Nowadays, a highly integrated valve?controlled cylinder(HIVC) is applied to drive the joints of legged robots. Although the adoption of HIVC has resulted in high?performance robot control, the hydraulic force system s...Nowadays, a highly integrated valve?controlled cylinder(HIVC) is applied to drive the joints of legged robots. Although the adoption of HIVC has resulted in high?performance robot control, the hydraulic force system still has problems, such as strong nonlinearity, and time?varying parameters. This makes HIVC force control very diffcult and complex. How to improve the control performance of the HIVC force control system and find the influence rule of the system parameters on the control performance is very significant. Firstly, the mathematical model of HIVC force control system is established. Then the mathematical expression for parameter sensitivity matrix is obtained by applying matrix sensitivity analysis(PSM). Then, aimed at the sinusoidal response under(three factors and three levels) working conditions, the simulation and the experiment are conducted. While the error between the simulation and experiment can't be avoided. Therefore, combined with the range analysis, the error in the two performance indexes of sinusoidal response under the whole working condition is analyzed. Besides, the sensitivity variation pattern for each system parameter under the whole working condition is figured out. Then the two sensitivity indexes for the three system parameters, which are supply pressure, proportional gain and initial displacement of piston, are proved experimentally. The proposed method significantly reveals the sensitivity characteristics of HIVC force control system, which can make the contribution to improve the control performance.展开更多
The development of high-sulfur-loading Li-S batteries is a key prerequisite for their commercial applications.This requires to surmount the huge polarization,severe polysulfide shuttling and drastic volume change caus...The development of high-sulfur-loading Li-S batteries is a key prerequisite for their commercial applications.This requires to surmount the huge polarization,severe polysulfide shuttling and drastic volume change caused by electrode thickening.High-strength polar binders are ideal for constructing robust and long-life high-loading sulfur cathodes but show very weak interfacial interaction with non-polar sulfur materials.To address this issue,this work devises a highly integrated sulfur@polydopamine/highstrength binder composite cathodes,targeting long-lasting and high-sulfur-loading Li-S batteries.The super-adhesion polydopamine(PD)can form a uniform nano-coating over the graphene/sulfur(G-S)surface and provide strong affinity to the cross-linked polyacrylamide(c-PAM)binder,thus tightly integrating sulfur with the binder network and greatly boosting the overall mechanical strength/conductivity of the electrode.Moreover,the PD coating and c-PAM binder rich in polar groups can form two effective blockades against the effusion of soluble polysulfides.As such,the 4.5 mg cm−2 sulfur-loaded G-S@PD-c-PAM cathode achieves a capacity of 480 mAh g−1 after 300 cycles at 1 C,while maintaining a capacity of 396 mAh g−1 after 50 cycles at 0.2 C when the sulfur loading rises to 9.1 mg cm−2.This work provides a system-wide concept for constructing high-loading sulfur cathodes through integrated structural design.展开更多
Fabricating high integration density,high resolution,and intrinsically stretchable patterns by patterned technologies remain challenging.Template printing enabled high-precision patterned fabrication at a facile opera...Fabricating high integration density,high resolution,and intrinsically stretchable patterns by patterned technologies remain challenging.Template printing enabled high-precision patterned fabrication at a facile operation.However,the pattern spacing constraint is the major limitation to high integration density.In this study,we develop an elastomer-assisted strategy to improve the template printing process,which involves patterning on the prestrain elastic substrate.This strategy overcomes the spacing limitation and enables the realization of a centimeter-scale pattern with submicron precision.Particularly,the integration density of fabricated intrinsically stretchable patterns can reach 1932 lines on a substrate of 0.5 cm2;the assembly lines with a feature size of 880 nm and an interval of 955 nm.Furthermore,we demonstrate a facile approach for constructing silver nanoparticle/liquid metal alloy composite conductive patterns.The as-prepared flexible electrodes can withstand up to 150%strain and a 2-mm bend radius.This method provides new insights into template printing technology.Additionally,it opens a route for the simultaneous construction of functional patterned arrays with large scale,high integration density,and intrinsic stretchability,which will be useful for the integrated fabrication of various flexible electronic devices.展开更多
