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Journal articles on the topic 'Nonlinear dissipation'

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Author: Grafiati

Published: 10 December 2022

Last updated: 29 January 2023

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1

Kamrin, K., and J. D. Goddard. "Symmetry relations in viscoplastic drag laws." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2172 (December 8, 2014): 20140434. http://dx.doi.org/10.1098/rspa.2014.0434.

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The following note shows that the symmetry of various resistance formulae, often based on Lorentz reciprocity for linearly viscous fluids, applies to a wide class of nonlinear viscoplastic fluids. This follows from Edelen's nonlinear generalization of the Onsager relation for the special case of strongly dissipative rheology, where constitutive equations are derivable from his dissipation potential. For flow domains with strong dissipation in the interior and on a portion of the boundary, this implies strong dissipation on the remaining portion of the boundary, with strongly dissipative traction–velocity response given by a dissipation potential. This leads to a nonlinear generalization of Stokes resistance formulae for a wide class of viscoplastic fluid problems. We consider the application to nonlinear Darcy flow and to the effective slip for viscoplastic flow over textured surfaces.

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2

Lévy, Laurent P., and Andrew T. Ogielski. "Dissipation in nonlinear response." Journal of Mathematical Physics 30, no. 3 (March 1989): 683–88. http://dx.doi.org/10.1063/1.528382.

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3

LIANG, JIANFENG. "HYPERBOLIC SMOOTHING EFFECT FOR SEMILINEAR WAVE EQUATIONS AT A FOCAL POINT." Journal of Hyperbolic Differential Equations 06, no. 01 (March 2009): 1–23. http://dx.doi.org/10.1142/s0219891609001745.

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For semi-linear dissipative wave equation □u + |ut|p - 1ut = 0, we consider finite energy solutions with singularities propagating along a focusing light cone. At the tip of cone, the singularities are focused and partially smoothed out under strong nonlinear dissipation, i.e. the solution gets up to 1/2 more L2 derivative after the focus. The smoothing phenomenon is in fact the result of simultaneous action of focusing and nonlinear dissipation.

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4

HANSEN, JAKOB, ALEXEI KHOKHLOV, and IGOR NOVIKOV. "PROPERTIES OF FOUR NUMERICAL SCHEMES APPLIED TO A NONLINEAR SCALAR WAVE EQUATION WITH A GR-TYPE NONLINEARITY." International Journal of Modern Physics D 13, no. 05 (May 2004): 961–82. http://dx.doi.org/10.1142/s021827180400502x.

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We study stability, dispersion and dissipation properties of four numerical schemes (Itera-tive Crank–Nicolson, 3rd and 4th order Runge–Kutta and Courant–Fredrichs–Levy Nonlinear). By use of a Von Neumann analysis we study the schemes applied to a scalar linear wave equation as well as a scalar nonlinear wave equation with a type of nonlinearity present in GR-equations. Numerical testing is done to verify analytic results. We find that the method of lines (MOL) schemes are the most dispersive and dissipative schemes. The Courant–Fredrichs–Levy Nonlinear (CFLN) scheme is most accurate and least dispersive and dissipative, but the absence of dissipation at Nyquist frequency, if fact, puts it at a disadvantage in numerical simulation. Overall, the 4th order Runge–Kutta scheme, which has the least amount of dissipation among the MOL schemes, seems to be the most suitable compromise between the overall accuracy and damping at short wavelengths.

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5

Shi, Yunlong, Baoshu Yin, Hongwei Yang, Dezhou Yang, and Zhenhua Xu. "Dissipative Nonlinear Schrödinger Equation for Envelope Solitary Rossby Waves with Dissipation Effect in Stratified Fluids and Its Solution." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/643652.

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We solve the so-called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency, andβeffect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipation on the evolution of envelope solitary Rossby wave is also discussed. The results show that the dissipation causes a slow decrease of amplitude of envelope solitary Rossby waves and a slow increase of width, while it has no effect on the propagation velocity. That is quite different from the KdV-type solitary waves. It is notable that dissipation has certain influence on the carrier frequency.

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6

Huang, K. M., S. D. Zhang, F. Yi, C. M. Huang, Q. Gan, Y. Gong, and Y. H. Zhang. "Nonlinear interaction of gravity waves in a nonisothermal and dissipative atmosphere." Annales Geophysicae 32, no. 3 (March 21, 2014): 263–75. http://dx.doi.org/10.5194/angeo-32-263-2014.

