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3D Numerical Simulation of Overbank Flow in Non-Orthogonal Curvilinear Coordinates 被引量:2
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作者 张明亮 沈永明 吴修广 《China Ocean Engineering》 SCIE EI 2005年第3期395-407,共13页
The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the... The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields with computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. A 3-D k-E turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overhank flow. The bodyfitted coordinate is adopted in the horizontal plane, the part grid is adopted in the vertical direction, and the wall-function method is employed to simulate the bed resistance. The model is applied to the simulation of the meandering channel with straight flood plain banks, and the main velocities and secondary velocities for both the longitudinal and cross sections are presented. Comparison and analysis show that the results of simulation are fit to reflect the results of experiment. These results show the application value of the model to 3D overhank flow. 展开更多
关键词 non-orthogonal curvilinear coordinates overbank flow wall-function method k-ε turbulence model
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Expression of strain tensor in orthogonal curvilinear coordinates
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作者 Xuyan Liu Yingfeng Ji Quanqiang Liang 《Geodesy and Geodynamics》 2010年第1期48-56,共9页
Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a func... Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal eurvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates. 展开更多
关键词 orthogonal Curvilinear coordinates OCC Cartesian coordinates strain tensor transformation matrix universal expression
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THE EQUATIONS OF COMPLETE DEPTH-AVERAGED TURBULENCE MODEL IN GENERAL ORTHOGONAL COORDINATES
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作者 丁剡 周雪漪 +1 位作者 余常昭 梁栋 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第1期53-63,共11页
For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of rive... For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of river bed are taken into account.The depth-averaged equations of k-εturbulence model are also obtained. Because it Accounts for the three-dimensional effect, this model is named as the complete Depth-averaged model.The boundaries of natural water bodies are usually curved.In this work, the derived equations in Cartesian coordinates are transformed into orthogonal coordinates. The obtained equations can be applied directly to numerical computation of practical problems. 展开更多
关键词 turbulent flow mathematical model depth-average general orthogonal coordinates
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Parabolic Wave Propagation Modelling in Orthogonal Coordinate Systems 被引量:1
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作者 袁德奎 林斌良 肖鸿 《海洋工程:英文版》 EI 2004年第3期445-456,共12页