The vigorous development in the field of energy conversion and storage devices directly contributes to the full utilization and convenient use of clean energy.However,some drawbacks of independent energy conversion an...The vigorous development in the field of energy conversion and storage devices directly contributes to the full utilization and convenient use of clean energy.However,some drawbacks of independent energy conversion and storage devices,including unstable,insufficient energy output and dependence on external power supply,are difficult to overcome by self-optimization,thus,hindering their further development and direct application.Coincidentally,the combination of above two devices can solve these problems,which conforms to their intrinsic needs for development.At the same time,the pursuit of portability and miniaturization also promotes the development of the power system toward a highly integrated direction.Therefore,we introduce several integration modes of energy conversion and storage systems,with emphasis on all-in-one power system,possessing the highest integration in this review.From the aspect of device configuration,working mechanisms and their performances,the all-inone power systems based on different energy sources(e.g.,mechanical,solar,thermal,and chemical energy)are discussed and analyzed.Finally,the design strategies are summarized and the potential development directions in the future are proposed.This review aims to provide a comprehensive overview of highly integrated energy conversion and storage system,and seeks to point out the opportunities and orientations of future research in this field.展开更多
Colorless‐to‐black switching has attracted widespread attention for smart windows and multifunctional displays because they are more useful to control solar energy.However,it still remains a challenge owing to the t...Colorless‐to‐black switching has attracted widespread attention for smart windows and multifunctional displays because they are more useful to control solar energy.However,it still remains a challenge owing to the tremendous difficulties in the design of completely reverse absorptions in transmissive and colored states.Herein,we report on an electrochemical device that can switch between colorless and black by using the electrochemical process of hybrid organic–inorganic perovskite MAPbBr_(3),which shows a high integrated contrast ratio of up to 73%from 400 to 800 nm.The perovskite solution can be used as the active layer to assemble the device,showing superior transmittance over the entire visible region in neutral states.By applying an appropriate voltage,the device undergoes reversible switching between colorless and black,which is attributed to the formation of lead and Br_(2)in the redox reaction induced by the electron transfer process in MAPbBr_(3).In addition,the contrast ratio can be modulated over the entire visible region by changing the concentration and the applied voltage.These results contribute toward gaining an insightful understanding of the electrochemical process of perovskites and greatly promoting the development of switchable devices.展开更多
To make high integrity lightweight metal castings,best practices are required in various stages of casting and heat treatment processes,including liquid metal composition and quality control,casting and gating/riser s...To make high integrity lightweight metal castings,best practices are required in various stages of casting and heat treatment processes,including liquid metal composition and quality control,casting and gating/riser system design,and process optimization.This paper presents best practices for liquid metal processing and quality assurance of molten metal in both melting and mold filling.Best practices for other aspects of lightweight metal casting will be published separately.展开更多
In this paper,high-power LED with many integrated chips is used as thermal resistance analysis research object, and we do thermal resistance testing technology research on it. We put forward the thermocouple point con...In this paper,high-power LED with many integrated chips is used as thermal resistance analysis research object, and we do thermal resistance testing technology research on it. We put forward the thermocouple point contact test method. According to the principle that LED forward voltage changes with temperature,LED heat sink to surface temperature distribution is studied directly in the test,and then we analyze the thermal resistance of high-power LED with many integrated chips when its secondary packaging is introduced. This method makes the measurement of thermal resistance of LED more rapid and convenient. It provides an effective assessment method for the analysis of high power LED device design and engineering application.展开更多
<div style="text-align:justify;"> Transceiver module and two-dimensional sum difference network are important components of phased array antenna. In this paper, multilayer printed board is used to inte...<div style="text-align:justify;"> Transceiver module and two-dimensional sum difference network are important components of phased array antenna. In this paper, multilayer printed board is used to integrate millimeter wave multi-channel transceiver circuit and sum difference network. The interconnection between them is realized through RF coaxial vertical transition. At the same time, the heat dissipation design and inter channel shielding design of the module are carried out. The RF and low frequency required by the module are completed through the wiring between and within the dielectric plate layers. Finally, 128 arrays are fabricated and verified by multi-channel passive test. The results show that the type transceiver module integrating with two-dimensional sum difference network has good performance, and 128 channels have excellent amplitude and phase characteristics. The integration technology has the characteristics of lightweight, miniaturization, high integration and low manufacturing cost. It can be widely used in miniaturized phased array antennas. </div>展开更多
