To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fract...To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.展开更多
The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.Howeve...The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.However,the inversion for the ES model suffers from nonuniqueness and instability,which remain unresolved.To mitigate these issues,we introduce both the minimum and flattest models into the model objective function as an alternative regularization approach in the spherical ES method.We first present the methods,then analyze the accuracy of forward calculation and test the proposed ES method in this study by using synthetic data.The experimental results from simulation data indicate that our proposed regularization effectively suppresses the Backus effect and mitigates inversion instability in the low-latitude region.Finally,we apply the proposed method to magnetic anomaly data from China Seismo-Electromagnetic Satellite-1(CSES-1)and Macao Science Satellite-1(MSS-1)magnetic measurements over Africa by constructing an ES model of the large-scale lithospheric magnetic field.Compared with existing global lithospheric magnetic field models,our ES model demonstrates good consistency at high altitudes and predicts more stable fields at low altitudes.Furthermore,we derive the reduction to the pole(RTP)magnetic anomaly fields and the apparent susceptibility contrast distribution based on the ES model.The latter correlates well with the regional tectonic framework in Africa and surroundings.展开更多
Porous spherical MnCo_(2)S_(4) was synthesized by a simple solvothermal method.Thanks to the well-designedbimetallic composition and the unique porous spherical structure,the MnCo_(2)S_(4) electrode exhibited an excep...Porous spherical MnCo_(2)S_(4) was synthesized by a simple solvothermal method.Thanks to the well-designedbimetallic composition and the unique porous spherical structure,the MnCo_(2)S_(4) electrode exhibited an exceptionalspecific capacitance of 190.8 mAh·g^(-1)at 1 A·g^(-1),greatly higher than the corresponding monometallic sulfides MnS(31.7 mAh·g^(-1))and Co_(3)S_(4)(86.7 mAh·g^(-1)).Impressively,the as-assembled MnCo_(2)S_(4)||porous carbon(PC)hybridsupercapacitor(HSC),showed an outstanding energy density of 76.88 Wh·kg^(-1)at a power density of 374.5 W·kg^(-1),remarkable cyclic performance with a capacity retention of 86.8% after 10000 charge-discharge cycles at 5 A·g^(-1),and excellent Coulombic efficiency of 99.7%.展开更多
Spherical harmonic analysis(SHA)and synthesis(SHS)are widely used by researchers in various fields.Both numerical integration and least-squares methods can be employed for analysis and synthesis.However,these approach...Spherical harmonic analysis(SHA)and synthesis(SHS)are widely used by researchers in various fields.Both numerical integration and least-squares methods can be employed for analysis and synthesis.However,these approaches,when calculated via summation,are computationally intensive.Although the Fast Fourier Transform(FFT)algorithm is efficient,it is traditionally limited to processing global grid points starting from zero longitude.In this paper,we derive an improved FFT algorithm for spherical harmonic analysis and synthesis.The proposed algorithm eliminates the need for grid points to start at zero longitude,thereby expanding the applicability of FFT-based methods.Numerical experiments demonstrate that the new algorithm retains the computational efficiency of conventional FFT while achieving accuracy comparable to the summation method.Consequently,it enables direct harmonic coefficient calculation from global grid data without requiring interpolation to align with zero longitude.Additionally,the algrithm can generate grid points with equi-angular spacing using the improved FFT algorithm,starting from non-zero longitudes.To address the loss of orthogonality in latitude due to discrete spherical grids,a quadrature weight factor-dependent on grid type(e.g.,regular or Gauss grid)-is incorporated,as summarized in this study.展开更多
Significant progress has been made in magnetic and inertial confinement fusion(MCF and ICF)energy development since the achievement of world record parameters on the T3 tokamak in 1968.In MCF,the triple product nτT h...Significant progress has been made in magnetic and inertial confinement fusion(MCF and ICF)energy development since the achievement of world record parameters on the T3 tokamak in 1968.In MCF,the triple product nτT has been elevated from 5×10^(17)m^(-3)·s·keV to 1×10^(21)m^(-3)·s·keV.At the same time,Q=Pfusion/Pheating,has increased from 1×10^(-9)to 0.67,with expectations to exceed 10 in the ITER experiment.In ICF,a Q value of approximately 2.4 was attained with a fusion energy output of around 5.2 MJ.展开更多
EHL-2 is an ENN second-generation device aimed at studying proton-boron(p-11B)fusion reactions in a spherical torus.The design parameters are Ti0~30 keV,Ti/Te>2,n_(e0)~1×10^(20)m^(-3),I_(p)~3 MA,B_(t)~3 T,and...EHL-2 is an ENN second-generation device aimed at studying proton-boron(p-11B)fusion reactions in a spherical torus.The design parameters are Ti0~30 keV,Ti/Te>2,n_(e0)~1×10^(20)m^(-3),I_(p)~3 MA,B_(t)~3 T,andτ_(E)~0.5 s.High ion temperature is one of the standard operation scenarios of EHL-2,aiming to reduce bremsstrahlung radiation while enhancing plasma parameters by elevating the ion to electron temperature ratio.In order to achieve high ion temperature,neutral beam injection is considered the primary heating method during the flat-top phase.The neutral beam system for EHL-2 comprises 3-5 beams with energy/power ranging from 60 keV/4 MW,80-100 keV/10 MW,to 200 keV/3 MW.This work conducts predictive analysis on core transport during the flat-top phase of EHL-2’s high-ion-temperature scenario utilizing ASTRA.The study delineates the potential operating range of core temperature and other parameters given the designed heating capacity.Specifically,the study presents predictive simulations based on CDBM,GLF23,Bohm-gyro-Bohm,and IFSPPPL transport models,evaluating the steady-state power balance,energy confinement time,and impact of various parameters such as plasma density and NBI power on core ion temperature.The simulations demonstrate that the design parameters of the EHL-2 high-Ti scenario,although sensitive to varying transport models,are hopefully attainable as long as adequate ion heating and controlled ion transport levels are ensured.展开更多
