binding can alter nonlinearity via the voltage dependence of the ionic double layer. PMID:19164024
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
Nonlinear Optics and Turbulence
1992-10-01
currently at Queen Mary College, London Patrick Dunne, (Ph.D., 1987, M.I.T., Hydrodynamic Stability, Nonlinear Waves), 1987-1988. Alecsander Dyachenko...U I I I U I I 3 9 3 V. BIOGRAPHIES A. FACULTY BRUCE BAYLY, 31, Ph.D. 1986, Princeton University. Postdoctoral visiting member 1986-88 at Courant...Caputo, A. C. Newell, and M. Shelley , "Nonlinear Wave Propagation Through a Random Medium and Soliton Tunneling", Integrable Systems and
Multiresonant layered plasmonic films
Energy Technology Data Exchange (ETDEWEB)
DeVetter, Brent M. [Pacific Northwest National Laboratory, Richland, Washington, United States; Bernacki, Bruce E. [Pacific Northwest National Laboratory, Richland, Washington, United States; Bennett, Wendy D. [Pacific Northwest National Laboratory, Richland, Washington, United States; Schemer-Kohrn, Alan [Pacific Northwest National Laboratory, Richland, Washington, United States; Alvine, Kyle J. [Pacific Northwest National Laboratory, Richland, Washington, United States
2017-01-01
Multi-resonant nanoplasmonic films have numerous applications in areas such as nonlinear optics, sensing, and tamper indication. While techniques such as focused ion beam milling and electron beam lithography can produce high-quality multi-resonant films, these techniques are expensive, serial processes that are difficult to scale at the manufacturing level. Here, we present the fabrication of multi-resonant nanoplasmonic films using a layered stacking technique. Periodically-spaced gold nanocup substrates were fabricated using self-assembled polystyrene nanospheres followed by oxygen plasma etching and metal deposition via magnetron sputter coating. By adjusting etch parameters and initial nanosphere size, it was possible to achieve an optical response ranging from the visible to the near-infrared. Singly resonant, flexible films were first made by performing peel-off using an adhesive-coated polyolefin film. Through stacking layers of the nanofilm, we demonstrate fabrication of multi-resonant films at a fraction of the cost and effort as compared to top-down lithographic techniques.
Enhanced Multi-Layer Fatigue-Analysis Approach for Unbonded Flexible Risers
Institute of Scientific and Technical Information of China (English)
杨和振; 姜豪; 杨启
2014-01-01
This paper proposes an enhanced approach for evaluating the fatigue life of each metallic layer of unbonded flexible risers. Owing to the complex structure of unbonded flexible risers and the nonlinearity of the system, particularly in the critical touchdown zone, the traditional method is insufficient for accurately evaluating the fatigue life of these risers. The main challenge lies in the transposition from global to local analyses, which is a key stage for the fatigue analysis of flexible pipes owing to their complex structure. The new enhanced approach derives a multi-layer stress-decomposition method to meet this challenge. In this study, a numerical model validated experimentally is used to demonstrate the accuracy of the stress-decomposition method. And a numerical case is studied to validate the proposed approach. The results demonstrate that the multi-layer stress-decomposition method is accurate, and the fatigue lives of the metallic layers predicted by the enhanced multi-layer analysis approach are rational. The proposed fatigue-analysis approach provides a practical and reasonable method for predicting fatigue life in the design of unbonded flexible risers.
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
Nonlinear polarization of ionic liquids: theory, simulations, experiments
Kornyshev, Alexei
2010-03-01
Room temperature ionic liquids (RTILs) composed of large, often asymmetric, organic cations and simple or complex inorganic or organic anions do not freeze at ambient temperatures. Their rediscovery some 15 years ago is widely accepted as a ``green revolution'' in chemistry, offering an unlimited number of ``designer'' solvents for chemical and photochemical reactions, homogeneous catalysis, lubrication, and solvent-free electrolytes for energy generation and storage. As electrolytes they are non-volatile, some can sustain without decomposition up to 6 times higher voltages than aqueous electrolytes, and many are environmentally friendly. The studies of RTILs and their applications have reached a critical stage. So many of them can be synthesized - about a thousand are known already - their mixtures can further provide ``unlimited'' number of combinations! Thus, establishing some general laws that could direct the best choice of a RTIL for a given application became crucial; guidance is expected from theory and modelling. But for a physical theory, RTILs comprise a peculiar and complex class of media, the description of which lies at the frontier line of condensed matter theoretical physics: dense room temperature ionic plasmas with ``super-strong'' Coulomb correlations, which behave like glasses at short time-scale, but like viscous liquids at long-time scale. This talk will introduce RTILs to physicists and overview the current understanding of the nonlinear response of RTILs to electric field. It will focus on the theory, simulations, and experimental characterisation of the structure and nonlinear capacitance of the electrical double layer at a charged electrode. It will also discuss pros and contras of supercapacitor applications of RTILs.