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Abstract. Starting from a set of fully nonlinear equations, this paper studies that two initial gravity wave packets interact to produce a third substantial packet in a nonisothermal and dissipative atmosphere. The effects of the inhomogeneous temperature and dissipation on interaction are revealed. Numerical experiments indicate that significant energy exchange occurs through the nonlinear interaction in a nonisothermal and dissipative atmosphere. Because of the variability of wavelengths and frequencies of interacting waves, the interaction in an inhomogeneous temperature field is characterised by the nonresonance. The nonresonant three waves mismatch mainly in the vertical wavelengths, but match in the horizontal wavelengths, and their frequencies also tend to match throughout the interaction. Below 80 km, the influence of atmospheric dissipation on the interaction is rather weak due to small diffusivities. With the further propagation of wave above 80 km, the exponentially increasing atmospheric dissipation leads to the remarkable decay and slowly upward propagation of wave energy. Even so, the dissipation below 110 km is not enough to decrease the vertical wavelength of wave. The dissipation seems neither to prevent the interaction occurrence nor to prolong the period of wave energy exchange, which is different from the theoretical prediction based on the linearised equations. The match relationship and wave energy evolution in numerical experiments are helpful in further investigating interaction of gravity waves in the middle atmosphere based on experimental observations.

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7

Vitali, David, and Paolo Grigolini. "Nonlinear effects in quantum dissipation." Physical Review A 42, no. 12 (December 1, 1990): 7091–106. http://dx.doi.org/10.1103/physreva.42.7091.

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8

Tian, Bo, and Yi-Tian Gao. "Painlevé Analysis and Symbolic Computation for a Nonlinear Schrödinger Equation with Dissipative Perturbations." Zeitschrift für Naturforschung A 51, no. 3 (March 1, 1996): 167–70. http://dx.doi.org/10.1515/zna-1996-0305.

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The nonlinear Schrödinger equations with small dissipative perturbations are of current importance in modeling weakly nonlinear dispersive media with dissipation. In this paper, the Painlevé formulation with symbolic computation is presented for one of those equations. An auto-Bäcklund transformation and some exact solutions are explicitly constructed

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9

Bona, J. L., F. Demengel, and K. Promislow. "Fourier splitting and dissipation of nonlinear dispersive waves." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 3 (1999): 477–502. http://dx.doi.org/10.1017/s0308210500021478.

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Presented herein is a new method for analysing the long-time behaviour of solutions of nonlinear, dispersive, dissipative wave equations. The method is applied to the generalized Korteweg–de Vries equation posed on the entire real axis, with a homogeneous dissipative mechanism included. Solutions of such equations that commence with finite energy decay to zero as time becomes unboundedly large. In circumstances to be spelled out presently, we establish the existence of a universal asymptotic structure that governs the final stages of decay of solutions. The method entails a splitting of Fourier modes into long and short wavelengths which permits the exploitation of the Hamiltonian structure of the equation obtained by ignoring dissipation. We also develop a helpful enhancement of Schwartz's inequality. This approach applies particularly well to cases where the damping increases in strength sublinearly with wavenumber. Thus the present theory complements earlier work using centre-manifold and group-renormalization ideas to tackle the situation wherein the nonlinearity is quasilinear with regard to the dissipative mechanism.

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10

Sedal, Audrey, and Alan Wineman. "Force reversal and energy dissipation in composite tubes through nonlinear viscoelasticity of component materials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2241 (September 2020): 20200299. http://dx.doi.org/10.1098/rspa.2020.0299.

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Fibre-reinforced, fluid-filled structures are commonly found in nature and emulated in devices. Researchers in the field of soft robotics have used such structures to build lightweight, impact-resistant and safe robots. The polymers and biological materials in many soft actuators have these advantageous characteristics because of viscoelastic energy dissipation. Yet, the gross effects of these underlying viscoelastic properties have not been studied. We explore nonlinear viscoelasticity in soft, pressurized fibre-reinforced tubes, which are a popular type of soft actuation and a common biological architecture. Relative properties of the reinforcement and matrix materials lead to a rich parameter space connecting actuator inputs, loading response and energy dissipation. We solve a mechanical problem in which both the fibre and the matrix are nonlinearly viscoelastic, and the tube deforms into component materials’ nonlinear response regimes. We show that stress relaxation of an actuator can cause the relationship between the working fluid input and the output force to reverse over time compared to the equivalent, non-dissipative case. We further show that differences in design parameter and viscoelastic material properties can affect energy dissipation throughout the use cycle. This approach bridges the gap between viscoelastic behaviour of fibre-reinforced materials and time-dependent soft robot actuation.

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11

Pavlov G. A. "Fluctuation-dissipation theorem and frequency moments of response functions of a dense plasma to an electromagnetic field." Technical Physics 92, no. 2 (2022): 191. http://dx.doi.org/10.21883/tp.2022.02.52945.149-21.

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The fluctuation-dissipative theorem and frequency moments for quadratic functions of the reaction of a dense plasma in a constant magnetic field to an electromagnetic field are considered. The frequency moments of the corresponding correlation functions are studied. A model approach is proposed to calculate quadratic reaction functions that determine nonlinear phenomena caused by the quadratic interaction of electromagnetic waves in a dense charged medium (Coulomb systems, plasma) in a constant magnetic field. Keywords: dense plasma, nonlinear fluctuation-dissipative theorem, quadratic reaction functions, nonlinear phenomena. Keywords: dense plasma, nonlinear fluctuation-dissipation theorem, quadratic response functions, nonlinear phenomena.