Activated carbon(AC)is considered to be an excellent adsorbent due to its high specific surface area and various functional groups.AC powders are available in sizes ranging from 44 to 150 μm.Its particle size prevent...Activated carbon(AC)is considered to be an excellent adsorbent due to its high specific surface area and various functional groups.AC powders are available in sizes ranging from 44 to 150 μm.Its particle size prevent its separation from the soil.Therefore,when AC powder is applied to Cd-contaminated soil,it only reduces the bioavailability of Cd and Cd is not necessarily removed but semi-immobilized.Recovery of adsorbent materials from the soil is therefore a preferred soil remediation method.In order to achieve the separation of Cd from soil and the recovery and reuse of AC,a batch of phenolic resin(PR)-carboxymethyl cellulose(CMC)-activated carbon(AC)composite(PCC-800)with uniform particle diameter(diameter 0.8 mm)and high compressive strength was prepared.PCC-800 composites were made of PR/CMC/AC calcined at 800℃ in a certain ratio.The Barrett-Joyner-Halender results showed that the PCC-800 spheres own a mesoporous structure.The compressive strength of PCC-800 pellets was 20.6 N.After first adsorption cycle,total Cd in the soil decreased by 52.18%while bioavailable Cd decreased to 25.68%of the original soil.After three cycles,the recovery rates of PCC-800 were 90.37%and the adsorption regeneration was 72.73%.The PCC-800 immobilized Cd by adsorption,precipitation and complexation reaction.This study demonstrates the potential for developing adsorbents that are both easily separable from soil and highly effective in adsorption.展开更多
The EXL-50U is China’s first large spherical torus device with a toroidal field reaching 1 T.The major radius of the EXL-50U ranges from 0.6 m to 0.8 m,with an aspect ratio of 1.4−1.8.The goal of plasma current in th...The EXL-50U is China’s first large spherical torus device with a toroidal field reaching 1 T.The major radius of the EXL-50U ranges from 0.6 m to 0.8 m,with an aspect ratio of 1.4−1.8.The goal of plasma current in the first experimental phase is 500 kA,and in the future second phase,the goal of plasma current is 1 MA.On the EXL-50U project,the ENN fusion team expeditiously accomplished a series of comprehensive tasks including physical and engineering design,main component construction installation,and system commissioning,all within a mere eighteen-month timeframe.In the experiments of 2024,the EXL-50U achieved a 500 kA limiter configuration discharge using ECRH(Electron Cyclotron Resonance Heating)for non-inductive current start-up and a current ramp-up with the synergetic effect of ECRH and central solenoid(CS).Preliminary divertor configuration plasmas were also obtained under 200 kA plasma current.The core ion temperature of 1 keV was achieved with low-power NBI heating,and the energy confinement time of 30 ms was reached with Ohmic heating in the flat-top phase.The current and future experiments of EXL-50U will strongly support the physical design and operational scenarios of EHL-2 in the areas of current drive,high ion temperature exploration,energy transport and confinement,and hydrogen-boron physical characteristics.At the same time,the experience in the design,construction,and commissioning of the engineering,heating,and diagnostics systems on EXL-50U is also very beneficial for enhancing the feasibility of the engineering design for EHL-2.展开更多
ENN He Long-2(EHL-2)is the next-generation large mega-Ampere(MA)spherical torus(ST)proposed and funded by the ENN company.The design parameters are:Ti0>30 keV,n_(e0)~1×10^(20)m^(-3),Ip~3 MA,Bt~3 T.One of the b...ENN He Long-2(EHL-2)is the next-generation large mega-Ampere(MA)spherical torus(ST)proposed and funded by the ENN company.The design parameters are:Ti0>30 keV,n_(e0)~1×10^(20)m^(-3),Ip~3 MA,Bt~3 T.One of the biggest challenges of EHL-2 is how to achieve several MA current flat-tops with limited voltage-seconds(Vs)of the center solenoid(CS)coils.In order to minimize the consumption of Vs,a fully non-inductive start-up by electron cyclotron resonance heating(ECRH)will be applied in EHL-2.The ramp-up phase will be accomplished with the synergetic mode between the CS and non-inductive methods.The strategy of non-inductive start-up and ramp-up with synergetic mode has been verified on EXL-50U’s experiments.Based on this strategy,numerical simulations indicate the feasibility of EHL-2 achieving 3 MA plasma current.A high-performance steady-state scenario with Ip~1.5 MA is also designed.In this scenario,the bootstrap current fraction fBS>70%,the safety factor q at the magnetic axis q0>2,the minimum safety factor qmin>1,the poloidal betaβp>3 and normalized betaβN>2.3.Each design iteration integrates the validation of physical models with the constraints of engineering implementation,gradually optimizing the performance of the heating and current drive(H&CD)systems.Numerical simulation results for general auxiliary H&CD systems such as neutral beam injection(NBI),electron cyclotron(EC)wave,ion cyclotron wave(ICW),and lower hybrid wave(LHW)are presented.These simulation results ensure that the 31 MW H&CD systems comprehensively cover all scenarios while maintaining engineering feasibility.展开更多
Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spher...Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spherical attractor is proposed,which is constructed using spherical coordinates.Dynamical analyses reveal that the hyperchaotic map exhibits global hyperchaos and high complexity,making it capable of generating more complex chaotic sequences suitable for image encryption.A hybrid encryption scheme based on a hyperchaotic map is proposed for two-dimensional(2D)images,three-dimensional(3D)models,and 3D point clouds.Firstly,the pixels of 2D image and the coordinate data of 3D image are fused into a plaintext cube,which is combined with Hash-512 to obtain the initial value of the hyperchaotic map.Chaotic sequences are utilized for cube space internal confusion and dynamic cross-diffusion.The encrypted images demonstrate high information entropy,and the test results show that the encryption scheme effectively protects the images.The proposed hybrid image encryption scheme provides an efficient solution for securing various types of images.展开更多
