THE STABILITY OF BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION AROUND THE HYDROSTATIC BALANCE

This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena.The Boussinesq system focused on here is anisotropic,and involves only horizontal dissipation and thermal damping.In the 2D case R^(2),due to the lack of vertical dissipation,the stability and large-time behavior problems have remained open in a Sobolev setting.For the spatial domain T×R,this paper solves the stability problem and gives the precise large-time behavior of the perturbation.By decomposing the velocity u and temperatureθinto the horizontal average(ū,θ)and the corresponding oscillation(ū,θ),we can derive the global stability in H~2 and the exponential decay of(ū,θ)to zero in H^(1).Moreover,we also obtain that(ū_(2),θ)decays exponentially to zero in H^(1),and thatū_(1)decays exponentially toū_(1)(∞)in H^(1)as well;this reflects a strongly stratified phenomenon of buoyancy-driven fluids.In addition,we establish the global stability in H^(3)for the 3D case R^(3).

Mechanical response and dilatancy characteristics of deep marble under different stress paths:A sight from energy dissipation

Dilatancy is a fundamental volumetric growth behavior observed during loading and serves as a key index to comprehending the intricate nonlinear behavior and constitutive equation structure of rock.This study focuses on Jinping marble obtained from the Jinping Underground Laboratory in China at a depth of 2400 m.Various uniaxial and triaxial tests at different strain rates,along with constant confining pressure tests and reduced confining pressure tests under different confining pressures were conducted to analyze the mechanical response and dilatancy characteristics of the marble under four stress paths.Subsequently,a new empirical dilatancy coefficient is proposed based on the energy dissipation method.The results show that brittle failure characteristics of marble under uniaxial compression are more obvious with the strain rate increasing,and plastic failure characteristics of marble under triaxial compression are gradually strengthened.Furthermore,compared to the constant confining pressure,the volume expansion is relatively lower under unloading condition.The energy dissipation is closely linked to the process of dilatancy,with a rapid increase of dissipated energy coinciding with the beginning of dilatancy.A new empirical dilatancy coefficient is defined according to the change trend of energy dissipation rate curve,of which change trend is consistent with the actual dilatancy response in marble under different stress paths.The existing empirical and theoretical dilatancy models are analyzed,which shows that the empirical dilatancy coefficient based on the energy background is more universal.

Paving continuous heat dissipation pathways for quantum dots in polymer with orangeinspired radially aligned UHMWPE fibers

Thermal management of nanoscale quantum dots(QDs)in light-emitting devices is a long-lasting challenge.The existing heat transfer reinforcement solutions for QDs-polymer composite mainly rely on thermal-conductive fillers.However,this strategy failed to deliver the QDs’heat generation across a long distance,and the accumulated heat still causes considerable temperature rise of QDs-polymer composite,which eventually menaces the performance and reliability of lightemitting devices.Inspired by the radially aligned fruit fibers in oranges,we proposed to eliminate this heat dissipation challenge by establishing long-range ordered heat transfer pathways within the QDs-polymer composite.Ultrahigh molecular weight polyethylene fibers(UPEF)were radially aligned throughout the polymer matrix,thus facilitating massive efficient heat dissipation of the QDs.Under a UPEF filling fraction of 24.46 vol%,the in-plane thermal conductivity of QDs-radially aligned UPEF composite(QDs-RAPE)could reach 10.45 W m^(−1) K^(−1),which is the highest value of QDs-polymer composite reported so far.As a proof of concept,the QDs’working temperature can be reduced by 342.5℃ when illuminated by a highly concentrated laser diode(LD)under driving current of 1000 mA,thus improving their optical performance.This work may pave a new way for next generation high-power QDs lighting applications.