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12

Kim, Daewook, Dojin Kim, Keum-Shik Hong, and Il Hyo Jung. "Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/716740.

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The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipationg. Lastly, numerical simulations in order to verify the analytical results are given.

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13

Maaita, Jamal-Odysseas, and Efthymia Meletlidou. "The Effect of Slow Invariant Manifold and Slow Flow Dynamics on the Energy Transfer and Dissipation of a Singular Damped System with an Essential Nonlinear Attachment." Journal of Nonlinear Dynamics 2014 (September 1, 2014): 1–10. http://dx.doi.org/10.1155/2014/208171.

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We study the effect of slow flow dynamics and slow invariant manifolds on the energy transfer and dissipation of a dissipative system of two linear oscillators coupled with an essential nonlinear oscillator with a mass much smaller than the masses of the linear oscillators. We calculate the slow flow of the system, the slow invariant manifold, the total energy of the system, and the energy that is stored in the nonlinear oscillator for different sets of the parameters and show that the bifurcations of the SIM and the dynamics of the slow flow play an important role in the energy transfer from the linear to the nonlinear oscillator and the rate of dissipation of the total energy of the initial system.

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14

Aburjania, G., K. Chargazia, O. Kharshiladze, and G. Zimbardo. "Self-organization of ULF electromagnetic wave structures in the shear flow driven dissipative ionosphere." Nonlinear Processes in Geophysics Discussions 1, no. 2 (August 26, 2014): 1431–64. http://dx.doi.org/10.5194/npgd-1-1431-2014.

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Abstract. This work is devoted to investigation of nonlinear dynamics of planetary electromagnetic (EM) ultra-low-frequency wave (ULFW) structures in the rotating dissipative ionosphere in the presence of inhomogeneous zonal wind (shear flow). Planetary EM ULFW appears as a result of interaction of the ionospheric medium with the spatially inhomogeneous geomagnetic field. The shear flow driven wave perturbations effectively extract energy of the shear flow increasing own amplitude and energy. These perturbations undergo self organization in the form of the nonlinear solitary vortex structures due to nonlinear twisting of the perturbation's front. Depending on the features of the velocity profiles of the shear flows the nonlinear vortex structures can be either monopole vortices, or dipole vortex, or vortex streets and vortex chains. From analytical calculation and plots we note that the formation of stationary nonlinear vortex structure requires some threshold value of translation velocity for both non-dissipation and dissipation complex ionospheric plasma. The space and time attenuation specification of the vortices is studied. The characteristic time of vortex longevity in dissipative ionosphere is estimated. The long-lived vortices transfer the trapped medium particles, energy and heat. Thus they represent structural elements of turbulence in the ionosphere.

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15

Hoyos Velasco, Carlos Ildefonso, Fredy Edimer Hoyos Velasco, and Julian M. Londoño Monsalve. "Nonlinear Dynamics Analysis of a Dissipation System with Time Delay." International Journal of Bifurcation and Chaos 28, no. 06 (June 15, 2018): 1830018. http://dx.doi.org/10.1142/s0218127418300185.

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This work is concerned with the bifurcational analysis of nonlinear dissipative systems affected by time delay. This issue typically arises when testing highly nonlinear energy dissipation devices, commonly used in vibration control of civil structures, and carried out experimentally via a hybrid technique known as Real-Time Dynamic Substructuring (RTDS) simulation. Unfortunately, the RTDS simulation is affected by time delay in the control feedback loop due to the actuator response, sensor reading and numerical processing. In essence, this paper focuses on studying the nonlinear dynamics induced by the interaction of a dynamical system with the nonlinear damper affected by the presence of time delay. Given the complexity of the system, numerical analysis is carried out in the context of bifurcational behavior, and bifurcation diagrams are computed using a continuation method. The bifurcational analysis presented here, provides a characterization of delay-induced nonlinear phenomena created by the interaction of the dynamical system with a delayed nonlinear response of the dissipation device. Nonlinear dynamics are also identified and characterized for different damper types when varying the damper model parameters, leading to the identification of system conditions at which the testing arrangement and test specimens can exhibit undesired dynamics.

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16

Panayotaros, Panayotis, and Felipe Rivero. "Multi-peak breather stability in a dissipative discrete Nonlinear Schrödinger (NLS) equation." Journal of Nonlinear Optical Physics & Materials 23, no. 04 (December 2014): 1450044. http://dx.doi.org/10.1142/s0218863514500441.

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We study the stability of breather solutions of a dissipative cubic discrete NLS with localized forcing. The breathers are similar to the ones found for the Hamiltonian limit of the system. In the case of linearly stable multi-peak breathers the combination of dissipation and localized forcing also leads to stability, and the apparent damping of internal modes that make the energy around multi-peak breathers nondefinite. This stabilizing effect is however accompanied by overdamping for relatively small values of the dissipation parameter, and the appearance of near-zero stable eigenvalues.

