Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions

In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.

Effect of the Geometrical Parameter of OpenMicrochannel on Pool Boiling Enhancement

High heat dissipation is required for miniaturization and increasing the power of electronic systems.Pool boiling is a promising option for achieving efficient heat dissipation at low wall superheat without the need for moving parts.Many studies have focused on improving heat transfer efficiency during boiling by modifying the surface of the heating element.This paper presents an experimental investigation on improving pool boiling heat transfer using an open microchannel.The primary goal of this work is to investigate the impact of the channel geometry characteristics on boiling heat transfer.Initially,rectangular microchannels were prepared on a circular copper test piece with a diameter of 20 mm.Then,the boiling characteristics of these microchannels were compared with those of a smooth surface under saturated conditions using deionized water.In this investigation,a wire-cutting electrical discharge machine(EDM)machine was used to produce parallel microchannels with channel widths of 0.2,0.4,and 0.8 mm.The fin thicknesses were 0.2,0.4,and 0.6 mm,while the channel depth remained constant at 0.4 mm.The results manifested that the surface featuring narrower fins and broader channels achieved superior performance.The heat transfer coefficient(HTC)was enhanced by a maximum of 248%,and the critical heat flux(CHF)was enhanced by a maximum of 101%compared to a plain surface.Eventually,the obtained results were compared with previous research and elucidated a good agreement.

Determination of indices and critical values of gas parameters of the first gas outburst in a coal seam of the Xieqiao Mine

Based on the important role in mine safety played by parameters of the first gas outburst, we propose a method of combining historic data, theoretical analysis and experimental research for the purpose of crit- ical values of gas parameters of the first gas outburst in a coal seam of the Xieqiao Mine. According to a characteristic analysis and a summary of the rules of coal and gas outbursts in the No.8 coal seam of a Hua- inan mine, we have investigated their effect on coal and gas outbursts in terms such as ground stress, gas, and coal structure. We have selected gas parameters and determined the critical values of each of the fol- lowing indices： gas content as 7.7 m^3/t, tectonic coal as 0.8 m thick, the absolute gas emission as 2 m3/min, the rate of change as 0.7 m3/min, the gas desorption index of a drilling chip KI as 0.26 mL/（g min^1/2） and the values of desorption indexes Ah2 as 200 Pa. From a verification of the production, the results indicate that application of each index and their critical values significantly improve the level of safety in the pro- duction process, relieve the burden upon the mine, save much labor and bring clear economic benefits.

On a New Equation for Critical Current Density Directly in Terms of the BCS Interaction Parameter, Debye Temperature and the Fermi Energy of the Superconductor

Recasting the BCS theory in the larger framework of the Bethe-Salpeter equation, a new equation is derived for the temperature-dependent critical current density jc(T) of an elemental superconductor (SC) directly in terms of the basic parameters of the theory, namely the dimensionless coupling constant [N(0)V], the Debye temperature θD and, additionally, the Fermi energy EF—unlike earlier such equations based on diverse, indirect criteria. Our approach provides an ab initio theoretical justification for one of the latter, text book equations invoked at T = 0 which involves Fermi momentum;additionally, it relates jc with the relevant parameters of the problem at T ≠ 0. Noting that the numerical value of EF of a high-Tc SC is a necessary input for the construction of its Fermi surface—which sheds light on its gap-structure, we also briefly discuss extension of our approach for such SCs.

Regularization and Choice of the Parameter for the Third Kind Nonlinear Volterra-Stieltjes Integral Equation Solutions

The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.

Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out.We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed region.Then,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is introduced.It is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may occur.More importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

Critical Parameters and Magnetocaloric Effect of the La_5/8Ca_3/8Mn_0.9750Pd_0.025O₃Compound

The La5/8Ca3/8Mn0.9750Pd0.025O3 compound was studied using DC magnetization measurements. The data were analyzed in the paramagnetic-ferromagnetic phase transition region by the Arrott plot method. The results show the Curie temperature TC ~ 247.8 K and the critical exponents of b = 0.48633, g = 1.18623 and d = 3.431682. The values of the critical exponents are between the mean- field theory and 3D Ising model. The magnetocaloric value is ~5 J/kgK, extracted from the M(H) curves.