To meet the application requirements for a Ka-band space-based TT&C terminal for a launch vehicle,this paper proposes the implementation scheme of a space-based TT&C terminal,analyzes and solves the miniaturiz...To meet the application requirements for a Ka-band space-based TT&C terminal for a launch vehicle,this paper proposes the implementation scheme of a space-based TT&C terminal,analyzes and solves the miniaturized design of equipment and the key technology for high-efficiency heat dissipation.The phased array antenna test shows that without external heat dissipation measures,the phased array antenna can work for a long time to meet the working requirements of launch vehicle,which has been verified in the LM-8 mission,and has wide engineering application prospects.展开更多
We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates ...We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.展开更多
In this paper,new Levin methods are presented for calculating oscillatory integrals with algebraic and/or logarithmic singularities.To avoid singularities,the technique of singularity separation is applied and then th...In this paper,new Levin methods are presented for calculating oscillatory integrals with algebraic and/or logarithmic singularities.To avoid singularities,the technique of singularity separation is applied and then the singular ODE occurring in classic Levin methods is converted into two kinds of non-singular ODEs.The solutions of one can be obtained explicitly,while the other kind of ODEs can be solved efficiently by collocation methods.The proposed methods can attain arbitrarily high asymptotic orders and also enjoy superalgebraic convergence with respect to the number of collocation points.Several numerical experiments are presented to validate the efficiency of the proposed methods.展开更多
Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are ...Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are derived in the frequency domain. By considering the coupling effect between the solid phase and the fluid phase and without any hypothesis for the fluid displacement, the model presented here is rigorous and close to the real materials. Owing to the use of extended homogeneous capacity precision integration method and precise element method, the model can be applied in higher frequency range than pure numerical methods. This model also easily adapts to various boundary conditions. Numerical results are given for two different porous plates under different excitations and boundary conditions.展开更多
In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a s...In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a system of coupled eigenvalue PDEs that is usually supplemented by interface boundary conditions that can be derived from a variational formulation of the problem.We analyze such a system for the envelope functions and show that a failure to restrict their Fourier expansion coeffi-cients to small k components would lead to the appearance of non-physical solutions.We survey the existing methodologies to eliminate this difficulty and propose a simple and effective solution.This solution is demonstrated on an example of a two-band model for both bulk materials and low-dimensional nanostructures.Finally,based on the above requirement of small k,we derive a model for nanostructures with cylindrical symmetry and apply the developed model to the analysis of quantum dots using an eight-band model.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.51605417)Key Project of Hebei Provincial Natural Science Foundation,China(Grant No.E2016203264)State Key Laboratory of Fluid Power and Mechatronic Systems(Zhejiang University)Open Fund Project(Grant No.GZKF-201502)
文摘Nowadays, a highly integrated valve?controlled cylinder(HIVC) is applied to drive the joints of legged robots. Although the adoption of HIVC has resulted in high?performance robot control, the hydraulic force system still has problems, such as strong nonlinearity, and time?varying parameters. This makes HIVC force control very diffcult and complex. How to improve the control performance of the HIVC force control system and find the influence rule of the system parameters on the control performance is very significant. Firstly, the mathematical model of HIVC force control system is established. Then the mathematical expression for parameter sensitivity matrix is obtained by applying matrix sensitivity analysis(PSM). Then, aimed at the sinusoidal response under(three factors and three levels) working conditions, the simulation and the experiment are conducted. While the error between the simulation and experiment can't be avoided. Therefore, combined with the range analysis, the error in the two performance indexes of sinusoidal response under the whole working condition is analyzed. Besides, the sensitivity variation pattern for each system parameter under the whole working condition is figured out. Then the two sensitivity indexes for the three system parameters, which are supply pressure, proportional gain and initial displacement of piston, are proved experimentally. The proposed method significantly reveals the sensitivity characteristics of HIVC force control system, which can make the contribution to improve the control performance.
