Product of Uniform Distribution and Stirling Numbers of the First Kind

Let Vk=u1u2……uk, ui＇s be i.i.d - U（0, 1）, the p.d.f of 1 - Vk＋l be the GF of the unsigned Stirling numbers of the first kind s（n, k）. This paper discusses the applications of uniform distribution to combinatorial analysis and Riemann zeta function; several identities of Stifling series are established, and the Euler＇s result for ∑ Hn/n^k-l, k ≥ 3 is given a new probabilistic proof.

The Uniform Distribution of SiC Particles in an A356-SiC_p Composite Produced by the Tilt-blade Mechanical Stirring

The tilt-blade mechanical stirring of A356-2.5vol.%SiCp liquid was conducted in a cylindrical crucible to solve the problem of nonhomogeneous radial distribution of SiC particles in conventional straight-blade mechanical stirring. The radial distribution of SiC particles in A356 liquid was studied under the conditions of 25° for horizontal tilt angle α of the blade, 200 r/min for rotating speed of stirrer and 10 mm/s for speed of moving up and down of stirrer. The results show that there exists a nonlinear relationship between circumferential tilt angle β of the blade and radial relative deviation d of SiCp content in A356 liquid. When β is smaller than 20°, the d of SiCp content in A356 liquid between the center and the periphery of crucible decreases with increasing β. Conversely, when β is bigger than 26°, d increases with increasing β. Only when β is about 20°, d can be equal to nought i.e. uniform radial distribution of SiC particles can be realized. It can be seen that the nonhomogeneous radial distribution of SiC particles in conventional straight-blade mechanical stirring can be eliminated in this tilt-blade mechanical stirring of A356-SiCp liquid.

Uniform Distribution Spread-spectrum Modulation Strategy for MMC to Reduce Conducted EMI and Switching Loss

Modular multilevel converters(MMCs)have been widely used owing to their superior performance.However,the rapid switching of power electronics devices causes serious electromagnetic interference(EMI).There are a large number of obvious EMI peaks in the frequency spectrum of the carrier phase-shifted constant-switching-frequency pulse-width modulation(CSFPWM).Spreading the EMI across a wider frequency range can help to reduce the EMI peaks.In this study,we designed a uniform distribution(UD)spread-spectrum modulation technology using the principle of uniform switching frequency distribution and minimum switching loss for MMC.Its feasibility is verified by theoretical derivation and simulation.Then,the effectiveness of UDPWM in reducing the EMI is verified in experiments with a prototype MMC testbed in the lab.Compared with traditional CSFPWM,UDPWM can reduce conducted EMI by 10-20 dB.Also,compared with random PWM(RPWM),UDPWM can improve efficiency and reduce total harmonic distortion(THD)of output voltage and current in MMC.

The monitoring of burden distribution uniformity and even sintering technology

After expanding the capacity by widening the trolley of the No. 3 sintering machine, severe uneven sintering occurred in the trolley＇ s lateral distribution, which affected the output and quality of sinter. In this study, the quantitative evaluation indices of the burden uniform distribution in the width direction of the sintering machine is introduced for the first time. By measuring the temperature of discharged gas, a plane temperature field is constructed. Through analyzing the temperature field and the burden layer＇ s differential thermal equilibrium, a mathematical model for evaluating the indices, which is an online reflection of the degree of uniform distribution, is built. Following the improvements in burden distribution equipment ,the optimization of the ignition system and the dynamic adjustment of the process ,the problem of uneven sintering in lateral distribution has been solved, and the quality and the yield of sinter have been improved.

Strengthening mechanisms based on reinforcement distribution uniformity for particle reinforced aluminum matrix composites

A modified mixed strengthening model was proposed for describing the yield strength of particle reinforced aluminum matrix composites.The strengthening mechanisms of the composites were analyzed based on the microstructures and compression mechanical properties.The distribution uniformity of reinforcements and cooperation relationship among dislocation mechanisms were considered in the modified mixed strengthening model by introducing a distribution uniformity factor u and a cooperation coefficient fc,respectively.The results show that the modified mixed strengthening model can accurately describe the yield strengths of Al3Ti/2024Al composites with a relative deviation less than1.2%,which is much more accurate than other strengthening models.The modified mixed model can also be used to predict the yield strength of Al3Ti/2024Al composites with different fractions of reinforcements.