Handbook of nonlinear optical crystals
Dmitriev, Valentin G; Nikogosyan, David N
1991-01-01
This Handbook of Nonlinear Optical Crystals provides a complete description of the properties and applications of nonlinear crystals In addition, it presents the most important equations for calculating the main parameters of nonlinear frequency converters This comprehensive reference work will be of great value to all scientists and engineers working in nonlinear optics, quantum electronics and laser physics
Institute of Scientific and Technical Information of China (English)
张丽
2015-01-01
The study of the nonlinear evolution of three-dimensional disturbances in the boundary layers has a great theoretical research significance to the hydrodynamic stability.PSE method is adopted to study the subharmonic resonance in the experiment,and comparison be-tween PSE results and experimental data is presented.The numerical results by PSE match the experiment results basically in quantitatively.In the qualitative comparison,the plane wave ex-periences a linear exponential growth in the beginning stage and parametric-resonance stage,and the subharmonic oblique waves also experience a linear exponential growth in the initial stage. However,when the nonlinear effects is relatively strong,the subharmonic oblique waves experi-ence a super exponential growth that is faster than the exponential growth predicted by the linear theory,and stmulate the plane wave to make it increase again.This result is a consistent with the theoretical description.%用抛物化稳定性方程（PSE）方法数值模拟了实验中三波共振中三维扰动的非线性作用情况，得到的计算结果与实验数据在定量上比较相符。研究表明扰动演化的定性行为与理论描述的结果是一致的，即二维波在初始阶段和参数共振阶段按照线性指数增长，三维波在初始阶段同样按照线性指数增长。在非线性作用比较强时，三维波快速增长起来，最终作用在二维波上，使其再次增长起来，从而引起转捩。
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Holographic Superconductors with Logarithmic Nonlinear Electrodynamics in an External Magnetic Field
Sheykhi, A.; Shamsi, F.
2017-03-01
Based on the matching method, we explore the effects of adding an external magnetic field on the s-wave holographic superconductors when the gauge field is in the form of the logarithmic nonlinear source. First, we obtain the critical temperature as well as the condensation operator in the presence of logarithmic nonlinear electrodynamics and understand that they depend on the nonlinear parameter b. We show that the critical temperature decreases with increasing b, which implies that the nonlinear gauge field makes the condensation harder. Then, we turn on the magnetic field in the bulk and find the critical magnetic field, B c , in terms of the temperature, which also depends on the nonlinear parameter b. We observe that for temperature smaller than the critical temperature, T superconductor with magnetic field in Maxwell theory.
Nonlinear internal wave penetration via parametric subharmonic instability
Ghaemsaidi, S J; Dauxois, T; Odier, P; Peacock, T
2016-01-01
We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.
Institute of Scientific and Technical Information of China (English)
ALLAKHVERDIEV K; BAYKARA T
2011-01-01
The experimental and studied results of the structural, optical and nonlinear optical properties on the highly anisotropic especially un-doped and doped layered semiconductor GaSe (gallium selenide) and related crystals, InSe, GaS and GaSe-GaS (solid solutions) are overviewed. It includes also the investigation results on optical properties performed by confocal Raman and photoluminescence (PL) microscopy. Some experimental results on optical properties of GaSe nanoparticles obtained via ultrasonication and laser ablation methods are considered also. The properties of ε-GaSe isemphasized,which has one of the highest coefficient x(2) of optical second-order nonlinearity and are crystallized into four different polytypes (e,Υ,β,δ), containing different number and arrangement of layers per unit cell. It is shown that GaSe may be considered as one of the best crystals for nonlinear applications in the IR range. More than 1 700 papers describe the physical properties of the GaAs and indicate that it is an outstanding material for applications to the teraherz (THz) spectral range. The domain structure of the crystal in connection with the Nonlinea Optical(NLO) properties is discussed by confocal Raman microscopy experiments. In spite most important physical properties of these materials are mainly investigated, further studies of optical absorption near the fundamental edge, PL, NLO properties in the IR and THz ranges as well as physical properties of their nanoparticles are necessary to understand the connection between the 2-D crystal structure and the physical properties. It is known that the nanoparticles of GaSe and GaSe- type crystals are highly interesting because they have a single tetra layer structure consisting of covalently bond - Se-Ga-Ga-Se- tetra layers. Some of GaSe-type crystals have band gaps in the range of 1.2-1.5 eV (InSe, GaTe) which make them and their nanoparticles suitable for photovoltaic applications.%概述了高度各向异性的,尤其
DEFF Research Database (Denmark)
Svegaard, Robin Sebastian Kaszmarczyk
2015-01-01
This article will introduce and take a look at a specific subset of the fan created remix videos known as vids, namely those that deal with feminist based critique of media. Through examples, it will show how fans construct and present their critique, and finally broach the topic of the critical ...