基金supported by the National Natural Science Foundation of China(21875155,51675275,21703185 and 21473119)Q.B.Z.acknowledges the Leading Project Foundation of Science Department of Fujian Province(2018H0034)Shenzhen Science and Technology Planning Project(JCYJ20170818153427106).
文摘The development of high-sulfur-loading Li-S batteries is a key prerequisite for their commercial applications.This requires to surmount the huge polarization,severe polysulfide shuttling and drastic volume change caused by electrode thickening.High-strength polar binders are ideal for constructing robust and long-life high-loading sulfur cathodes but show very weak interfacial interaction with non-polar sulfur materials.To address this issue,this work devises a highly integrated sulfur@polydopamine/highstrength binder composite cathodes,targeting long-lasting and high-sulfur-loading Li-S batteries.The super-adhesion polydopamine(PD)can form a uniform nano-coating over the graphene/sulfur(G-S)surface and provide strong affinity to the cross-linked polyacrylamide(c-PAM)binder,thus tightly integrating sulfur with the binder network and greatly boosting the overall mechanical strength/conductivity of the electrode.Moreover,the PD coating and c-PAM binder rich in polar groups can form two effective blockades against the effusion of soluble polysulfides.As such,the 4.5 mg cm−2 sulfur-loaded G-S@PD-c-PAM cathode achieves a capacity of 480 mAh g−1 after 300 cycles at 1 C,while maintaining a capacity of 396 mAh g−1 after 50 cycles at 0.2 C when the sulfur loading rises to 9.1 mg cm−2.This work provides a system-wide concept for constructing high-loading sulfur cathodes through integrated structural design.
基金Beijing National Laboratory for Molecular Sciences,Grant/Award Numbers:BNLMSCXXM‐202005,2019BMS20003National Natural Science Foundation of China,Grant/Award Number:2018YFA0703200+3 种基金K.C.Wong Education Foundation,and China Postdoctoral Science Foundation,Grant/Award Number:2020M670466External Cooperation Program of Chinese Academy of Sciences,Grant/Award Number:GJHZ201948CAS‐VPST Silk Road Science Fund 2022,Grant/Award Number:121111KYSB20210006National Key R&D Program of China,Grant/Award Numbers:52003276,22175185,52003273,51803217,51773206,91963212,51961145102,22002171。
文摘Fabricating high integration density,high resolution,and intrinsically stretchable patterns by patterned technologies remain challenging.Template printing enabled high-precision patterned fabrication at a facile operation.However,the pattern spacing constraint is the major limitation to high integration density.In this study,we develop an elastomer-assisted strategy to improve the template printing process,which involves patterning on the prestrain elastic substrate.This strategy overcomes the spacing limitation and enables the realization of a centimeter-scale pattern with submicron precision.Particularly,the integration density of fabricated intrinsically stretchable patterns can reach 1932 lines on a substrate of 0.5 cm2;the assembly lines with a feature size of 880 nm and an interval of 955 nm.Furthermore,we demonstrate a facile approach for constructing silver nanoparticle/liquid metal alloy composite conductive patterns.The as-prepared flexible electrodes can withstand up to 150%strain and a 2-mm bend radius.This method provides new insights into template printing technology.Additionally,it opens a route for the simultaneous construction of functional patterned arrays with large scale,high integration density,and intrinsic stretchability,which will be useful for the integrated fabrication of various flexible electronic devices.