Global security threats have motivated organizations to adopt robust and reliable security systems to ensure the safety of individuals and assets.Biometric authentication systems offer a strong solution.However,choosi...Global security threats have motivated organizations to adopt robust and reliable security systems to ensure the safety of individuals and assets.Biometric authentication systems offer a strong solution.However,choosing the best security system requires a structured decision-making framework,especially in complex scenarios involving multiple criteria.To address this problem,we develop a novel quantum spherical fuzzy technique for order preference by similarity to ideal solution(QSF-TOPSIS)methodology,integrating quantum mechanics principles and fuzzy theory.The proposed approach enhances decision-making accuracy,handles uncertainty,and incorporates criteria relationships.Criteria weights are determined using spherical fuzzy sets,and alternatives are ranked through the QSFTOPSIS framework.This comprehensive multi-criteria decision-making(MCDM)approach is applied to identify the optimal gate security system for an organization,considering critical factors such as accuracy,cost,and reliability.Additionally,the study compares the proposed approach with other established MCDM methods.The results confirm the alignment of rankings across these methods,demonstrating the robustness and reliability of the QSF-TOPSIS framework.The study identifies the infrared recognition and identification system(IRIS)as the most effective,with a score value of 0.5280 and optimal security system among the evaluated alternatives.This research contributes to the growing literature on quantum-enhanced decision-making models and offers a practical framework for solving complex,real-world problems involving uncertainty and ambiguity.展开更多
Direct numerical simulations of a uniform flow past a fixed spherical droplet are performed to investigate the parameter range within which the axisymmetric flow becomes unstable due to an external flow bifurcation.Th...Direct numerical simulations of a uniform flow past a fixed spherical droplet are performed to investigate the parameter range within which the axisymmetric flow becomes unstable due to an external flow bifurcation.The hydrodynamics is governed by three dimensionless parameters:the viscosity ratioμ*,the external Reynolds numbers Re^(e),and internal Reynolds numbers Re^(i),respectively.The drop-to-fluid density ratio is related to these parameters asρ*=μ*Re^(i)/Re^(e).This study focuses on highly viscous droplets withμ*≥5,where wake instability is driven by the vorticity flux transferred from the droplet surface into the surrounding fluid.By analysing the wake structure,we confirm that the onset of the external bifurcation is linked to the tilting of the azimuthal vorticityωϕ,in the wake and that the bifurcation occurs once the isocontours ofωϕalign nearly perpendicular to the symmetry axis.We propose an empirical criterion for predicting the onset of the external bifurcation,formulated in terms of the maximum vorticity on the external side of the droplet surface.This criterion is applicable for sufficiently high Re^(i) and holds over a wide range ofμ*and Re^(e).Additionally,we examine the bifurcation sequence for two specific external Reynolds numbers,Re^(e)=300 and Re^(e)=500,and show that,beyond a critical viscosity ratio,the axisymmetric wake first transitions to a steady planar-symmetric state before undergoing a secondary Hopf bifurcation.Finally,we highlight the influence of Re^(i) on external bifurcation and show that,at moderate Re^(i),wake instability may set in at a lower vorticity threshold than predicted by our criterion.These findings provide new insights into the external flow bifurcation of viscous droplets.展开更多
EHL-2 is a compact,high-field spherical tokamak designed to explore the potential of an advanced p-11B nuclear fusion reactor.Due to its high plasma current and thermal energy,it is crucial to mitigate the impact asso...EHL-2 is a compact,high-field spherical tokamak designed to explore the potential of an advanced p-11B nuclear fusion reactor.Due to its high plasma current and thermal energy,it is crucial to mitigate the impact associated with disruptions to ensure the safe operation of EHL-2.This paper evaluates the performance requirements of the disruption prediction system on EHL-2,with a particular focus on applying generalizable knowledge transfer from existing devices to future ones.Furthermore,the key characteristics of disruption mitigation strategies are analyzed,and their overall mitigation performance on EHL-2 is assessed.This insight provides valuable guidance for optimizing the engineering design of EHL-2 and identifying its optimal operational regime.展开更多
EHL-2 spherical torus(ST)is one of the key steps of p-^(11)B(proton-boron or hydrogen-boron)fusion energy research in ENN.The fusion produced energy is carried mainly by alpha particles of average energy 3 MeV,which i...EHL-2 spherical torus(ST)is one of the key steps of p-^(11)B(proton-boron or hydrogen-boron)fusion energy research in ENN.The fusion produced energy is carried mainly by alpha particles of average energy 3 MeV,which ideally can be converted to electricity with high efficiency(>80%).However,there exist serious difficulties to realize such conversion in a fusion device,due to the high energy density and high voltage required.To comprehensively describe the progress of the EHL-2 physics design,this work presents preliminary considerations of approaches for achieving energy conversion,highlighting critical issues for further investigation.Specifically,we provide an initial simulation of alpha particle extraction in the EHL-2 ST configuration as a starting point for p-^(11)B fusion energy conversion.展开更多
The EHL-2 spherical torus is designed to demonstrate proton-boron(p-11B)fusion within a compact spherical tokamak.Its planned heating system includes a negative ion-based neutral beam injection(N-NBI),two positive ion...The EHL-2 spherical torus is designed to demonstrate proton-boron(p-11B)fusion within a compact spherical tokamak.Its planned heating system includes a negative ion-based neutral beam injection(N-NBI),two positive ion-based NBI systems(P-NBI),electron cyclotron resonance heating(ECRH),ion cyclotron resonance heating(ICRH),and high harmonic fast wave(HHFW),with a total power output of 31 MW.According to scaling law estimates,the device is capable of achieving H-mode operation.The plasma density,,n_(e,min)at the minimum L-H power threshold,P_(lh),is estimated to be 4.4×10^(19)m^(-3).The pedestal parameters were calculated using the REPED model.Assuming B as the primary impurity ion,the predicted pedestal width and height are lower compared to the typical case with carbon impurities.The pedestal collisionality for EHL-2 is estimated to range between 0.06 and 0.17,indicating the potential for significant energy loss due to edge localized modes(ELMs).The heat flux on the divertor plate has been calculated using the JOREK code.The peak heat fluxes during ELM bursts are approximately 31.0 MW/m^(2)at the lower inboard target and 39.5 MW/m^(2)at the lower outboard target.A preliminary design of the resonant magnetic perturbation(RMP)coils has been completed to both control type-I ELMs and correct error fields.The system comprises 16 coils arranged into 24 pairs.In ELM control mode,a 14/2 component is generated at 1.7 G/kAt,with a current of 4.9 kA required to achieveσChirikow=1 at the resonant surface,where the normalized poloidal magnetic flux is 0.85.In error field(EF)modulation mode,2/1 and 3/1 components are generated at 3.5 G/kAt and 2.8 G/kAt,respectively.展开更多
