Nonlinear Decay Research Articles

Dynamics of glass-forming liquids. XIX. Rise and decay of field induced anisotropy in the non-linear regime.

For glycerol and three monohydroxy alcohols, we have measured the non-linear dielectric effects resulting from the application and removal of a high dc bias electric field. The field effects are detected by virtue of a small amplitude harmonic field, from which time resolved changes in the dielectric loss are derived. The changes in permittivity are dominated by modifications of the time constants (rather than amplitudes) which display two contributions: a heating-like decrease of relaxation times that originates from the time dependent field when the bias is switched on and off and a slowing down of the dynamics resulting from the field induced reduction of configurational entropy. As observed for the electro-optical Kerr effect, the rise of the entropy change is slower than its decay, a feature that we rationalize on the basis of the quadratic dependence of the entropy change on polarization. For glycerol, the observed steady state level of the field induced shift of the glass transition temperature (+84 mK) matches the expectation based on the entropy change and its impact on dynamics via the Adam-Gibbs relation (+88 mK). For the alcohols, these non-linear effects rise and decay on the time scales of the prominent dielectric Debye process, underscoring the relation of these features to polarization anisotropy, opposed to mechanical or enthalpy relaxation which are orders of magnitude faster in these systems. A model is discussed which captures the observed magnitudes as well as time dependences in a near quantitative fashion. It is demonstrated that the high bias field modifies the response of polarization to the ac field, including a temporary change in the low field susceptibility.

LANGMUIR WAVE DECAY IN INHOMOGENEOUS SOLAR WIND PLASMAS: SIMULATION RESULTS

Langmuir turbulence excited by electron flows in solar wind plasmas is studied on the basis of numerical simulations. In particular, nonlinear wave decay processes involving ion-sound (IS) waves are considered in order to understand their dependence on external long-wavelength plasma density fluctuations. In the presence of inhomogeneities, it is shown that the decay processes are localized in space and, due to the differences between the group velocities of Langmuir and IS waves, their duration is limited so that a full nonlinear saturation cannot be achieved. The reflection and the scattering of Langmuir wave packets on the ambient and randomly varying density fluctuations lead to crucial effects impacting the development of the IS wave spectrum. Notably, beatings between forward propagating Langmuir waves and reflected ones result in the parametric generation of waves of noticeable amplitudes and in the amplification of IS waves. These processes, repeated at different space locations, form a series of cascades of wave energy transfer, similar to those studied in the frame of weak turbulence theory. The dynamics of such a cascading mechanism and its influence on the acceleration of the most energetic part of the electron beam are studied. Finally, the role of the decay processes in the shaping of the profiles of the Langmuir wave packets is discussed, and the waveforms calculated are compared with those observed recently on board the spacecraft Solar TErrestrial RElations Observatory and WIND

Hybrid (Vlasov-fluid) simulation of ion-acoustic solitonic chain formation in plasmas with super-thermal electrons

Nonlinear decay of a localized perturbation into ion-acoustic solitons in the presence of both trapped and super-thermal electrons (Abbasi et al 2008 Plasma Phys. Control. Fusion 50 095007) is revisited. The motivation is to present a benchmark by introducing a more precise model, the hybrid (Vlasov-fluid) model. In this way, it is possible to address the restrictions that a simple modified Korteweg de–Vries (mKdV) model has. For instance, the lack of vital information in phase space associated with the evolution of electron velocity distribution, its perturbative nature which limits it to weak nonlinear case, and special spatio-temporal scaling based on which the mKdV is derived. From these points of view, the hybrid model is a more convenient model that can be extended to more complex situations. Remarkable differences between the results of the two models lead us to conclude that the mKdV model can only monitor the general aspects of the dynamics, and the precise picture, including the correct spatio-temporal scales and the properties of solitons, should be studied within the framework of hybrid model.

Long time dynamics of a multidimensional nonlinear lattice with memory

This work is devoted to study the nature of vibrations arising in a multidimensional nonlinear periodic lattice structure with memory. We prove the existence of a global attractor. In the homogeneous case under a restriction on the nonlinear term we obtain decay rates of the total energy. These rates could be exponential, polynomial or several other intermediate types.

