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.

Influence of Interconnection Configuration on Thermal Dissipation of ULSI Interconnect Systems

The effects of adjacent metal layers and space between metal lines on the temperature rise of multilevel ULSI interconnect lines are investigated by modeling a three-layer interconnect. The heat dissipation of various metallization technologies concerning the metal and low-k dielectric employment is simulated in detail. The Joule heat generated in the interconnect is transferred mainly through the metal lines in each metal layer and through the path with the smallest thermal resistance in each Ield layer. The temperature rises of Al metallization are approximately pAl/pCu times higher than those of Cu metallization under the same conditions. In addition, a thermal problem in 0.13μm globe interconnects is studied for the worst case, in which there are no metal lines in the lower interconnect layers. Several types of dummy metal heat sinks are investigated and compared with regard to thermal efficiency,influence on parasitic capacitance,and optimal application by combined thermal and electrical simula- tion.

Noisy-power dissipation and efficiency in NiO/Fe_2O_3 wet grinding by planetary ball mill

The relationship between the efficiency of NiO/Fe2O3 wet grinding and noisy-power dissipation was studied. The optimal grinding parameters were found as: a slurry water content of 64.10%-85.47%, ball number ratio of 360/20, revolution speed of 300.9 r/min, powder-filling ratio of 10.88%, ball-filling ratio of 20.53%-23.88%, and grinding time of approximately 6 h. The discrete element method(DEM) was employed to analyze relationship between the noisy-power dissipation and the grinding efficiency, and equations describing the relationship were derived. The mean particle size of the ground powder decreased with a decrease in the degree of noisy-power dissipation, while the grinding efficiency and the amount of specific impact power used decreased with an increase in the degree of noisy-power dissipation.

Analytical model for power dissipation in cell membranes in suspensions exposed to electric fields

Due to interaction among cells, it is too complex to build an exactanalytical model for the power dissipation within the cell membrane in suspensions exposed toexternal fields. An approximate equivalence method is proposed to resolve this problem. Based on theeffective medium theory, the transmembrane voltage on cells in suspensions was investigated by theequivalence principle. Then the electric field in the cell membrane was determined. Finally,analytical solutions for the power dissipation within the cell membrane in suspensions exposed toexternal fields were derived according to the Joule principle. The equations show that theconductive power dissipation is predominant within the cell membrane in suspensions exposed todirect current or lower frequencies, and dielectric power dissipation prevails at high frequenciesexceeding the relaxation frequency of the exposed membrane.

An approach to estimate tidal dissipation with single-point high-frequency ground wave radar data

Using the single-point ground wave （GW） radar data at Shensi Station and the water level data at three stations （Shengsi, Luchaogang and Daishan）, the authors obtained the flow vectors from the radial velocity of GW radar observation, and calculate four sub-tidal harmonic constants （O1, K1, M2 and S2）. The tidal characteristics derived from the GW radar dataset agreed well with those from the tidal gauge data. The authors also analyzed the tidal energy flux and tidal energy dissipation rate. There was a good relationship between the tidal energy dissipation rate and topography. The study showed a good way to calculate tidal energy dissipation rate using GW radar data.

Dissipation of chlorpyrifos on pakchoi inside and outside greenhouse

The dissipation of chlorpyrifos on pakchoi inside and outside greenhouse was studied. The decline curve of chlorpyrifos on pakchoi could be described as first-order kinetic. The experimental data showed that both the hermetic environment of greenhouse and season affected dissipation rates of chlorpyrifos on pakchoi. Chlorpyrifos declined faster outside greenhouse than inside greenhouse. Chlorpyrifos residues at pre-harvest time were below the maximum residue limits(MRLs) fixed in China, whereas the values inside greenhouse were higher than those outside greenhouse by almost 50%. The recommended pre-harvest time established under conditions of open field might not always fit to greenhouse production.

