Weak Dissipation Research Articles

Random perturbations of nonlinear oscillators: Homogenization and large deviations

This paper considers two prototypical strongly nonlinear oscillators with weak dissipation and noise: a pendulum which is acted on by a small noisy torque and opposed by a friction; and the noisy Duffing-van der Pol oscillator. But over a long time the weak dissipative and noise effects can be significant. This paper develops asymptotic techniques based on averaging and large deviations to study the effects of weak noise on the escape from the domain of attraction of stable equilibrium points and limit cycles in phase-space.

Effect of surface heat dissipation on thermocapillary convection of low Prandtl number fluid in a shallow annular pool

In order to understand the effect of surface heat dissipation on thermocapillary convection of low Prandtl number in a shallow annular pool, a series of three-dimensional numerical simulations were carried out by using the finite volume method. Results indicate that with the increase of surface heat dissipation, the thermocapillary convection intensity increases at first, and then decreases slightly; furthermore, the center of the thermocapillary convective cell moves gradually to the hot outer wall. With the increase of Marangoni number, the stable axisymmetric flow bifurcates orderly to the three-dimensional steady flow and the three-dimensional oscillatory flow at a weak surface heat dissipation. However, it bifurcates directly to the three-dimensional oscillatory flow at a strong heat dissipation. After thermocapillary convection destabilizes, the hydrothermal waves appear at the weak surface heat dissipation, but the longitudinal rolls near the outer wall are dominant at the strong heat dissipation. The flow pattern transition is always accompanied by the variations of the temperature fluctuation amplitude, the oscillatory frequency and the wave number.

Self-localization of Bose–Einstein condensates in optical lattices

Mean field and beyond mean field model calculations of Bose–Einstein condensates trapped in optical lattices have shown that initially homogeneous condensates can evolve into self-trapped, strongly localized states in the presence of weak boundary dissipation, a phenomenon called self-localization. A dynamical phase transition from extended to localized states can be observed when the effective nonlinearity exceeds a critical threshold . We investigate this phase transition to self-localization in the mean field approximation of the discrete nonlinear Schrödinger equation. We quantitatively characterize the properties of the discrete breathers, i.e. the nonlinear localized solutions, at the phase transition. This leads us to propose and numerically verify an analytical lower bound for the critical nonlinearity based on the idea of self-induced Anderson localization.

Stochastic Response Characteristic and Equivalent Damping of Weak Nonlinear Energy Dissipation System under Biaxial Earthquake Action

The random response characteristic of weak nonlinear structure under biaxial earthquake excitation is investigated. The structure has a SDOF (single degree of freedom) with supporting braces and viscoelastic dampers. First, it adopts integral constitutive relation and establishes a differential and integral equations of motion. Then, according to the principle of energy balance, the equation is linearized. Finally, based on the stochastic averaging method, the general analytical solution of the variance of the displacement and velocity response and the equivalent damping is deduced and derived. At the same time, the joint probability density function of the amplitude and phase and displacement and velocity of the energy dissipation structure are also given. The dynamic characteristics of a structure with viscoelastic dampers are determined as a solution to the variance of displacement response, so the equivalent damping is taken into consideration as a solution to replace the original nonlinear damping. It means it has established a unified analytical solution of stochastic response analysis and equivalent damping of a SDOF nonlinear dissipation structure with the brace under biaxial earthquake action in this paper.

Decomposition of flexible joint robot mathematical model

The mathematical model of the manipulator with flexible joints is investigated under the condition of weak dissipation. The method of asymptotic decomposition is used to reduce dimension and to simplify the structure of the model. The decoupling coordinate transformation is constructed as an asymptotic series. It converts original multirate system to block triangular form with independent slow subsystem.

Global regularity of the 2D liquid crystal equations with weak velocity dissipation

In this paper we consider an initial value problem for the two-dimensional liquid crystal equations. We establish the global regularity of solutions to the equations with a weak velocity dissipation and obtain the global smooth solutions to the 2D liquid crystal equations with damping for small initial data.

Effect of SiO2 Buffer Layer Thickness on Performance and Reliability of Flexible Polycrystalline Silicon TFTs Fabricated on Polyimide

This letter investigates flexible polycrystalline silicon thin film transistor performance variation due to different buffer layer thicknesses. In flexible electronics, thermal expansion stress during device fabrication is inevitable. A thicker SiO2 buffer demonstrates better endurance to thermal expansion stress from the polyimide substrate during device annealing. However, if the SiO2 buffer thickness is above a critical point, its weak heat dissipation capability causes the optimal ELA crystallization condition to shift. A thermal expansion stress simulation and TEM photos were utilized to verify performance variation. Furthermore, a similar trend was observed in electrical characteristics after negative bias temperature instability.