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17

Goddard, Joe, and Ken Kamrin. "Dissipation potentials from elastic collapse." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2226 (June 2019): 20190144. http://dx.doi.org/10.1098/rspa.2019.0144.

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Generalizing Maxwell's (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond. 157 , 49–88 ( doi:10.1098/rstl.1867.0004 )) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtl's (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8 , 85–106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T , with a nonlinear viscous response that becomes a plastic response for T → 0 . We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner–Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes.

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18

Yadollahi, Shahla, Mostafa Ramezani, Mehdi Razzaghi-Kashani, and Ahmad-Reza Bahramian. "NONLINEAR VISCOELASTIC DISSIPATION IN VULCANIZATES CONTAINING CARBON BLACK AND SILANIZED SILICA HYBRID FILLERS." Rubber Chemistry and Technology 91, no. 3 (July 1, 2018): 537–47. http://dx.doi.org/10.5254/rct.18.82611.

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ABSTRACT Different mechanisms of large-strain viscoelastic dissipation in vulcanizates containing carbon black or silanized silica and their synergistic effects in hybrid filler tread vulcanizates were investigated. In addition, the pure effects of fillers were examined while the degree of chemical cross-linking in the rubber matrix was similar in the vulcanizates. The results revealed that nonlinear viscoelastic loss modulus under strain-controlled dynamic tests, as a measure of dissipation mechanism, is high in both carbon black and silanized silica tread vulcanizates. However, a synergistic effect in reducing loss modulus was observed in the hybrid filler vulcanizates. Conversely, storage modulus in the vulcanizates containing more silanized silica is distinguishably higher and results in a lower loss factor representing load-controlled cyclic deformation of vulcanizates, such as in the heat buildup test. Both loss factor and heat build-up reduced nonlinearly as the amount of silanized silica increased in the vulcanizates, verifying the synergistic effect of hybrid carbon black–silanized silica filler in reducing dissipative mechanisms in large-strain dynamic loadings. This feature is highly favorable for the tire industry, where the lowering of viscoelastic dissipation in tread vulcanizates is of great importance.

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19

LeMesurier, Brenton J. "Multi-focusing and sustained dissipation in the dissipative nonlinear Schrödinger equation." Mathematics and Computers in Simulation 55, no. 4-6 (March 2001): 503–17. http://dx.doi.org/10.1016/s0378-4754(00)00307-4.

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20

MOON, K. "QUANTUM PHASE TRANSITIONS IN DISSIPATIVE JOSEPHSON JUNCTION ARRAYS." International Journal of Modern Physics B 19, no. 01n03 (January 30, 2005): 471–74. http://dx.doi.org/10.1142/s0217979205028839.

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Quantum phase slips can induce a phase transition in a single Josephson junction by varying coupling strength RS to the dissipative environment. We study the finite Josephson junction array with dissipations. For the infinite arrays with no dissipation, a quantum KT phase transition can occur by varying the ratio of the Josephson coupling strength EJ to the charging energy Ec due to the unbinding of instanton pairs. At finite temperature and array size, there will be a rich interplay between instantons and quantum phase slips.

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21

Su, Chuan-Qi, Yong-Yan Wang, Nan Qin, Yan-Chun Wang, and Guo-Dong Zhang. "Research on the dissipative characteristics of unsteady heat conduction for the one-dimensional sphere." Modern Physics Letters B 32, no. 25 (September 5, 2018): 1850293. http://dx.doi.org/10.1142/s0217984918502937.

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In this paper, the dissipative characteristics of unsteady heat conduction process for the one-dimensional sphere is studied. The dissipation function can be regarded as a Lyapunov function for the heat conduction system, which determines the evolution direction of the system and the stability of the steady state. By use of the vector formula, the relationship between the thermal potential and dissipation function is derived, and its similarity with the dissipation system of mechanical energy is shown. The expression of dissipation function is obtained when the boundary temperature is fixed. In addition, an example for optimization of heat conduction process is discussed based on the entransy dissipation extremum principle.

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22

Richet, O., C. Muller, and J. M. Chomaz. "Impact of a Mean Current on the Internal Tide Energy Dissipation at the Critical Latitude." Journal of Physical Oceanography 47, no. 6 (June 2017): 1457–72. http://dx.doi.org/10.1175/jpo-d-16-0197.1.