Mechanical behavior of rock under uniaxial tension:Insights from energy storage and dissipation

Many rock engineering projects show that the growth of tensile cracks is often an important cause of engineering disasters,and the mechanical behavior of rocks is essentially the transmission,storage,dissipation and release of energy.To investigate the tensile behavior of rock from the perspective of energy,uniaxial tension tests(UTTs)and uniaxial compression tests(UCTs)were carried out on three typical rocks(granite,sandstone and marble).Different unloading points were set before the peak stress to separate elastic energy and dissipated energy.The input energy density ut,elastic energy density ue,and dissipated energy density ud at each unloading point were calculated by integrating stress-strain curves.The results show that there is a strong linear relationship between the three energy parameters and the square of the unloading stress in UCT,but this linear relationship is weaker in UTT.The ue and ud increase linearly with the increase in ut in UCT and UTT.Based on the phenomenon that ue and ud increase linearly with ut,the applicability of W_(et)^(p) index in UTT was proved and the relative energy storage capacity and absolute energy distribution characteristics of three rocks in UCT and UTT were evaluated.The tensile behavior of marble and sandstone in UTT can be divided into two stages vaguely according to the energy distribution,but granite is not the case.In addition,based on dissipated energy,the damage evolution of three types of rocks in UCT and UTT was discussed.This study provides some new insights for understanding the tensile behavior of rock.

Interrelationships between Length of the Day, Moon Distance, Phanerozoic Geodynamic Cycles, Tidal Dissipation and Earth’s Core: Review and Analysis

The rotation of the Earth and the related length of the day (LOD) are predominantly affected by tidal dissipation through the Moon and the growth of the Earth’s core. Due to the increased concentration of mass around the rotation axis of the spinning Earth during the growth of the core the rotation should have been accelerated. Controversially the tidal dissipation by the Moon, which is mainly dependent on the availability of open shallow seas and the kind of Moon escape from a nearby position, acts towards a deceleration of the rotating Earth. Measurements of LOD for Phanerozoic and Precambrian times open ways to solve questions concerning the geodynamical history of the Earth. These measurements encompass investigations of growth patterns in fossils and depositional patterns in sediments (Cyclostratigraphy, Tidalites, Stromatolites, Rhythmites). These patterns contain information on the LOD and on the changing distance between Earth and Moon and can be used as well for a discussion about the growth of the Earth’s core. By updating an older paper with its simple approach as well as incorporating newly published results provided by the geoscientific community, a moderate to fast growth of the core in a hot early Earth will be favored controversially to the assumption of a delayed development of the core in an originally cold Earth. Core development with acceleration of Earth’s rotation and the contemporaneous slowing down due to tidal dissipation during the filling of the ocean may significantly interrelate.

Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation

To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.

Mechanism of Thermally Radiative Prandtl Nanofluids and Double-Diffusive Convection in Tapered Channel on Peristaltic Flow with Viscous Dissipation and Induced Magnetic Field

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.

Research on heat dissipation characteristics of magnetic fluid bearings under multiple field coupling effects

This paper analyzes the sources of heat losses in magnetic fluid bearings,proposes various cou-pling relationships of physical fields,divides the coupled heat transfer surfaces while ensuring the continuity of heat flux density,and analyzes the overall heat dissipation pathways of the bearings.By changing parameters such as input current,rotor speed,and inlet oil flow rate,the study applies a multi-physics field coupling method to investigate the influence of different parameters on the temper-ature field and heat dissipation patterns of the bearings,which is then validated through experi-ments.This research provides a theoretical basis for the optimal design of magnetic fluid bearing sys-tems.

Effects of Viscous Dissipation and Periodic Heat Flux on MHD Free Convection Channel FlowwithHeat Generation

This study investigates the influence of periodic heat flux and viscous dissipation on magnetohydrodynamic(MHD)flow through a vertical channel with heat generation.A theoretical approach is employed.The channel is exposed to a perpendicular magnetic field,while one side experiences a periodic heat flow,and the other side undergoes a periodic temperature variation.Numerical solutions for the governing partial differential equations are obtained using a finite difference approach,complemented by an eigenfunction expansion method for analytical solutions.Visualizations and discussions illustrate how different variables affect the flow velocity and temperature fields.This offers comprehensive insights into MHD flow behavior and its interactions with the magnetic field,heat flux,viscous dissipation,and heat generation.The findings hold significance for engineering applications concerning fluid dynamics and heat transfer,offering valuable knowledge in this field.The study concludes that the transient velocity and temperature profiles exhibit periodic patterns under periodic heat flow conditions.A temperature reduction is observed with an increase in the wall temperature phase angle.In contrast,an increase in the heat flux phase angle values raises the temperature values.