Assessment of the SiC＿p Distribution Uniformity in SiC＿p／Al Composites Made by Powder Metallurgy

In the manufacture of SiC_p/Al completes via powder metallurgy, the method of assessing the distri-bution uniformity of SiC particles is very important. The SiC_p distribution uniformity on each processingprocedure at the macro- and micro-mixed stages was investigated and the methods for determining mix-ture quality were put forward.

Analysis of distribution uniformity of nodes in wireless sensor networks

Wireless sensor networks have several special characteristics which make against the network coverage, such as shortage of energy, difficulty with energy supply and so on. In order to prolong the lifetime of wireless sensor networks, it is necessary to balance the whole network load. As the energy consumption is related to the situation of nodes, the distribution uniformity must be considered. In this paper, a new model is proposed to evaluate the nodes distribution uniformity by considering some parameters which include compression discrepancy, sparseness discrepancy, self discrepancy, maximum cavity radius and minimum cavity radius. The simulation results show that the presented model could be helpful for measuring the distribution uniformity of nodes scattered randomly in wireless sensor networks.

Optimum Energy Harvesting for Series-Connected Power Sources with Uniform Voltage Distribution

This paper presents a power system architecture where SIPO （series-input parallel-output） converters are controlled to achieve uniform inpt voltages across their respective series-connected power sources while also tracking the system optimum power point; the system optimum power point is the maximum power drawn from the series-connected power sources while their voltages are kept uniformly distributed. With proper uniform input voltage distribution control, near maximum use of the power sources is achieved by employing only one MPT （maximum power tracking） controller instead of multiple MPT controllers dedicated for their respective power sources. Provided that the maximum power point voltages of the input power sources are similar, the resulting system architecture offers near-maximum power transfer with a lower parts count. A feasibility study using computer simulation has successfully validated two SIPO power architectures and their control concepts for optimum power transfer.

Design and Structure Optimization of Plenum Chamber with Airfoil Baffle to Improve Its Outlet Velocity Uniformity in Heat Setting Machines

The plenum chamber of a heat setting machine is a key structure for distributing hot air to different air channels.Its outlet velocity uniformity directly determines the heating uniformity of textiles,significantly affecting the heat setting performance.In a traditional heat setting machine,the outlet airflow maldistribution of the plenum chamber still exists.In this study,a novel plenum chamber with an airfoil baffle was established to improve the uniformity of the velocity distribution at the outlet in a heat setting machine.The structural influence of the plenum chamber on the velocity distribution was investigated using a computational fluid dynamics program.It was found that a chamber with a smaller outlet partition thickness had a better outlet velocity uniformity.The structural optimization of the plenum chamber was conducted using the particle swarm optimization algorithm.The outlet partition thickness,the transverse distance and the longitudinal distance of the optimized plenum chamber were 20,686.2 and 274.6 mm,respectively.Experiments were carried out.The experimental and simulated results showed that the optimized plenum chamber with an airfoil baffle could improve the outlet velocity uniformity.The air outlet velocity uniformity index of the optimized plenum chamber with an airfoil baffle was 4.75%higher than that of the plenum chamber without an airfoil baffle and 5.98%higher than that of the conventional chamber with a square baffle in a commercial heat setting machine.

Optimal Design and Experimental Study of Tightly Coupled SCR Mixers for Diesel Engines

Two types of tightly coupled Selective Catalytic Reduction(SCR)mixers were designed in this study,namely Mixer 1 integrated with an SCR catalyst and Mixer 2 arranged separately.Computational Fluid Dynamics(CFD)software was utilized to model the gas flow,spraying,and pyrolysis reaction of the aqueous urea solution in the tightly coupled SCR system.The parameters of gas flow velocity uniformity and ammonia distribution uniformity were simulated and calculated for both Mixer 1 and Mixer 2 in the tightly coupled SCR system to compare their advantages and disadvantages.The simulation results indicated that Mixer 1 exhibited a gas velocity uniformity of 0.972 and an ammonia distribution uniformity of 0.817,whereas Mixer 2 demonstrated a gas velocity uniformity of 0.988 and an ammonia distribution uniformity of 0.964.Mixer 2 performed better in the simulation analysis.Furthermore,a 3D-printed prototype of Mixer 2 was manufactured and installed on an engine test bench to investigate ammonia distribution uniformity and NOX conversion efficiency.The experimental investigations yielded the following findings:1)The ammonia distribution uniformity of Mixer 2 was measured as 0.976,which closely aligned with the simulation result of 0.964,with a deviation of 1.2%from the model calculations;2)As exhaust temperature increased,the ammonia distribution uniformity gradually improved,while an increase in exhaust flow rate resulted in a decrease in ammonia distribution uniformity;3)When utilizing Mixer 2,the NOX conversion efficiency reached 84.7%at an exhaust temperature of 200°C and 97.4%at 250°C.Within the exhaust temperature range of 300°C to 450°C,the NOX conversion efficiency remained above 98%.This study proposed two innovative mixer structures,conducted simulation analysis,and performed performance testing.The research outcomes indicated that the separately arranged Mixer 2 exhibited superior performance.The tightly coupled SCR systemequippedwith Mixer 2 achieved excellent levels of gas velocity uniformity,ammonia distribution uniformity,and NOX conversion efficiency.These findings can serve as valuable references for the design and development of ultra-low emission after-treatment systems for diesel engines in the field of diesel engine aftertreatment.