Existence, regularity and approximation of global attractors for weakly dissipative p-Laplace equations

A global attractor in $L^2$ is shown for weakly dissipative $p$-Laplace equations on the entire Euclid space, where the weak dissipativeness means that the order of the source is lesser than $p-1$. Half-time decomposition and induction techniques are utilized to present the tail estimate outside a ball. It is also proved that the equations in both strongly and weakly dissipative cases possess an $(L^2,L^r)$-attractor for $r$ belonging to a special interval, which contains the critical exponent $p$. The obtained attractor is proved to be approximated by the corresponding attractor inside a ball in the sense of upper strictly and lower semicontinuity.

Random Perturbations of Autoresonance in Oscillating Systems with Small Dissipation

We consider the system of differential equations describing the initial step of capture of nonlinear oscillations in autoresonance under weak dissipation. We study the stability in probability of resonance solutions with unboundedly growing amplitude under persistent random perturbations. Bibliography: 11 titles. Illustrations: 1 Figure

Flow patterns and efficiency-power characteristics of a self-propelled, heaving rigid flat plate

The aim of the present study is to characterize the flow patterns, propulsion efficiency and power requirements associated with a self-propelled-heaving thin flat plate in a quiescent medium. In this regard, a numerical model using a shifting discontinuous-grid and based upon multi-relaxation-time lattice Boltzmann method is developed to probe the resulting aerodynamics. The influence of kinematic parameters namely flapping Reynolds number Ref (20−100) and plunging amplitude β (0.2–1), and the density ratio ρ* (101−102) on forward flight is pursued. Depending on the kinematics, various periodic vortex shedding characteristics of the plunging plate are observed that lead to modification of the angle of attack as a result of wing-wake interaction and downward jet. The presence of strong vortex dipole at the trailing edge with an attached leading edge vortex are factors responsible for maximum thrust generation. A wing-wake interaction which occurs at low β and high Ref due to weak vortex dissipation and presence of vortex dipole at the trailing edge acting in tandem can lead to achieving high propulsion efficiency. Through surrogate modelling, a set of Pareto-optimal solutions that describe the tradeoff between efficiency and input power for forward flight is presented and offers insight into the design and development of next generation flapping wing micro-air vehicles.

Global regularity for a class of 2D tropical climate model

In this paper, we establish the global regularity of a modified version of the tropical climate model originally derived by Frierson–Majda–Pauluis (2004) [6] which couples the barotropic and baroclinic modes of the velocity and the typical midtropospheric temperature. In proving the global regularity, to bypass the difficulty caused by the very weak dissipation (any small power α>0) of the barotropic mode, we utilize the “weakly nonlinear” energy estimate approach and the Maximal LtqLxp regularity for the heat kernel.

Energy localization in weakly dissipative resonant chains.

Localization of energy in oscillator arrays has been of interest for a number of years, with special attention paid to the role of nonlinearity and discreteness in the formation of localized structures. This work examines a different type of energy localization arising due to the presence of dissipation in nonlinear resonance arrays. As a basic model, we consider a Klein-Gordon chain of finite length subjected to a harmonic excitation applied at an edge of the chain. It is shown that weak dissipation may be a key factor preventing the emergence of resonance in the entire chain, even if its nondissipative analog is entirely captured into resonance. The resulting process in the dissipative oscillator array represents large-amplitude resonant oscillations in a part of the chain adjacent to the actuator and small-amplitude oscillations in the distant part of the chain. The conditions of the emergence of resonance as well as the conditions of energy localization are derived. An agreement between the obtained analytical results and numerical simulations is demonstrated.

Identifying storm-induced wave origins using SAR wave mode data

Because of weak dissipation effects, swells generated by fierce storms can propagate across an entire ocean basin; therefore, observing swell generation and decay and retrieving storm characteristics from a swell by satellite remote sensing are possible. In this study, based on the dispersion relation and geometrical optics principle, we used SAR wave mode data from 2003 to 2010 provided by GlobWave to track swells with peak wavelengths of more than 300 m to locate a storm-generated far-traveling swell and present the swell field related to this “static” origin. Through a comparison with ECMWF wind datasets, we conducted validations and explored some conditions that cause misjudgments in swell origins. Finally, we obtained the spatiotemporal distribution characteristics of satellite-observed swell origins (i.e., the fierce wind condition) and their evolution. This work can be used as a reference for wave models, providing early swell warnings, determining air-sea surface interactions, and determining global climate change.

