Study of a Hydraulic Jump in an Asymmetric Trapezoidal Channel with Different Sluice Gates

In this study,the main properties of the hydraulic jump in an asymmetric trapezoidal flume are analyzed experimentally,including the so-called sequent depths,characteristic lengths,and efficiency.In particular,an asymmetric trapezoidal flume with a length of 7 m and a width of 0.304 m is considered,with the bottom of the flume transversely inclined at an angle of m=0.296 and vertical lateral sides.The corresponding inflow Froude number is allowed to range in the interval(1.40<F1<6.11).The properties of this jump are compared to those of hydraulic jumps in channels with other types of cross-sections.A relationship for calculating hydraulic jump efficiency is proposed for the considered flume.For F1>5,the hydraulic jump is found to be more effective than that occurring in triangular and symmetric trapezoidal channels.Also,when■mes>8 and■>5,the hydraulic jump in the asymmetrical trapezoidal channel downstream of a parallelogram sluice gate is completely formed as opposed to the situation where a triangular sluice is considered.

A Generalized Array Factor for Time-Modulated Hexagonal Based Antenna Array Geometry With Novel Trapezoidal Switching

The concept of the time-modulated array has been emerging as an alternative to the complex phase shifters,which lowers the cost of the array feeding network due to the utilization of radio frequency(RF)switches.The various forms of hexagonal antenna array geometries can be used for applications like surveillance tracking in phased array radar and wireless communication systems.This work proposes the generalized array factor(AF)for the hexagonal antenna array geometry based on time modulation.The time modulation in generalized hexagonal geometry can maintain the fixed static amplitude excitation,giving more flexibility over time.Furthermore,a novel trapezoidal switching function is also proposed and applied to the generalized array factor to enable future researchers to use this array factor in the field of advancement to observe how switching schemes like trapezoidal and rectangular affect the array pattern's side lobe level(SLL).The generalized equation can be utilized for the analysis and synthesis of radiation characteristics of the time-modulated hexagonal array(TMHA),time-modulated concentric hexagonal array(TMCHA),time-modulated hexagonal cylindrical array(TMHCA),and time-modulated hexagonal concentric cylindrical array(TMHCCA).The numerical result illustrates the generation of AF of time-modulated hexagonal structures and also shows that the trapezoidal switching sequence outperforms the rectangular switch using the cat swarm optimization(CSO)approach.

Sliding behaviors of the trapezoidal roof rock block under a lateral dynamic disturbance

The surrounding rock of underground space is always affected by external dynamic disturbance from the side position,such as blasting vibration from a stope at the same level or seismic waves from adjacent strata.A series of laboratory tests,numerical simulations and theoretical analyses were carried out in this study to disclose the sliding mechanism of roof rock blocks under lateral disturbance.Firstly,the experiments on trapezoidal key block under various clamping loads and disturbance were conducted,followed by numerical simulations using the fast Lagrangian analysis of continua(FLAC3D).Then,based on the conventional wave propagation model and the classical shear-slip constitutive model,a theoretical model was proposed to capture the relative displacement between blocks and the sliding displacement of the key block.The results indicate that the sliding displacement of the key block increased linearly with the disturbance energy and decreased exponentially with the clamping load when the key block was disturbed to slide(without instability).Meanwhile,when the key block was disturbed to fall,two types of instability process may appear as immediate type or delayed type.In addition,the propagation of stress waves in the block system exhibited obvious low-velocity and lowfrequency characteristics,resulting in the friction reduction effect appearing at the contact interface,which is the essential reason for the sliding of rock blocks.The results can be applied to practical underground engineering and provide valuable guidance for the early detection and prevention of rockfalling disasters.

Composite Fractional Trapezoidal Rule with Romberg Integration

The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator.This would be achieved by first establishing a fractional-order version of the 2-point Trapezoidal rule and then by proposing another fractional-order version of the(n+1)-composite Trapezoidal rule.In particular,the so-called divided-difference formula is typically employed to derive the 2-point Trapezoidal rule,which has accordingly been used to derive a more accurate fractional-order formula called the(n+1)-composite Trapezoidal rule.Additionally,in order to increase the accuracy of the proposed approximations by reducing the true errors,we incorporate the so-called Romberg integration,which is an extrapolation formula of the Trapezoidal rule for integration,into our proposed approaches.Several numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme.