Linear numerical calculation method for obtaining critical point,pore fluid,and framework parameters of gas-bearing media

Up to now, the primary method for studying critical porosity and porous media are experimental measurements and data analysis. There are few references on how to numerically calculate porosity at the critical point, pore fluid-related parameters, or framework-related parameters. So in this article, we provide a method for calculating these elastic parameters and use this method to analyze gas-bearing samples. We first derive three linear equations for numerical calculations. They are the equation of density p versus porosity Ф, density times the square of compressional wave velocity p Vp^2 versus porosity, and density times the square of shear wave velocity pVs^2 versus porosity. Here porosity is viewed as an independent variable and the other parameters are dependent variables. We elaborate on the calculation steps and provide some notes. Then we use our method to analyze gas-bearing sandstone samples. In the calculations, density and P- and S-velocities are input data and we calculate eleven relative parameters for porous fluid, framework, and critical point. In the end, by comparing our results with experiment measurements, we prove the viability of the method.

An experimental study on the relationship between acoustic parameters and mechanical properties of frozen silty clay

To study the influence of temperature and water content on ultrasonic wave velocity and to establish the relationship between ultrasonic wave velocity and frozen silty clay strength, ultrasonic tests were conducted to frozen silty clay by using RSM-SY5（T） nonmetal supersonic test meter, and the tensile strength and compressive strength of silty clay were measured under various negative temperatures. Test and analysis results indicate that, ultrasonic wave velocity rapidly changes in the temperature range of-1 ℃ to -5 ℃. Ultrasonic wave velocity increased with an increase of water content until the water content reached the critical water content, while decreased with an increase of water content after the water content exceeded the critical water content. This study showed that there was strong positive correlation between the ul- trasonic wave velocity and the frozen soil strength. As ultrasonic wave velocity increased, either tensile strength or com- pressive strength increased. Based on the experimental data, the relationship between ultrasonic wave velocity and frozen silty clay strength was obtained through regression analysis. It was found that the ultrasonic test technique can be used to test frozen soils and lay the foundation for the determination of frozen soil strength.

Chemometric identification of canonical metabolites linking critical process parameters to monoclonal antibody production during bioprocess development

A deeper understanding of the biological events occurring when bioprocess parameters changed will be of great value in improving the monoclonal antibodies (mAbs) production. Design of experiment (DoE) was applied to investigate the effect of process parameters (pH, temperature shift and dissolve oxygen (DO)) on protein titer. The key metabolites connecting the critical process parameters (CPPs) with monoclonal antibody production were identified by different chemometrics tools. Finally, the biological events of marker metabolites relating with titer improvement were concluded. pH and temperature shift were identified as CPPs that affect the target protein titer. A series of metabolites influenced by the altered CPPs and correlated with protein titer were screened by principal component analysis (PCA) and Pearson' correlation test. The marker metabolites and their pathways linking CPPs to target protein titer in different culture phases were summarized. Metabolomics and chemometrics are promising data-driven tools to shine light into the biological black box between the bioprocess parameters and process performance.

A Study of Estimating the Safe Storage Life, Self-accelerating Decomposition Temperature and Critical Temperature of Thermal Explosion of Double-base Propellant Using Isothermal and Non-isothermal Decomposition Behaviours

A method of estimating the safe storage life （τ）, self-accelerating decomposition temperature （TsADT） and critical temperature of thermal explosion （Tb） of double-base propellant using isothermal and non-isothermal decomposition behaviours is presented. For double-base propellant composed of 56±1wt% of nitrocellulose （NC）, 27±0.5wt% of nitroglycerine （NG）, 8.15±0.15wt% of dinitrotoluene （DNT）, 2.5±0.1wt% of methyl centralite, 5.0±0.15wt% of catalyst and 1.0±0.1wt% of other, the values of r of 49.4 years at 40℃, of TSAOT of 151.35℃ and of Tb of 163.01℃ were obtained.