Impact of Viscous Dissipation and Ohmic Heating on Natural Convection Heat Transfer in Thermo-Magneto Generated Plume

The present investigation centers on the impact of viscous dissipation and ohmic heating on the plume generated by a line heat source under the impact of an aligned magnetic field.In this study,the flow model is adapted to incorporate ohmic heating and viscous dissipation by including the respective terms in the energy equation.A mathematical model is formulated as a system of coupled partial differential equations to analyze the flow problem.Subsequently,a numerical solution is derived with stream function formulation for the system of coupled partial differential equations,which transmutes it into ordinary differential equations.To achieve this,the numerical properties of the problem are established through the utilization of the Shooting method in tandem with the MATLAB tool bvp4c.The graphical representations of both missing and specified boundary conditions depict the effects of the magnetic parameter,viscous dissipation variable,magnetic force parameter,Prandtl number,and magnetic Prandtl number.These are accompanied by a discussion of their respective physical implications.The observed results claimed that the velocity,current density,and temperature distribution decrease for enhancing magnetic parameters.Meanwhile,the skin friction and magnetic flux drop while the heat transfer rate increases with an increment in magnetic parameters.These fluid flow and heat transfer characteristics were observed to decrease for increasing viscous dissipation.The current work is novel in incorporating ohmic heating viscous dissipation in energy equations coupled with Max-well and magnetic induction equations.

Heat dissipation enhancement method for finned heat sink for AGV motor driver's IGBT module

With the widespread use of high-power and highly integrated insulated gate bipolar transistor(IGBT),their cooling methods have become challenging.This paper proposes a liquid cooling scheme for heavy-duty automated guided vehicle(AGV)motor driver in port environment,and improves heat dissipation by analyzing and optimizing the core component of finned heat sink.Firstly,the temperature distribution of the initial scheme is studied by using Fluent software,and the heat transfer characteristics of the finned heat sink are obtained through numerical analysis.Secondly,an orthogonal test is designed and combined with the response surface methodology to optimize the structural parameters of the finned heat sink,resulting in a 14.57%increase in the heat dissipation effect.Finally,the effectiveness of heat dissipation enhancement is verified.This work provides valuable insights into improving the heat dissipation of IGBT modules and heat sinks,and provides guidance for their future applications.

The Effects of Thermal Radiation and Viscous Dissipation on the Stagnation Point Flow of a Micropolar Fluid over a Permeable Stretching Sheet in the Presence of Porous Dissipation

In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.

ZERO DISSIPATION LIMIT TO A RAREFACTION WAVE WITH A VACUUM FOR A COMPRESSIBLE,HEAT CONDUCTING REACTING MIXTURE

In this paper,we study the zero dissipation limit with a vacuum for the reacting mixture Navier-Stokes equations.For proper smooth initial data that the initial density tends to zero as the relevant physical coefficients tend to zero,we demonstrate that the solution tends to a rarefaction wave connected to a vacuum on the left side coupled with a zero mass fraction of reactant.What is more,the uniform convergence rate is obtained.

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

The control of dissipation and amplification of solitary waves in an electrical model of a microtubule is demonstrated.This model consists of a shunt nonlinear resistance–capacitance(J(V)–C(V)) circuit and a series resistance–inductance(R–L) circuit. Through linear dispersion analysis, two features of the network are found, that is, low bandpass and bandpass filter characteristics. The effects of the conductance’s parameter λ on the linear dispersion curve are also analyzed. It appears that an increase of λ induces a decrease(an increase) of the width of the bandpass filter for positive(negative) values of λ. By applying the reductive perturbation method, we derive the equation governing the dynamics of the modulated waves in the system. This equation is the well-known nonlinear Schr?dinger equation extended by a linear term proportional to a hybrid parameter σ, i.e., a dissipation or amplification coefficient. Based on this parameter, we successfully demonstrate the hybrid behavior(dissipation and amplification) of the system. The exact and approximate solitary wave solutions of the obtained equation are derived, and the effects of the coefficient σ on the characteristic parameters of these waves are investigated. Using the analytical solutions found, we show numerically that the waves that are propagated throughout the system can be dissipated, amplified, or remain stable depending on the network parameters. These results are not only in agreement with the analytical predictions, but also with the existing experimental results in the literature.

