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.

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.

Rate Equation of Small Particle-Air Bubble Attachment in Turbulent Flow of Flotation Cells

A rate equation of small particle-air bubble attachment in the turbulent now of flotation cells has beenderived. The equation, integrating both the collision probability and adhesion probability together, represents theprobability of attachment between particle and bubble in the turbulent flow. 'Capture efficiency' f(a) is introducedinto the rate equation to reflect the influence of energy hairier on the attachment rate. Three typical situations of particle-bubble interaction in flotation process have been discussed. For a completely hydrophobic particle-bubble system,f(a) = 1. This means that all collision leads to attachment. Whereas for hydrophilic particle-bubble systems, .f(a) =0. Thus no adhesion of particle on bubble occurs at all. In real notation circumstances, however, there always existsa certain energy barrier between the particle and the bubble. Therefore, f(a) = 0～1. In such cases, not all collisionsresult in particle-bubble attachment.

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.

A thermodynamic Approach to Rate Equations in Continuum Physics

The paper addresses the formulation of rate equations, via objective time derivatives, within continuum physics. The concept of objectivity is reviewed and distinction is made with material frame-indifference whose meaning is restricted to the invariance of the balance equations relative to Galilean frames. Objective time derivatives are defined to leave the tensor character of the appropriate field invariant within the set of Euclidean frames. Rate equations are required to involve objective time derivatives and to be consistent with the second law of thermodynamics. Here the general structure of objective time derivatives is established and the known derivatives of the physical literature are shown to be particular cases. Next, to fix ideas, a rate equation is considered for the model of heat conduction via a generalization of the Maxwell-Cattaneo equation with higher-order gradients as in the Guyer-Krumhansl equation. The thermodynamic restrictions are investigated and the expected effects, of the selected derivative of the heat flux, on the stress tensor are derived.

Improved Dissipation Rate Equation for Swirling and Rotating Pipe Flows

The nature of turbulent swirling and rotating flow in a straight pipe is investigated using a family of near-wall two-equation models. Specifically, the viability of three different near-wall two-equation models is assessed. These models are asymptotically consistent near the wall. The first two models, one with isotropic and another with anisotropic eddy viscosity invoked, solved a dissipation rate equation with no explicit correction made to account for swirl and flow rotation. The third model assumes an isotropic eddy viscosity but solves an improved dissipation rate equation that has explicit corrections made to account for swirl and flow rotation. Calculations of turbulent flows in the swirl number range 0.25 - 1.3 with and without a central recirculation region reveal that, with the exception of the third model, neither one of the other two models can replicate the mean field at the swirl numbers tested. Furthermore, taking stress anisotropy into account also fails to model swirl effect correctly. Significant improvements can be realized from the third model, which is based on an improved dissipation rate equation and the assumption of isotropic eddy viscosity. The predicted mean flow and turbulence statistics correlate well with measurements at low swirl. At high swirl, the two-equation model with an improved dissipation rate equation can still be used to model swirling and rotating pipe flows with a central recirculation region. However, its simulation of flows without a central recirculation region is not as satisfactory.

Rate equation model analysis on the infrared and upconversion emission of Er/Yb co-doped borate-silicate glass

Er/Yb co-doped borate-silicate glasses with various Yb concentrations were fabricated by high-temperature solid-reaction method.The photoluminescence spectra around 1.55 μm and the visible upconversion spectra were measured.The radiative lifetime of Er-4I13/2,com-pared with the measured one,was obtained by Judd-Ofelt theory based on the absorption spectra.A rate equation model for Er/Yb co-doped system has been established based on the data obtained from the measurements,including the absorption and emissio...

Trimming Behavior of H_2-Loaded Silica Fiber Modeled by Rate Equations

Photosensitivity behavior of H2-loaded silica fiber was modeled by rate equations for activated particles. The theoretical deductions give a close explanation to experimental phenomena on post-exposure growth in fiber gratings.

Kinetics of celestite conversion to acidic strontium oxalate hydrate in aqueous solution of oxalic acid

Conversion of SrSO4 to acidic strontium oxalate hydrate(H[Sr(C2O4)1.5(H2O)]) in aqueous H2C2O4 solutions proceeds as a consecutive reaction. In the first step of the consecutive reaction, SrSO4 reacts with H2C2O4 and pseudomorphic conversion to SrC2 O4·H2O occurs. In the second step, SrC2 O4·H2O reacts with H2C2O4 to form H[Sr(C2 O4)1.5(H2O)]. Sr(HC2 O4)(C2 O4)0.5·H2 O crystallizes during cooling of the reaction mixture to room temperature if the solution reaches the saturation concentration of (H[Sr(C2O4)1.5(H2O)]. The aims of this study are the derivation of reaction rate equations and the determination of the kinetic parameters such as pre-exponential factor, apparent activation energy and order of H2C2O4 concentration for each reaction step.Fractional conversions of SrSO4 were calculated using the quantitative amounts of dissolved S and Sr. It was determined that the reaction rate increased at the initial time of reaction by increasing the temperature using solutions with approximately same H2C2O4 concentrations. The reaction extends very slowly after a certain time in solutions with low H2C2O4 concentration and ends by the formation of a protective layer of SrC2O4-H2O around the surfaces of solid particles. Fractional conversion of SrSO4 is increased by increasing concentration of H2C2O4 at constant temperature. Kinetic model equations were derived using shrinking core model for each step.