We study the confinement of a spinless charged particle to a spherical quantum dot under the influence of a linear electric field.The spherical quantum dot is described by a short-range potential given by the power-ex...We study the confinement of a spinless charged particle to a spherical quantum dot under the influence of a linear electric field.The spherical quantum dot is described by a short-range potential given by the power-exponential potential.Then,by analysing the region near the spherical quantum dot centre,we discuss two cases where the energy levels can be obtained for s-waves and how the linear electric field modifies the spectrum of energy of the spherical quantum dot.展开更多
Magnetic levitation of the fusion target by coating a thin MgB_(2)superconducting shell on its outer surface has recently been proposed in inertial confinement fusion(ICF)to realize a noncontact support of the target ...Magnetic levitation of the fusion target by coating a thin MgB_(2)superconducting shell on its outer surface has recently been proposed in inertial confinement fusion(ICF)to realize a noncontact support of the target at~20 K to boost the implosion performance and fusion yield.To avoid possible effects on target ablation,the coated MgB_(2)shell is anticipated to be as thin as possible while fulfilling the target levitation requirements.Under this circumstance,the fabrication of an MgB_(2)shell with reduced thickness has been explored using a hybrid physical-chemical vapour deposition method.By gradually decreasing the deposition time,a set of MgB_(2)shells were grown on 1 mm diameter Si_(3)N_(4)spheres with the thickness reducing from 720 nm to 200 nm.The spherical shells all have a polycrystalline structure characterized by closely packed hexagonal grains,with both the grain size and thickness diminishing as the shell thickness decreases.The superconducting transition temperature Tcof the shells,as determined by both resistance and magnetization measurements,is in the range of 38-40 K and all shells exhibit ideal diamagnetism at low temperatures.For the thinnest shell of 200 nm,the superconducting critical current density Jcat 20 K reaches 8.0×10^(6)A/cm^(2)and 2.1×10^(5)A/cm^(2)under zero and 2 T applied field,respectively.The results indicate that it is experimentally feasible to fabricate MgB_(2)spherical shells with a thickness as low as 200 nm while maintaining the high Tcand Jc,thereby taking a further step towards the application of the shell in superconducting magnetic levitation for ICF.展开更多
A dimensionless load-displacement model based on the energy-density equivalence principle is proposed to obtain the stress-strain relationships of metallic materials under monotonic indentations with various diameters...A dimensionless load-displacement model based on the energy-density equivalence principle is proposed to obtain the stress-strain relationships of metallic materials under monotonic indentations with various diameters of spherical indenters.Finite element simulations are carried out to verify the constitutive relations from the new model,involving indentations made with various spherical indenters.For each indenter,some quasi-static spherical indentation tests are conducted on the materials with 40 preset constitutive relationships.The results indicate that the stress-strain curves predicted by the model align with the preset curves under 200 loading conditions.Moreover,the goodness-of-fit between the predicted stress-strain curves and the preset curves exceeds0.96 for all indenters and materials.In the end,the indentation tests are conducted by the spherical indenters with the diameters of 1.587 mm for fifteen metallic materials and1 mm for eight metallic materials.The results show that the stress-strain curves obtained by the spherical indentation based on the new model closely match those obtained from the uniaxial tensile tests.The relative errors for both the proof strength at 0.2%plastic extension and the tensile strength are below 5%.展开更多
A series of CoS_(2-x)Se_(x)(x=0.05,0.1,0.2,0.3,and 2)composite catalysts were synthesized on carbon fiber paper via the hydrothermal method with Se doping.By precisely controlling the reaction temperature and Se dopin...A series of CoS_(2-x)Se_(x)(x=0.05,0.1,0.2,0.3,and 2)composite catalysts were synthesized on carbon fiber paper via the hydrothermal method with Se doping.By precisely controlling the reaction temperature and Se doping level,a hollow spherical catalyst structure composed of CoSSe was successfully synthesized,which exhibited exceptional activity for hydrogen evolution in acidic solutions.The influences of Se doping on the microstructure and catalytic mechanism of hydrogen evolution reaction(HER)of these composites were systematically investigated.The experimental results reveal that the hollow spherical sample displays an overpotential value of 143 mV along with a Tafel slope value of 69.8 mV·dec^(-1)at a current density of 10 mA·cm^(-2)in an acid aqueous solution.Furthermore,it demonstrates remarkable cycling stability after undergoing 3000 cycles.The comprehensive analysis indicates that Se doping optimizes the electronic structure and enhances conductivity,meanwhile the unique hollow spherical architecture increases active sites for HER and significantly improves overall electrocatalytic performance.展开更多
This study proposes a numerically efficient technique for computing the far-field scattered by a spherical target placed near the seabed.The bottom is supposed to be a homogeneous liquid attenuating half-space.The tra...This study proposes a numerically efficient technique for computing the far-field scattered by a spherical target placed near the seabed.The bottom is supposed to be a homogeneous liquid attenuating half-space.The transmitter and receiver are situated at different points of a homogeneous water half-space.The distances between the transmitter,receiver,and object of interest are assumed to be much larger than the acoustic wavelength in water.The scattered far-field is ascertained using Hackman and Sammelmann’s general approach.The arising scattering coefficients of a sphere are assessed using the steepest descent approach.The branch cut contribution is also considered.The obtained formulas for the form-function can be used for acoustically rigid or soft scatterers,as well as elastic targets or spherical elastic shells.Numerical simulations are conducted for an acoustically rigid sphere.Asymptotic expressions for the scattering coefficients allow a decrease in the number of summands in the formula for the target strength and a significant reduction in computational time.展开更多
基金funded by the project of the Major Scientific and Technological Projects of CNOOC in the 14th Five-Year Plan(No.KJGG2022-0701)the CNOOC Research Institute(No.2020PFS-03).