DEFF Research Database (Denmark)
Svegaard, Robin Sebastian Kaszmarczyk
2015-01-01
This article will introduce and take a look at a specific subset of the fan created remix videos known as vids, namely those that deal with feminist based critique of media. Through examples, it will show how fans construct and present their critique, and finally broach the topic of the critical...
Keimer, Bernhard; Sachdev, Subir
2011-01-01
This is a review of the basic theoretical ideas of quantum criticality, and of their connection to numerous experiments on correlated electron compounds. A shortened, modified, and edited version appeared in Physics Today. This arxiv version has additional citations to the literature.
Existence of solutions for elliptic systems with critical Sobolev exponent
Directory of Open Access Journals (Sweden)
Pablo Amster
2002-06-01
Full Text Available We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.
Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model
Köllner, Thomas; Boeck, Thomas; Schumacher, Jörg
2017-05-01
The combined effects of buoyancy-driven Rayleigh-Bénard convection (RC) and surface tension-driven Marangoni convection (MC) are studied in a triple-layer configuration which serves as a simplified model for a liquid metal battery (LMB). The three-layer model consists of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Convection is triggered by the temperature gradient between the hot electrolyte and the colder electrodes, which is a consequence of the release of resistive heat during operation. We present a linear stability analysis of the state of pure thermal conduction in combination with three-dimensional direct numerical simulations of the nonlinear turbulent evolution on the basis of a pseudospectral method. Five different modes of convection are identified in the configuration, which are partly coupled to each other: RC in the upper electrode, RC with internal heating in the molten salt layer, and MC at both interfaces between molten salt and electrode as well as anticonvection in the middle layer and lower electrode. The linear stability analysis confirms that the additional Marangoni effect in the present setup increases the growth rates of the linearly unstable modes, i.e., Marangoni and Rayleigh-Bénard instability act together in the molten salt layer. The critical Grashof and Marangoni numbers decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found for realistic current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated RC. The global turbulent momentum transfer is comparable with turbulent convection in the classical Rayleigh-Bénard case. In summary, our studies show that incorporating Marangoni effects generates smaller flow structures, alters the velocity magnitudes, and enhances the turbulent heat transfer across the triple-layer configuration.
NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD
Institute of Scientific and Technical Information of China (English)
DU Guo-jun; MA Jian-qing
2006-01-01
Based on yon Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the anslytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero,critical load is obtained.
Quantification and prediction of rare events in nonlinear waves
Sapsis, Themistoklis; Cousins, Will; Mohamad, Mustafa
2014-11-01
The scope of this work is the quantification and prediction of rare events characterized by extreme intensity, in nonlinear dispersive models that simulate water waves. In particular we are interested for the understanding and the short-term prediction of rogue waves in the ocean and to this end, we consider 1-dimensional nonlinear models of the NLS type. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or Gabor coefficients) where a critical energy can trigger the formation of an extreme event. The unstable character of these critical localized modes is analysed directly through the system equation and it is shown that it is defined as the result of the system nonlinearity and the wave dissipation (that mimics wave breaking). These unstable modes are randomly triggered through the dispersive ``heat bath'' of random waves that propagate in the nonlinear medium. Using these properties we formulate low-dimensional functionals of these Gabor coefficients that allow for the prediction of extreme event well before the strongly nonlinear interactions begin to occur. The prediction window is further enhanced by the combination of the developed scheme with traditional filtering schemes.