Longtime Well-posedness for the 2D Groma–Balogh Model

In this paper, we consider the cauchy problem for the 2D Groma–Balogh model (Acta Mater 47:3647–3654, 1999). From the works Cannone et al. (Arch Ration Mech Anal 196:71–96, 2010) and El Hajj (Ann Inst Henri Poincare Anal Nonlineaire 27:21–35, 2010), one can see global well-posedness for this model is an open question. However, we can prove longtime well-posedness. In particular, we show that this model admits a unique solution with the lifespan \(T^\star \) satisfying \(T^\star \log ^2(1+T^\star )\gtrsim \epsilon ^{-2}\) if the initial data is of size \(\epsilon \). To achieve this, we first establish some new decay estimates concerning the operator \(e^{-{\mathcal {R}}_{12}^2t}\). Then, we prove the longtime well-posedness by utilizing the weak dissipation to deal with the nonlinear terms.

Magnetosonic shock wave in collisional pair-ion plasma

Nonlinear propagation of magnetosonic shock wave has been studied in collisional magnetized pair-ion plasma. The masses of both ions are same but the temperatures are slightly different. Two fluid model has been taken to describe the model. Two different modes of the magnetosonic wave have been obtained. The dynamics of the nonlinear magnetosonic wave is governed by the Korteweg-de Vries Burgers' equation. It has been shown that the ion-ion collision is the source of dissipation that causes the Burgers' term which is responsible for the shock structures in equal mass pair-ion plasma. The numerical investigations reveal that the magnetosonic wave exhibits both oscillatory and monotonic shock structures depending on the strength of the dissipation. The nonlinear wave exhibited the oscillatory shock wave for strong magnetic field (weak dissipation) and monotonic shock wave for weak magnetic field (strong dissipation). The results have been discussed in the context of the fullerene pair-ion plasma experiments.

Hysteresis of noninteracting and spin-orbit-coupled atomic Fermi gases with relaxation

Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating magnetic field in the relaxation approximation clearly demonstrates rate-dependent hysteresis. A noninteracting atomic Fermi gas in an optical ring potential, when driven by a periodic artificial gauge field and subjected to dissipation, is shown to exhibit hysteresis loops of atomic current due to a competition of the driving time and the relaxation time. This is in contrast to electronic systems exhibiting equilibrium persistent current driven by magnetic flux due to rapid relaxation. Universal behavior of the dissipated energy in one hysteresis loop is observed in both the magnetic and atomic systems, showing linear and inverse-linear dependence on the relaxation time in the strong and weak dissipation regimes. While interactions in general invalidate the framework for rate-dependent hysteresis, an atomic Fermi gas with artificial spin-orbit coupling exhibits hysteresis loops of atomic currents. Cold-atoms in ring-shape potentials are thus promising in demonstrating rate-dependent hysteresis and its associated phenomena.

Experimental research on seismic behavior of SRC-RC transfer columns

It was found that the lateral stiffness changes obvious at the transfer position of the section configuration from SRC to RC. This particular behavior leads to that the transfer columns become as the important elements in SRC-RC hybrid structures. A comprehensive study was conducted to investigate the seismic behavior of SRC-RC transfer columns based on a low cyclic loading test of 16 transfer columns compared with 1 RC column. Test results shows three failure modes for transfer columns, which are shear failure, bond failure and bend failure. Its seismic behavior was completely analyzed about the failure mode, hysteretic and skeleton curves, bearing capacity deformation ability, stiffness degradation and energy dissipation. It is further determined that displacement ductility coefficient of transfer columns changes from 1.97 to 5.99. The stiffness of transfer columns are at the interval of SRC and RC, and hence transfer columns can play the role of transition from SRC to RC. All specimens show similar discipline of stiffness degradation and the process can be divided into three parts. Some specimens of transfer column lose bearing capacity swiftly after shear cracking and showed weak energy dissipation ability, but the others show better ability of energy dissipation than RC column.

Quantum synchronization in a star-type cavity QED network

We propose and analyze a quantum synchronization sharing scheme among the nodes of a star-type quantum network. Utilizing dark state resonances, we show the biggish differences between two subsystems can be corrected by magnified effective coupling although each subsystem is of relative weak coupling intensity and high dissipation effects. Moreover, we elucidate that the quantum synchronization contains available classical and quantum correlations simultaneously. In particular, synchronization measure shows high consistency with quantum concurrence for qubit system, which means it possesses nonlocality and can ensure the advantage of quantum information processing. Finally, a brief discussion about parameter selection is given so that our scheme can be applied expediently in relevant experiments.

Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition

The study of dynamic fracture is based on the dynamic energy-dissipation balance. It is easy to see that this condition is always satisfied by a stationary crack together with a displacement satisfying the system of elastodynamics. Therefore to predict crack growth a further principle is needed. In this paper we introduce a weak maximal dissipation condition that, together with elastodynamics and energy balance, provides a model for dynamic fracture, at least within a certain class of possible crack evolutions. In particular, we prove the existence of dynamic fracture evolutions satisfying this condition, subject to smoothness constraints, and exhibit an explicit example to show that maximal dissipation can indeed rule out stationary cracks.

Expansion shock waves in regularized shallow-water theory.

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin-Bona-Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.