Modeling of the Dyeing Uptake Rate for Direct Dyestuff on Cotton in Batch Dyeing Process Based on Grey System Theory

The grey system theory, with the characteristics of fewer modeling data and higher accuracy, was employed to model the batch dyeing process for the purpose of accurate online control. The GM（1, 1） and GM （0, N） models of the grey system theory were discussed for their feasibilities of modding for batch dyeing process. The combination of direct dyestuff Fast Red F3B on cotton was chosen as a representative of the common dyeing method for describing the modeling process. Firstly, the GM（ 1, 1 ） model and the GM（1, 1） combined with GM（0, N） model were employed to model the equilibrium percentage of dyeing uptake rate. Secondly, an integrated dyeing uptake rate model with three factors （ temperature, salt concentration, and pH） was established based on the adsorption rate equation. Experimental results show that this model has higher accuracy and beetler generalization ability, which can predict the results of batch dyeing process. Due to the application of grey system theory, the model has a lot of advantages, such as being easy to determine the parameter value and small amount of calculation. So it can also be suitable for the same type of combination of dyestuff-fahric by changing the parameters value only.

Interaction between Topographic Conditions and Entrainment Rate in Numerical Simulations of Debris Flow

Debris flow simulations are useful for predicting the sediment supplied to watersheds from upstream areas. However, the topographic conditions upstream are more complicated than those downstream and the relationship between the topographic conditions and debris flow initiation is not well understood. This study compared the use of several entrainment rate equations in numerical simulations of debris flows to examine the effect of topographic conditions on the flow. One-dimensional numerical simulations were performed based on the shallow water equations and three entrainment rate equations were tested. These entrainment rate equations were based on the same idea that erosion and the deposition of debris flows occur via the difference between the equilibrium and current conditions of debris flows, while they differed in the expression of the concentration, channel angle, and sediment amount. The comparison was performed using a straight channel with various channel angles and a channel with a periodically undulating surface. The three entrainment rate equations gave different amounts of channel bed degradation and hydrographs for a straight channel with a channel angle greater than 21° when water was supplied from upstream at a steady rate. The difference was caused by the expression of the entrainment rate equations. For channels with little undulation, the numerical simulations gave results almost identical to those for straight channels with the same channel angle. However, for channels with large undulations, the hydrographs differed from those for straight channels with the same channel angle when the channel angle was less than 21°. Rapid erosion occurred and the hydrograph showed a significant peak, especially in cases using the entrainment equation expressed by channel angle. This was caused by the effects of the steep undulating sections, since the effect increased with the magnitude of the undulation, suggesting that a debris flow in an upstream area develops differently according to the topographic conditions. These results also inferred that numerical simulations of debris flow can differ depending on the spatial resolution of the simulation domain, as the resolution determines the reproducibility of the undulations.

A Two-Step Growth Curve: Approach to the von Bertalanffy and Gompertz Equations

Many curves have been proposed and debated to model individual growth of marine invertebrates. Broadly, they fall into two classes, first order (e.g. von Bertalanffy) and sigmoidal (e.g. Gompertz). We provide an innovative approach which demonstrates that the growth curves are not mutually exclusive but that either may arise from a simple three-stage growth model with two steps (k1 and k2) depending on the ratio of the growth parameters . The new approach predicts sigmoidal growth when is close to 1, but if either growth from stage A to stage B or B to C is fast relative to the other, the slower of the two steps becomes the growth limiting step and the model reduces to first order growth. The resulting curves indicate that there is a substantial difference in the estimated size at time t during the period of active growth. This novel two-step rate model generates a growth surface that allows for changes in the rate parameters over time as reflected in the new parameter n(t) = k1(t) - k2(t). The added degree of freedom brings about individual growth trajectories across the growth surface that is not easily mapped using conventional growth modeling techniques. This two (or more) stage growth model yields a growth surface that allows for a wide range of growth trajectories, accommodating staged growth, growth lags, as well as indeterminate growth and can help resolve debates as to which growth curves should be used to model animal growth. This flexibility can improve estimates of growth parameters used in population models influencing model outcomes and ultimately management decisions.=

NEW PRINCIPLES OF WORK AND ENERGY AS WELLAS POWER AND ENERGY RATE FORCONTINUUM FIELD THEORIES

New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola's theorems were naturally derived in all and without any additional requirement. Finally, some new balance laws of energy and energy rate for generalized continuum mechanics were established. The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.

