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.

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)

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.

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 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.=

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.

Numerical Computing for a Class of Free Multipoint Boundary Value Problem of O.D.E in the Intervention of Exchange Rate

In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenillas and Femaado Zapatero. A numerical example was given for illustrating the validity of this method.

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.

Kinetics of oxidative coupling of methane:Bridging the gap between comprehension and description

The development of notions about the mechanism of the oxidative coupling of methane （OCM） over oxide catalysts and corresponding progress in its kinetic description are reviewed and discussed. The latter becomes essential at the stage of scaling up and optimization of the process in pilot and industrial reactors. It is demonstrated that the main achievements in the development of kinetic models can be reached by combining the approaches conventionally used in homogeneous gas-phase kinetics and in heterogeneous catalysis. In particular, some important features of the OCM process can be described if several elementary reactions of free radical species （formation and transformation） with surface active sites are included into the detailed scheme of methane oxidation in gas. However, some important features, such as a non-additive character of the reciprocal influence of methane and ethane in the case of their simultaneous presence in the reaction mixture, cannot yet be described and comprehended in the framework of schemes developed so far. Possible ways towards an advanced kinetic model, accounting the main principles of catalyst functioning （redox nature of active sites） and pathways of product formation （via free radicals） are traced.

Competing role of catalysis-coagulation and catalysis-fragmentation in kinetic aggregation behaviours

We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K（i,j;l） l^v and the catalysis-fragmentation rate kernel F（i,j; l） l^μ, where l is the size of the catalyst aggregate, and v and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters v and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters v and μ, but also depend on the values of these two parameters. When v 〉 μ and v ≥0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution αk（t） obeys the conventional or generalized scaling law; when v 〈 μ and v ≥ 0 or v 〈 0 but μ≥ 0, the catalysis-fragmentation process may play a dominating role and ak（t） approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ακ（t） obeys a modified scaling law.

An equivalent circuit model for terahertz quantum cascade lasers:Modeling and experiments

Terahertz quantum cascade lasers（THz QCLs） emitted at 4.4 THz are fabricated and characterized. An equivalent circuit model is established based on the five-level rate equations to describe their characteristics. In order to illustrate the capability of the model, the steady and dynamic performances of the fabricated THz QCLs are simulated by the model.Compared to the sophisticated numerical methods, the presented model has advantages of fast calculation and good compatibility with circuit simulation for system-level designs and optimizations. The validity of the model is verified by the experimental and numerical results.

A theoretical and experimental investigation of an in-band pumped gain-switched thulium-doped fiber laser

In this paper, the theoretical rate equation model of an in-band pumped gain-switched thulium-doped fiber （TDF） laser is investigated. The analytical formulations of pump energy threshold, peak power extraction efficiency, and pulse extraction efficiency are derived through analyzing the interaction process between the pump pulse and the laser pulse. They are useful for understanding, designing, and optimizing the in-band pumped TDF lasers in a 1.9 μm-2.1 μm wavelength region. The experiment with an all-fiber gain-switched TDF laser pumped by a 1.558-μm pulse amplifier is conducted, and our experimental results show good agreement with theoretical analysis.

Nonaffine Network Structural Model for Molten Low-Density Polyethylene and High-Density Polyethylene in Oscillatory Shear

We propose molten polymer's entanglement network deformation to be nonaffine and use transient network structural theory with the revised Liu's kinetics rate equation and the revised upper convected Maxwell constitutive equation to establish a nonaffine network structural constitutive model for studying the rheological behavior of molten Low Density Polyethylene (LDPE) and High Density Polyethylene (HDPE) in oscillatory shear. As a result, when the strain amplitude or frequency increases, the shear stress amplitude increases. At the same time, the accuracy of the nonaffine network model is higher than that of affine network model. It is clear that there is a small amount of nonaffine network deformation for LDPE melts which have long chain branches, and there is a larger amount of nonaffine network deformation in oscillatory shear for HDPE melts which has no long chain branches. So we had better consider the network deformation nonaffine when we establish the constitutive equations of polymer melts in oscillatory shear.

Kinetics of catalytically activated duplication in aggregation growth

We propose a catalytically activated duplication model to mimic the coagulation and duplication of the DNA polymer system under the catalysis of the primer RNA. In the model, two aggregates of the same species can coagulate themselves and a DNA aggregate of any size can yield a new monomer or double itself with the help of RNA aggregates. By employing the mean-field rate equation approach we analytically investigate the evolution behaviour of the system. For the system with catalysis-driven monomer duplications, the aggregate size distribution of DNA polymers αk（t） always follows a power law in size in the long-time limit, and it decreases with time or approaches a time-independent steady-state form in the case of the duplication rate independent of the size of the mother aggregates, while it increases with time increasing in the case of the duplication rate proportional to the size of the mother aggregates. For the system with complete catalysis-driven duplications, the aggregate size distribution αk（t） approaches a generalized or modified scaling form.

Spectroscopic properties of Er/Ce-codoped La_3Ga_5SiO_(14)

The Er-single-doped and Er/Ce-codoped La3Ga5SiO14 polycrystalline powders are synthesized by the solid-phase synthesis method. The room-temperature luminescence spectra of the samples are investigated. The Near-infrared- region spectroscopic properties of Er3＋ ions in the La3GasSiO14 systems are analysed with Judd-Ofelt theory and rate equations. The effective deactivating effect of Ce3＋ ions on Er3＋ ions is confirmed.

Studies on aluminum powder combustion in detonation environment

The combustion mechanism of aluminum particles in a detonation environment characterized by high temperature(in unit 10^(3)K),high pressure(in unit GPa),and high-speed motion(in units km/s)was studied,and a combustion model of the aluminum particles in detonation environment was established.Based on this model,a combustion control equation for aluminum particles in detonation environment was obtained.It can be seen from the control equation that the burning time of aluminum particle is mainly affected by the particle size,system temperature,and diffusion coefficient.The calculation result shows that a higher system temperature,larger diffusion coefficient,and smaller particle size lead to a faster burn rate and shorter burning time for aluminum particles.After considering the particle size distribution characteristics of aluminum powder,the application of the combustion control equation was extended from single aluminum particles to nonuniform aluminum powder,and the calculated time corresponding to the peak burn rate of aluminum powder was in good agreement with the experimental electrical conductivity results.This equation can quantitatively describe the combustion behavior of aluminum powder in different detonation environments and provides technical means for quantitative calculation of the aluminum powder combustion process in detonation environment.