Algorithms for automatic measurement of SIS-type hysteretic underdamped Josephson junction’s parameters by current-voltage characteristics

Some electrical parameters of the SIS-type hysteretic underdamped Josephson junction(JJ)can be measured by its current-voltage characteristics(IVCs).Currents and voltages at JJ are commensurate with the intrinsic noise level of measuring instruments.This leads to the need for multiple measurements with subsequent statistical processing.In this paper,the digital algorithms are proposed for the automatic measurement of the JJ parameters by IVC.These algorithms make it possible to implement multiple measurements and check these JJ parameters in an automatic mode with the required accuracy.The complete sufficient statistics are used to minimize the root-mean-square error of parameter measurement.A sequence of current pulses with slow rising and falling edges is used to drive JJ,and synchronous current and voltage readings at JJ are used to realize measurement algorithms.The algorithm performance is estimated through computer simulations.The significant advantage of the proposed algorithms is the independence from current source noise and intrinsic noise of current and voltage meters,as well as the simple implementation in automatic digital measuring systems.The proposed algorithms can be used to control JJ parameters during mass production of superconducting integrated circuits,which will improve the production efficiency and product quality.

Multiplicity of Solutions for Nonlinear Biharmonic Equation Involving Critical Parameter and Critical Exponent

By using variational method, the multiplicity of solutions for nonlinear biharmonic equation involving critical parameter and critical exponent are established.

Experimental verification of parameter m in Hoeke-Brown failure criterion considering the effects of natural fractures

HoekeBrown failure criterion is one of the widely used rock strength criteria in rock mechanics and mining engineering.Based on the theoretical expression of HoekeBrown parameter m of an intact rock,the parameter m has been modified by crack parameters for fractured rocks.In this paper,the theoretical value range and theoretical expression form of the parameter m in HoekeBrown failure criterion were discussed.A critical crack parameter B was defined to describe the influence of the critical crack when the stress was at the peak,while a parameter b was introduced to represent the distribution of the average initial fractures.The parameter m of a fractured rock contained the influences of critical crack(B),confining pressure(s3)and initial fractures(b).Then the triaxial test on naturally fractured limestones was conducted to verify the modification of the parameter m.From the ultrasonic test and loading test results of limestones,the parameter m can be obtained,which indicated that the confining pressure at a high level reduced the differences of m among all the specimens.The confining pressure s3 had an exponential impact on m,while the critical crack parameter B had a negative correlation with m.Then the expression of m for a naturally fractured limestone was also proposed.

Influence of gas pressure state on the motion parameters of coal-gas flow in the outburst hole

Carried on the one-dimensional analysis to the motion state of coal-gas flow in the outburst hole, and deduced the relational expression between the motion parameters （containing of velocity, flow rate and density etc.） of bursting coal-gas flow and gas pressure in the hole, then pointed out the critical state change of coal-gas flow under different pressure conditions which had the very tremendous influence on both stability and destructiveness of the entire coal and gas outburst system. The mathematical processing and results of one-dimensional flow under the perfect condition are simple and explicit in this paper, which has the certain practical significance.

Recovery of oil and free fatty acids from spent bleaching earth using sub-critical water technology supported with kinetic and thermodynamic study

This work represents the extraction of oil with high free fatty acid content from spent bleaching earth using sub-critical water technology as a greener production pathway. The extraction efficiencies under different conditions were investigated. The studied parameters include temperatures in the range of 180 to 270°C, the feed to solventfeed-to-solvent (in this case water) ratio (1:1, 1:2, 1:3, 1:4 and 1:5) and extraction times in the range of 5-60 minutes. The results showed that the optimum temperature, feed to solventfeed-to-solvent ratio, and extraction time were 270°C, 1:3, and 20 minutes, respectively. In another experiment, the extracted free fatty acids were converted into mono-, di-, and triglycerides through esterification with glycerol to increase the value added of the extracted products. The kinetics of the extraction process was found to be corresponding to an irreversible consecutive unimolecular-type first order reaction, consisting of the extraction step followed by the decomposition reaction step. Both reaction rates of extraction and decomposition were estimated using the reaction rate equations utilizing the nonlinear regression method. The apparent activation energy was calculated to be 46.1 kJ·mol-1. This result indicates a diffusion controlled reaction. For more exploration and deep understanding of the extraction mechanism, other thermodynamic parameters were also calculated and analyzed including,ΔH#, ΔS#, and ΔG# of the extraction step.