Apparent recovery of C18 polyunsaturated fatty acids from feed in cow milk: A meta-analysis of the importance of dietary fatty acids and feeding regimens in diets without fat supplementation

A meta-analysis was conducted using the results of 82 experiments (78 publications, 266 treatments) to investigate the importance of dietary C18 fatty acids (FA) and feeding regimen for milk C18 FA profile and apparent recovery of selected FA relative to intake of these FA or their precursors. Feeding treatments based on lipid-supplemented diets were excluded. Feeding regimens were defined as grazing [including partial and full-time grazing, at dietary concentrate proportions from 0 to 44% dry matter (DM)], forage-based indoor feeding [>65% forage of total DM intake (DMI)], and concentrate-based indoor feeding (forage DMI ≤65% of DMI). Linoleic acid (LLA), α-linolenic acid (ALA), and total C18 FA proportions in milk fat increased linearly with the respective dietary FA content in all feeding regimens tested. This effect was highest in the forage-based indoor feeding. Slopes were lowest for the grazing regimens, especially regarding ALA and the sum of all C18 FA, whereas the intercepts of the prediction equations of milk ALA and total C18 FA proportions were highest for grazing regimens. This indicates that, in grazing cows, factors other than dietary FA contents determine the C18 FA composition of the milk fat. At equal dietary LLA contents, the type of feeding regimen showed no significant effect on LLA proportion in milk fat. Milk fat proportions of rumenic acid and vaccenic acid were positively related to the sum of dietary ALA and LLA contents. Grazing regimens led to the strongest enrichment of rumenic acid and vaccenic acid in milk fat. The apparent recovery of ALA, LLA, and total C18 FA (secreted, % of intake), an estimate for transfer efficiency, decreased with increasing dietary content. This relationship followed a nonlinear decay function. When the dietary content of these FA exceeded a certain threshold (about 0.2, 0.8, and 2.8% of DM for ALA, LLA, and total C18 FA, respectively) the recovery in milk remained constant at about 5, 10, and 82% of the ingested ALA, LLA, and total C18 FA, respectively. At dietary proportions below 0.01% ALA and 1.5% total C18 FA of DM, their apparent recovery in milk fat exceeded 100%. In conclusion, a general inverse relationship between dietary C18 FA and the corresponding apparent recovery in milk fat seems to exist. Within this frame, the effect of different types of feeding regimens on the eventual milk C18 FA profile varies. Among them, grazing pasture appears to provide the most variable properties.

Optical limiting of laser radiation and light quenching in colloidal solutions of CdSe/ZnS semiconductor quantum dots and hybrid systems

The photodynamics of power optical limiting is studied in colloidal solutions of quantum dots by exiting the system in the absorption band with 0.4-ns 532-nm pulses. Based on a parallel analysis of the dependence of the nonlinear transmission and luminescence decay kinetics of the investigated solutions, the conclusion is drawn that the main mechanism of the optical limiting of nanosecond laser radiation pulses is light quenching of the so-called dark states in quantum dots. The efficiency of limiting is determined by the dynamics of the population of these states. It is shown that CdSe/ZnS QDs–C60 hybrid system has the same efficiency in both the single-pulse and 10-Hz reptation rate modes.

Weathering and Chemical Degradation of Methyl Eugenol and Raspberry Ketone Solid Dispensers for Detection, Monitoring, and Male Annihilation of Bactrocera dorsalis and Bactrocera cucurbitae (Diptera: Tephritidae) in Hawaii.

Solid male lure dispensers containing methyl eugenol (ME) and raspberry ketone (RK), or mixtures of the lures (ME + RK), and dimethyl dichloro-vinyl phosphate (DDVP) were evaluated in area-wide pest management bucket or Jackson traps in commercial papaya (Carica papaya L.) orchards where both oriental fruit fly, Bactrocera dorsalis (Hendel), and melon fly, Bactrocera cucurbitae (Coquillett), are pests. Captures of B. dorsalis with fresh wafers in Jackson and bucket traps were significantly higher on the basis of ME concentration (Mallet ME [56%] > Mallet MR [31.2%] > Mallet MC [23.1%]). Captures of B. cucurbitae with fresh wafers in Jackson and bucket traps were not different regardless of concentration of RK (Mallet BR [20.1%] = Mallet MR [18.3%] = Mallet MC [15.9%]). Captures of B. dorsalis with fresh wafers, compared with weathered wafers, were significantly different after week 12; captures of B. cucurbitae were not significantly different after 16 wk. Chemical analyses revealed presence of RK in dispensers in constant amounts throughout the 16-wk trial. Degradation of both ME and DDVP over time was predicted with a high level of confidence by nonlinear asymptotic exponential decay curves. Results provide supportive data to deploy solid ME and RK wafers (with DDVP) in fruit fly traps for detection programs, as is the current practice with solid TML dispensers placed in Jackson traps. Wafers with ME and RK might be used in place of two separate traps for detection of both ME and RK responding fruit flies and could potentially reduce cost of materials and labor by 50%.