This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild slope equation in the orthogonal coordinate system. Two types of coordinate systems are stud... This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the conformal system. The computational results show that the conformal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical conformal grid system. 展开更多
关键词 orthogonal coordinates conformal mapping parabolic mild slope equation numerical grid generation
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Curve integral with path independent in orthogonal curvilinear coordinate system
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作者 YU Huai-min LUO Guang +1 位作者 XIANG Yu-cui YUAN Meng 《Journal of Chongqing University》 CAS 2018年第2期70-76,共7页
It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or... It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made. 展开更多
关键词 CURVE integral orthogonal curvilinear coordinATE system coordinATE transformation green’s THEOREM STOKES FORMULA
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COORDINATES OF PRINCIPAL STRESSES FOR ELASTIC PLANE PROBLEM
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作者 黄民丰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第2期157-162,共6页
In this paper, the equilibrium equations on orthogonal curve coordinates made of curves of principal stresses are disscused and their properties in process of solution are presented through a simple example. Therefore... In this paper, the equilibrium equations on orthogonal curve coordinates made of curves of principal stresses are disscused and their properties in process of solution are presented through a simple example. Therefore, it is deduced that there is another way to solve problems in elasticity, i.e., by assumption of orthogonal curves of principal stresses. 展开更多
关键词 ELASTICITY equilibrium equation principal stress plane problem orthogonal curve coordinates
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基于混合协作NOMA的安全MEC能耗优化
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作者 余雪勇 傅新程 朱洪波 《系统工程与电子技术》 EI CSCD 北大核心 2024年第3期1116-1124,共9页
非正交多址接入(non-orthogonal multiple access,NOMA)技术的广泛应用改变了传统物理层安全对用户传输速率的限制,在降低时延的同时会引起系统能耗增加。针对安全通信与降低能耗问题,提出一种基于混合协作NOMA的安全边缘计算传输方法... 非正交多址接入(non-orthogonal multiple access,NOMA)技术的广泛应用改变了传统物理层安全对用户传输速率的限制,在降低时延的同时会引起系统能耗增加。针对安全通信与降低能耗问题,提出一种基于混合协作NOMA的安全边缘计算传输方法。该方法对每个用户数据处理过程设计了多时隙混合协作方案,根据不同用户的信道条件分别设置卸载决策,保证用户间公平,并推导出系统保密中断概率的闭合表达式。然后以最小化系统能耗为目标,采用基于块坐标下降的三步迭代优化算法求得最优卸载方案。仿真结果显示,所提出的传输方法能在保证信息安全的条件下有效地减少系统能耗。 展开更多
关键词 非正交多址接入 物理层安全 移动边缘计算 中断概率 块坐标下降
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焊接机器人管-管相贯线焊接工艺试验研究
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作者 邹义龙 胡卫欢 +1 位作者 胡一龙 张海东 《河北建筑工程学院学报》 CAS 2024年第2期187-191,共5页
相贯线焊缝是工业生产中典型的焊缝形式之一。相贯线是复杂的空间曲线,采用手工焊接的方法很难保证焊接质量,而利用机器人焊接相贯线焊缝可以大大提高焊接效率和产品质量的稳定性。
关键词 关节坐标系 轨迹重复精度 焊接机器人 正交相贯线
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赤水嘉定群一段红层砂岩机制砂工程特性研究
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作者 黄富全 杨根兰 +2 位作者 史文兵 程斌 江兴元 《水利水电技术(中英文)》 北大核心 2024年第8期116-126,共11页