基金NSFC,Grant/Award Numbers:22075019,22035005National Key R&D Program of China,Grant/Award Number:2017YFB1104300。
文摘The vigorous development in the field of energy conversion and storage devices directly contributes to the full utilization and convenient use of clean energy.However,some drawbacks of independent energy conversion and storage devices,including unstable,insufficient energy output and dependence on external power supply,are difficult to overcome by self-optimization,thus,hindering their further development and direct application.Coincidentally,the combination of above two devices can solve these problems,which conforms to their intrinsic needs for development.At the same time,the pursuit of portability and miniaturization also promotes the development of the power system toward a highly integrated direction.Therefore,we introduce several integration modes of energy conversion and storage systems,with emphasis on all-in-one power system,possessing the highest integration in this review.From the aspect of device configuration,working mechanisms and their performances,the all-inone power systems based on different energy sources(e.g.,mechanical,solar,thermal,and chemical energy)are discussed and analyzed.Finally,the design strategies are summarized and the potential development directions in the future are proposed.This review aims to provide a comprehensive overview of highly integrated energy conversion and storage system,and seeks to point out the opportunities and orientations of future research in this field.
基金Natural Science Foundation of Hebei Province(China),Grant/Award Numbers:B2020203013,B2021203016Science and Technology Project of Hebei Education Department(China),Grant/Award Number:QN2020137+3 种基金Cultivation Project for Basic Research Innovation of Yanshan University(China),Grant/Award Number:2021LGZD015Subsidy for Hebei Key Laboratory of Applied Chemistry after Operation Performance(China),Grant/Award Number:22567616HNatural Science Foundation of Heilongjiang Province(China),Grant/Award Number:LH2022B025Fundamental Research Funds for the Provincial Universities of Heilongjiang Province(China),Grant/Award Number:KYYWF10236190104。
文摘Colorless‐to‐black switching has attracted widespread attention for smart windows and multifunctional displays because they are more useful to control solar energy.However,it still remains a challenge owing to the tremendous difficulties in the design of completely reverse absorptions in transmissive and colored states.Herein,we report on an electrochemical device that can switch between colorless and black by using the electrochemical process of hybrid organic–inorganic perovskite MAPbBr_(3),which shows a high integrated contrast ratio of up to 73%from 400 to 800 nm.The perovskite solution can be used as the active layer to assemble the device,showing superior transmittance over the entire visible region in neutral states.By applying an appropriate voltage,the device undergoes reversible switching between colorless and black,which is attributed to the formation of lead and Br_(2)in the redox reaction induced by the electron transfer process in MAPbBr_(3).In addition,the contrast ratio can be modulated over the entire visible region by changing the concentration and the applied voltage.These results contribute toward gaining an insightful understanding of the electrochemical process of perovskites and greatly promoting the development of switchable devices.
文摘To make high integrity lightweight metal castings,best practices are required in various stages of casting and heat treatment processes,including liquid metal composition and quality control,casting and gating/riser system design,and process optimization.This paper presents best practices for liquid metal processing and quality assurance of molten metal in both melting and mold filling.Best practices for other aspects of lightweight metal casting will be published separately.
基金Sponsored by the Heilongjiang Provincial Project(Grant No.12511121)the Harbin City Innovation Talent Project(Grant No.2011RFXXG019)the National Science and Technology Support Project(Grant No.2012BAH28F02)
文摘In this paper,high-power LED with many integrated chips is used as thermal resistance analysis research object, and we do thermal resistance testing technology research on it. We put forward the thermocouple point contact test method. According to the principle that LED forward voltage changes with temperature,LED heat sink to surface temperature distribution is studied directly in the test,and then we analyze the thermal resistance of high-power LED with many integrated chips when its secondary packaging is introduced. This method makes the measurement of thermal resistance of LED more rapid and convenient. It provides an effective assessment method for the analysis of high power LED device design and engineering application.