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AbstractPrevious numerical studies of the dissipation of internal tides in idealized settings suggest the existence of a critical latitude (~29°) where dissipation is enhanced. But observations only indicate a modest enhancement at this latitude. To resolve this difference between observational and numerical results, the authors study the latitudinal dependence of internal tides’ dissipation in more realistic conditions. In particular, the ocean is not a quiescent medium; the presence of large-scale currents or mesoscale eddies can impact the propagation and dissipation of internal tides. This paper investigates the impact of a weak background mean current in numerical simulations. The authors focus on the local dissipation of high spatial mode internal waves near their generation site. The vertical profile of dissipation and its variation with latitude without the mean current are consistent with earlier studies. But adding a weak mean current has a major impact on the latitudinal distribution of dissipation. The peak at the critical latitude disappears, and the dissipation is closer to a constant, albeit with two weak peaks at ~25° and ~35° latitude. This disappearance results from the Doppler shift of the internal tides’ frequency, which hinders the nonlinear transfer of energy to small-scale secondary waves via the parametric subharmonic instability (PSI). The new two weak peaks correspond to the Doppler-shifted critical latitudes of the left- and right-propagating waves. The results are confirmed in simulations with simple sinusoidal topography. Thus, although nonlinear transfers via PSI are efficient at dissipating internal tides, the exact location of the dissipation is sensitive to large-scale oceanic conditions.

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23

Li, Tao, Zikai Gao, and Keyu Xia. "Nonlinear-dissipation-induced nonreciprocal exceptional points." Optics Express 29, no. 11 (May 21, 2021): 17613. http://dx.doi.org/10.1364/oe.426474.

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24

Vekstein, G. E., and E. R. Priest. "Nonlinear magnetic reconnection with collisionless dissipation." Physics of Plasmas 2, no. 8 (August 1995): 3169–78. http://dx.doi.org/10.1063/1.871149.

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25

Bona, Jerry L., and Jiahong Wu. "Zero-Dissipation Limit for Nonlinear Waves." ESAIM: Mathematical Modelling and Numerical Analysis 34, no. 2 (March 2000): 275–301. http://dx.doi.org/10.1051/m2an:2000141.

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26

Sonnino, Giorgio, Jarah Evslin, and Alberto Sonnino. "Minimum Dissipation Principle in Nonlinear Transport." Entropy 17, no. 12 (October 30, 2015): 7567–83. http://dx.doi.org/10.3390/e17117567.

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27

Imboden, Matthias, Oliver Williams, and Pritiraj Mohanty. "Nonlinear dissipation in diamond nanoelectromechanical resonators." Applied Physics Letters 102, no. 10 (March 11, 2013): 103502. http://dx.doi.org/10.1063/1.4794907.

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28

Bousse, Nicholas Eric, James Marion Lehto Miller, Anne Louise Alter, Christopher Patrick Cameron, Hyun-Keun Kwon, Gabrielle Davis Vukasin, and Thomas W. Kenny. "Negative Nonlinear Dissipation in Microelectromechanical Beams." Journal of Microelectromechanical Systems 29, no. 5 (October 2020): 954–59. http://dx.doi.org/10.1109/jmems.2020.3006800.

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29

Wei, Xing. "Linear and nonlinear responses to harmonic force in rotating flow." Journal of Fluid Mechanics 796 (May 4, 2016): 306–17. http://dx.doi.org/10.1017/jfm.2016.267.

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For understanding the dissipation in a rotating flow when resonance occurs, we study the rotating flow driven by the harmonic force in a periodic box. Both the linear and nonlinear regimes are studied. The various parameters such as the force amplitude $a$, the force frequency ${\it\omega}$, the force wavenumber $k$ and the Ekman number $E$ are investigated. In the linear regime, the dissipation at the resonant frequency scales as $E^{-1}k^{-2}$, and it is much stronger than the dissipation at the non-resonant frequencies on large scales and at low Ekman numbers. In the nonlinear regime, at the resonant frequency the effective dissipation (dissipation normalised with the square of the force amplitude) is lower than in the linear regime and it decreases with increasing force amplitude. This nonlinear suppression effect is significant near the resonant frequency but negligible far away from the resonant frequency. Opposite to the linear regime, in the nonlinear regime at the resonant frequency the lower Ekman number leads to lower dissipation because of the stronger nonlinear effect. This work implies that the previous linear calculations overestimated the tidal dissipation, which is important for understanding the tides in stars and giant planets.

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30

Watanabe, Tomonari. "Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term." Journal of Hyperbolic Differential Equations 12, no. 02 (June 2015): 249–76. http://dx.doi.org/10.1142/s0219891615500071.

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We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

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31

Hui-chuan, Shen. "Dissipation mechanics and exact solutions for nonlinear equations of dissipative type—Principle and application of dissipation mechanics (I)." Applied Mathematics and Mechanics 7, no. 12 (December 1986): 1125–42. http://dx.doi.org/10.1007/bf01896976.

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32

Rosenberg, Duane, Annick Pouquet, and Raffaele Marino. "Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence." Atmosphere 12, no. 2 (January 26, 2021): 157. http://dx.doi.org/10.3390/atmos12020157.

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We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.

