Nonlinear Dissipation Research Articles

Blow‐up of solutions of wave equation with a nonlinear boundary condition and interior focusing source of variable order of growth

In this paper, being investigated an initial‐boundary value problem for a one‐dimensional wave equation with a nonlinear source of variable order and nonlinear dissipation at the boundary. The existence of a local solution of the problem under consideration is proved. Then the question of the absence of global solutions is investigated. Depending on the relationship between the order of growth of the nonlinear source and the nonlinear boundary dissipation, different results are obtained on the blow‐up of weak solutions in a finite time interval.

Dissipative Phase Transition in Systems with Two-Photon Drive and Nonlinear Dissipation near the Critical Point.

In this paper, we examine dissipative phase transition (DPT) near the critical point for a system with two-photon driving and nonlinear dissipations. The proposed mean-field theory, which explicitly takes into account quantum fluctuations, allowed us to describe properly the evolutionary dynamics of the system and to demonstrate new effects in its steady-state. We show that the presence of quantum fluctuations leads to a power-law dependence of the anomalous average at the phase transition point, with which the critical exponent is associated. Also, we investigate the effect of the quantum fluctuations on the critical point renormalization and demonstrate the existence of a two-photon pump “threshold”. It is noteworthy that the obtained results are in a good agreement with the numerical simulations.

Significance of magnetized Darcy-Forchheimer stratified rotating Williamson hybrid nanofluid flow: A case of 3D sheet

The rising challenges of thermal transportation in compact density heat exchangers demand an efficient solution. The adequate thermal transportation for various heat exchangers can be achieved by mild homogeneous mixing of metallic/nonmetallic materials in the bulk base fluid. In this way, the base fluid's thermal efficiency is boosted. So, hybrid nanofluid constituted by mixing two or more nano species in the bulk base fluid is more effective than nanofluids. Therefore, the current research aims to determine the heat transfer properties of a 3D rotating Williamson hybrid nanofluid with Darcy-Forchheimer, dual stratifications, nonlinear thermal radiation, magnetic field, viscous dissipation, activation energy, and Joule heating effects for a stretched surface. The Al2O3 and Zn nanoparticles are mixed with base fluid C2H6O2. Partial differential equations are used to formulate the flow problem. Due to the nonlinear nature of the resulting governing differential equations, these partial differential equations are converted into ordinary differential equations using a feasible similarity transformation. The reduced mathematical structure is solved numerically with the help of MATLAB software Bvp4c package's boundary value problem solver. This study showed a higher degree of symmetry and accuracy of data than the previous ones. The primary velocity declined, and secondary velocity was enhanced for nanofluid and hybrid nanofluid by increasing the Williamson parameter's values, which is consistent with prior observations. Additionally, the temperature and concentration of both fluids are decreased for the boosted inputs of thermal stratification and concentration stratification parameters, respectively.

A five-parameter constitutive model for hysteresis shearing and energy dissipation of rock joints

Rock joints exhibit hysteresis shearing behavior and produce energy dissipation under shear cyclic loads, which however cannot be accurately depicted by existing constitutive models. This paper establishes a constitutive model for hysteresis shearing and associated energy dissipation of rock joints. Analytical expressions of the model during cyclic shearing processes are derived. Derivation of the model indicates no energy dissipation in the elastic stage. When the shear load exceeds elastic boundary, nonlinear energy dissipation takes place. Validations with experiments show that the proposed model provides good conformities with direct shear curves and hysteresis loops, and can predict the energy dissipation characteristics of rock joints under different working conditions. Compared to the constitutive models using Weibull’s distribution, the proposed one is smooth at the elastic boundary and can accurately capture the maximum shear stress. Unlike the existing incremental-type models, the proposed one provides clear and direct analytical expressions for both shear stress and energy dissipation during the whole displacement domain, which is more convenient in application.