Effects of Ulva prolifera dissipation on the offshore environment based on remote sensing images and field monitoring data

Outbreaks of Ulva prolifera have continued in the South Yellow Sea of China(SYS)since 2007,becoming a serious marine ecological disaster.Large amounts of U.prolifera drift to the coast of the Shandong Peninsula to dissipate under the action of southeast monsoons and ocean surface currents.This causes serious harm to the ecological environment and economic activities of coastal cities.To investigate the impact of U.prolifera dissipation,this study extracted the spatiotemporal distribution of U.prolifera in the SYS from 2012 to 2020 based on the Google Earth Engine.The outbreak cycle of U.prolifera was determined by fitting analysis of outbreak time and coverage area through MATLAB.This study also looked at the effect of U.prolifera dissipation on water quality through field monitoring data.The results showed that the growth curve of the U.prolifera has a significant Gaussian distribution.The U.prolifera dissipates in Haiyang,China,in July and August every year and affects the offshore environment.Water quality parameters of seawater at different depths had significant differences after the U.prolifera dissipation.Changes in pH,chemical oxygen demand,nitrite nitrogen,nitrate nitrogen,ammonia nitrogen,chlorophyll a,total phosphorus,and suspended solids were more significant in surface seawater than in deeper water.Changes in the concentrations of dissolved oxygen and total nitrogen were more significant in the deep seawater(1.63 and 1.1 times higher than those in the surface seawater,respectively).The dissipation of U.prolifera releases a large amount of carbon and nitrogen into the seawater,which provides rich nutrients for phytoplankton and may cause secondary disasters such as red tide.These findings are useful for further understanding the rules of U.prolifera dissipation,as well as preventing and controlling green tide disasters.

Response Spectrum Analysis of 7-story Assembled Frame Structure with Energy Dissipation System

Viscoelastic damper is an effective passive damping device,which can reduce the seismic response of the structure by increasing the damping and dissipating the vibration energy of structures.It has a wide application prospect in actual structural vibration control because of simple device and economical material.In view of the poor seismic behaviors of assembled frame structure connections,various energy dissipation devices are proposed to improve the seismic performance.The finite element numerical analysis method is adopted to analyze relevant energy dissipation structural parameters.The response spectrum of a 7-story assembled frame structure combined the ordinary steel support,ordinary viscoelastic damper,and viscoelastic damper with displacement amplification device is analyzed.The analysis results show that the mechanical behavior of assembled frame structure with ordinary steel supports are not significantly different from those without energy dissipation devices.The assembled frame structure with viscoelastic damper has better seismic performance and energy dissipation,especially for the viscoelastic damper with displacement amplification devices.The maximum value of inter-story displacement angle decreases by 32.24%;the maximum floor displacement decreases by 31.91%,and the base shear decreases by 13.62%compared with the assembled frame structures without energy dissipation devices.The results show that the seismic fortification ability of the structure is significantly improved,and the overall structure is more uniformly stressed.The damping structure with viscoelastic damper mainly reduces the dynamic response of the structure by increasing the damping coefficient,rather than by changing the natural vibration period of the structure.This paper provides an effective theoretical basis and reference for improving the energy dissipation system and the seismic performance of assembled frame structures.