Chen, Xianping; Tan, Chunjian; Yang, Qun; Meng, Ruishen; Liang, Qiuhua; Jiang, Junke; Sun, Xiang; Yang, D Q; Ren, Tianling
2016-06-28
Development of nanoelectronics requires two-dimensional (2D) systems with both direct-bandgap and tunable electronic properties as they act in response to the external electric field (E-field). Here, we present a detailed theoretical investigation to predict the effect of atomic structure, stacking order and external electric field on the electrical properties of few-layer boron-phosphide (BP). We demonstrate that the splitting of bands and bandgap of BP depends on the number of layers and the stacking order. The values for the bandgap show a monotonically decreasing relationship with increasing layer number. We also show that AB-stacking BP has a direct-bandgap, while ABA-stacking BP has an indirect-bandgap when the number of layers n > 2. In addition, for a bilayer and a trilayer, the bandgap increases (decreases) as the electric field increases along the positive direction of the external electric field (E-field) (negative direction). In the case of four-layer BP, the bandgap exhibits a nonlinearly decreasing behavior as the increase in the electric field is independent of the electric field direction. The tunable mechanism of the bandgap can be attributed to a giant Stark effect. Interestingly, the investigation also shows that a semiconductor-to-metal transition may occur for the four-layer case or more layers beyond the critical electric field. Our findings may inspire more efforts in fabricating new nanoelectronics devices based on few-layer BP.
Song, Dong; Opris, Ioan; Chan, Rosa H M; Marmarelis, Vasilis Z; Hampson, Robert E; Deadwyler, Sam A; Berger, Theodore W
2012-01-01
The prefrontal cortex (PFC) has been postulated to play critical roles in cognitive control and the formation of long-term memories. To gain insights into the neurobiological mechanism of such high-order cognitive functions, it is important to understand the input-output transformational properties of the PFC micro-circuitry. In this study, we identify the functional connectivity between the Layer 2/3 (input) neurons and the Layer 5 (output) neurons using a previously developed generalized Volterra model (GVM). Input-output spike trains are recorded from the PFCs of nonhuman primates performing a memory-dependent delayed match-to-sample task with a customized conformal ceramic multi-electrode array. The GVM describes how the input spike trains are transformed into the output spike trains by the PFC micro-circuitry and represents the transformation in the form of Volterra kernels. Results show that Layer 2/3 neurons have strong and transient facilitatory effects on the firings of Layer 5 neurons. The magnitude and temporal range of the input-output nonlinear dynamics are strikingly different from those of the hippocampal CA3-CA1. This form of functional connectivity may have important implications to understanding the computational principle of the PFC.
Nonlinear electrophoresis in the presence of dielectric decrement
Figliuzzi, B.; Chan, W. H. R.; Buie, C. R.; Moran, J. L.
2016-08-01
The nonlinear phenomena that occur in the electric double layer (EDL) that forms at charged surfaces strongly influence electrokinetic effects, including electro-osmosis and electrophoresis. In particular, saturation effects due to either dielectric decrement or ion crowding effects are of paramount importance. Dielectric decrement significantly influences the ionic concentration in the EDL at high ζ potential, leading to the formation of a condensed layer near the particle's surface. In this article, we present a model incorporating both steric effects due to the finite size of ions and dielectric decrement to describe the physics in the electric double layer. The model remains valid in both weakly and strongly nonlinear regimes, as long as the electric double layer remains in quasiequilibrium. We apply this model to the study of two archetypal problems in electrokinetics, namely the electrophoresis of particles with fixed surface charges and the electrophoresis of ideally polarizable particles.