Effect of periodic heat transfer on the transient thermal behavior of a convective-radiative fully wet porous moving trapezoidal fin

A moving trapezoidal profiled convective-radiative porous longitudinal fin wetted in a single-phase fluid is considered in the current article.The periodic variation in the fin base temperature is taken into account along with the temperature sensitive thermal conductivity and convective heat transfer coefficients.The modeled problem,which is resolved into a non-linear partial differential equation(PDE),is made dimensionless and solved by employing the finite difference method(FDM).The results are displayed through graphs and discussed.The effects of amplitude,frequency of oscillation,wet nature,Peclet number,and other relevant quantities on the distribution of temperature through the fin length and with the dimensionless time are investigated.It is deciphered that the periodic heat transfer gives rise to the wavy nature of the fin thermal profile against time.The analysis is beneficial in the design of fin structures for applications like solar collectors,space/airborne applications,and refrigeration industries.

High frequency doubling efficiency THz GaAs Schottky barrier diode based on inverted trapezoidal epitaxial cross-section structure

A high-performance terahertz Schottky barrier diode(SBD)with an inverted trapezoidal epitaxial cross-sectional structure featuring high varactor characteristics and reverse breakdown characteristics is reported in this paper.Inductively coupled plasma dry etching and dissolution wet etching are used to define the profile of the epitaxial layer,by which the voltage-dependent variation trend of the thickness of the metal-semiconductor contact depletion layer is modified.The simulation of the inverted trapezoidal epitaxial cross-section SBD is also conducted to explain the physical mechanism of the electric field and space charge region area.Compared with the normal structure,the grading coefficient M increases from 0.47 to 0.52,and the capacitance modulation ratio(C^(max)/C_(min))increases from 6.70 to 7.61.The inverted trapezoidal epitaxial cross-section structure is a promising approach to improve the variable-capacity ratio by eliminating the accumulation of charge at the Schottky electrode edge.A 190 GHz frequency doubler based on the inverted trapezoidal epitaxial cross-section SBD also shows a doubling efficiency of 35%compared to that 30%of a normal SBD.

Analysis of Friction and Heat Transfer Characteristics of Tubes with Trapezoidal Cut Twisted Tape Inserts

The thermo-hydraulic properties of circular tubes with a twisted tape inside(used accordingly to induce turbulence and enhance heat transfer through the tube wall)are described for Reynolds Numbers ranging from 830 to 1990.Tapes twisted with the three distinct twist ratios are considered,namely,6,4.4 and 3.Air is used as the working fluid in several tests.For the sake of comparison,the standard tube with no insert is also examined.It is shown that in the presence of the twisted tape,the‘frictional factor’,‘Nusselt Number’and the‘thermal performance factor’are much higher than those obtained for the plain tube.Moreover,the tapes having the lowest twist ratio,i.e.,3,are more effective than the others in terms of heat transfer augmentation.The‘thermal performance factor’is greater than one for all the twisted tapes used in the experiments,which confirms the enhanced performances of the heat exchanger and the related savings in terms of total energy.

Text Sentiment Analysis Based on Multi-Layer Bi-Directional LSTM with a Trapezoidal Structure

Sentiment analysis,commonly called opinion mining or emotion artificial intelligence(AI),employs biometrics,computational linguistics,nat-ural language processing,and text analysis to systematically identify,extract,measure,and investigate affective states and subjective data.Sentiment analy-sis algorithms include emotion lexicon,traditional machine learning,and deep learning.In the text sentiment analysis algorithm based on a neural network,multi-layer Bi-directional long short-term memory(LSTM)is widely used,but the parameter amount of this model is too huge.Hence,this paper proposes a Bi-directional LSTM with a trapezoidal structure model.The design of the trapezoidal structure is derived from classic neural networks,such as LeNet-5 and AlexNet.These classic models have trapezoidal-like structures,and these structures have achieved success in the field of deep learning.There are two benefits to using the Bi-directional LSTM with a trapezoidal structure.One is that compared with the single-layer configuration,using the of the multi-layer structure can better extract the high-dimensional features of the text.Another is that using the trapezoidal structure can reduce the model’s parameters.This paper introduces the Bi-directional LSTM with a trapezoidal structure model in detail and uses Stanford sentiment treebank 2(STS-2)for experiments.It can be seen from the experimental results that the trapezoidal structure model and the normal structure model have similar performances.However,the trapezoidal structure model parameters are 35.75%less than the normal structure model.

Modeling of Coupled Heat and Mass Transfer in a Trapezoidal Porous Bed on a Grid

We investigate heat and mass transfer in an isosceles trapezoidal cavity, filled with charcoal considered as a granular porous medium. The Darcy-Brinkman-Forchheimer flow model is coupled to the energy and mass equations with the assumption of non-thermal equilibrium. These equations are discretized by the finite volume method with an offset mesh and then solved by the line-by-line method of Thomas. The coupling between pressure and velocity is obtained by Semi-Implicit Method for Pressure Linked Equations. (SIMPLE) algorithm. The results show that the temperature in the cavity increases when the inclination angle of the sides walls decreases. The 15° inclination is selected as being able to offer better thermal performance in the cookstove combustion chamber.

Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method

In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.

Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems

Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.

Effect of loading rates on crack propagating speed,fracture toughness and energy release rate using single-cleavage trapezoidal open specimen under impact loads

The former studies indicate that loading rates significantly affect dynamic behavior of brittle materials,for instance,the dynamic compressive and tensile strength increase with loading rates.However,there still are many unknown or partially unknown aspects.For example,whether loading rates have effect on crack dynamic propagating behavior(propagation toughness,velocity and arrest,etc).To further explore the effect of loading rates on crack dynamic responses,a large-size single-cleavage trapezoidal open(SCTO)specimen was proposed,and impacting tests using the SCTO specimen under drop plate impact were conducted.Crack propagation gauges(CPGs)were employed in measuring impact loads,crack propagation time and velocities.In order to verify the testing result,the corresponding numerical model was established using explicit dynamic software AUTODYN,and the simulation result is basically consistent with the experimental results.The ABAQUS software was used to calculate the dynamic SIFs.The universal function was calculated by fractal method.The experimental-numerical method was employed in determining initiation toughness and propagation toughness.The results indicate that crack propagating velocities,dynamic fracture toughness and energy release rates increase with loading rates;crack delayed initiation time decreases with loading rates.

Effect of trapezoidal collars as a scour countermeasure around wing-wall abutments

Local scour around bridge abutments is a widespread problem that can result in structural failure. Collars can be used as a countermeasure to reduce the scour depth. In this study, the temporal scour development around a wing-wall abutment was investigated with and without collars. The tests were carried out under clear-water conditions for different abutment lengths, with collars of different sizes placed at the bed level. When no collar was used in the experiments, 70% of the maximum scour depth occurred in less than 2 h. However, when a collar with a width greater than the length of the abutment was used, no scour was observed for up to 200 min from the beginning of the experiments. The results show that an increase in the collar width not only led to a lag time for the onset of scouring but also reduced the maximum scour depth. Moreover, an increased collar width led to a better performance in mitigating scouring around smaller abutments. Generally, the scour depth decreased by 9%-37% with different collar widths.

Control over Surrounding Rocks Deformation of Soft Floor and Whole-Coal Gateways with Trapezoidal Supports

In Gengcun Colliery, Yima Coal Group Co. Ltd.the characteristics of the gateways of thick coal seam and the coal seam is with fully mechanized sublevel caving mining are that the thickness of roof coal seam of gateways is larger, their surrounding rocks are the whole-coal mass and the coal seam is prone to Spontaneous Combustion. With the natural equilibrium arch theory, the reasonable adjacent distance of No.11 mine-type metal supports was calculated in trapezoidal gateways based on these characteristics. Then, in-situ supporting experiments were carried out. The results indicate that under the action of virgin rock stress, the width of broken rocks zone of surrounding rocks is 1.7–2.0 m in return heading and 1.1–1.3 m in going headway. And their surrounding rocks belong to the Ⅳ-type soften rock and the Ⅲ-type common surrounding rock respectively. Therefore, under the movable abutment pressure, the gateways deformation is serious. It is suggested that the designed gateways have to use pre-broadened cross section to suit their deformation. At the same time, the accumulated water on gateway floor must be drained in time. These measures were taken in the 1302 and 1304 coal faces in Gengcun Colliery, and the satisfactory results have been obtained.

Microstructure and Mechanical Strength Predictive Modeling in Al 5052-Trapezoidal Grooved SS 304 Explosive Cladding

Aluminum alloy plates were explosively cladded to stainless steel plates with trapezoidal grooves on the mating surface.The process parameters viz,loading ratio,standoff distance and flyer plate thickness were varied based on the Taguchi analogy.The variation in the process parameters alters the kinetic energy dissipation and the deformation work performed at the interface,and dictates the interfacial wave amplitude and the mechanical strength of the dissimilar explosive clad.The optimum level of process parameters for attaining higher tensile and shear strength is computed by signal-to-noise ratio.Further,a mathematical model is developed for calculating tensile and shear strength of the clad,based on the regression analysis using statistical software Minitab-16,and the level of fit is determined by analysis of variance.