Local Bifurcation Analysis of Parameter-Excited Resonance of Pipes under Thermal Load

The stability and local bifurcation of the lateral parameter-excited resonance of pipes induced by the pulsating fluid velocity and thermal load are studied. A mathematical model for a simply supported pipe is developed according to Hamilton principle. The Galerkin method is adopted to discretize the partial differential equations to the ordinary differential equations. The method of multiple scales and the singularity theory are utilized to analyze the stability and bifurcation of the trivial and non-trivial solutions. The transition sets and bifurcation diagrams are obtained both in the unfolding parameter space and physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and verify the stability and local bifurcation analyses. The critical thermal rates are obtained both by the numerical simulation and the local bifurcation analysis. The natural frequency of lateral vibration decreases as the mean fluid velocity or the thermal rate increases according to the numerical results. The present work can provide valuable information for the design of the pipeline and controllers to prevent structural instability.

Molecular Simulation of Critical Parameters of Nano-Confined n-Alkanes

TraPPE force field combined with grand-canonical transition-matrix Monte Carlo simulation were used to investigate the vapor-liquid coexistence curve and critical properties of methane,ethane,propane,and n-butane in slit pores ranging from 6?to 40?.Long range correction for intermolecular potential in slit pore model was developed,and the fact indicating that its influence on various thermodynamic properties is not negligible was found.The simulation results show that the thermodynamic properties of nano-confined alkanes shift tremendously from the bulk state.The critical temperature under confinement experiences a roughly linear decrease with an inverse in the slit width,while the critical pressure and the critical density have a relative increment related with carbon number on both the large slit width region and the small slit width region.Further analysis on z-density profiles of alkanes revealed that the complex behaviors of shift in critical parameters are the results of interplay between fluid-fluid and fluid-wall interaction.

Rigorous back analysis of shear strength parameters of landslide slip

A rigorous back analysis of shear strength parameters of landslide slip was presented. Kinematical element method was adopted to determine factor of safety and critical failure surface, which overcomes the disadvantage of limit equilibrium method. The theoretical relationship between the combination of shear strength parameters and stability state was studied. The results show that the location of critical slip surface, F/tan f and F/c depend only on the value of c/tan f. The failure surface moves towards the inside of slope as c/tan f increases. According to the information involving factor of safety and critical failure surface in a specific cross-section, strength parameters can be back calculated based on the above findings. Three examples were given for demonstrating the validity of the present method. The shear strength parameters obtained by back analysis are almost consistent with their correct solutions or test results.

Influences of aerodynamic loads on hunting stability of high-speed railway vehicles and parameter studies

The influences of steady aerodynamic loads on hunting stability of high-speed railway vehicles were investigated in this study.A mechanism is suggested to explain the change of hunting behavior due to actions of aerodynamic loads：the aerodynamic loads can change the position of vehicle system（consequently the contact relations）,the wheel/rail normal contact forces,the gravitational restoring forces/moments and the creep forces/moments.A mathematical model for hunting stability incorporating such influences was developed.A computer program capable of incorporating the effects of aerodynamic loads based on the model was written,and the critical speeds were calculated using this program.The dependences of linear and nonlinear critical speeds on suspension parameters considering aerodynamic loads were analyzed by using the orthogonal test method,the results were also compared with the situations without aerodynamic loads.It is shown that the most dominant factors a ff ecting linear and nonlinear critical speeds are different whether the aerodynamic loads considered or not.The damping of yaw damper is the most dominant influencing factor for linear critical speeds,while the damping of lateral damper is most dominant for nonlinear ones.When the influences of aerodynamic loads are considered,the linear critical speeds decrease with the rise of cross wind velocity,whereas it is not the case for the nonlinear critical speeds.The variation trends of critical speeds with suspension parameters can be significantly changed by aerodynamic loads.Combined actions of aerodynamic loads and suspension parameters also a ff ect the critical speeds.The effects of such joint action are more obvious for nonlinear critical speeds.