Prost, Amaury; Poisson, Florian; Bossy, Emmanuel
2015-09-01
We investigate theoretically the photoacoustic generation by a gold nanosphere in water in the thermoelastic regime. Specifically, we consider the long-pulse illumination regime, in which the time for electron-phonon thermalization can be neglected and photoacoustic wave generation arises solely from the thermoelastic stress caused by the temperature increase of the nanosphere or its liquid environment. Photoacoustic signals are predicted based on the successive resolution of a thermal diffusion problem and a thermoelastic problem, taking into account the finite size of the gold nanosphere, thermoelastic and elastic properties of both water and gold, and the temperature dependence of the thermal expansion coefficient of water. For sufficiently high illumination fluences, this temperature dependence yields a nonlinear relationship between the photoacoustic amplitude and the fluence. For nanosecond pulses in the linear regime, we show that more than 90 % of the emitted photoacoustic energy is generated in water, and the thickness of the generating layer around the particle scales close to the square root of the pulse duration. The amplitude of the photoacoustic wave in the linear regime is accurately predicted by the point-absorber model introduced by Calasso et al. [Phys. Rev. Lett. 86, 3550 (2001), 10.1103/PhysRevLett.86.3550], but our results demonstrate that this model significantly overestimates the amplitude of photoacoustic waves in the nonlinear regime. We therefore provide quantitative estimates of a critical energy, defined as the absorbed energy required such that the nonlinear contribution is equal to that of the linear contribution. Our results suggest that the critical energy scales as the volume of water over which heat diffuses during the illumination pulse. Moreover, thermal nonlinearity is shown to be expected only for sufficiently high ultrasound frequency. Finally, we show that the relationship between the photoacoustic amplitude and the
Guo, Yan
2010-01-01
This note concerns a nonlinear ill-posedness of the Prandtl equation and an invalidity of asymptotic boundary-layer expansions of incompressible fluid flows near a solid boundary. Our analysis is built upon recent remarkable linear ill-posedness results established by G\\'erard-Varet and Dormy [2], and an analysis in Guo and Tice [5]. We show that the asymptotic boundary-layer expansion is not valid for non-monotonic shear layer flows in Sobolev spaces. We also introduce a notion of Weak Lipschitz well-posedness and prove that the nonlinear Prandtl equation is not well-posed in this sense near non-stationary and non-monotonic shear flows. On the other hand, we are able to verify that Oleinik's monotonic solutions are well-posed.
Critical reading and critical thinking Critical reading and critical thinking
Directory of Open Access Journals (Sweden)
Loni Kreis Taglieber
2008-04-01
Full Text Available The purpose of this paper is to provide, for L1 and L2 reading and writing teachers, a brief overview of the literature about critical reading and higher level thinking skills. The teaching of these skills is still neglected in some language classes in Brazil, be it in L1 or in L2 classes. Thus, this paper may also serve as a resource guide for L1 and/or L2 reading and writing teachers who want to incorporate critical reading and thinking into their classes. In modern society, even in everyday life people frequently need to deal with complicated public and political issues, make decisions, and solve problems. In order to do this efficiently and effectively, citizens must be able to evaluate critically what they see, hear, and read. Also, with the huge amount of printed material available in all areas in this age of “information explosion” it is easy to feel overwhelmed. But often the information piled up on people’s desks and in their minds is of no use due to the enormous amount of it. The purpose of this paper is to provide, for L1 and L2 reading and writing teachers, a brief overview of the literature about critical reading and higher level thinking skills. The teaching of these skills is still neglected in some language classes in Brazil, be it in L1 or in L2 classes. Thus, this paper may also serve as a resource guide for L1 and/or L2 reading and writing teachers who want to incorporate critical reading and thinking into their classes. In modern society, even in everyday life people frequently need to deal with complicated public and political issues, make decisions, and solve problems. In order to do this efficiently and effectively, citizens must be able to evaluate critically what they see, hear, and read. Also, with the huge amount of printed material available in all areas in this age of “information explosion” it is easy to feel overwhelmed. But often the information piled up on people’s desks and in their minds is of
Energy Technology Data Exchange (ETDEWEB)
Davis, C.G.
1990-01-01
The advent of nonlinear pulsation theory really coincides with the development of the large computers after the second world war. Christy and Stobbie were the first to make use of finite difference techniques on computers to model the bumps'' observed in the classical Cepheid light and velocity curves, the so-called Hertzsprung'' sequence. Following this work a more sophisticated analysis of the light and velocity curves from the models was made by Simon and Davis using Fourier techniques. Recently a simpler amplitude equation formalism has been developed that helps explain this resonance mechanism. The determination of Population I Cepheid masses by nonlinear methods will be discussed. For the lower mass objects, such as RR Lyrae and BL Her. stars, we find general agreement using evolutionary masses and nonlinear pulsation theory. An apparent difficulty of nonlinear pulsation theory occurs in the understanding of double'' mode pulsation, which will also be discussed. Recent studies in nonlinear pulsation theory have dealt with the question of mode selection, period doubling and the trends towards chaotic behavior such as is observed in the transition from W Virginis to RV Tauri-like stars. 10 refs., 1 fig., 2 tabs.
