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"Dissipation"
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A proof of Onsager's conjecture
For any α < 1/3, we construct weak solutions to the 3D incompressible Euler equations in the class
CtCx
α
that have nonempty, compact support in time on R × T3 and therefore fail to conserve the total kinetic
energy. This result, together with the proof of energy conservation for α < 1/3 due to [Eyink] and [Constantin, E, Titi], solves Onsager's conjecture that the
exponent α = 1/3 marks the threshold for conservation of energy for weak solutions in the class
Lt
∞Cx
α. The previous best results were solutions in the class
CtCx
α
for α < 1/5, due to [Isett], and in the class
Lt
1
Cx
α
for α < 1/3 due to [Buckmaster, De Lellis, Székelyhidi], both based
on the method of convex integration developed for the incompressible Euler equations by [De Lellis, Székelyhidi]. The present proof combines the method of convex integration and a
new “Gluing Approximation” technique. The convex integration part of the proof relies on the “Mikado flows” introduced by [Daneri, Székelyhidi] and the framework of estimates
developed in the author's previous work.
Journal Article
Spectral Wave Dissipation Over a Roughness‐Varying Barrier Reef
The present paper reports on a field experiment performed over a shallow, roughness‐varying barrier reef at Maupiti island, French Polynesia. The spectral wave energy balance is examined, outside the breaking zone and accounting for non‐linear transfers and mean current, to estimate the wave friction factor. This latter varies from 0.05 to 4, with dependence on the ratio between near‐bed orbital amplitude and roughness height well predicted by an adjusted parameterization from Madsen (1995). The present results are discussed with respect to other field data recovered on coral and rocky grounds. Plain Language Summary Coral reefs are essential for humanity and ecosystems in many tropical areas. In the context of global change and reef degradation, coral reef management requires efficient hydrodynamic models. An important feature of coral reefs is that they act as sheltering barrier for coastlines, by attenuating wave energy. However, due to the complexity of coral structure, there is still a major challenge in predicting the efficiency of coral reef to dissipate wave energy, and how it will evolve with a rising sea level and probable damaged coral systems. This paper demonstrates that, when adjusted, the existing parameterization of bottom friction are able to correctly predict the wave attenuation. Furthermore, the results are in line with those obtained on other reef or rocky sites, which gives confidence to the analysis. Key Points Application of the wave‐current boundary layer theory to in‐situ measurement of frictional wave dissipation over coral reef Non‐linear energy transfers and mean current contribution are considered in the wave energy balance The adjusted parameterization is able to predict the present observations together with other published data on rough seabeds
Journal Article
Dissipative Hyperbolic Geometric Flowon Modified Riemann Extensions
We study the properties of modified Riemann extensions evolving under dissipative hyperbolic geometric flow with examples.
Journal Article
Exploring the collision, acoustic and thermal energy dissipation distribution of discrete mass
This research delves into the transfer and loss of energy in a discrete mass when subjected to forced vibration. Using discrete element method (DEM), we analyzed the dynamic behavior of regular spherical granular assemblies and the energy distribution characteristics under different excitation frequencies and reduced accelerations. Moreover, the energy transfer and dissipation process of granular assemblies under different vibration states are studied using an experimental method. The results show that the granular assemblies will produce collision energy dissipation, thermal energy dissipation, acoustic energy dissipation and other forms of energy dissipation in the forced vibration state and the proportion of different energy dissipation under different excitation is given. The collision and friction of granular assemblies are the key to affecting other forms of energy dissipation. When the excitation increases, the energy dissipation forms are generated inside the granular assemblies, and the proportion of collision energy dissipation of the granular assemblies increases. The acoustic energy above 20 kHz occupies the main part of the acoustic energy dissipation. Thermal energy consumption always exists, which takes a long time to play a role. The granular also have other forms of energy loss, which is hard to be measured, including Rayleigh waves generated by granular collision. In this study, the relationship between the forced vibration state of the granular assemblies and the energy loss distribution is established. Various types of energy transfer and conversion distribution which further enriches the energy dissipation of discrete element calculation of the granular assemblies is discussed and provides a reference for the energy loss analysis of the granular assemblies.
