Effect of mixing rate and temperature on primary Si phase of hypereutectic Al-20Si alloy during control ed diffusion solidification(CDS) process

Controlled Diffusion Solidification(CDS) is a promising process relied on mixing two liquid alloys of precisely controlled chemistry and temperature in order to produce a predetermined alloy composition. In this study, the CDS was employed to prepare hypereutectic Al-20%Si(mass fraction) alloy using Al-30%Si and pure Al of different temperatures. The mixing rate was controlled using three small crucibles with a hole of different diameters in their bottom. The effect of mixing rate and temperature on the microstructure of the primary Si-phase during the mixing of molten Al and Al-30%Si was studied. The results showed that when the diameter of the small crucible bottom hole is 16 mm, a higher mass mixing rate 0.217 kg·s-1 would results in a lower stream velocity 0.414 m·s-1. Conversely a lower mass mixing rate 0.114 kg·s-1(the diameter of the small crucible bottom hole is 8 mm) would result in a higher fluid stream velocity 0.879 m·s-1. A lower mass mixing rate would be better to refine the primary Si than a higher mass mixing rate. Meanwhile, the morphology and distribution of primary Si could also be improved. Especially, when Al-30%Si alloy at 820 °C was mixed with pure Al at 670 °C in the case of a mass mixing rate of 0.114 kg·s-1 and a pouring temperature of 680 °C, the average size of the primary Si phase would be only 18.2 μm. Its morphology would mostly be octahedral and the primary Si would distribute uniformly in the matrix microstructure. The lower mass mixing rate(0.114 kg·s-1) will enhance the broken tendency of Al-30%Si steam and the mixing agitation of resultant melt, so the primary Si phase can be better refined.

Ruin Probability with Variable Premium Rate and Disturbed by Diffusion in a Markovian Environment

We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method. Key words ruin probability - variable premium rate - diffusion process - Markov intensity CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)

ENTROPY PRODUCTION RATE OF THE MINIMAL DIFFUSION PROCESS

The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point at infinity is absorbing is proved.

On pricing of corporate securities in the case of jump-diffusion

Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over time. In this paper, we extend the pricing model for corporate bond and determine the default probability in jump-diffusion model to address this issue. To make the problem clearly, we first investigate the case that the firm value follows a geometric Brownian motion under similar assumptions to those in Black and Scholes（1973）, Briys and de Varenne（1997）, i.e, the default barrier is KD （t, T） and the recovery rate is （1 -w）, where D （t, T） is the price of zero coupon default free bond and w is a constant （0 〈 w 〈 1）. By changing the numeraire, we obtain the closed-form solution for both the price of bond and default probability. Further, we consider the case of jump-diffusion and suppose that a firm will go bankruptcy if its value Vt 〈 KD （t, T） and at the same time, the bondholder will receive （1 - w） vt/k By introducing the Green function of PDE with absorbing boundary and converting the problem to an II-type Volterra integral equation, we get the closed-form expressions in series form for bond price and corresponding default probability. Numerical results are presented to show the impact of different parameters to credit spread of bond.

Boosting rate performance of layered lithium-rich cathode materials by oxygen vacancy induced surface multicomponent integration

The rapid development of electric vehicles and portable energy storage systems demands improvements in the energy density and cost-effectiveness of lithium-ion batteries,a domain in which Lithium-rich layered cathode(LLO)materials inherently excel.However,these materials face practical challenges,such as low initial Coulombic efficiency,inferior cycle/rate performance,and voltage decline during cycling,which limit practical application.Our study introduces a surface multi-component integration strategy that incorporates oxygen vacancies into the pristine LLO material Li1.2Mn_(0.6)Ni_(0.2)O_(2).This process involves a brief citric acid treatment followed by calcination,aiming to explore rate-dependent degradation behavior.The induced surface oxygen vacancies can reduce surface oxygen partial pressure and diminish the generation of O_(2)and other highly reactive oxygen species on the surface,thereby facilitating the activation of Li ions trapped in tetrahedral sites while overcoming transport barriers.Additionally,the formation of a spinel-like phase with 3D Li+diffusion channels significantly improves Li^(+)diffusion kinetics and stabilizes the surface structure.The optimally modified sample boasts a discharge capacity of 299.5 mA h g^(-1)at a 0.1 C and 251.6 mA h g^(-1)at a 1 C during the initial activation cycle,with an impressive capacity of 222.1 mA h g^(-1)at a 5 C.Most notably,it retained nearly 70%of its capacity after 300 cycles at this elevated rate.This straightforward,effective,and highly viable modification strategy provides a crucial resolution for overcoming challenges associated with LLO materials,making them more suitable for practical application.

DECAY RATE FOR DEGENERATE CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS

We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension convection diffusion equation. On the other hand, in the second part of this article, we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions.

Some Properties of Solutions for a Degenerate Diffusion System

In this paper, we prove some properties of solutions to a class of degener-ate diffusion systems which arise from modeling interacting evolution of two biological groups.