Detecting nonlinearity and chaos in epidemic data
Energy Technology Data Exchange (ETDEWEB)
Ellner, S.; Gallant, A.R. [North Carolina State Univ., Raleigh, NC (United States). Dept. of Statistics; Theiler, J. [Santa Fe Inst., NM (United States)]|[Los Alamos National Lab., NM (United States)
1993-08-01
Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude of epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.
Nonlinear effect induced in thermally poled glass waveguides
Institute of Scientific and Technical Information of China (English)
REN Yi-tao
2006-01-01
Thermally poled germanium-doped channel waveguides are presented. Multilayer waveguides containing a silicon oxynitride layer were used as charge trapper in this investigation on the effect of the internal field inside the waveguide. Compared to waveguides without the trapping layer, experimental results showed that the induced linear electro-optic (EO) coefficient increases about 20% after poling, suggesting strongly that the internal field is relatively enhanced, and showed it is a promising means for improving nonlinearity by poling in waveguides.
Energy Technology Data Exchange (ETDEWEB)
Stirling, W.G. [Liverpool Univ., Dep. of Physics, Liverpool (United Kingdom); Perry, S.C. [Keele Univ. (United Kingdom). Dept. of Physics
1996-12-31
We outline the theoretical and experimental background to neutron scattering studies of critical phenomena at magnetic and structural phase transitions. The displacive phase transition of SrTiO{sub 3} is discussed, along with examples from recent work on magnetic materials from the rare-earth (Ho, Dy) and actinide (NpAs, NpSb, USb) classes. The impact of synchrotron X-ray scattering is discussed in conclusion. (author) 13 figs., 18 refs.
Superconducting nano-layer coating without insulator
Kubo, Takayuki
2014-01-01
The superconducting nano-layer coating without insulator layer is studied. The magnetic-field distribution and the forces acting on a vortex are derived. Using the derived forces, the vortex-penetration field and the lower critical magnetic field can be discussed. The vortex-penetration field is identical with the multilayer coating, but the lower critical magnetic field is not. Forces acting on a vortex from the boundary of two superconductors play an important role in evaluations of the free energy.
On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation
Directory of Open Access Journals (Sweden)
Mohammed Guedda
2007-05-01
Full Text Available This paper concerns the singular solutions of the equation $$ f''' +kappa ff''-eta {f'}^2 = 0, $$ where $eta < 0$ and $kappa = 0$ or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, $f'$ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (the blow-up point. In particular, we shall examine in detail the behavior of $f$ near the blow-up point.
A Nonlinear Stability Theory for Plane Boundary-Layer Flows
1980-07-01
flows , Poiseuille flows and Couette flows . For example, 3 for plane Polseutlle flow with...published results for plane Poiseuille flow and the Orr-Sonunerfeld solutions for ~lasius flow and a numerical solution of Navier-Stokes flow along a flat...TWO-POINT BOUNDARY-VALUE PROBLEM .......... 21 4. NUMERICAL RESULTS ............................................. 44 4.1 Plane Poiseuille Flow
Coriolis effect on thermal convection in a couple-stress fluid-saturated rotating rigid porous layer
Energy Technology Data Exchange (ETDEWEB)
Shivakumara, I.S.; Devaraju, N. [Bangalore University, UGC-Centre for Advanced studies in Fluid Mechanics, Department of Mathematics, Bangalore (India); Sureshkumar, S. [Siddaganga Institute of Technology, Department of Mathematics, Tumkur (India)
2011-04-15
Both linear and weakly nonlinear stability analyses are performed to study thermal convection in a rotating couple-stress fluid-saturated rigid porous layer. In the case of linear stability analysis, conditions for the occurrence of possible bifurcations are obtained. It is shown that Hopf bifurcation is possible due to Coriolis force, and it occurs at a lower value of the Rayleigh number at which the simple bifurcation occurs. In contrast to the nonrotating case, it is found that the couple-stress parameter plays a dual role in deciding the stability characteristics of the system, depending on the strength of rotation. Nonlinear stability analysis is carried out by constructing a set of coupled nonlinear ordinary differential equations using truncated representation of Fourier series. Sub-critical finite amplitude steady motions occur depending on the choice of physical parameters but at higher rotation rates oscillatory convection is found to be the preferred mode of instability. Besides, the stability of steady bifurcating equilibrium solution is discussed using modified perturbation theory. Heat transfer is calculated in terms of Nusselt number. Also, the transient behavior of the Nusselt number is investigated by solving the nonlinear differential equations numerically using the Runge-Kutta-Gill method. It is noted that increase in the value of Taylor number and the couple-stress parameter is to dampen the oscillations of Nusselt number and thereby to decrease the heat transfer. (orig.)