文摘To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures.
基金supported by the National Natural Science Foundation of China(Grant Nos.42250103 and 42174090)the Opening Fund of Key Laboratory of Geological Survey and Evaluation of Ministry of Education(Grant No.GLAB2023ZR02)the MOST Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources(Grant No.MSFGPMR2022-4).
文摘The equivalent source(ES)method in the spherical coordinate system has been widely applied to processing,reduction,field modeling,and geophysical and geological interpretation of satellite magnetic anomaly data.However,the inversion for the ES model suffers from nonuniqueness and instability,which remain unresolved.To mitigate these issues,we introduce both the minimum and flattest models into the model objective function as an alternative regularization approach in the spherical ES method.We first present the methods,then analyze the accuracy of forward calculation and test the proposed ES method in this study by using synthetic data.The experimental results from simulation data indicate that our proposed regularization effectively suppresses the Backus effect and mitigates inversion instability in the low-latitude region.Finally,we apply the proposed method to magnetic anomaly data from China Seismo-Electromagnetic Satellite-1(CSES-1)and Macao Science Satellite-1(MSS-1)magnetic measurements over Africa by constructing an ES model of the large-scale lithospheric magnetic field.Compared with existing global lithospheric magnetic field models,our ES model demonstrates good consistency at high altitudes and predicts more stable fields at low altitudes.Furthermore,we derive the reduction to the pole(RTP)magnetic anomaly fields and the apparent susceptibility contrast distribution based on the ES model.The latter correlates well with the regional tectonic framework in Africa and surroundings.
文摘Porous spherical MnCo_(2)S_(4) was synthesized by a simple solvothermal method.Thanks to the well-designedbimetallic composition and the unique porous spherical structure,the MnCo_(2)S_(4) electrode exhibited an exceptionalspecific capacitance of 190.8 mAh·g^(-1)at 1 A·g^(-1),greatly higher than the corresponding monometallic sulfides MnS(31.7 mAh·g^(-1))and Co_(3)S_(4)(86.7 mAh·g^(-1)).Impressively,the as-assembled MnCo_(2)S_(4)||porous carbon(PC)hybridsupercapacitor(HSC),showed an outstanding energy density of 76.88 Wh·kg^(-1)at a power density of 374.5 W·kg^(-1),remarkable cyclic performance with a capacity retention of 86.8% after 10000 charge-discharge cycles at 5 A·g^(-1),and excellent Coulombic efficiency of 99.7%.
基金supported by The National Natural Science Foundation of China(42374004).
文摘Spherical harmonic analysis(SHA)and synthesis(SHS)are widely used by researchers in various fields.Both numerical integration and least-squares methods can be employed for analysis and synthesis.However,these approaches,when calculated via summation,are computationally intensive.Although the Fast Fourier Transform(FFT)algorithm is efficient,it is traditionally limited to processing global grid points starting from zero longitude.In this paper,we derive an improved FFT algorithm for spherical harmonic analysis and synthesis.The proposed algorithm eliminates the need for grid points to start at zero longitude,thereby expanding the applicability of FFT-based methods.Numerical experiments demonstrate that the new algorithm retains the computational efficiency of conventional FFT while achieving accuracy comparable to the summation method.Consequently,it enables direct harmonic coefficient calculation from global grid data without requiring interpolation to align with zero longitude.Additionally,the algrithm can generate grid points with equi-angular spacing using the improved FFT algorithm,starting from non-zero longitudes.To address the loss of orthogonality in latitude due to discrete spherical grids,a quadrature weight factor-dependent on grid type(e.g.,regular or Gauss grid)-is incorporated,as summarized in this study.
文摘Significant progress has been made in magnetic and inertial confinement fusion(MCF and ICF)energy development since the achievement of world record parameters on the T3 tokamak in 1968.In MCF,the triple product nτT has been elevated from 5×10^(17)m^(-3)·s·keV to 1×10^(21)m^(-3)·s·keV.At the same time,Q=Pfusion/Pheating,has increased from 1×10^(-9)to 0.67,with expectations to exceed 10 in the ITER experiment.In ICF,a Q value of approximately 2.4 was attained with a fusion energy output of around 5.2 MJ.
基金supported by the ENN Group and ENN Energy Research Institutesupported by National Natural Science Foundation of China(No.12475210).
文摘EHL-2 is an ENN second-generation device aimed at studying proton-boron(p-11B)fusion reactions in a spherical torus.The design parameters are Ti0~30 keV,Ti/Te>2,n_(e0)~1×10^(20)m^(-3),I_(p)~3 MA,B_(t)~3 T,andτ_(E)~0.5 s.High ion temperature is one of the standard operation scenarios of EHL-2,aiming to reduce bremsstrahlung radiation while enhancing plasma parameters by elevating the ion to electron temperature ratio.In order to achieve high ion temperature,neutral beam injection is considered the primary heating method during the flat-top phase.The neutral beam system for EHL-2 comprises 3-5 beams with energy/power ranging from 60 keV/4 MW,80-100 keV/10 MW,to 200 keV/3 MW.This work conducts predictive analysis on core transport during the flat-top phase of EHL-2’s high-ion-temperature scenario utilizing ASTRA.The study delineates the potential operating range of core temperature and other parameters given the designed heating capacity.Specifically,the study presents predictive simulations based on CDBM,GLF23,Bohm-gyro-Bohm,and IFSPPPL transport models,evaluating the steady-state power balance,energy confinement time,and impact of various parameters such as plasma density and NBI power on core ion temperature.The simulations demonstrate that the design parameters of the EHL-2 high-Ti scenario,although sensitive to varying transport models,are hopefully attainable as long as adequate ion heating and controlled ion transport levels are ensured.
