INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM

In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.

Influences of Co-Flow and Counter-Flow Modes of Reactant Flow Arrangement on a PEMFC at Start-Up

To investigate the influences of co-flowand counter-flowmodes of reactant flowarrangement on a proton exchange membrane fuel cell(PEMFC)during start-up,unsteady physical and mathematical models fully coupling the flow,heat,and electrochemical reactions in a PEMFC are established.The continuity equation and momentum equation are solved by handling pressure-velocity coupling using the SIMPLE algorithm.The electrochemical reaction rates in the catalyst layers(CLs)of the cathode and anode are calculated using the Butler-Volmer equation.The multiphase mixture model describes the multiphase transport process of gas mixtures and liquid water in the fuel cell.After validation,the influences of co-flow and counter-flow modes on the PEMFC performance are investigated,including the evolution of the current density,flow field,temperature field,and reactant concentration field during start-up,as well as the steady distribution of the current density,reactant concentration,andmembrane water content when the start-up stabilizes.Co-flow and counter-flow modes influence the current density distribution and temperature distribution.On the one hand,the co-flow mode accelerates the start-up process of the PEMFC and leads to a more evenly distributed current density than the counter-flow mode.On the other hand,the temperature difference between the inlet and outlet sections of the cell is up to 10.1℃ under the co-flow mode,much larger than the 5.0℃ observed in the counter-flow mode.Accordingly,the counter-flowmode results in a more evenly distributed temperature and a lower maximum temperature than the co-flow case.Therefore,in the flow field design of a PEMFC,the reactant flow arrangements can be considered to weigh between better heat management and higher current density distribution of the cell.

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

Effects of counter-current driven by electron cyclotron waves on neoclassical tearing mode suppression

Through theoretical analysis,we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode(NTM).The equation is used with this model to obtain the modified Rutherford equation with co-current and counter-current contributions.Consistent with the reported experimental results,numerical simulations have shown that the localized counter external current can only partially suppress NTM when it is far from the resonant magnetic surface.Under some circumstances,the Ohkawa mechanism dominated current drive(OKCD)by electron cyclotron waves can concurrently create both co-current and counter-current.In this instance,the minimal electron cyclotron wave power that suppresses a particular NTM was calculated by the Rutherford equation.The result is marginally less than when taking co-current alone into consideration.As a result,to suppress NTM using OKCD,one only needs to align the co-current with a greater OKCD peak well with the resonant magnetic surface.The effect of its lower counter-current does not need to be considered because the location of the counter-current deviates greatly from the resonant magnetic surface.

KINETIC MODELING OF ESTERIFICATION OF EPOXY RESIN IN THE PRESENCE OF TRIPHENYLPHOSPHINE FOR PRODUCING VINYL ESTER RESIN: MECHANISTIC RATE EQUATION

Due to its mechanical properties and ease of use, vinyl ester resin is enjoying increasing consideration. This resin normally is produced by reaction between epoxy resin and unsaturated carboxylic acid. In the present study, bis-phenol A based epoxy resin and methacrylic acid was used to produce vinyl ester resin. The reaction was conducted under both stoichiometric and non-stoichiometric conditions in the presence of triphenylphosphine as catalyst. The stoichiometric and non-stoichiometric experiments were conducted at 95, 100, 105 and 110℃ and at 90 and 95℃, respectively. The first order rate equation and mechanism based rate equation were examined. Parameters are evaluated by least square method. A comparison of mechanism based rate equation and experimental data show an excellent agreement. Finally, Arrhenius equation and activation energy were presented.

Estimating Crash Rate of Freeway Segments Using Simultaneous Equation Model

This study develops crash rate prediction models based on the premise that crash frequencies observed from adjacent paired non-weaving and weaving freeway segments are spatially correlated and therefore requires a simultaneous equation modeling approach. Simultaneous equation models for paired freeway non-weaving segments and weaving segments along with combined three freeway segments upstream and downstream were developed to investigate the relationship of crash rate with freeway characteristics. The endogenous variables have significant coefficients which indicate that unobserved variables exist on these contiguous segments, resulting in different crash rates. AADT is a variable that can show the interaction between the traffic and crashes on these contiguous segments. The results corroborate such an interaction. By comparing the simultaneous equation model and the multiple linear regression model, it is shown that more model parameters in the simultaneous models are significant than those from linear regression model. This demonstrates the existence of the correlation between the interchange and between-interchange segments. It is crucial that some variables like segment length can be identified significant in the simultaneous model, which provides a way to quantify the safety impact of freeway development.