Influence of dissipation on solitary wave solution to generalized Boussinesq equation

This paper uses the theory of planar dynamic systems and the knowledge of reaction-diffusion equations,and then studies the bounded traveling wave solution of the generalized Boussinesq equation affected by dissipation and the influence of dissipation on solitary waves.The dynamic system corresponding to the traveling wave solution of the equation is qualitatively analyzed in detail.The influence of the dissipation coefficient on the solution behavior of the bounded traveling wave is studied,and the critical values that can describe the magnitude of the dissipation effect are,respectively,found for the two cases of b_3<0 and b_3>0 in the equation.The results show that,when the dissipation effect is significant(i.e.,r is greater than the critical value in a certain situation),the traveling wave solution to the generalized Boussinesq equation appears as a kink-shaped solitary wave solution;when the dissipation effect is small(i.e.,r is smaller than the critical value in a certain situation),the traveling wave solution to the equation appears as the oscillation attenuation solution.By using the hypothesis undetermined method,all possible solitary wave solutions to the equation when there is no dissipation effect(i.e.,r=0)and the partial kink-shaped solitary wave solution when the dissipation effect is significant are obtained;in particular,when the dissipation effect is small,an approximate solution of the oscillation attenuation solution can be achieved.This paper is further based on the idea of the homogenization principles.By establishing an integral equation reflecting the relationship between the approximate solution of the oscillation attenuation solution and the exact solution obtained in the paper,and by investigating the asymptotic behavior of the solution at infinity,the error estimate between the approximate solution of the oscillation attenuation solution and the exact solution is obtained,which is an infinitesimal amount that decays exponentially.The influence of the dissipation coefficient on the amplitude,frequency,period,and energy of the bounded traveling wave solution of the equation is also discussed.

Anisotropic characteristics of layered backfill:Mechanical properties and energy dissipation

Layered backfill is commonly used in mining operations,and its mechanical behavior is strongly influenced by delamination parameters.In this study,13 specimens with different numbers of delamination and delamination angle were prepared to investigate the anisotropic mechanical behavior,energy dissipation characteristics and crack development of backfill.P-wave velocity,uniaxial compression,scanning electron microscope(SEM),and acoustic emission(AE)experiments were conducted.The results indicate that:(1)The P-wave velocity has linear and elliptical relationships with the number of delamination surface and delamination angle,respectively;the strength,delamination parameters and P-wave velocity show a high degree of coincidence in terms of their function relationship,which can realize the rapid prediction of strength.(2)The microstructure of the delaminated surface is looser than that of the matrix,leading to a decrease in strength and an increase at the pore-fissure compaction stage.The number and angle of delamination increase linearly with the anisotropy coefficient.(3)The energy evolution in angle-cut backfill can be divided into four stages,with a decrease in the proportion of elastic energy at the initiation stress and peak stress with increasing number of delamination planes and delamination angle.(4)Crack development increases with the number of delamination surface and delamination angle,resulting in a decrease in energy dissipation coefficient and peak AE energy.These findings provide valuable insights for the design of filling materials and processes in mining operations.

Nonlinearly induced entanglement in dissipatively coupled optomechanical system

Nonlinearly induced steady-state photon–phonon entanglement of a dissipative coupled system is studied in the bistable regime. Quantum dynamical characteristics are analysed by solving the mean-field and fluctuation equations of the system. It is shown that dissipative coupling can induce bistable behaviour for the effective dissipation of the system.Under suitable parameters, one of the steady states significantly reduces the dissipative effect of the system. Consequently,a larger steady-state entanglement can be achieved compared to linear dynamics. Furthermore, the experimental feasibility of the parameters is analysed. Our results provide a new perspective for the implementation of steady-state optomechanical entanglement.

Simulation of nanofluid natural convection based on single-particle hydrodynamics in energy-conserving dissipative particle dynamics(eDPD)

In the present study,the nanofliud natural convection is investigated by the energy-conserving dissipative particle dynamics(eDPD)method,where the nanoparticles are considered at the single-particle level.The thermal expansion coefficientβand the viscosityμof the simulated system containing nanoparticles are calculated and found to be in close alignment with the previous simulation results.The single-particle hydrodynamics in e DPD enables simulations of nanofluid natural convection with higher Rayleigh numbers and greater nanoparticle volume fractions.Additionally,this approach is utilized to simulate the nanoparticle distribution during the enhanced heat transfer process in the nanofluid natural convection.The localized aggregation of nanoparticles enhances the heat transfer performance of the nanofluid under specific Rayleigh numbers and nanoparticles volume fractions.