Entropy Rate of Thermal Diffusion

The thermal diffusion of a free particle is a random process and generates entropy at a rate equal to twice the particle’s temperature, (in natural units of information per second). The rate is calculated using a Gaussian process with a variance of which is a combination of quantum and classical diffusion. The solution to the quantum diffusion of a free particle is derived from the equation for kinetic energy and its associated imaginary diffusion constant;a real diffusion constant (representing classical diffusion) is shown to be . We find the entropy of the initial state is one natural unit, which is the same amount of entropy the process generates after the de-coherence time, .

GLOBAL BLOWUP AND BLOWUP RATE ESTIMATES OF SOLUTIONS FOR A CLASS OF NONLINEAR NON-LOCAL REACTION-DIFFUSION PROBLEMS

In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the solution is given.

Pricing Study on Two Kinds of Power Options in Jump-Diffusion Models with Fractional Brownian Motion and Stochastic Rate

In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end.

Experimental study on effects of gas flow rate on soot characteristics in diffusion flames coupled with plasma

This study examined the evolution of morphology and nanostructure of soot particles from the plasma-flame interaction for various gas flow rates.The current study used both optical diagnostic and sampling methods to explore the soot production and combustion characteristics.Soot particles were characterized at the same positions downstream from the flame zone by thermophoretic sampling and transmission electron microscopy.Moreover,X-ray diffraction analysis,and thermogravimetric analysis were performed to study the nanostructure and oxidation reactivity of soot.A reduction in soot concentration was found with the plasma addition,which illustrated an inhibition effect of plasma on soot emission.The increased gas flow rate promoted soot concentration since a growing number of carbons participated in the combustion process.Depending on the gas flow rate(carbon content)variation and plasma activation,either liquid-like soot material with irregularly shaped protrusions or chain-like structure,or a mixture of both,were generated from the diffusion flames.The soot produced by plasma-flame interaction also demonstrated a high correlation between nanostructure and reactivity.The soot from lower carbon content with plasma activation had a shorter fringe length and larger fringe tortuosity related to higher oxidation reactivity.On the contrary,soot from the highest carbon content without plasma-flame interaction exhibited prevalent fullerene-like nanostructures with evident large or small shells and also had a higher carbonization degree resulting in lower oxidation reactivity.

A Three-Dimensional Model of Transport and Diffusion of Seeding Agents within Stratus

It is essential to learn the temporal and spatial concentration distributions and variations of seeding agents in cloud seeding of precipitation enhancement. A three-dimensional puff trajectory model incorporating a mesoscale nonhydrostatic model has been formulated, and is applied to simulating the transporting and diffusive characteristics of multiple line sources of seeding agents within super-cooled stratus. Several important factors are taken into consideration that affect the diffusion of seeding materials such as effects of topography and vertical wind shear, temporal and spatial variation of seeding parameters and wet deposition. The particles of seeding agents are assumed to be almost inert, they have no interaction with the particles of the cloud or precipitation except that they are washed out by precipitation. The model validity is demonstrated by the analyses and comparisons of model results, and checked by the sensitivity experiments of diffusive coefficients and atmospheric stratification. The advantage of this model includes not only its exact reflection of heterogeneity and unsteadiness of background fields, but also its good simulation of transport and diffusion of multiple line sources. The horizontal diffusion rate and the horizontal transport distance have been proposed that they usually were difficult to obtain in other models. In this simulation the horizontal diffusion rate is 0.82 m s(-1) for average of one hour, and the horizontal average transport distance reaches 65 km after 1 4 which are closely related to the background Fields.

Diffusion of Acetic Acid Across Oil/Water Interface in Emulsification-Internal Gelation Process for Preparation of Alginate Gel Beads

Alginate has been widely used in cell microencapsulation and drug delivery systems in the form of gel beads or microcapsules.Although an alternative novel emulsification-internal gelation technology has been established and both the properties and the potential applications of the beads in drug delivery systems have been studied,the mechanism has not been well understood compared with the traditional droplet method（external gelation technology）.On the basis of our previous knowledge that the novel technology is composed of complicatedly consecutive processes with multistep diffusion and reaction,and the diffusion of acetic acid across oil/water interface being the prerequisite that determines the occurrence and rate for the reactions and the structures and properties of final produced gel beads,a special emphasis was placed on the diffusion process.With the aid of diffusion modeling and simple experimental design,the diffusion rate constant and diffusion coefficient of acetic acid across oil/water interface were determined to be in the orders of magnitude of 10-6 and 10-16,respectively.This knowledge will be of particular importance in understanding and interpreting the formation,structure of the gel beads and the relationship between the structure and properties and guiding the preparation and quality control of the gel beads.