Kaur, Nimardeep; Singh, Kuldeep; Saini, N. S.
2017-09-01
The nonlinear propagation of ion acoustic solitary waves (IASWs) is investigated in an unmagnetized plasma composed of a positive warm ion fluid, two temperature electrons obeying kappa type distribution and penetrated by a positive ion beam. The reductive perturbation method is used to derive the nonlinear equations, namely, Korteweg-de Vries (KdV), modified KdV (mKdV), and Gardner equations. The characteristic features of both compressive and rarefactive nonlinear excitations from the solution of these equations are studied and compared in the context with the observation of the He+ beam in the polar cap region near solar maximum by the Dynamics Explorer 1 satellite. It is observed that the superthermality and density of cold electrons, number density, and temperature of the positive ion beam crucially modify the basic properties of compressive and rarefactive IASWs in the KdV and mKdV regimes. It is further analyzed that the amplitude and width of Gardner solitons are appreciably affected by different plasma parameters. The characteristics of double layers are also studied in detail below the critical density of cold electrons. The theoretical results may be useful for the observation of nonlinear excitations in laboratory and ion beam driven plasmas in the polar cap region near solar maximum and polar ionosphere as well in Saturn's magnetosphere, solar wind, pulsar magnetosphere, etc., where the population of two temperature superthermal electrons is present.
Xiang, Wei; Zhang, Beiping; Zhou, Tao; Wu, Xiaohui; Mao, Juan
2016-04-01
This study demonstrated the synergistic degradation of 4-chlorophenol (4-CP) achieved in a magnetic field (MF) enhanced zero-valent iron (ZVI)/H2O2 Fenton-like (FL) system and revealed an interesting correlative dependence relationship between MF and the pristine iron oxides layer (FexOy) on ZVI particles. First, a comparative investigation between the FL and MF-FL systems was conducted under different experimental conditions. The MF-FL system could suppress the duration of initial lag degradation phase one order of magnitude in addition of the significant enhancement in overall 4-CP degradation. Monitoring of intermediates/products indicated that MF would just accelerate the Fenton reactions to produce hydroxyl radical more rapidly. Evolutions of simultaneously released dissolved iron species suggested that MF would not only improve mass-transfer of the initial heterogeneous reactions, but also modify the pristine ZVI surface. Characterizations of the specific prepared ZVI samples evidenced that MF would induce a special evolution mechanism of the ZVI particles surface depending on the existence of FexOy layer. It comprised of an initial rapid point dissolution of FexOy and a following pitting corrosion of the exposed Fe0 reactive sites, finally leading to appearance of a particular rugged surface topography with numerous adjacent Fe0 pits and FexOy tubercles.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Duff, Francis; McGarry, Donald; Zasada, David; Foote, Scott
2009-05-01
The MITRE Sensor Layer Prototype is an initial design effort to enable every sensor to help create new capabilities through collaborative data sharing. By making both upstream (raw) and downstream (processed) sensor data visible, users can access the specific level, type, and quantities of data needed to create new data products that were never anticipated by the original designers of the individual sensors. The major characteristic that sets sensor data services apart from typical enterprise services is the volume (on the order of multiple terabytes) of raw data that can be generated by most sensors. Traditional tightly coupled processing approaches extract pre-determined information from the incoming raw sensor data, format it, and send it to predetermined users. The community is rapidly reaching the conclusion that tightly coupled sensor processing loses too much potentially critical information.1 Hence upstream (raw and partially processed) data must be extracted, rapidly archived, and advertised to the enterprise for unanticipated uses. The authors believe layered sensing net-centric integration can be achieved through a standardize-encapsulate-syndicateaggregate- manipulate-process paradigm. The Sensor Layer Prototype's technical approach focuses on implementing this proof of concept framework to make sensor data visible, accessible and useful to the enterprise. To achieve this, a "raw" data tap between physical transducers associated with sensor arrays and the embedded sensor signal processing hardware and software has been exploited. Second, we encapsulate and expose both raw and partially processed data to the enterprise within the context of a service-oriented architecture. Third, we advertise the presence of multiple types, and multiple layers of data through geographic-enabled Really Simple Syndication (GeoRSS) services. These GeoRSS feeds are aggregated, manipulated, and filtered by a feed aggregator. After filtering these feeds to bring just the type