Optical modification of nonlinear crystals for quasi-parametric chirped-pulse amplification

Quasi-parametric chirped-pulse amplification (QPCPA), which features a theoretical peak power much higher than those obtained with Ti:sapphire laser or optical parametric chirped-pulse amplification, is promising for future ultra-intense lasers. The doped rare-earth ion used for idler dissipation is critical for effective QPCPA, but is usually not compatible with traditional crystals. Thus far, only one dissipative crystal of Sm3+-doped yttrium calcium oxyborate has been grown and applied. Here we introduce optical means to modify traditional crystals for QPCPA applications. We theoretically demonstrate two dissipation schemes by idler frequency doubling and sum-frequency generation with an additional laser. In contrast to absorption dissipation, the proposed nonlinear dissipations ensure not only high signal efficiency but also high small-signal gain. The demonstrated ability to optically modify crystals will facilitate the wide application of QPCPA.

Optimal $$L^2$$-decay of solutions to a nonlinear Schrödinger equation with sub-critical dissipative nonlinearity

Optimal $$L^2$$-decay of solutions to a nonlinear Schrödinger equation with sub-critical dissipative nonlinearity

Qubit decoherence and symmetry restoration through real-time instantons

A parametrically driven quantum oscillator, stabilized by a nonlinear dissipation, exhibits a spontaneous breaking of the parity symmetry. It results in the quantum bi-stability, corresponding to a Bloch sphere of dark states. This makes such a driven-dissipative system an attractive candidate for a qubit. The parity symmetry breaking is exact both on the classical level and within the quantum mechanical perturbation theory. Here we show that non-perturbative quantum effects lead to the symmetry restoration and result in exponentially small but finite qubit decoherence rate. Technically the symmetry restoration is due to real time instanton trajectories of the Keldysh path integral, which represents the Lindbladian evolution of the driven-dissipative oscillator.

Nonlinear dynamic response dissipation of plates with heterogeneous orthotropic distributions of shape memory alloy micro-wires undergoing 3D phase-transformations

Nonlinear dynamic response dissipation of plates with heterogeneous orthotropic distributions of shape memory alloy micro-wires undergoing 3D phase-transformations

Design optimization of fuzzy controllers in building structures using the crystal structure algorithm (CryStAl)

The current study uses a recently-developed metaheuristic method called Crystal Structure Algorithm (CryStAl) to achieve optimized vibration control in structural engineering. More specifically, this algorithm, which is inspired by the well-established crystallographic principles underlying the formation of crystalline solids in nature, is applied to the optimization of fuzzy logic controllers in building structures. To demonstrate the capability of this method in solving real engineering problems, two real-size building structures, one with three and the other with twenty stories, are considered. The fuzzy controllers are implemented through an active control system to control the seismically-induced vibrations of the structures intelligently. The evaluation criteria utilized to assess the overall performance of the optimization method applied to the fuzzy control system are presented and discussed. Through nonlinear structural analyses, the ductility, energy dissipation, and other nonlinear characteristics of the structures are also considered as the structural responses to be controlled. The computational results obtained from this novel metaheuristic algorithm are compared with those of the other expert systems from the optimization literature. The findings of this paper demonstrate that the Crystal Structure Algorithm is capable of outranking the other methods in the majority of considered cases.

Finite-Time Stabilization of the Fractional Model of the Driven Dissipative Nonlinear Pendulum

Finite-time stabilization of the driven dissipative nonlinear pendulum is investigated in this paper. First, asymptotic and nonasymptotic convergence towards stable and unstable orbits of the ordinary model of the driven dissipative nonlinear pendulum is considered. It is shown that the existence of nonasymptotic convergence does not contradict the fact that time-reversal invariance holds true for the ordinary model of the driven dissipative nonlinear pendulum. Then, finite-time stabilization of unstable orbits of the fractional model of the driven dissipative nonlinear pendulum is discussed. The proposed stabilization technique is based on a proper selection of initial conditions and does not require any feedback loops. Computational experiments are used to illustrate the efficacy of the proposed finite-time stabilization techniques.