Dissipation of chlorpyrifos in pakchoi-vegetated soil in a greenhouse

The dissipation of chlorpyrifos in pakchoi-vegetated soil was investigated in the summer and autumn in a greenhouse and field, respectively. The dissipation of chlorpyrifos in pakchoi-grown soil was comparatively described by fitting the residue data to seven models （lst-order, 1.5th-order, 2nd-order, RF lst-order, RF 1.5th-order, RF 2nd-order, and bi-exponential or two-compartment models）. Statistical analysis was performed using the SPSS 11.5 statistical package. The bi-exponential model was selected as the optimal model according to the coefficient of determination r^2. The dissipation half-lives （DT50） of chlorpyrifos in pakchoi-vegetated soil at the recommended dose in the summer and autumn, calculated by the bi-exponential model, were 0.6 and 1.2 d in a greenhouse, 0.4 and 1.0 d in a field, respectively; the corresponding values at double dose were 1.2 and 2.1 d in a greenhouse, 0.5 and 1.3 d in a field, respectively. The kinetic data indicate the dissipation of chlorpyrifos in pakchoi-grown soil in a greenhouse is slower than that in a field, and dissipates slower in the autumn than in the summer.

Determination of Forchlorfenuron Dissipation and Residue in Cucumbers and Red Soil

To assess the risks of forchlorfenuron after application, a residue analysis method for ferchlorfenuron in cucumbers and the red soil of Southern China was established, and the dissipation behavior and residue characteristics of forchlorfenuron were studied under field conditions. The field trials, including dissipation and residue experiments, were conducted in Hunan, Yunnan and Hainan Provinces. Forchlorfenuron was applied at 32 a.i.g ha^-1 rate for the dissipation study and both 21 and 32 a.i.g ha^-1 for the residue study. Representative cucumbers and soil samples were collected at predetermined intervals for HPLC for UV- detector analysis. The average recoveries of the method were 80.8%-92.0% with coefficients variation （CV） between 0.4% and 11.8%. The detection limit of forchlorfenuron in cucumbers and soil samples was 0.003 mg·kg^-1 and the minimum detectable amount was 3.0× 10^-10 g. The half life of forchlorfenuron in cucumbers in the three provinces changed as： Yunnan （5.50 days）, Hunan （5.88 days）, and Hainan （6.53 days） and in the soil was observed： Hainan （6.54 days）, Hunan （7.64 days）, and Yunnan （8.39 days）. The maximum terminal residue in cucumbers at 32 a.i.g ha^-1 rate after 5 days was 0.009 mg·kg^-1 （Yunnan） followed by 0.0085 mg·kg^-1 （Hainan） and 0.0082 mg·kg^-1（Hunan） which was below MRL value of 0.01 mg·kg^-1 established by the USA, EPA. So a waiting period of 5 days should be established after spaying on cucumbers to avoid hazard to human beings.

ZERO DISSIPATION LIMIT OF THE COMPRESSIBLE HEAT-CONDUCTING NAVIER-STOKES EQUATIONS IN THE PRESENCE OF THE SHOCK

The zero dissipation limit of the compressible heat-conducting Navier–Stokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient κ and the viscosity coefficient ε satisfy κ = O（ε）, κ/ε≥ c 〉 0, as ε→ 0 （see （1.3））, if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier–Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3].

Study on Wave Dissipation of the Structure Combined by Baffle and Submerged Breakwater

This paper proposes a structure combined by baffle and submerged breakwater （abbreviated to SCBSB in the following texts）. Such a combined structure is conducive to the water exchange in the harbor, and has strong capability on wave dissipation. Our paper focuses on the discussion of two typical structures, i.e., the submerged baffle and rectangular breakwater combined with the upper baffle respectively, which are named as SCBSB 1 and SCBSB2 for short. The eigenfunction method corrected by experimental results is used to investigate the wave dissipation characteristics. It shows that the calculated results agree well with the experimental data and the minimum value of the wave transmission coefficient can be obtained when the distance between the front and rear structures is from 1/4 to 1/2 of the incident wave length.