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TRUEBA, JOSÉ L., JOAQUÍN RAMS, and MIGUEL A. F. SANJUÁN. "ANALYTICAL ESTIMATES OF THE EFFECT OF NONLINEAR DAMPING IN SOME NONLINEAR OSCILLATORS." International Journal of Bifurcation and Chaos 10, no. 09 (September 2000): 2257–67. http://dx.doi.org/10.1142/s0218127400001419.

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This paper reports on the effect of nonlinear damping on certain nonlinear oscillators, where analytical estimates provided by the Melnikov theory are obtained. We assume general nonlinear damping terms proportional to the power of velocity. General and useful expressions for the nonlinearly damped Duffing oscillator and for the nonlinearly damped simple pendulum are computed. They provide the critical parameters in terms of the damping coefficient and damping exponent, that is, the power of the velocity, for which complicated behavior is expected. We also consider generalized nonlinear damped systems, which may contain several nonlinear damping terms. Using the idea of Melnikov equivalence, we show that the effect of nonlinear dissipation can be equivalent to a linearly damped nonlinear oscillator with a modified damping coefficient.

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34

CHEN, YONG-CONG. "LINEAR, NONLINEAR, AND TIME-DEPENDENT RESPONSE OF A DISSIPATIVE QUANTUM PARTICLE IN PERIODIC COSINE POTENTIALS." International Journal of Modern Physics B 07, no. 28 (December 30, 1993): 4647–86. http://dx.doi.org/10.1142/s0217979293003802.

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We review some of our recent results on the dynamics of a dissipative quantum particle in periodic cosine potentials. The dissipation is modeled by the Caldeira-Leggett prescription. Exact real-time Wigner distributions for the particle alone can be obtained in powers of V0 (the strength of the cosine potentials), which is suitable for calculations of various time-dependent averages. Special interest is devoted to summing over the whole series. For Ohmic dissipation, we have the following results: (a) The Kubo-Einstein relation for the linear response is shown to hold rigorously to all orders. (b) In the small viscosity limit, nearly exact analytic expressions for the nonlinear mobility and the nonlinear time-dependent response are found. (c) The resummation can also be performed in certain regimes of the dissipative Hafstadter problem in two dimensions. These results we believe can have useful applications in experiments in Josephson junctions and other mesoscopic systems.

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35

Oppenheim, Irwin. "Nonlinear nonequilibrium thermodynamics I. Linear and nonlinear fluctuation-dissipation theorems." Journal of Statistical Physics 77, no. 5-6 (December 1994): 1109–10. http://dx.doi.org/10.1007/bf02183157.

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36

Oppenheim, Irwin. "Nonlinear nonequilibrium thermodynamics I. Linear and nonlinear fluctuation-dissipation theorems." Journal of Statistical Physics 77, no. 3-4 (November 1994): 949–50. http://dx.doi.org/10.1007/bf02179473.

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37

ABDUSALAM, H. A., and E. S. FAHMY. "TRAVELING WAVE SOLUTIONS FOR NONLINEAR WAVE EQUATION WITH DISSIPATION AND NONLINEAR TRANSPORT TERM THROUGH FACTORIZATIONS." International Journal of Computational Methods 04, no. 04 (December 2007): 645–51. http://dx.doi.org/10.1142/s0219876207001321.

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In this work, we use the factorization method to find explicit exact particular traveling wave solutions for the nonlinear wave equation with dissipation and nonlinear transport term. The two-parameter solution is obtained by using the particular solution and the known solutions for the Newell–Whitehead equation, Kolmogorov–Petrovsky–Piscounov equation, Fitzhugh–Nagumo equation, and the Burgers equation with cubic nonlinearity obtained as special cases from the solutions of the nonlinear wave equation with dissipation and nonlinear term.

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38

Herrmann, Leopold. "Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation." Czechoslovak Mathematical Journal 35, no. 2 (1985): 278–94. http://dx.doi.org/10.21136/cmj.1985.102016.

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39

Gottlieb, O. "Bifurcations of a Nonlinear Small-Body Ocean-Mooring System Excited by Finite-Amplitude Waves." Journal of Offshore Mechanics and Arctic Engineering 119, no. 4 (November 1, 1997): 234–38. http://dx.doi.org/10.1115/1.2829101.

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We investigate the response of a nonlinear small-body ocean-mooring system excited by finite-amplitude waves. The system is characterized by a coupled geometrically nonlinear restoring force defined by a single elastic tether. The nonlinear hydrodynamic exciting force includes both dissipative and convective terms that are not negligible in a finite wave amplitude environment. Stability of periodic motion is determined numerically and the bifurcation structure includes ultrasubharmonic and quasi-periodic response. The dissipation mechanism is found to control stability thresholds, whereas the convective nonlinearity governs the evolution to chaotic system response.