Research on Identification Model of Continuous Compaction Based on Energy Dissipation

A continuous compaction control energy model suitable for contact decoupling between the vibrating wheel and the filling body surface is established through analyzing the energy state of the filling body in the compaction detection stage and calculating nonlinear vibration energy dissipation rate based on the basic principle of continuous compaction control technology and the principle of energy conservation. The significance of the parameters contained in the energy model is analyzed, and the energy index-dissipation measured value (DMV) for evaluating the continuous compaction quality is put forward in combination with engineering practice. The feasibility of DMV is verified, and the applicability of DMV is discussed according to the field test results. The results show that the variation range of the DMV index is about 1.66–2.73 times of the Evd index, the DMV has good repeatability and sensitivity for both coarse-grained and fine-grained filler, and it is less affected by the interference caused by the small fluctuation of mechanical parameters, and has good stability for the local unevenness of filler in horizontal direction. The engineering application shows that the correlation coefficient between energy index DMV and Evd index reach more than 0.87, there is a good correlation between DMV and the conventional quality inspection index Evd, indicating that the energy model is applicable.

Stability results for laminated beam with thermo-visco-elastic effects and localized nonlinear damping

In this article, we investigate a one-dimensional thermoelastic laminated beam system with nonlinear damping and viscoelastic dissipation on the effective rotation angle and through heat conduction in the interfacial slip equations. Under minimal conditions on the relaxation function and the relationship between the coefficients of the wave propagation speed of the first two equations, we show that the solution energy has an explicit and optimal decay rate from which the exponential and polynomial stability are just particular cases. Moreover, we establish a weaker decay result in the case of non-equal wave of speed propagation and give some examples illustrate our results. This work extends and improves the earlier results in the literature, particularly the result of Mukiawa et al. (2021).

Convective Acceleration in Porous Media

Convective acceleration occurs in porous media flows due to the spatial variations of the nonuniform flow channel geometry of natural pores. This article demonstrates that the influence of convective acceleration in a nonuniform a pore channel is analogous to that of a constricting pipe channel. Their fluid mechanical behaviour can be comparable, provided that their geometrical characteristics are described precisely in the same manner, and from the same point of reference with regards to the fluid velocity in the flow channels. The analogy of the dissipation mechanisms in nonlinear porous media flow to the "minor loss" approach in fluid mechanics of pipes is therefore appropriate. Conventional nonuniform pipe channel geometries obtain dissipation coefficients within the range 0 < CKL < 0.2. These pipe geometries are relevant reference points for natural porous media, and it is thus expected that most natural pore geometries will obtain values within this range. This assumption holds true for the nine different 3D porous media samples presented here. However, the results show that the rate of change in the pore geometry, and consequently the magnitude of induced convective acceleration, depends on: the area ratio a of the pore channel, the angle of approach θ and the rounding of the pore channel geometry. The rounding of the pore channel reduces the dissipation coefficient, as the rate of change becomes smoother along the channel length. The results also indicate that the pore tortuosity increase the magnitude of nonlinear dissipation, in good agreement with pipe flow behaviour. This knowledge can help improve our interpretation of experimental data and enhance the predictability of porous media equations that incorporate the appropriate dissipation coefficients CKL as a variable.Article HighlightsThe analogy of porous media flow to the "minor loss" approach in fluid mechanics of pipes is appropriate, and the angle of approach θ and the area ratio a of the pore channel govern the magnitude of induced convective acceleration in porous mediaThe rounding of the pore channel geometry reduces the magnitude of induced convective accelerationThe tortuosity of a pore influences the dissipation coefficient CKL and increase the magnitude of induced convective acceleration