Green's functions for uniformly distributed loads acting on an inclined line in a poroelastic layered site

Based on one type of practical Biot＇s equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green＇s functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green＇s functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.

Effect of Different Types of Structural Configuration on Air Distribution in a Compact Purification Device

In some old industrial plants,in order to meet the increasingly strict requirements of pollutant emission limits,it is necessary to install the compact filtration and/or purification devices in a given narrow machine room.Different types of structural configuration might influence air distribution inside these devices.The unreasonable air distribution might lead each part of filtration or purification media to operating at largely different air flow rates.Based on a computational fluid dynamics(CFD)model,this study explores the influence of different outlet positions and different upper heights on the flow field inside chamber.The porous medium model is employed to simulate the air flow in porous media.The changing structural configurations include three positioning cases of the outlet opening and eight height cases of the upper chamber.The root mean square is defined as the non-uniformity coefficient to evaluate the uniformity of air flow distribution.The results show that the farther distance between inlet and outlet openings will bring more uniform air distribution,and the increasing height of upper chamber totally trends to exhibit more uniform air distribution.

Thermal explosion of a reactive gas mixture at constant pressure for non-uniform and uniform temperature systems

In this study,the approximate and exact solutions for the stationary-state of the solids model with neglecting reactant consumption for both non-uniform and uniform temperature systems were applied on gas ignition under a constant pressure condition.The criticality conditions for a slab,an infinite cylinder,and a sphere are determined and discussed using dimensionless temperatures under constant ambient and surface temperatures for a non-uniform temperature system.Exact solution for a Semenov model with convection heat loss was also presented.The solution of the Semenov problem for constant volume or density as a solid and constant pressure were compared.The critical parameterδis calculated and compared with those of Frank-Kamenetskii solution values.The validation of the calculated ignition temperatures with other exact solution and experimental results were offered.The relation between critical parameters form Semenov and F.K.models solution was introduced.

Investigation of distribution uniformity of distributor for biogas slurry application based on CFD analysis

A horizontal distributor for biogas slurry application was proposed to explore the distribution performance through CFD analysis and verified by field test.The rheological properties of biogas slurry were analyzed at first,and key parameters were obtained for the next simulation.The effects of distribution modes,inlet direction,and outlets number on the velocity distribution of flow field and mass flow rate of the horizonal distributor were investigated by CFD simulations.Results of rheological properties indicated that biogas slurry was a non-Newtonian fluid and exhibited shear-thinning behavior.It can be well described by power-law model.The simulation results showed that the geometry of rotor,especially the block numbers was the main factor that determining the fluid movement and trajectory of distribution and output.The mode rotor 1 with two blocks reached the lowest variable coefficient of mass flow rate(4.49%),indicating a higher degree of uniformity.The upward inlet direction would obtain less dead zone,and the distributor with an even outlets number would possess more uniform distribution and less dead zone.The field test of the distributor with rotor 1,upward inlet direction,and 24 outlets has been carried on to verify the simulation results,the variable coefficient of mass flow was 13.06%,which was slightly higher than the simulation(9.23%),but it still within the range of requirement(<15%).The proposed model and the findings of this work are of guiding significance for the study of the utilization technology and equipment of liquid biogas residue.