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40

Anjana Aishwarya, M., and N. Srujana. "Nonlinear Analysis of a RC Structure for Different Damping Models." IOP Conference Series: Earth and Environmental Science 1086, no. 1 (September 1, 2022): 012014. http://dx.doi.org/10.1088/1755-1315/1086/1/012014.

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Abstract Damping is an important property of the structure as it helps in the dissipation of vibratory energy which is generally caused by the dynamic loads acting on the structure. Limiting the response amplitudes that are caused due to imposed vibrations is always challenging for the structure’s stability and safety. Three types damping models; viscous damping, structural damping and coulomb friction damping are proposed so far in the literature. Among these models viscous damping is highlighted due to the fact of high energy dissipation in the structure. In the present analysis, comparison of these three damping models in a G+5 RCC structure with respect to the energy dissipation by considering strain energy. The structure is analysed for the response amplitudes for the different damping models. The damping coefficient present in the structure is identified using linear time history analysis. Non-linear time history analysis is performed using time stepping methods to assess the response amplitudes of the structure. Using the non- linear responses, the amount of energy dissipated in each model and the loss factors are estimated. Also, the energy dissipations in the structure are compared for two different ground motions. Viscous damping model is found to be the suitable model in reducing effect of vibrations coming to the structure. For the structure having viscous damping model, frequency response curves of response amplification and phase angle are plotted. Therefore, non-linear behaviour of the structure can be estimated to some extent.

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41

Kaihatu, James, Deirdre Devery, Richard Erwin, and John Goertz. "THE INTERACTION BETWEEN SHORT OCEAN SWELL AND TRANSIENT LONG WAVES: DISSIPATIVE AND NONLINEAR EFFECTS." Coastal Engineering Proceedings 1, no. 33 (December 14, 2012): 20. http://dx.doi.org/10.9753/icce.v33.waves.20.

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The dissipation and nonlinear effects of random swell interaction with transient long waves are studied. Results from a laboratory experiment in which random swell was generated both with and without a co-existing transient long wave are analyzed. An instantaneous dissipation mechanism for estimating both instantaneous and bulk dissipation from data is used to determine the characteristics of dissipation for both cases. Fourier analysis of the free surface measurements and dissipation estimates reveals that the presence of the transient long wave does not have an appreciable impact on the known dissipation characteristics of random swell. However, the use of wavelet analysis, centered on the long wave in the time series, shows that the dissipation characteristics of the combined short-long wave signals deviate considerably from that of swell alone, indicating that smearing of the long wave signal by the Fourier analysis is sufficiently strong to affect dissipation estimates. A wavelet-based bispectral algorithm is used to determine the nonlinear wave-wave coupling in both swell and combined swell-long wave signals; the results indicate that there can be broader ranges of frequencies in which nonlinear coupling is present for the case of the combined short-long wave signal.

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42

Ha, Seung-Ji, and Gordon E. Swaters. "Finite-Amplitude Baroclinic Instability of Time-Varying Abyssal Currents." Journal of Physical Oceanography 36, no. 1 (January 1, 2006): 122–39. http://dx.doi.org/10.1175/jpo2838.1.

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Abstract The weakly nonlinear baroclinic instability characteristics of time-varying grounded abyssal flow on sloping topography with dissipation are described. Specifically, the finite-amplitude evolution of marginally unstable or stable abyssal flow both at and removed from the point of marginal stability (i.e., the minimum shear required for instability) is determined. The equations governing the evolution of time-varying dissipative abyssal flow not at the point of marginal stability are identical to those previously obtained for the Phillips model for zonal flow on a β plane. The stability problem at the point of marginally stability is fully nonlinear at leading order. A wave packet model is introduced to examine the role of dissipation and time variability in the background abyssal current. This model is a generalization of one introduced for the baroclinic instability of zonal flow on a β plane. A spectral decomposition and truncation leads, in the absence of time variability in the background flow and dissipation, to the sine–Gordon solitary wave equation that has grounded abyssal soliton solutions. The modulation characteristics of the soliton are determined when the underlying abyssal current is marginally stable or unstable and possesses time variability and/or dissipation. The theory is illustrated with examples.

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43

Riseborough, Peter S. "Influence of nonlinear dissipation on quantum tunneling." Physical Review B 43, no. 16 (June 1, 1991): 13269–73. http://dx.doi.org/10.1103/physrevb.43.13269.

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44

Schneggenburger, Christoph, Heinz Günther, and Wolfgang Rosenthal. "Shallow water wave modelling with nonlinear dissipation." Deutsche Hydrographische Zeitschrift 49, no. 2-3 (September 1997): 431–44. http://dx.doi.org/10.1007/bf02764049.

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45

Jou, D., and M. Zakari. "Nonlinear transport coefficients and fluctuation-dissipation theorem." Physics Letters A 203, no. 2-3 (July 1995): 129–32. http://dx.doi.org/10.1016/0375-9601(95)00386-h.