文摘Activated carbon(AC)is considered to be an excellent adsorbent due to its high specific surface area and various functional groups.AC powders are available in sizes ranging from 44 to 150 μm.Its particle size prevent its separation from the soil.Therefore,when AC powder is applied to Cd-contaminated soil,it only reduces the bioavailability of Cd and Cd is not necessarily removed but semi-immobilized.Recovery of adsorbent materials from the soil is therefore a preferred soil remediation method.In order to achieve the separation of Cd from soil and the recovery and reuse of AC,a batch of phenolic resin(PR)-carboxymethyl cellulose(CMC)-activated carbon(AC)composite(PCC-800)with uniform particle diameter(diameter 0.8 mm)and high compressive strength was prepared.PCC-800 composites were made of PR/CMC/AC calcined at 800℃ in a certain ratio.The Barrett-Joyner-Halender results showed that the PCC-800 spheres own a mesoporous structure.The compressive strength of PCC-800 pellets was 20.6 N.After first adsorption cycle,total Cd in the soil decreased by 52.18%while bioavailable Cd decreased to 25.68%of the original soil.After three cycles,the recovery rates of PCC-800 were 90.37%and the adsorption regeneration was 72.73%.The PCC-800 immobilized Cd by adsorption,precipitation and complexation reaction.This study demonstrates the potential for developing adsorbents that are both easily separable from soil and highly effective in adsorption.
基金supported by ENN Group and ENN Energy Research Institute.
文摘The EXL-50U is China’s first large spherical torus device with a toroidal field reaching 1 T.The major radius of the EXL-50U ranges from 0.6 m to 0.8 m,with an aspect ratio of 1.4−1.8.The goal of plasma current in the first experimental phase is 500 kA,and in the future second phase,the goal of plasma current is 1 MA.On the EXL-50U project,the ENN fusion team expeditiously accomplished a series of comprehensive tasks including physical and engineering design,main component construction installation,and system commissioning,all within a mere eighteen-month timeframe.In the experiments of 2024,the EXL-50U achieved a 500 kA limiter configuration discharge using ECRH(Electron Cyclotron Resonance Heating)for non-inductive current start-up and a current ramp-up with the synergetic effect of ECRH and central solenoid(CS).Preliminary divertor configuration plasmas were also obtained under 200 kA plasma current.The core ion temperature of 1 keV was achieved with low-power NBI heating,and the energy confinement time of 30 ms was reached with Ohmic heating in the flat-top phase.The current and future experiments of EXL-50U will strongly support the physical design and operational scenarios of EHL-2 in the areas of current drive,high ion temperature exploration,energy transport and confinement,and hydrogen-boron physical characteristics.At the same time,the experience in the design,construction,and commissioning of the engineering,heating,and diagnostics systems on EXL-50U is also very beneficial for enhancing the feasibility of the engineering design for EHL-2.
基金supported by ENN Group and ENN Energy Research Institute.The authors would like to express their gratitude for the contributions of the ENN fusion team and collaborators,such as Tiantian Sun,Haojie Ma,and Yong Guo,in supporting these endeavours.The authors also acknowledge the support of the National SuperComputer Center in Tianjin and Beijing PARATERA Tech Corp.,Ltd.,for providing HPC resources that have contributed to the research results reported in this paper.This work was partly supported by National Natural Science Fundation of China(Nos.12375215 and 12475210).
文摘ENN He Long-2(EHL-2)is the next-generation large mega-Ampere(MA)spherical torus(ST)proposed and funded by the ENN company.The design parameters are:Ti0>30 keV,n_(e0)~1×10^(20)m^(-3),Ip~3 MA,Bt~3 T.One of the biggest challenges of EHL-2 is how to achieve several MA current flat-tops with limited voltage-seconds(Vs)of the center solenoid(CS)coils.In order to minimize the consumption of Vs,a fully non-inductive start-up by electron cyclotron resonance heating(ECRH)will be applied in EHL-2.The ramp-up phase will be accomplished with the synergetic mode between the CS and non-inductive methods.The strategy of non-inductive start-up and ramp-up with synergetic mode has been verified on EXL-50U’s experiments.Based on this strategy,numerical simulations indicate the feasibility of EHL-2 achieving 3 MA plasma current.A high-performance steady-state scenario with Ip~1.5 MA is also designed.In this scenario,the bootstrap current fraction fBS>70%,the safety factor q at the magnetic axis q0>2,the minimum safety factor qmin>1,the poloidal betaβp>3 and normalized betaβN>2.3.Each design iteration integrates the validation of physical models with the constraints of engineering implementation,gradually optimizing the performance of the heating and current drive(H&CD)systems.Numerical simulation results for general auxiliary H&CD systems such as neutral beam injection(NBI),electron cyclotron(EC)wave,ion cyclotron wave(ICW),and lower hybrid wave(LHW)are presented.These simulation results ensure that the 31 MW H&CD systems comprehensively cover all scenarios while maintaining engineering feasibility.
基金Project supported by the Basic Scientific Research Projects of Department of Education of Liaoning Province,China(Grant No.LJ212410152049)the Technological Innovation Projects in the field of artificial intelligence of Liaoning Province,China(Grant No.2023JH26/10300011)。
文摘Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spherical attractor is proposed,which is constructed using spherical coordinates.Dynamical analyses reveal that the hyperchaotic map exhibits global hyperchaos and high complexity,making it capable of generating more complex chaotic sequences suitable for image encryption.A hybrid encryption scheme based on a hyperchaotic map is proposed for two-dimensional(2D)images,three-dimensional(3D)models,and 3D point clouds.Firstly,the pixels of 2D image and the coordinate data of 3D image are fused into a plaintext cube,which is combined with Hash-512 to obtain the initial value of the hyperchaotic map.Chaotic sequences are utilized for cube space internal confusion and dynamic cross-diffusion.The encrypted images demonstrate high information entropy,and the test results show that the encryption scheme effectively protects the images.The proposed hybrid image encryption scheme provides an efficient solution for securing various types of images.