Driven nonlinear damping and mode coupling in a superconducting levitated magnet

The magnetic flux pinning phenomenon enables high-$Q$ trapping of a magnet above a superconductor. In practice, the trapped magnet can undergo nonlinear mode coupling and dissipation as its vibration can induce variations of the magnetic field and vortex displacement on the superconductor surface. Here we study nonlinear interactions between vibrational modes of a levitated magnetic mirror above a superconducting disk in vacuum conditions. We observe that by exciting one vibrational mode of the levitated mirror, the vibrational noise of another mode can be suppressed by more than 17 dB. We attribute this unique noise suppression mechanism to the mode coupling and nonlinear dissipation caused by the driven magnetic inhomogeneity of the levitated object. The results suggest that noise reduction of a vibrational mode is possible by driving another orthogonal mode.

Static and Dynamic Mechanical Characterization of Polydimethylsiloxane (PDMS) under Uniaxial Tensile Loading

The present study is based on performing mechanical characterization of polydimethylsiloxane (PDMS) under tensile loading. PDMS samples are developed by mixing prepolymer and curing agent with 10:1 ratio. Mechanical characterization of the PDMS samples is carried out using static and dynamic mechanical testing methods. In particular, the material is characterized under monotonic loading, different strain rates, and force-controlled cyclic loading. The monotonic loading tests are performed at different grip tightening levels to optimize gripping that avoids slipping and reaches failure point. The strain rate dependency and cyclic loading tests are performed to study the viscoelastic behaviour of the material. Strain rate dependency tests are carried out at the strain rates of 6.7×10-3 s-1, 3.2×10-2 s-1, and 6.2×10-2 s-1. The hysteresis tests are performed at the force rates of 0.1 – 2 N/s. The obtained results show that fixing the testing specimen made of soft hyperviscoelastic material such as PDMS is challenging and can significantly affect its stress-strain behaviour and mechanical properties. A higher strain rate increases the stiffness of the material due to the viscoelastic nature of the material. Observing the stress-strain curves, with respect to the lowest strain rate case, the curve for 6.2×10-2 s-1 strain rate diverges at 40% strain compared to 3.2×10-2 s-1 strain rate curve that diverges at 80% strain. The material shows a nonlinear hysteresis behaviour and similar energy dissipation for the considered force-controlled cyclic loading cases.

A proposed method for selecting and scaling recorded seismic accelerations according to TCVN-9386:2012

Accelerogram is a significant input in seismic analysis of structures, particularly for performance-based seismic designs and for advanced technologies using nonlinear energy dissipation devices. However, in seismic regions like Vietnam, earthquake data is generally scarce. Vietnam Standard TCVN-9386:2012 mentions the use of recorded accelerogram for seismic analysis, although it contains shortcomings. The paper aims to detail the procedure of selecting and scaling recorded seismic accelerations according to requirements specified by TCVN-9386:2012. The target response spectrum and the fundamental vibration period of the considered structure are critical factors for the selecting and scaling process. The proposed procedure essentially includes converting the two original horizontal accelerations to the principal directions, correcting the relative proportion between the two acceleration components, determining the period range of interest, calculating the scaling factors, and verifying the 10% matching criteria. An example is conducted on a typical set of accelerations to detail the application of the proposed procedure. The results show that the response spectra of calibrated accelerations are consistent with the target spectrum and satisfy the requirements of TCVN-9386:2012, suggesting that the proposed method can be applied to the seismic analysis of structures with high reliability.

Numerical investigation for non-axisymmetric Homann stagnation point flow of a SWCNT/MWCNT-water nanofluid over a disk

In this article, the non-axisymmetric MHD Homann stagnation point flow over an impermeable rigid cylindrical disk is discussed. Thermal convection is also studied in the Homann flow of water by adding the multi-wall carbon nanotube/ single-wall carbon nanotube (MWCNT/SWCNT) as nanoparticles. The analysis of energy transport in nanofluids is done by adopting the dynamic and static models namely the Buongiorno and Xue models for nanofluids, respectively. Furthermore, the effect of non-linear thermal radiations and viscous dissipation on thermal energy transport is also examined. The appropriate transformations are used in order to obtain the similar differential equations. The resulting non-linear transformed coupled equations are solved by the bvp4c method in MATLAB. It is noted that for MWCNT-Water nanofluid there is significant enhancement in the heat conduction rate as compared to SWCNT-Water nanofluid.