Accurate characterization of bubble mixing uniformity in a circular region using computational geometric theory

The present study proposes a novel method based on the geometric theory for measuring the distribution of bubble swarms in the circular region of a direct-contact heat exchanger.It was determined that the mixing is uniform when the average distance between the bubble swarms in the unit circular region is approximately 0.9054,which is the standard reference value.The effect of sample size(i.e.,the number of bubbles)on mixing uniformity was investigated to determine the optimal sample size.It was verified that the metric's accuracy and stability were higher with a sample size of 155.Accordingly,it was proposed to increase the sample size by filling irregular bubbles using a segmentation method,which enabled a further accurate assessment of the mixing uniformity.The mixing uniformity of bubble swarms in the circular region and its maximum internal connection with the square region was accurately quantified.It was revealed that the relative average error increased by approximately 3.47% due to information loss.The proposed method was demonstrated to be rotationally invariant.The present study provided novel insights into evaluating mixing uniformity,which would guide enhanced heat transfer and the effective evaluation of the spatiotemporal characteristics of transient mixing in circular regions or the cross-sections of chemical transport pipelines.

A Mathematical Model for Designing Optimal Shape for the Cone Used in Z-flow Type Radial Flow Adsorbers

Nonuniform flow distribution along the radial direction usually exists in a Z-flow type radial flow adsorber,which will decrease the utilization of adsorbent and the switching time and may result in operating safety problems in cryogenic air separation.In order to improve the uniformity of the flow distribution along the radial direction in the adsorber,a differential equation is derived through pressure drop analysis in the Z-flow type radial adsorber with a cone in the middle of the central pipe.The differential equation determines the ideal cross-sectional radii of the cone along the axis.The result shows that the cross-sectional radius of the cone should gradually decrease from 0.3 m to zero along the axis to ensure that the process air is distributed uniformly in the Z-flow type radial flow adsorber and the shape of the cone is a little convex.The flow distribution without the cone in the central pipe is compared under different bed porosities.It is demonstrated that the proposed differential equation can provide theoretical support for designing Z-flow type radial flow adsorbers.

A CLASS OF RANDOM NUMBER GENERATORS BASED ON WEYL SEQUENCE

The generation of good pseudo-random numbers is the base of many important fields in scientific computing, such as randomized algorithms and numerical solution of stochastic differential equations. In this paper, a class of random number generators （RNGs） based on Weyl sequence is proposed. The uniformity of those RNGs is proved theoretically. Statistical and numerical computations show the efficiency of the methods.

A LEVEL-VALUE ESTIMATION METHOD FOR SOLVING GLOBAL OPTIMIZATION

A level-value estimation method was illustrated for solving the constrained global optimization problem. The equivalence between the root of a modified variance equation and the optimal value of the original optimization problem is shown. An alternate algorithm based on the Newton＇s method is presented and the convergence of its implementable approach is proved. Preliminary numerical results indicate that the method is effective.

A Histogram-Based Static-Error Correction Technique for Flash ADCs

High-speed, high-accuracy data converters are attractive for use in most RF applications. Such converters allow direct conversion to occur between the digital baseband and the antenna. However, high speed and high accuracy make the analog components in a converter more complex, and this complexity causes more power to be dissipated than if a traditional approach were taken. A static calibration technique for flash analog-to-digital converters （ADCs） is discussed in this paper. The calibration is based onhistogram test methods, and equivalent errors in the flash ADC comparators are estimated in the digital domain without any significant changes being made to the ADC comparators. In the trimming process, reference voltages are adjusted to compensate for static errors. Behavioral-level simulations of a moderate-resolution 8-bit flash ADC show that, for typical errors, ADC performance is considerably improved by the proposed technique. As a result of calibration, the differential no.nlinearities （DNLs） are reduced on average from 4 LSB to 0.5 LSB, and the integral nonlinearities （INLs） are reduced on average from 4.2 LSB to 0.35 LSB. Implementation issues for this proposed technique are discussed in our subsequent paper, “A Histogram-Based Static-Error Correction Technique for Flash ADCs： Implementation Aspects. ”

Random step maneuver algorithm with normally distributed starting times

The random step maneuver with uniformly distributed starting times has the disadvantage that it cannot focus the starting time on the more efficiency time. It decreases the penetration probability. To resolve this problem, a random step penetration algorithm with normal distribution starting time is proposed. Using the shaping filters and adjoint system method, the miss distance with different starting times can be acquired. According to the penetration standard, the time window ensuring successful penetration can be calculated and it is used as the 3σ bound of the normally distributed random maneuver. Simulation results indicate that the normally distributed random maneuver has higher penetration probability than the uniformly distributed random maneuver.