文摘<div style="text-align:justify;"> Transceiver module and two-dimensional sum difference network are important components of phased array antenna. In this paper, multilayer printed board is used to integrate millimeter wave multi-channel transceiver circuit and sum difference network. The interconnection between them is realized through RF coaxial vertical transition. At the same time, the heat dissipation design and inter channel shielding design of the module are carried out. The RF and low frequency required by the module are completed through the wiring between and within the dielectric plate layers. Finally, 128 arrays are fabricated and verified by multi-channel passive test. The results show that the type transceiver module integrating with two-dimensional sum difference network has good performance, and 128 channels have excellent amplitude and phase characteristics. The integration technology has the characteristics of lightweight, miniaturization, high integration and low manufacturing cost. It can be widely used in miniaturized phased array antennas. </div>
文摘To meet the application requirements for a Ka-band space-based TT&C terminal for a launch vehicle,this paper proposes the implementation scheme of a space-based TT&C terminal,analyzes and solves the miniaturized design of equipment and the key technology for high-efficiency heat dissipation.The phased array antenna test shows that without external heat dissipation measures,the phased array antenna can work for a long time to meet the working requirements of launch vehicle,which has been verified in the LM-8 mission,and has wide engineering application prospects.
基金The work is supported by Royal Society International Exchanges(grant IE141214)the Projects of International Cooperation and Exchanges NSFC-RS(Grant No.11511130052)+1 种基金the Key Science and Technology Program of Shaanxi Province of China(Grant No.2016GY-080)the Fundamental Research Funds for the Central Universities.
文摘We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.
基金supported by National Natural Science Foundation of China(Grant No.11771454)Research Fund of National University of Defense Technology(Grant No.ZK19-19)。
文摘In this paper,new Levin methods are presented for calculating oscillatory integrals with algebraic and/or logarithmic singularities.To avoid singularities,the technique of singularity separation is applied and then the singular ODE occurring in classic Levin methods is converted into two kinds of non-singular ODEs.The solutions of one can be obtained explicitly,while the other kind of ODEs can be solved efficiently by collocation methods.The proposed methods can attain arbitrarily high asymptotic orders and also enjoy superalgebraic convergence with respect to the number of collocation points.Several numerical experiments are presented to validate the efficiency of the proposed methods.
基金Project supported by the National Natural Science Foundation of China(nos.11162001,11502056 and 51665006)
文摘Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are derived in the frequency domain. By considering the coupling effect between the solid phase and the fluid phase and without any hypothesis for the fluid displacement, the model presented here is rigorous and close to the real materials. Owing to the use of extended homogeneous capacity precision integration method and precise element method, the model can be applied in higher frequency range than pure numerical methods. This model also easily adapts to various boundary conditions. Numerical results are given for two different porous plates under different excitations and boundary conditions.
文摘In this paper we analyze a long standing problem of the appearance of spurious,non-physical solutions arising in the application of the effective mass theory to low dimensional nanostructures.The theory results in a system of coupled eigenvalue PDEs that is usually supplemented by interface boundary conditions that can be derived from a variational formulation of the problem.We analyze such a system for the envelope functions and show that a failure to restrict their Fourier expansion coeffi-cients to small k components would lead to the appearance of non-physical solutions.We survey the existing methodologies to eliminate this difficulty and propose a simple and effective solution.This solution is demonstrated on an example of a two-band model for both bulk materials and low-dimensional nanostructures.Finally,based on the above requirement of small k,we derive a model for nanostructures with cylindrical symmetry and apply the developed model to the analysis of quantum dots using an eight-band model.