Spinning rigid bodies driven by orbital forcing: the role of dry friction

A "circular orbital forcing" makes a chosen point on a rigid body follow a circular motion while the body spins freely around that point. We investigate this problem for the planar motion of a body subject to dry friction. We focus on the effect called reverse rotation (RR), where spinning and orbital rotations are antiparallel. Similar reverse dynamics include the rotations of Venus and Uranus, journal machinery bearings, tissue production reactors, and chiral active particles. Due to dissipation, RRs are possible only as a transient. Here the transient or flip time $t_\textrm{f}$ depends on the circular driving frequency $\omega$, unlike the viscous case previously studied. We find $t_\textrm{f}\sim\omega^{\gamma-1}\mu^{-\gamma/2}$, where $\mu$ is the friction coefficient and $\gamma=0$ ($\gamma=2$) for low (high) $\omega$. Whether RRs really occur depends on the initial conditions as well as on $\mu$ and $H$, a geometrical parameter. The critical $H_\textrm{c}(\mu)$ where RRs become possible follows a $q$-exponential with $q\simeq1.9$, a more restrictive RR scenario than in the wet case. We use animations to visualize the different dynamical regimes that emerge from the highly nonlinear dissipation mechanism of dry friction. Our results are valid across multiple investigated rigid body shapes.

Influence of a strong low-frequency wave on the propagation of weak ultrasonic pulses in a rod resonator made of annealed polycrystalline copper

An experimental study of an influence of a strong low-frequency wave on the propagation of weak ultrasonic pulses in an acoustic resonator made of annealed polycrystalline copper has been carried out. The measurements were carried out with harmonic excitation of the resonator at its first four longitudinal modes in the range from 2 to 15 kHz, the frequency of ultrasonic pulses varied from 65 to 400 kHz. The analysis of the observed nonlinear effects was carried out within the framework of the polycrystal equation of state obtained on the basis of a modified string model of the Granato-Lucke dislocation. The values of the parameters of dissipative and reactive nonlinearity of dislocations in annealed copper are determined. Keywords: dislocation dissipative and reactive nonlinearity, polycrystalline copper, elastic waves.

Turbulence-driven magnetic reconnection and the magnetic correlation length: Observations from Magnetospheric Multiscale in Earth's magnetosheath

Turbulent plasmas generate a multitude of thin current structures that can be sites for magnetic reconnection. The Magnetospheric Multiscale (MMS) mission has recently enabled the detailed examination of such turbulent current structures in Earth's magnetosheath and revealed that a novel type of reconnection, known as electron-only reconnection, can occur. In electron-only reconnection, ions do not have enough space to couple to the newly reconnected magnetic fields, suppressing ion jet formation and resulting in thinner sub-proton-scale current structures with faster super-Alfvénic electron jets. In this study, MMS observations are used to examine how the magnetic correlation length (λC) of the turbulence, which characterizes the size of the large-scale magnetic structures and constrains the length of the current sheets formed, influences the nature of turbulence-driven reconnection. We systematically identify 256 reconnection events across 60 intervals of magnetosheath turbulence. Most events do not appear to have ion jets; however, 18 events are identified with ion jets that are at least partially coupled to the reconnected magnetic field. The current sheet thickness and electron jet speed have a weak anti-correlation, with faster electron jets at thinner current sheets. When λC≲20 ion inertial lengths, as is typical near the sub-solar magnetosheath, a tendency for thinner current sheets and potentially faster electron jets is present. The results are consistent with electron-only reconnection being more prevalent for turbulent plasmas with relatively short λC and may be relevant to the nonlinear dynamics and energy dissipation in turbulent plasmas.