Replacement of annular domain with trapezoidal domain in computational modeling of nonaqueous-phase-liquid dissolution-front propagation problems

In order to simulate the instability phenomenon of a nonaqueous phase liquid(NAPL) dissolution front in a computational model, the intrinsic characteristic length is commonly used to determine the length scale at which the instability of the NAPL dissolution front can be initiated. This will require a huge number of finite elements if a whole NAPL dissolution system is simulated in the computational model. Even though modern supercomputers might be used to tackle this kind of NAPL dissolution problem, it can become prohibitive for commonly-used personal computers to do so. The main purpose of this work is to investigate whether or not the whole NAPL dissolution system of an annular domain can be replaced by a trapezoidal domain, so as to greatly reduce the requirements for computer efforts. The related simulation results have demonstrated that when the NAPL dissolution system under consideration is in a subcritical state, if the dissolution pattern around the entrance of an annulus domain is of interest, then a trapezoidal domain cannot be used to replace an annular domain in the computational simulation of the NAPL dissolution system.However, if the dissolution pattern away from the vicinity of the entrance of an annulus domain is of interest, then a trapezoidal domain can be used to replace an annular domain in the computational simulation of the NAPL dissolution system. When the NAPL dissolution system under consideration is in a supercritical state, a trapezoidal domain cannot be used to replace an annular domain in the computational simulation of the NAPL dissolution system.

Wave Attenuation Properties of Double Trapezoidal Submerged Breakwaters on Flat-Bed

This paper investigates the wave attenuation properties of the double trapezoidal submerged breakwaters on the flat-bed by conducting physical experiments subjected to linear and cnoidal incident waves.The method of Goda's two points is used to separate the heights of incident,reflected and transmitted waves based on the experimental data.The possible factors affecting the wave attenuation properties of the double trapezoidal submerged breakwaters(i.e.,the relative submerged water depth,relative breakwater spacing,wave steepness and relative wave height) are investigated with respect to the reflection and transmission coefficients.The results show that there is a range,within which the breakwater spacing has little impact on the reflection coefficient,and the transmission coefficient tends to be a constant.The influence of the wave steepness is reduced while the breakwater spacing is too large or too small.Within the range of the relative wave height tested in this study,the reflection and transmission coefficients increase and decrease with the relative wave height,respectively.The double trapezoidal submerged breakwaters model indicates a good attenuation effect for larger wave steepness,big relative wave height and within the range of the relative breakwater spacing between 12.5 and 14 according to linear and cnoidal waves.The changes of wave energy spectra between the double submerged breakwaters on the flat-bed are investigated by the fast Fourier transform(FFT) method,showing that wave energy dissipation can be reached more effectively when the relative breakwater spacing is 12.5.

The Application of Trapezoidal Fuzzy AHP on Evaluation Item Weight Calculation of Highway Network Programming Schemes

The fuzzy theory is invited in this paper to calculate weights of evaluation items, which is a very important stage in highway network evaluation. Highway network evaluation is a composite of various attributes that lack of pertinency and comparability, and their commonality is that they are more or less tainted with uncertainty, with different daily decision making problems of diverse intensity, the results can be misleading if the fuzziness of human decision-making is not taken into account. So we introduce fuzzy theory into the measurement of evaluating weights to overcome the issue and Analytic Hierarchy Process in scheme ranking. It is testified to be a more reliable way through the case study of Yangtze River Delta highway network evaluation.

Scattering loss in optical waveguide with trapezoidal cross section

To get the scattering loss of the trapezoidal core waveguide,a new analysis model is presented based on the perturbation equivalent method and modified effective-index method.Firstly,the trapezoidal core waveguide is successfully equivalent to the rectangular one with both restricting the same optical field energy by adopting the perturbation method,Then,the equivalent rectangular core waveguide is decomposed into two slab waveguides by employing the modified effective-index method,The trapezoidal core waveguide scattering theory model is established based on the slab waveguide scattering theory.With the sidewalls surface roughness in the range from 0 to 100 nm in the single model trapezodial core waveguide,optical simulation shows excellent agreement with the results from the scattering loss model presented.The relationship between the dimension and side-wall roughness with the scattering loss can be determined in the trapezoidal core waveguide by the scattering loss model.

Positioning-control Based on Trapezoidal Velocity Curve for High-precision Basis Weight Control Valve

Traditionally, basis weight control valve is driven by a constant frequency pulse signal. Therefore, it is difficult for the valve to match the control precision of basis weight. Dynamic simulation research using Matlab/Simulink indicates that there is much more overshoot and fluctuating during the valve-positioning process. In order to improve the valve-positioning precision, the control method of trapezoidal velocity curve was studied. The simulation result showed that the positioning steady-state error was less than 0.0056%, whereas the peak error was less than 0.016% by using trapezoidal velocity curve at 10 positioning steps. A valve-positioning precision experimental device for the stepper motor of basis weight control valve was developed. The experiment results showed that the error ratio of 1/10000 positioning steps was 4% by using trapezoidal velocity curve. Furthermore, the error ratio of 10/10000 positioning steps was 0.5%. It proved that the valve-positioning precision of trapezoidal velocity curve was much higher than that of the constant frequency pulse signal control strategy. The new control method of trapezoidal velocity curve can satisfy the precision requirement of 10000 steps.