Limiting Absorption Principle for the Dissipative Helmholtz Equation

Adapting Mourre's commutator method to the dissipative setting, we prove a limiting absorption principle for a class of abstract dissipative operators. A consequence is the uniform resolvent estimate for the high-frequency Helmholtz equation when trapped classical trajectories meet the region where the absorption coefficient is non-zero. We also give the resolvent estimate in Besov spaces.     

Reducing Occupational Noise Propagated from Centrifugal Fan through Dissipative Silencers: A Field Study

Acoustic performance of dissipative silencer was evaluated to determine the effectiveness of perforated duct porosity and absorbent material density in reducing occupational noise exposure propagated from centrifugal fan. Design charts were applied to predict noise reduction and length of a dissipative silencer. Dissipative silencers with various punched duct porosity (14%, 30% and 40%) and sound absorbent density (80 Kg/m³, 120 Kg/m³, and 140 Kg/m³) were designed and fabricated. According to ISO9612 and ISO11820, noise level was measured before and after installing all nine test silencers at fixed workstations around the discharge side of a centrifugal fan in a manufacturing plant. On average, the noise level at the discharge side of a fan without silencer was measured to be 93.6 dBA, whereas it was significantly mitigated by 67.4 dBA to 70.1 dBA after installing all silencers. Dynamic insertion loss for a dissipative silencer with 100 cm length was predicted to be 27.9 dB, which was in agreement with experimental ones. Although, there was no significant differences between insertion loss of silencers, the one with 30% porosity and 120 Kg/m³ rock wool density had the highest insertion loss of 26.2 dBA. Dissipative silencers noticeably reduced centrifugal fan noise exposures. Increasing sound absorbent density and duct porosity up to a certain limit could probably be effective in noise reduction of dissipative silencers.     

Impact of higher-order effects on dissipative soliton in metamaterials

We study the influence of higher-order effects such as third order dispersion (TOD), fourth order dispersion (FOD), quintic nonlinearity (QN), self steepening (SS) and second order nonlinear dispersion (SOND) on the dynamics of dissipative soliton (DS) in metamaterials. Considering each higher-order effect as a perturbation to the system and following Lagrangian variational method, we demonstrate stable dynamics of DS as a result of the interplay between different higher-order effects. We also perform numerical analysis to confirm the analytical results.     

A Dissipative Reaction Network Drives Transient Solid–Liquid and Liquid–Liquid Phase Cycling of Nanoparticles

Transient states maintained by energy dissipation are an essential feature of dynamic systems where structures and functions are regulated by fluxes of energy and matter through chemical reaction networks. Perfected in biology, chemically fueled dissipative networks incorporating nanoscale components allow the unique properties of nanomaterials to be bestowed with spatiotemporal adaptability and chemical responsiveness. We report the transient dispersion of gold nanoparticles in water, powered by dissipation of a chemical fuel. A dispersed state that is generated under non-equilibrium conditions permits fully reversible solid–liquid or liquid–liquid phase transfer. The molecular basis of the out-of-equilibrium process is reversible covalent modification of nanoparticle-bound ligands by a simple inorganic activator. Activator consumption by a coupled dissipative reaction network leads to autonomous cycling between phases. The out-of-equilibrium lifetime is tunable by adjusting the pH value, and reversible phase cycling is reproducible over several cycles.     

Convectional,sedimentation, and drying dissipative patterns of colloidal crystals of poly (methyl methacrylate) spheres on a cover glass

Direct observation of the convectional dissipative patterns was successful during the course of dryness of colloidal crystals of poly (methyl methacrylate) spheres on a cover glass. Formation processes of the convectional patterns of spoke-like lines were observed as a function of sphere size and also sphere concentration. During dryness of the suspensions, the brilliant iridescent colors changed beautifully. Macro- and microscopic drying patterns and thickness profiles of the dried film were observed. Sharp broad rings were observed especially at low sphere concentrations. The water evaporation accompanied with the convectional flow of water and the colloidal spheres played an important role for these dissipative structure formation.     

耗散粒子动力学和纳维边界条件在微米纳米流体力学模拟中的应用

耗散粒子动力学是一种粗粒化的计算模拟方法,在微米和纳米流体力学中有着广泛的应用.由于界面在微小体积流体中的重要性,边界条件的选取在微米和纳米流体的研究中起到了关键性的作用.我们简单地介绍了耗散粒子动力学的模拟方法,并以此为基础,介绍了能够实现纳维边界条件的可调滑移长度的边界条件模拟方法.通过条纹状图案修饰的超疏水表面的流体力学行为研究,和高分子链在微米纳米流体器件中的运动研究2个例子,耗散粒子动力学结合纳维边界条件的模拟方法的实用性和可靠性得到了证实.     

On the critical nonlinear damped wave equation with large initial data

We study the nonlinear damped wave equation

(0.1)     

Perspectives on spin hydrodynamics in ferromagnetic materials

The field of spin hydrodynamics aims to describe magnetization dynamics from a fluid perspective. For ferromagnetic materials, there is an exact mapping between the Landau-Lifshitz equation and a set of dispersive hydrodynamic equations. This analogy provides ample opportunities to explore novel magnetization dynamics and magnetization states that can lead to potential applications that rely entirely on magnetic materials, for example, long-distance transport of information. This article provides an overview of the theoretical foundations of spin hydrodynamics and their physical interpretation in the context of spin transport. We discuss other proposed applications for spin hydrodynamics as well as our view on challenges and future research directions.     

A hydrodynamic approach to multidimensional dissipation-based Schrödinger models from quantum Fokker-Planck dynamics

In this paper we are concerned with the modeling of quantum dissipation and diffusion effects at the level of the multidimensional Schrödinger equation. Our starting point is the quantum Fokker-Planck master equation describing dissipative interactions (of mass and energy) of the particle ensemble with a thermal bath in thermodynamic equilibrium. When considering its associated hydrodynamic system, which rules the temporal evolution of the local density and the mean fluid-flow velocity, and imposing physically admissible closure relations, these equations can be seen as describing the fluid-mechanical evolution of the macroscopic amplitude and phase of an envelope wavefunction, thus giving rise to a family of dissipative Schrödinger equations of logarithmic type whose steady state and radial dynamics are analyzed. Also, numerical comparison with the exactly solvable models for the free particle and the damped harmonic oscillator is performed.