文摘Global security threats have motivated organizations to adopt robust and reliable security systems to ensure the safety of individuals and assets.Biometric authentication systems offer a strong solution.However,choosing the best security system requires a structured decision-making framework,especially in complex scenarios involving multiple criteria.To address this problem,we develop a novel quantum spherical fuzzy technique for order preference by similarity to ideal solution(QSF-TOPSIS)methodology,integrating quantum mechanics principles and fuzzy theory.The proposed approach enhances decision-making accuracy,handles uncertainty,and incorporates criteria relationships.Criteria weights are determined using spherical fuzzy sets,and alternatives are ranked through the QSFTOPSIS framework.This comprehensive multi-criteria decision-making(MCDM)approach is applied to identify the optimal gate security system for an organization,considering critical factors such as accuracy,cost,and reliability.Additionally,the study compares the proposed approach with other established MCDM methods.The results confirm the alignment of rankings across these methods,demonstrating the robustness and reliability of the QSF-TOPSIS framework.The study identifies the infrared recognition and identification system(IRIS)as the most effective,with a score value of 0.5280 and optimal security system among the evaluated alternatives.This research contributes to the growing literature on quantum-enhanced decision-making models and offers a practical framework for solving complex,real-world problems involving uncertainty and ambiguity.
基金supported by the Deutsche Forschungsgemeinschaft(DFG)(Grant No.501298479)。
文摘Direct numerical simulations of a uniform flow past a fixed spherical droplet are performed to investigate the parameter range within which the axisymmetric flow becomes unstable due to an external flow bifurcation.The hydrodynamics is governed by three dimensionless parameters:the viscosity ratioμ*,the external Reynolds numbers Re^(e),and internal Reynolds numbers Re^(i),respectively.The drop-to-fluid density ratio is related to these parameters asρ*=μ*Re^(i)/Re^(e).This study focuses on highly viscous droplets withμ*≥5,where wake instability is driven by the vorticity flux transferred from the droplet surface into the surrounding fluid.By analysing the wake structure,we confirm that the onset of the external bifurcation is linked to the tilting of the azimuthal vorticityωϕ,in the wake and that the bifurcation occurs once the isocontours ofωϕalign nearly perpendicular to the symmetry axis.We propose an empirical criterion for predicting the onset of the external bifurcation,formulated in terms of the maximum vorticity on the external side of the droplet surface.This criterion is applicable for sufficiently high Re^(i) and holds over a wide range ofμ*and Re^(e).Additionally,we examine the bifurcation sequence for two specific external Reynolds numbers,Re^(e)=300 and Re^(e)=500,and show that,beyond a critical viscosity ratio,the axisymmetric wake first transitions to a steady planar-symmetric state before undergoing a secondary Hopf bifurcation.Finally,we highlight the influence of Re^(i) on external bifurcation and show that,at moderate Re^(i),wake instability may set in at a lower vorticity threshold than predicted by our criterion.These findings provide new insights into the external flow bifurcation of viscous droplets.
基金supported by the ENN Group,the ENN Energy Research Institute and National Natural Science Foundation of China(No.12205122).
文摘EHL-2 is a compact,high-field spherical tokamak designed to explore the potential of an advanced p-11B nuclear fusion reactor.Due to its high plasma current and thermal energy,it is crucial to mitigate the impact associated with disruptions to ensure the safe operation of EHL-2.This paper evaluates the performance requirements of the disruption prediction system on EHL-2,with a particular focus on applying generalizable knowledge transfer from existing devices to future ones.Furthermore,the key characteristics of disruption mitigation strategies are analyzed,and their overall mitigation performance on EHL-2 is assessed.This insight provides valuable guidance for optimizing the engineering design of EHL-2 and identifying its optimal operational regime.
文摘EHL-2 spherical torus(ST)is one of the key steps of p-^(11)B(proton-boron or hydrogen-boron)fusion energy research in ENN.The fusion produced energy is carried mainly by alpha particles of average energy 3 MeV,which ideally can be converted to electricity with high efficiency(>80%).However,there exist serious difficulties to realize such conversion in a fusion device,due to the high energy density and high voltage required.To comprehensively describe the progress of the EHL-2 physics design,this work presents preliminary considerations of approaches for achieving energy conversion,highlighting critical issues for further investigation.Specifically,we provide an initial simulation of alpha particle extraction in the EHL-2 ST configuration as a starting point for p-^(11)B fusion energy conversion.
基金the auspices of National Natural Science Foundations of China(Nos.12075284 and 12205157)supported by the High-End Talents Program of Hebei Province,Innovative Approaches towards Development of Carbon-Free Clean Fusion Energy(No.2021HBQZYCSB006).
文摘The EHL-2 spherical torus is designed to demonstrate proton-boron(p-11B)fusion within a compact spherical tokamak.Its planned heating system includes a negative ion-based neutral beam injection(N-NBI),two positive ion-based NBI systems(P-NBI),electron cyclotron resonance heating(ECRH),ion cyclotron resonance heating(ICRH),and high harmonic fast wave(HHFW),with a total power output of 31 MW.According to scaling law estimates,the device is capable of achieving H-mode operation.The plasma density,,n_(e,min)at the minimum L-H power threshold,P_(lh),is estimated to be 4.4×10^(19)m^(-3).The pedestal parameters were calculated using the REPED model.Assuming B as the primary impurity ion,the predicted pedestal width and height are lower compared to the typical case with carbon impurities.The pedestal collisionality for EHL-2 is estimated to range between 0.06 and 0.17,indicating the potential for significant energy loss due to edge localized modes(ELMs).The heat flux on the divertor plate has been calculated using the JOREK code.The peak heat fluxes during ELM bursts are approximately 31.0 MW/m^(2)at the lower inboard target and 39.5 MW/m^(2)at the lower outboard target.A preliminary design of the resonant magnetic perturbation(RMP)coils has been completed to both control type-I ELMs and correct error fields.The system comprises 16 coils arranged into 24 pairs.In ELM control mode,a 14/2 component is generated at 1.7 G/kAt,with a current of 4.9 kA required to achieveσChirikow=1 at the resonant surface,where the normalized poloidal magnetic flux is 0.85.In error field(EF)modulation mode,2/1 and 3/1 components are generated at 3.5 G/kAt and 2.8 G/kAt,respectively.