Feasibility and Diagnostic Accuracy for Assessment of Coronary Artery Stenosis of Prospectively Electrocardiogram-gated High-pitch Spiral Acquisition Mode Dual-source CT Coronary Angiography in Patients with Relatively Higher Heart Rates: in Comparison wit

Objective To prospectively investigate the diagnostic accuracy for coronary artery stenosis of prospectively electrocardiogram-triggered spiral acquisition mode (high pitch mode) dual-source computed tomography coronary angiography (CTCA) in patients with relatively higher heart rates (HR) compared with catheter coronary angiography (CCA). Methods Forty-seven consecutive patients with relatively higher HR (>65 and <100 bpm) (20 male, 27 female; age 55±10 years) who both underwent dual-source CTCA and CCA were prospectively included in this study. All patients were performed CTCA using high pitch mode setting at 20%-30% of the R-R interval for the image acquisition. All coronary segments were evaluated by two blinded and independent observers with regard to image quality on a three-point scale (1: excellent to 3: non-diagnostic) and for the presence of significant coronary stenoses (defined as diameter narrowing exceeding 50%). Considered CCA as the standard of reference, the sensitivity, specificity, positive predictive value and negative predictive value were calculated. Radiation dose values were calculated using the dose-length product. Results Image quality was rated as being score 1 in 92.4% of segments, score 2 in 6.1% of segmentsand score 3 in 1.5% of segments. The average image quality score per segment was 1.064±0.306. The HR variability of patients with image score 1, 2 and 3 were 2.29±1.06 bpm, 5.17±1.37 bpm, 8.88±1.53 bpm, respectively. The average HR variability of patients with different image scores were significantly different (F=170.402, P=0.001). The sensitivity, specificity, positive and negative predictive values were 92.6%, 97.0%, 87.6%, 98.3%, respectively, per segment and 90.0%, 95.2%, 85.3%, 96.9%, respectively, per vessel and 100%, 63.6%, 90.0%, 100%, respectively, per patient. The effective radiation dose was on average 0.86±0.16 mSv. Conclusion In patients with HR more than 65 bpm and below 100 bpm without cardiac arrhythmia, the prospectively electrocardiogram-gated high-pitch spiral acquisition mode with image acquired timing set at 20%-30% of the R-R interval provides a high diagnostic accuracy for the assessment of coronary stenoses combined with a 1.5% of non-diagnostic coronary segments and a radiation dose below 1 mSv.

EQUATIONS OF MOTION AND BOUNDARY CONDITIONS OF INCREMENTAL RATE TYPE FOR POLAR CONTINUA

The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang.

CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL FORCES

For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article [15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H^3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H^3 and bounded in L6/5.

How Users Perceive Infrastructure Development Affects Their Transport Mode Choice

Transport infrastructure development and perception vary across and within countries, influencing mode choice among road users. This study explores how road users perceive the development of infrastructure modes, service attributes, embedded safety levels, and commuting modes. Additionally, the research examines whether participants’ environmental backgrounds impact their mode choice patterns. The study gathered responses from 1169 participants residing in two regions of Amman, Jordan, each with distinct infrastructure development and population densities. Participants completed a standardized questionnaire, and several statistical techniques were employed for analysis. The findings revealed that facilities’ infrastructure attributes, development, and safety were assessed using three indices. Both participant groups perceived these indices differently on average. Residents of low population density areas with relatively developed infrastructure showed more consistent assessments, irrespective of their most frequently used mode of transportation, tending towards lower scores. Interestingly, subjective ratings of infrastructure development were higher (4.96) than attribute-based ratings (4.32). Despite their generally low-quality perception, public transportation services received the highest appraisal (4.9). Conversely, pedestrian infrastructure complementing public transport received the lowest assessment (4.57), only slightly higher than street environments (4.59). The study found weak associations between subjective service characteristics ratings. Traveler and trip characteristics influenced mode choice and trips more than infrastructure perception. In conclusion, the study suggests that policies should be developed to encourage green transportation, ensure social equality and safety. In addition, the study contributes to understanding perceptions about transport infrastructure, modes of transportation, and the factors that influence sustainable and equitable transportation systems.

Pricing Stochastic Barrier Options under Hull-White Interest Rate Model

A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.

Growth rate of peeling mode in the near separatrix region of diverted tokamak plasma

An analytical expression of the peeling mode in the near separatrix region of diverted tokamak plasma is derived. It is shown that in diverted plasmas both with single and double X points, though the perturbed potential energy of the unstable peeling mode tends to be large, its growth rate becomes very small due to the even larger kinetic energy. Compared to some recent studies that give qualitatively correct results about this growth rate, our result is directly related with the diverted equilibrium quantities suitable for application to realistic experiments.

A Numerical Simulation of Air Flow in the Human Respiratory System Based on Lung Model

The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.

Analysis Expression of Rate Equation for Vertical Cavity Lasers

An analysis solution of rate equation is derived for vertical cavity surface-emitting lasers. Based on the enhanced spontaneous emission caused by VCSELs and influence of nonradiative recombination, the relation between output properties and structural parameters of multi-quantum wells (MQWs) is obtained. It was found that the characteristic curve of a“thresholdless”laser is strongly nonradiative depopulation-dependent. When the nonradiative depopulation is no zero, the light-current characteristic is not linearly even for an ideal closed microcavity. The light output is increased by the enhanced well number and by the reduced width. In particular, a lower threshold current density for MQW structure in the short cavity is realized by us, meanwhile the sharpness of the variation depends on spontaneous emission factor.