Micromechanical poroelastic finite element and shear-lag models of tendon predict large strain dependent Poisson’s ratios and fluid expulsion under tensile loading

As tendons are loaded, they reduce in volume and exude fluid to the surrounding medium. Experimental studies have shown that tendon stretching results in a Poisson’s ratio greater than 0.5, with a maximum value at small strains followed by a nonlinear decay. Here we present a computational model that attributes this macroscopic observation to the microscopic mechanism of the load transfer between fibrils under stretch. We develop a finite element model based on the mechanical role of the interfibrillar-linking elements, such as thin fibrils that bridge the aligned fibrils or macromolecules such as glycosaminoglycans (GAGs) in the interfibrillar sliding and verify it with a theoretical shear-lag model. We showed the existence of a previously unappreciated structure–function mechanism whereby the Poisson’s ratio in tendon is affected by the strain applied and interfibrillar-linker properties, and together these features predict tendon volume shrinkage under tensile loading. During loading, the interfibrillar-linkers pulled fibrils toward each other and squeezed the matrix, leading to the Poisson’s ratio larger than 0.5 and fluid expulsion. In addition, the rotation of the interfibrillar-linkers with respect to the fibrils at large strains caused a reduction in the volume shrinkage and eventual nonlinear decay in Poisson’s ratio at large strains. Our model also predicts a fluid flow that has a radial pattern toward the surrounding medium, with the larger fluid velocities in proportion to the interfibrillar sliding.

WEST NILE VIRUS ANTIBODY DECAY RATE IN FREE-RANGING BIRDS.

Antibody duration, following a humoral immune response to West Nile virus (WNV) infection, is poorly understood in free-ranging avian hosts. Quantifying antibody decay rate is important for interpreting serologic results and for understanding the potential for birds to serorevert and become susceptible again. We sampled free-ranging birds in Chicago, Illinois, US, from 2005 to 2011 and Atlanta, Georgia, US, from 2010 to 2012 to examine the dynamics of antibody decay following natural WNV infection. Using serial dilutions in a blocking enzyme-linked immunosorbent assay, we quantified WNV antibody titer in repeated blood samples from individual birds over time. We quantified a rate of antibody decay for 23 Northern Cardinals (Cardinalis cardinalis) of 0.198 natural log units per month and 24 individuals of other bird species of 0.178 natural log units per month. Our results suggest that juveniles had a higher rate of antibody decay than adults, which is consistent with nonlinear antibody decay at different times postexposure. Overall, most birds had undetectable titers 2 yr postexposure. Nonuniform WNV antibody decay rates in free-ranging birds underscore the need for cautious interpretation of avian serology results in the context of arbovirus surveillance and epidemiology.

Understanding nonlinear saturation in zonal-flow-dominated ion temperature gradient turbulence

We propose a quantitative model of ion temperature gradient driven turbulence in toroidal magnetized plasmas. In this model, the turbulence is regulated by zonal flows, i.e. mode saturation occurs by a zonal-flow-mediated energy cascade (‘shearing’), and zonal flow amplitude is controlled by nonlinear decay. Our model is tested in detail against numerical simulations to confirm that both its assumptions and predictions are satisfied. Key results include (1) a sensitivity of the nonlinear zonal flow response to the energy content of the linear instability, (2) a persistence of zonal-flow-regulated saturation at high temperature gradients, (3) a physical explanation of the nonlinear saturation process in terms of secondary and tertiary instabilities, and (4) dependence of heat flux in terms of dimensionless parameters.