文摘We study the confinement of a spinless charged particle to a spherical quantum dot under the influence of a linear electric field.The spherical quantum dot is described by a short-range potential given by the power-exponential potential.Then,by analysing the region near the spherical quantum dot centre,we discuss two cases where the energy levels can be obtained for s-waves and how the linear electric field modifies the spectrum of energy of the spherical quantum dot.
文摘Magnetic levitation of the fusion target by coating a thin MgB_(2)superconducting shell on its outer surface has recently been proposed in inertial confinement fusion(ICF)to realize a noncontact support of the target at~20 K to boost the implosion performance and fusion yield.To avoid possible effects on target ablation,the coated MgB_(2)shell is anticipated to be as thin as possible while fulfilling the target levitation requirements.Under this circumstance,the fabrication of an MgB_(2)shell with reduced thickness has been explored using a hybrid physical-chemical vapour deposition method.By gradually decreasing the deposition time,a set of MgB_(2)shells were grown on 1 mm diameter Si_(3)N_(4)spheres with the thickness reducing from 720 nm to 200 nm.The spherical shells all have a polycrystalline structure characterized by closely packed hexagonal grains,with both the grain size and thickness diminishing as the shell thickness decreases.The superconducting transition temperature Tcof the shells,as determined by both resistance and magnetization measurements,is in the range of 38-40 K and all shells exhibit ideal diamagnetism at low temperatures.For the thinnest shell of 200 nm,the superconducting critical current density Jcat 20 K reaches 8.0×10^(6)A/cm^(2)and 2.1×10^(5)A/cm^(2)under zero and 2 T applied field,respectively.The results indicate that it is experimentally feasible to fabricate MgB_(2)spherical shells with a thickness as low as 200 nm while maintaining the high Tcand Jc,thereby taking a further step towards the application of the shell in superconducting magnetic levitation for ICF.
基金Project supported by the National Natural Science Foundation of China(Nos.11872320 and 12072294)。
文摘A dimensionless load-displacement model based on the energy-density equivalence principle is proposed to obtain the stress-strain relationships of metallic materials under monotonic indentations with various diameters of spherical indenters.Finite element simulations are carried out to verify the constitutive relations from the new model,involving indentations made with various spherical indenters.For each indenter,some quasi-static spherical indentation tests are conducted on the materials with 40 preset constitutive relationships.The results indicate that the stress-strain curves predicted by the model align with the preset curves under 200 loading conditions.Moreover,the goodness-of-fit between the predicted stress-strain curves and the preset curves exceeds0.96 for all indenters and materials.In the end,the indentation tests are conducted by the spherical indenters with the diameters of 1.587 mm for fifteen metallic materials and1 mm for eight metallic materials.The results show that the stress-strain curves obtained by the spherical indentation based on the new model closely match those obtained from the uniaxial tensile tests.The relative errors for both the proof strength at 0.2%plastic extension and the tensile strength are below 5%.
基金Funded by the Breeding Project of Anhui Polytechnic University(No.2019YQQ027)the Scientific Research Foundation of Anhui Polytechnic University(No.xjky2022016)+1 种基金the Open Research Found of Anhui Key Laboratory of High-performance Non-ferrous Metal Materials(No.YSJS-2023-07)the Innovative Entrepreneurship Training Program for College Students in Anhui Province(No.S202210363391)。
文摘A series of CoS_(2-x)Se_(x)(x=0.05,0.1,0.2,0.3,and 2)composite catalysts were synthesized on carbon fiber paper via the hydrothermal method with Se doping.By precisely controlling the reaction temperature and Se doping level,a hollow spherical catalyst structure composed of CoSSe was successfully synthesized,which exhibited exceptional activity for hydrogen evolution in acidic solutions.The influences of Se doping on the microstructure and catalytic mechanism of hydrogen evolution reaction(HER)of these composites were systematically investigated.The experimental results reveal that the hollow spherical sample displays an overpotential value of 143 mV along with a Tafel slope value of 69.8 mV·dec^(-1)at a current density of 10 mA·cm^(-2)in an acid aqueous solution.Furthermore,it demonstrates remarkable cycling stability after undergoing 3000 cycles.The comprehensive analysis indicates that Se doping optimizes the electronic structure and enhances conductivity,meanwhile the unique hollow spherical architecture increases active sites for HER and significantly improves overall electrocatalytic performance.
基金Supported by the Ministry of Science and Higher Education of the Russian Federation as a part of World-class Research Center Program:Advanced Digital Technologies(contract No.075-15-2022-312 dated 20 April 2022).
文摘This study proposes a numerically efficient technique for computing the far-field scattered by a spherical target placed near the seabed.The bottom is supposed to be a homogeneous liquid attenuating half-space.The transmitter and receiver are situated at different points of a homogeneous water half-space.The distances between the transmitter,receiver,and object of interest are assumed to be much larger than the acoustic wavelength in water.The scattered far-field is ascertained using Hackman and Sammelmann’s general approach.The arising scattering coefficients of a sphere are assessed using the steepest descent approach.The branch cut contribution is also considered.The obtained formulas for the form-function can be used for acoustically rigid or soft scatterers,as well as elastic targets or spherical elastic shells.Numerical simulations are conducted for an acoustically rigid sphere.Asymptotic expressions for the scattering coefficients allow a decrease in the number of summands in the formula for the target strength and a significant reduction in computational time.