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)

Preparation of ultrafine WC-Co powder via fluidized bed

In this study,the effects of reaction parameters on the deep-reduction and carbonization process of WO_(2)-Co to WC-Co were studied.The results indicate that the oxygen loss rate of WO_(2) is positively correlated with temperature and methane partial pressure.The partial pressure of methane has no significant effect on the formation rate of WC.The carbon content and particle size of the product increase with the increase of CH_(4) partial pressure.By synergistically regulating the reaction temperature to 950℃,the CH_(4) partial pressure to 1.25%,and the reaction time to 60 min,ultrafine WC-Co powder without η phase can be obtained.The particle size of the composite powder is 128 nm,with total carbon content of 6.16%,free carbon content of 0.4%,and residual oxygen content of 0.05%,respectively.The growth rate relationship of tungsten carbide is as follows:δ(t)=1.21×10^(-13)exp(-12809.72/T)√t.

A Four-Level Theory on Energy Transfer of the Light-Harvesting Complex Ⅱ in PS Ⅱ in Higher Plants

With reference to the recent achivements about the structure, spectra and kinetics of light_harvesting complex (LHCⅡ) in PSⅡ of higher plants, a four_level model was provided to simulate the energy transfer process from LHC Ⅱ to the reaction center. On the basis of this model, a set of rate equation was established. Analysis of its algebra solution led to a general picture of energy transfer process in LHC Ⅱ of higher plants and the strong interaction among pigment molecules in this process. Based on the spectra, kinetics and biological structural data providing some information of energy transfer path and energy dissipation mechanism, it has been found that energy transfer mainly happened between the pigments whose energy level was most closely adjacent, the loss of energy had a close relation to the process of energy transfer and tended to increase with the decrease of energy level. The protective mechanism of antenna system was also discussed.

Adsorptive Removal of Copper Ions from Aqueous Solution Using Cross-linked Magnetic Chitosan Beads

The performance of cross-linked magnetic chitosan, coated with magnetic fluids and cross-linked with ePichlorohydrin, was investigated for the adsorption of Copper （Ⅱ） from aqueous solutions. Infrared spectra of chitosan before and after modification showed that the coating and cross-linking are effective. Experiments were performed at different pH of solution and contact time, and appropriate conditions for the adsorption of Cu（Ⅱ） were determined. Experimental equilibrium data were correlated with Langmuir and Freundlich isotherms for determination of the adsorption potential. The results showed that the Langmuir isotherm was better compared with the Freundlich isotherm, and the uptake of Cu（Ⅱ） was 78.13 mg·g^- 1. The kinetics of adsorption corresponded with the first-order Langergren rate equation, and Langergren rate constants were determined.

227-W output all-fiberized Tm-doped fiber laser at 1908 nm

In this paper, we report that a diode-pumped thulium-doped double clad silica fiber laser can provide powers of up to 227 W at 1908 nm, corresponding to a slope efficiency of 54.3%, and an optical-to-optical efficiency of 51.2%. The output power, to the best of our knowledge, is the highest output at 1908 nm. The beam quality M2 factor is about 1.56. Also discussed in this paper is the dependence of the laser performance on fiber length.

Study on the green upconversion saturation in Er^(3+) doped oxyfluoride tellurite glass

The upconversion emission spectra of Er^3＋ doped oxyfluoride tellurite glasses excited by 808 nm laser diode （LD） were measured. The dependence of 550 nm upconversion emission on the excitation intensity was analyzed. Quadratic intensity dependence was only observed at weak excitation intensity. With increasing the excitation intensity, saturation was turned out. The experimental results were fitted to a model based on the rate equations.

Theoretical study and optimization of a high power mid-infrared erbium-doped ZBLAN fibre laser

Based on the rate equations describing the erbium-doped fluoride glass （ZBLAN） fibre lasers with different pumping configurations being taken into account, this paper presents theoretical calculations related to the dynamic population density and the operation performance of a high power mid-infrared all-fibre erbium-doped ZBLAN fibre laser. It shows that the ground-state absorption, excited-state absorption and energy-transfer-upconversion processes co-exist and produce a population balance, causing the laser to operate stably at a continuous wave state. A good agreement between the theoretical results and recent experimental measurement is obtained. Furthermore, the laser structure parameters including fibre length, reflectance of output fibre Bragg grating and pumping configurations are quantitatively optimised to achieve the best performance. The results show, as expected, that the slope efficiency of the fibre laser can be improved significantly through optimisation, which then provides an important guide for the design of high-performance mid-infrared erbium-doped ZBLAN fibre lasers.