EVOLUTION OF FAST MAGNETOACOUSTIC PULSES IN RANDOMLY STRUCTURED CORONAL PLASMAS

We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in the context of large-scale propagating waves in the solar atmosphere. We perform one-dimensional numerical simulations of fast wave pulses propagating perpendicular to a constant magnetic field in a low-β plasma with a random density profile across the field. Both linear and nonlinear regimes are considered. We study how the evolution of the pulse amplitude and width depends on their initial values and the parameters of the random structuring. Acting as a dispersive medium, a randomly structured plasma causes amplitude attenuation and width broadening of the fast wave pulses. After the passage of the main pulse, secondary propagating and standing fast waves appear. Width evolution of both linear and nonlinear pulses can be well approximated by linear functions; however, narrow pulses may have zero or negative broadening. This arises because narrow pulses are prone to splitting, while broad pulses usually deviate less from their initial Gaussian shape and form ripple structures on top of the main pulse. Linear pulses decay at an almost constant rate, while nonlinear pulses decay exponentially. A pulse interacts most efficiently with a random medium with a correlation length of about half of the initial pulse width. This detailed model of fast wave pulses propagating in highly structured media substantiates the interpretation of EIT waves as fast magnetoacoustic waves. Evolution of a fast pulse provides us with a novel method to diagnose the sub-resolution filamentation of the solar atmosphere.

Non-Gilbert-damping Mechanism in a Ferromagnetic Heusler Compound Probed by Nonlinear Spin Dynamics.

The nonlinear decay of propagating spin waves in the low-Gilbert-damping Heusler film Co_{2}Mn_{0.6}Fe_{0.4}Si is reported. Here, two initial magnons with frequency f_{0} scatter into two secondary magnons with frequencies f_{1} and f_{2}. The most remarkable observation is that f_{1} stays fixed if f_{0} is changed. This indicates, that the f_{1} magnon mode has the lowest instability threshold, which, however, cannot be understood if only Gilbert damping is present. We show that the observed behavior is caused by interaction of the magnon modes f_{1} and f_{2} with the thermal magnon bath. This evidences a significant contribution of the intrinsic magnon-magnon scattering mechanisms to the magnetic damping in high-quality Heusler compounds.

PyFDAP: automated analysis of fluorescence decay after photoconversion (FDAP) experiments.

We developed the graphical user interface PyFDAP for the fitting of linear and non-linear decay functions to data from fluorescence decay after photoconversion (FDAP) experiments. PyFDAP structures and analyses large FDAP datasets and features multiple fitting and plotting options. PyFDAP was written in Python and runs on Ubuntu Linux, Mac OS X and Microsoft Windows operating systems. The software, a user guide and a test FDAP dataset are freely available for download from http://people.tuebingen.mpg.de/mueller-lab.

Nonlinear Pitch Decay Motion of a Floating Offshore Wind Turbine Structure

Model tests were conducted on three generic floating wind turbine systems in 2011 and reported in a series of papers at the 31st Ocean, Offshore, and Arctic Engineering Conference in 2012. These tests were conducted at the MARIN facility in The Netherlands, by a consortium of universities, government research organizations, and industry. As part of the testing program, decay tests in platform pitch were conducted with and without wind forcing. It was found that for spar and semisubmersible type structures, resonant pitch motion was damped due to wind in storm sea conditions. The nonlinear decay motion of a floating wind turbine platform is modeled using a one degree-of-freedom nonlinear oscillation equation about a mean offset angle. Attention is paid to the turbine thrust coefficient and its variability with respect to oncoming flow speed, which in turn is affected by the structure pitch motion. The equation of motion reveals that the mean offset position has an important role in the stiffness, damping, and consequently the natural period of pitch motion. Several important dimensionless parameters are introduced. The paper discusses a simple thrust model for an offshore wind turbine (OWT) based on rudiments of blade element theory. Using the simplified thrust coefficient formulation, the increase in platform pitch damping due to wind is formulated. Experimental data reported from prior tests described above show good agreement with the theoretical model.

An adaptive non-linear great deluge algorithm for the patient-admission problem

The patient-admission scheduling problem is a combinatorial optimisation problem that is receiving attention in health care practice. This is because hospitals are experiencing increasing pressure to optimise the usage of their resources while simultaneously increasing patients’ comfort. The goal of this work is to propose a meta-heuristic approach called an adaptive non-linear great deluge algorithm to address patient admission problems. We investigate the effect of adaptively updating the non-linear decay rate of the water level in the great deluge algorithm during the course of optimisation. The great deluge algorithm needs only to set up the water level as its basic parameter, which makes it naturally very attractive for solving optimisation problems. The performance of the proposed approach is verified using standard benchmark datasets. Empirical results demonstrate that the proposed algorithm obtains competitive results when compared to other approaches in the scientific literature.

Nonlinear decay of random waves described by an integrodifferential equation.