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46

Lange, H., B. Toomire, and P. F. Zweifel. "Time‐dependent dissipation in nonlinear Schrödinger systems." Journal of Mathematical Physics 36, no. 3 (March 1995): 1274–83. http://dx.doi.org/10.1063/1.531120.

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47

Ladyzhenskaya, O. A. "Attractors of nonlinear evolution problems with dissipation." Journal of Soviet Mathematics 40, no. 5 (March 1988): 632–40. http://dx.doi.org/10.1007/bf01094189.

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48

Zhang, Jiangyi, Vicente Romero-García, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Dimitrios Frantzeskakis. "Dark Solitons in Acoustic Transmission Line Metamaterials." Applied Sciences 8, no. 7 (July 20, 2018): 1186. http://dx.doi.org/10.3390/app8071186.

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We study dark solitons, namely density dips with a phase jump across the density minimum, in a one-dimensional, weakly lossy nonlinear acoustic metamaterial, composed of a waveguide featuring a periodic array of side holes. Relying on the electroacoustic analogy and the transmission line approach, we derive a lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. The latter, using the method of multiple scales, is reduced to a defocusing nonlinear Schrödinger equation, which leads to dark soliton solutions. The dissipative dynamics of these structures is studied via soliton perturbation theory. We investigate the role—and interplay between—nonlinearity, dispersion and dissipation on the soliton formation and dynamics. Our analytical predictions are corroborated by direct numerical simulations.

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49

BÜHLER, OLIVER. "On the vorticity transport due to dissipating or breaking waves in shallow-water flow." Journal of Fluid Mechanics 407 (March 25, 2000): 235–63. http://dx.doi.org/10.1017/s0022112099007508.

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Theoretical and numerical results are presented on the transport of vorticity (or potential vorticity) due to dissipating gravity waves in a shallow-water system with background rotation and bottom topography. The results are obtained under the assumption that the flow can be decomposed into small-scale gravity waves and a large-scale mean flow. The particle-following formalism of ‘generalized Lagrangian-mean’ theory is then used to derive an ‘effective mean force’ that captures the vorticity transport due to the dissipating waves. This can be achieved without neglecting other, non-dissipative, effects which is an important practical consideration. It is then shown that the effective mean force obeys the so-called ‘pseudomomentum rule’, i.e. the force is approximately equal to minus the local dissipation rate of the wave's pseudomomentum. However, it is also shown that this holds only if the underlying dissipation mechanism is momentum-conserving. This requirement has important implications for numerical simulations, and these are discussed.The novelty of the results presented here is that they have been derived within a uniform theoretical framework, that they are not restricted to small wave amplitude, ray-tracing or JWKB-type approximations, and that they also include wave dissipation by breaking, or shock formation. The theory is tested carefully against shock-capturing nonlinear numerical simulations, which includes the detailed study of a wavetrain subject to slowly varying bottom topography. The theory is also cross-checked in the appropriate asymptotic limit against recently formulated weakly nonlinear theories. In addition to the general finite-amplitude theory, detailed small-amplitude expressions for the main results are provided in which the explicit appearance of Lagrangian fields can be avoided. The motivation for this work stems partly from an on-going study of high-altitude breaking of internal gravity waves in the atmosphere, and some preliminary remarks on atmospheric applications and on three-dimensional stratified versions of these results are given.

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50

Fan, Xiao-Wei, Long-He Xu, Xing-Si Xie, Yu-Sheng Sun, and Zhong-Xian Li. "Hysteresis analysis of pre-pressed spring self-centering energy dissipation braces using different models." Advances in Structural Engineering 22, no. 12 (May 22, 2019): 2662–71. http://dx.doi.org/10.1177/1369433219849844.

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The ability of an idealized piecewise-linear restoring force model and a nonlinear mechanical model to describe the hysteretic performances of the pre-pressed spring self-centering energy dissipation braces was evaluated based on experimental data. The hysteretic behaviors predicted by these two proposed models were compared with the experimental results of a typical prototype brace, and the results demonstrated that the two models can explain the brace force-time responses, and that the nonlinear mechanical model is more effective in describing the stiffness transition and energy dissipation of the brace. The two proposed models can be used for the design of the pre-pressed spring self-centering energy dissipation brace specimens, and the nonlinear mechanical model may be more useful for designing the structures with the pre-pressed spring self-centering energy dissipation braces. An orthogonal experiment was applied to analyze the influences of the key parameters on the performances of pre-pressed spring self-centering energy dissipation braces based on the nonlinear mechanical model. The results indicate that the friction slip force of energy dissipation mechanism, the pre-pressed force of self-centering mechanism, and the post-activation stiffness significantly affect the hysteretic performances and equivalent viscous damping ratios of the bracing system, while the changes in other parameters only produce slight effects. The determination of the pre-pressed force of the self-centering mechanism should be coordinated with the friction slip force of the energy dissipation mechanism to achieve a better hysteretic performance of the pre-pressed spring self-centering energy dissipation brace.

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