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Nonlinear optomechanical paddle nanocavities
Kaviani, Hamidreza; Wu, Marcelo; Ghobadi, Roohollah; Barclay, Paul E
2014-01-01
A photonic crystal optomechanical system combining strong nonlinear optomechanical coupling, low effective mass and large optical mode spacing is introduced. This nanoscale "paddle nanocavity" device supports mechanical resonances with effective mass of 300--600 fg which couple nonlinearly to co-localized optical modes with a quadratic optomechanical coupling coefficient $g^{(2)} > 2\\pi\\times400$ MHz/nm$^2$, and a two phonon to single photon optomechanical coupling rate $\\Delta \\omega_0 > 2\\pi\\times 16$ Hz. This coupling relies on strong phonon-photon interactions in a structure whose optical mode spectrum is highly non--degenerate. Simulations indicate that nonlinear optomechanical readout of thermally driven motion in these devices should be observable for T $> 50 $ mK, and that measurement of phonon shot noise is achievable.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Nonlinear Photonic Crystal Fibers
DEFF Research Database (Denmark)
Hansen, Kim Per
2004-01-01
, leading to reduced mode confinement and dispersion flexibility. In this thesis, we treat the nonlinear photonic crystal fiber – a special sub-class of photonic crystal fibers, the core of which has a diameter comparable to the wavelength of the light guided in the fiber. The small core results in a large...... nonlinear coefficient and in various applications, it is therefore possible to reduce the required fiber lengths quite dramatically, leading to increased stability and efficiency. Furthermore, it is possible to design these fibers with zero-dispersion at previously unreachable wavelengths, paving the way...... for completely new applications, especially in and near the visible wavelength region. One such application is supercontinuum generation. Supercontinuum generation is extreme broadening of pulses in a nonlinear medium (in this case a small-core fiber), and depending on the dispersion of the fiber, it is possible...
Schmidt, Bruno E; Ernotte, Guilmot; Clerici, Matteo; Morandotti, Roberto; Ibrahim, Heide; Legare, Francois
2016-01-01
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new dipole radiation whose amplitude, frequency and phase differ from the incoming fields. Such high fields are typically achieved with ultra-short, femtosecond (1fs = 10-15 sec.) laser pulses containing very broad frequency spectra. Here, the matter not only couples incoming and outgoing fields but also causes different spectral components to interact and mix through a convolution process. In this contribution, we describe how frequency domain nonlinear optics overcomes the shortcomings arising from this convolution in conventional time domain nonlinear optics1. We generate light fields with previously inaccessible properties because the uncontrolled coupling of amplitudes and phases is turned off. For example, arbitrary phase functions are transferred linearly to the second har...
Nonlinear optomechanics with graphene
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Multidimensional nonlinear descriptive analysis
Nishisato, Shizuhiko
2006-01-01
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...
Nonlinear airship aeroelasticity
Bessert, N.; Frederich, O.
2005-12-01
The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.
Artificial Neural Networks for Nonlinear Dynamic Response Simulation in Mechanical Systems
DEFF Research Database (Denmark)
Christiansen, Niels Hørbye; Høgsberg, Jan Becker; Winther, Ole
2011-01-01
It is shown how artificial neural networks can be trained to predict dynamic response of a simple nonlinear structure. Data generated using a nonlinear finite element model of a simplified wind turbine is used to train a one layer artificial neural network. When trained properly the network is able...
Nonlinear electro-mechanobiological behavior of cell membrane during electroporation
Deng, Peigang
2012-01-01
A nonlinear electroporation (EP) model is proposed to study the electro-mechanobiological behavior of cell membrane during EP, by taking the nonlinear large deformation of the membrane into account. The proposed model predicts the critical transmembrane potential and the activation energy for EP, the equilibrium pore size, and the resealing process of the pore. Single-cell EP experiments using a micro EP chip were conducted on chicken red blood cells at different temperatures to determine the activation energy and the critical transmembrane potential for EP. The experimental results are in good agreement with the theoretical predictions. © 2012 American Institute of Physics.