Formation and Growth Kinetics of Intermediate Phases in Ni-Al Diffusion Couples

Formation and growth of the intermediate phases in the Ni-Al diffusion couples prepared by pouring technique were investigated. Electron probe microanalysis, scanning electron microscopy and X-ray diffraction were used to characterize the product phases in the joints. The results show that two intermediate phases form in the sequence of NiAl3 and Ni2Al3 during solidification. After annealed, Ni2Al3 and NiAl3 still exist in the joints of the couples. The reasons for the formation of Ni2Al3 and NiAl3, as well as the absence of NiAl, Ni5Al3 and Ni3Al were discussed, respectively. The growth kinetics of both product phase layers indicates that their growth obeys the parabolic rate law. The activation energies and frequency factors for NiAl3 and Ni2Al3 phases were also calculated according to the Arrhenius equation.

Diffusion Characteristics and Removal of Cyclohexane in Polyolefin Elastomer Melt

The diffusion coefficient of volatiles in polymer solutions is a crucial parameter to describe the mass transfer efficiency and ability of volatiles.In this research,polyolefin elastomer(POE)was used as a polymer,and cyclohexane was used as a volatile.A gravimetric analysis was applied to measure the diffusion coefficient of cyclohexane in POE.The devolatilization rate of the POE-cyclohexane system under different conditions was measured.The effects of temperature,film sample thickness,and initial concentration of volatiles on the devolatilization rate were discussed.Based on the devolatilization rate data,the average diffusion coefficient of cyclohexane in POE was obtained by fitting with a mathematical model.The experimental results indicate that the devolatilization rate increased with increasing temperature and initial concentration of volatiles,but it decreased with increasing sample thickness.As the thickness increased,the overall diffusion resistance increased.As the temperature increased,the molecular movement increased,resulting in the increase of average diffusion coefficient.The relationship between the diffusion coefficient of the POE-cyclohexane system and temperature follows the Arrhenius law.The diffusion activation energy E=6201.73 J/mol,and the pre-exponential factor of the diffusion coefficient D0=2.64×10^(-10) m^(2)/s.This work can provide basic data for exploring the devolatilization of POE polymers and serves as a useful reference for enhancing the effect of devolatilization.

Kinetic equation based on non-steady-state diffusion of oxygen in solid copper

The kinetics of internal oxidation of dilute Cu-Al alloys, containing 0.4475%-2.214%Al (mole fraction) was investigated over the temperature range of 1023-1273K and the depth of internal oxidation was measured by microscopy. Based on non-steady-state diffusion, a rate equation is derived to describe the kinetics of internal oxidation of plate: X=k-t-, where X is the oxidation depth, t is the oxidation time. For the internal oxidation of Cu-Al alloys employed in the synthesis of alumina dispersion strengthened copper, the permeability of oxygen in solid copper is obtained from the internal oxidation measurements. Investigation shows that the depth of the internal oxidation is a parabolic function of time, the typical shape of the front of internal oxidation is of planar morphology, and there is no evidence for preferential diffusion along grain boundaries.

CONVERGENCE RATES TO NONLINEAR DIFFUSIVE WAVES FOR SOLUTIONS TO NONLINEAR HYPERBOLIC SYSTEM

This article is involved with the asymptotic behavior of solutions for nonlinear hyperbolic system with external friction. The global existence of classical solutions is proven,and L^p convergence rates are obtained. Compared with the results obtained by Hsiao and Liu, better convergence rates are obtained in this article.

Effect of alternative magnetic field on the diffusion layer growth in Al/Zn couple

The influence of an alternative magnetic field on the growth of the diffusionlayer in Al-Zn diffusion couple was studied. The thickness of the diffusion layer was examined. Theresults show that the alternative magnetic field increases the thickness of the diffusion layer andthe effect increases with the intensity and frequency of the alternative magnetic field increasing. The growth of the diffusion layer obeys the parabolic rate law and the growth rateincreases with the application of the alternative magnetic field. This growth rate change ismanifested through a change in the frequency factor k_0 and not through a change in the activationenergy Q. The frequency factor k_0 for the diffusion layer growth with the alternative magneticfield is 5.03 cm^2/s and the one without the magnetic field is 3.84 cm^2/s.

BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS

In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.

Effect of thermal diffusion and electrostatic force on evolution of wind-blown sand flow

A theoretical model is suggested to mathematically describe the effect of thermal diffusion from a sand-bed on evolution of a wind-blown sand flow. An upward wind field is engendered by the thermal diffusion and the coupling interaction among the horizontal and upward wind flow, saltating grains, and a kind of electrostatic force exerted on the grains are considered in this theoretical model. The numerical results show that the effect of the thermal diffusion on the evolution process of wind-blown groan flow is quite obvious and very similar to the effect of the electrostatic force on the evolution. Not only the time for the entire system to reach a steady state （called the duration time）, the transport rate of grains, the mass-flux profiles and the trajectory of saltating grains are affected by the thermal diffusion and the electrostatic force exerted on saltating grains, but also the wind profiles and the temperature profiles at the steady state are affected by the wind-blown sand flow.