Journal Article
Ultrahigh energy-dissipation elastomers by precisely tailoring the relaxation of confined polymer fluids
Energy-dissipation elastomers relying on their viscoelastic behavior of chain segments in the glass transition region can effectively suppress vibrations and noises in various fields, yet the operating frequency of those elastomers is difficult to control precisely and its range is narrow. Here, we report a synergistic strategy for constructing polymer-fluid-gels that provide controllable ultrahigh energy dissipation over a broad frequency range, which is difficult by traditional means. This is realized by precisely tailoring the relaxation of confined polymer fluids in the elastic networks. The symbiosis of this combination involves: elastic networks forming an elastic matrix that displays reversible deformation and polymer fluids reptating back and forth to dissipate mechanical energy. Using prototypical poly (n-butyl acrylate) elastomers, we demonstrate that the polymer-fluid-gels exhibit a controllable ultrahigh energy-dissipation property (loss factor larger than 0.5) with a broad frequency range (10
−2
~ 10
8
Hz). Energy absorption of the polymer-fluid-gels is over 200 times higher than that of commercial damping materials under the same dynamic stress. Moreover, their modulus is quasi-stable in the operating frequency range.
In most cases the frequency range of a damping material is adapted to a specific application. Huang et al. design a gel filled with a polymeric fluid that bypasses this problem and offers an unusually broad window over which vibrational energy is effectively dissipated.
Journal Article
Topological dissipation in a time-multiplexed photonic resonator network
Topological phases feature robust edge states that are protected against the effects of defects and disorder. These phases have largely been studied in conservatively coupled systems, in which non-trivial topological invariants arise in the energy or frequency bands of a system. Here we show that, in dissipatively coupled systems, non-trivial topological invariants can emerge purely in a system’s dissipation. Using a highly scalable and easily reconfigurable time-multiplexed photonic resonator network, we experimentally demonstrate one- and two-dimensional lattices that host robust topological edge states with isolated dissipation rates, measure a dissipation spectrum that possesses a non-trivial topological invariant, and demonstrate topological protection of the network’s quality factor. The topologically non-trivial dissipation of our system exposes new opportunities to engineer dissipation in both classical and quantum systems. Moreover, our experimental platform’s straightforward scaling to higher dimensions and its ability to implement inhomogeneous, non-reciprocal and long range couplings may enable future work in the study of synthetic dimensions.
Topological phenomena have mostly been studied in conservative systems. Experiments on optical resonator networks now show that topologically non-trivial characteristics can also emerge in dissipation.
Journal Article
Magnetization switching by magnon-mediated spin torque through an antiferromagnetic insulator
Widespread applications of magnetic devices require an efficient means to manipulate the local magnetization. One mechanism is the electrical spin-transfer torque associated with electron-mediated spin currents; however, this suffers from substantial energy dissipation caused by Joule heating. We experimentally demonstrated an alternative approach based on magnon currents and achieved magnon-torque–induced magnetization switching in Bi2Se3/antiferromagnetic insulator NiO/ferromagnet devices at room temperature. The magnon currents carry spin angular momentum efficiently without involving moving electrons through a 25-nanometer-thick NiO layer. The magnon torque is sufficient to control the magnetization, which is comparable with previously observed electrical spin torque ratios. This research, which is relevant to the energy-efficient control of spintronic devices, will invigorate magnon-based memory and logic devices.
Journal Article
Anomalous Dissipation for the Forced 3D Navier–Stokes Equations
In this paper, we consider the forced incompressible Navier–Stokes equations with vanishing viscosity on the three-dimensional torus. We show that there are (classical) solutions for which the dissipation rate of the kinetic energy is bounded away from zero, uniformly in the viscosity parameter, while the body forces are uniformly bounded in some reasonable regularity class.
Journal Article
Electric-field-driven non-volatile multi-state switching of individual skyrmions in a multiferroic heterostructure
Electrical manipulation of skyrmions attracts considerable attention for its rich physics and promising applications. To date, such a manipulation is realized mainly via spin-polarized current based on spin-transfer torque or spin–orbital torque effect. However, this scheme is energy consuming and may produce massive Joule heating. To reduce energy dissipation and risk of heightened temperatures of skyrmion-based devices, an effective solution is to use electric field instead of current as stimulus. Here, we realize an electric-field manipulation of skyrmions in a nanostructured ferromagnetic/ferroelectrical heterostructure at room temperature via an inverse magneto-mechanical effect. Intriguingly, such a manipulation is non-volatile and exhibits a multistate feature. Numerical simulations indicate that the electric-field manipulation of skyrmions originates from strain-mediated modification of effective magnetic anisotropy and Dzyaloshinskii–Moriya interaction. Our results open a direction for constructing low-energy-dissipation, non-volatile, and multistate skyrmion-based spintronic devices.
Spin-polarized current manipulation of magnetic skyrmions is energy consuming. Here, the authors achieve an electric-field manipulation of individual skyrmions in a nanostructured ferromagnetic/ferroelectrical heterostructure at room temperature via an inverse magneto-mechanical effect.
Journal Article