The evolution of random nonlinear waves (high-intensity noise) in a dissipative and dispersive media is studied. To describe wave processes, the mathematical model in the form of a nonlinear integrodifferential equation is used. The concrete integrand kernels are determined by both frequency-dependent absorption and velocity of the wave. The nonlinear energy loss of broadband noise is considered in two limiting cases: (i) at the initial stage of propagation, when the wave profile contains a small number of shock fronts, and (ii) at the later stage when the wave reshapes to a sawtoothlike one with randomly located shocks.

Quadratic autocatalysis with non-linear decay

We provide a detailed, and thorough, investigation into the concentration multiplicity and dynamic stability of a prototype non-linear chemical mechanism: quadratic autocatalysis subject to non-linear decay in a continuously stirred tank reactor. This model was previously investigated in the literature using numerical path-following techniques. The contribution of this study is the application of singularity theory and degenerate Hopf-bifurcation theory to obtain analytical representations of many of the features of interest in this system. In particular, we use these presentations to identify critical values of an unfolding parameter below which specified phenomenon are no longer exhibited.

Effect of water vapor on the determination of aerosol direct radiative effect based on the AERONET fluxes

Abstract. The aerosol direct radiative effect (ADRE) is defined as the change in the solar radiation flux, F, due to aerosol scattering and absorption. The difficulty in determining ADRE stems mainly from the need to estimate F without aerosols, F0, with either radiative transfer modeling and knowledge of the atmospheric state, or regression analysis of radiation data down to zero aerosol optical depth (AOD), if only F and AOD are observed. This paper examines the regression analysis method by using modeled surface data products provided by the Aerosol Robotic Network (AERONET). We extrapolated F0 by two functions: a straight linear line and an exponential nonlinear decay. The exponential decay regression is expected to give a better estimation of ADRE with a few percent larger extrapolated F0 than the linear regression. We found that, contrary to the expectation, in most cases the linear regression gives better results than the nonlinear. In such cases the extrapolated F0 represents an unrealistically low water vapor column (WVC), resulting in underestimation of attenuation caused by the water vapor, and hence too large F0 and overestimation of the magnitude of ADRE. The nonlinear ADRE is generally 40–50% larger in magnitude than the linear ADRE due to the extrapolated F0 difference. Since for a majority of locations, AOD and WVC have a positive correlation, the extrapolated F0 with the nonlinear regression fit represents an unrealistically low WVC, and hence too large F0. The systematic underestimation of F0 with the linear regression is compensated by the positive correlation between AOD and water vapor, providing the better result.

The nonlinear decay of vortex flows in a rotating fluid

The manifestations of the cyclone-anticyclone asymmetry effect, which is observed in nature [1–3] and in laboratory experiments with a rotating fluid [4–6], have been studied in the scope of the vorticity evolution generalized equation. Under laboratory conditions, asymmetry is observed as a faster decay of cyclonic vortices as compared to anticyclonic ones. This effect has been analytically described simply based on the problem of the vortex spot decay and spatially periodic vortex lattice. It has been indicated that anticyclonic vortices compress and cyclonic ones expand when a lattice damps. Examples of exact solutions of the vorticity equation [7] (describing, specifically, collapsing of an axisymmetric vortex core with anticyclonic vorticity) have been constructed. The effect of the Ekman friction on the interaction between singular vortices is discussed.

Improvements to longitudinal Clean Development Mechanism sampling designs for lighting retrofit projects

An improved model for reducing the cost of long-term monitoring in Clean Development Mechanism (CDM) lighting retrofit projects is proposed. Cost-effective longitudinal sampling designs use the minimum numbers of meters required to report yearly savings at the 90% confidence and 10% relative precision level for duration of the project (up to 10years) as stipulated by the CDM. Improvements to the existing model include a new non-linear Compact Fluorescent Lamp population decay model based on the Polish Efficient Lighting Project, and a cumulative sampling function modified to weight samples exponentially by recency. An economic model altering the cost function to a net present value calculation is also incorporated. The search space for such sampling models is investigated and found to be discontinuous and stepped, requiring a heuristic for optimisation; in this case the Genetic Algorithm was used. Assuming an exponential smoothing rate of 0.25, an inflation rate of 6.44%, and an interest rate of 10%, results show that sampling should be more evenly distributed over the study duration than is currently considered optimal, and that the proposed improvements in model accuracy increase monitoring costs by 21.4% in present value terms.