Effect of toroidal mode coupling on explosive dynamics of m/n=3/1 double tearing mode

The CLT code was used to quantitatively study the impact of toroidal mode coupling on the explosive dynamics of the m/n=3/1 double tearing mode.The focus of this study was on explosive reconnection processes,in which the energy bursts and the main mode no longer dominates when the separation between two rational surfaces is relatively large in the medium range.The development of higher m and n modes is facilitated by a relatively large separation between two rational surfaces,a small q_(min)(the minimum value of the safety factor),or low resistivity.The relationships between the higher m and n mode development,explosive reconnection rate,and position exchange of 3/1 islands are summarized for the first time.Separation plays a more important role than q_(min)in enhancing the development of higher m and n modes.At a relatively large separation,the good development of higher m and n modes greatly reduces the reconnection rate and suppresses the development of the main mode,resulting in the main mode not being able to develop sufficiently large to generate the position changes of 3/1 islands.

THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT

Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<1.In this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)dt+vdt-θ(∫_(0)^(t)(X_(t)^(H)-X_(s)^(H))ds)dt,whereθ<0,σ,v∈ℝ.The process is an analogue of self-attracting diffusion(Cranston,Le Jan.Math Ann,1995,303:87–93).Our main aim is to study the large time behaviors of the process.We show that the solution X^(H)diverges to infinity as t tends to infinity,and obtain the speed at which the process X^(H)diverges to infinity.

THE OPTIMAL LARGE TIME BEHAVIOR OF3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR DAMPING

We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.

Pre-reduction of WO_(3)-Co_(3)O_(4)by H_(2)-C_(2)H_4 in a fluidized bed

In order to avoid the formation ofηphase(W_(6)Co_(6)C or W_(3)Co_(3)C)that adversely affects the sintering process and its products in the preparation process of ultra-fine WC-Co powder,a technical route of prereduction of WO_(3)-Co_(3)O_(4)to WO_(2)-Co and then deep reduction carbonization to WC-Co powder has been proposed.This study mainly investigates the influence of gas partial pressure on the pre-reduction process of WO_(3)-Co_(3)O_(4)under a mixed atmosphere of H_(2)-C_(2)H_(4)-Ar at 600℃and establishes the kinetic equations of pre-reduction and carbon evolution.The results indicate that increasing the partial pressure of hydrogen is conducive to the rapid and complete conversion of WO_(3) to WO_(2).High carbon content can be generated by the deposition of C_(2)H_(4),and it hinders the diffusion of the reducing gas;WO_(3)still cannot be completely reduced to WO_(2)as the partial pressure of C_(2)H_(4) increases to 60%.For the carbon evolution of C_(2)H_(4),the carbon amount is positively related to the H_(2)partial pressure,but it shows the highest amount and evolution rate when the ethylene partial pressure is 20%.Based on the reduction rate curves of WO_(3) and carbon evolution rate curves of C_(2)H_(4),the rate equations of pre-reduction and carbon evolution of WO_(3)-Co_(3)O_(4)system at 600℃are established.The pre-reduction reaction belongs to the first-order reaction,and its equation is expressed as follows:r=-(dw_(WO_(3)))/dt=(9±0.15)×10^(-2)×P_(H_(2))^(0.44)P_(C_(2)H_(4))&(0.57)The carbon deposition rate equation of C_(2)H_(4) can be expressed as follows:r=-(dc_C)/dt=r_f-r_b≌7.35×10^(-2)×P_(C_(2)H_(4))^(0.31)

Steady State Creep Rate Equation of Inconel 718 Superalloy

The steady state creep rate equdtion of a nickel base superalloy Inconel 718, strengthened by coherent ordered disc-shaped bct γ^(11) phase and coherent spherical fcc γ~1 phase precipitates, has been established in the stress and temperature ranges of 620-840 MN m^(-2) and 853-943K, respecti- vely. Constant stress tensile creep tests were used to medsure the values of steady state creep rate, ε_s, and the consecutive stress reduction method was used to measure the back stress during creep deformation. The values of effective stress exponent, n_e, were detemined from the slopes of the lgε_s vs. lg(σ_a-σ_0)/G plots. The effect of grain size, d, on steady state creep rdte has been also studied in this investigation, and the grain size sensitive exponents m were detemined from the slopes of lgε_s vs. lg(b/d) plots. The creep rate equations of Inconel 718, in the above stress and temperature ranges, have been proposed to be ε_s=1.6×10^(-5)(D_1Gb/KT) (b/d )^(0.19)[(σ_a-σ_0)/G]^(1.35) in diffusional creep region, and ε_s =75(D_1Gb/KT) (b/d)^(-0.42)[(σ_a-σ_0)/G]^(5.5) in dislocation power law creep region.

Optimal convergence rates for three-dimensional turbulent flow equations

In this paper, the convergence turbulent flow equations are considered. By rates of solutions to the three-dimensional combining the LP-Lq estimate for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H3-framework. More precisely, the optimal convergence rates of the solutions and their first-order derivatives in the L2-norm are obtained when the LP-norm of the perturbation is bounded for some p ε [1, 6）.