【目的】赤水以丹霞地貌而著名,但赤水红层区常见坡面防护材料颜色以冷色调为主,与红层景区原岩颜色极不协调。为了研制一种符合赤水红层区景观协调新型坡面防护材料,以红层砂岩为原料破碎为机制砂,并测试机制砂基础特性。【方法】利用... 【目的】赤水以丹霞地貌而著名,但赤水红层区常见坡面防护材料颜色以冷色调为主,与红层景区原岩颜色极不协调。为了研制一种符合赤水红层区景观协调新型坡面防护材料,以红层砂岩为原料破碎为机制砂,并测试机制砂基础特性。【方法】利用红层砂岩机制砂为掺料配置机制砂砂浆,测试砂浆在不同级配下3 d、7 d、28 d抗压强度、保水率以及稠度,获取机制砂砂浆最优级配,并在最优级配下利用正交试验测试不同砂胶比、石粉掺量以及保水剂掺量下机制砂砂浆性能。【结果】研究结果表明:在最优级配试验中,砂浆28 d抗压强度随着细度模数的增大而增大,保水率与稠度在细度模数为2.98时性能最优。在最优配比试验中,砂胶比、石粉掺量、保水剂掺量与机制砂砂浆抗压强度、抗折强度、拉伸粘结强度、核磁共振孔隙率成反比,石粉掺量对砂浆色差值影响最大。【结论】红层砂岩机制砂基本特性满足规范要求,级配特性呈现“哑铃状”;机制砂砂浆最优级配细度模数为3.31;机制砂砂浆配比在砂胶比2.5、石粉掺量22%、保水剂掺量0.22%条件下,抗压强度、抗折强度、拉伸粘结强度、核磁共振孔隙率以及颜色性能最优。利用红层砂岩机制砂配置所得机制砂砂浆满足M10砂浆标准且砂浆颜色与砂岩颜色接近。 展开更多
关键词 红层砂岩 坡面防护 景观协调 机制砂 正交试验 力学性能 影响因素 抗压强度
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泰勒级数准则的船体分段测量数据配准解析解
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作者 杨贵强 王炬成 李瑞 《哈尔滨工程大学学报》 EI CAS CSCD 北大核心 2024年第11期2094-2099,共6页
为提高船体分段测量数据与CAD模型间的配准定位效率,本文给出了一个基于泰勒级数准则的点集配准解析解,直接求解配准变换参数。通过分析最小二乘解析解的求解特点,考虑到配准变换参数的齐次表示问题,引入特征因子构建新的齐次变换矩阵,... 为提高船体分段测量数据与CAD模型间的配准定位效率,本文给出了一个基于泰勒级数准则的点集配准解析解,直接求解配准变换参数。通过分析最小二乘解析解的求解特点,考虑到配准变换参数的齐次表示问题,引入特征因子构建新的齐次变换矩阵,建立配准齐次表示模型。利用泰勒级数展开齐次变换矩阵的最近正交矩阵,得到齐次变换矩阵的无限次估计解。在此基础上,根据配准齐次表示模型的最大化,计算旋转矩阵的近似解析最优解。以理论模型和甲板分段实测数据为例子验证。本文结果表明了提出算法的有效性及实用性,为船体分段快速测量分析提供算法依据。 展开更多
关键词 船体分段 精度控制 齐次坐标 泰勒级数 点集配准 解析解 最小二乘 特征因子 最近正交矩阵
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多星姿态协同中的几何鲁棒控制
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作者 胡洋 刘学超 +1 位作者 李化义 曹芊 《系统工程与电子技术》 EI CSCD 北大核心 2024年第9期3118-3127,共10页
针对多星系统的姿态协同控制问题,通过不变扩展卡尔曼滤波(invariant extended Kalman filter,InEKF)对航天器进行姿态估计,将航天器的姿态估计与传递矩阵独立;结合无向通信拓扑构建多星特殊正交群(special orthogonal group,SO(3))姿... 针对多星系统的姿态协同控制问题,通过不变扩展卡尔曼滤波(invariant extended Kalman filter,InEKF)对航天器进行姿态估计,将航天器的姿态估计与传递矩阵独立;结合无向通信拓扑构建多星特殊正交群(special orthogonal group,SO(3))姿态模型,推导SO(3)上姿态协同误差。然后,基于SO(3)提出基于一致性理论的姿态协同控制算法。其中,利用径向基函数神经网络对虚拟扰动进行拟合补偿,所提出的算法考虑空间扰动,以保证协同控制器适用于整个姿态空间,实现多星姿态协同、跟踪期望姿态和执行器能力约束下的协同。根据LaSalle不变集理论对系统进行分析,证明系统具有全局渐近稳定性。最后,利用六星航天器系统校验了所提姿态协同控制算法的有效性。 展开更多
关键词 多航天器 特殊正交群 协同控制 径向基函数 不变扩展卡尔曼滤波
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平面刚体系统的参数预调节保辛算法
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作者 吴志刚 徐小明 《计算力学学报》 CAS CSCD 北大核心 2024年第1期101-107,共7页
保辛积分方法在约束哈密顿系统中有着重要的应用,是因为其在长时间仿真中表现出极好的稳定性。然而随着仿真时长增加,保辛格式通常具有较大的相位误差累积。本文提出了一种平面多刚体系统的参数预调节保辛积分方法。通过推导具有待定参... 保辛积分方法在约束哈密顿系统中有着重要的应用,是因为其在长时间仿真中表现出极好的稳定性。然而随着仿真时长增加,保辛格式通常具有较大的相位误差累积。本文提出了一种平面多刚体系统的参数预调节保辛积分方法。通过推导具有待定参数的改进的拉格朗日方程,并将其与已有保辛格式相结合并预先调节相关参数取值,可以大幅降低数值解的相位误差。理论分析与数值结果表明参数预调节保辛积分方法不仅保持了辛结构,而且具有很低的相位误差累积。因此,参数预调节保辛积分方法可应用于长时间仿真分析。 展开更多
关键词 平面刚体系统 笛卡尔坐标 正交投影 保辛算法 高精度
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智能反射面辅助的非正交多址系统协作多点传输方案研究
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作者 李志成 王鸿 《南京邮电大学学报(自然科学版)》 北大核心 2024年第2期45-52,共8页
智能反射面(Intelligent Reflection Surface,IRS)和非正交多址接入(Non-Orthogonal Multiple Access,NOMA)被认为是6G的关键创新型技术,将两者融合可以大幅提高通信系统的频谱效率与能量效率。文中针对IRS辅助的双小区协作多点与非正... 智能反射面(Intelligent Reflection Surface,IRS)和非正交多址接入(Non-Orthogonal Multiple Access,NOMA)被认为是6G的关键创新型技术,将两者融合可以大幅提高通信系统的频谱效率与能量效率。文中针对IRS辅助的双小区协作多点与非正交多址接入融合系统展开研究,具体地,将IRS部署于两小区中间的小区边缘附近,用来提升边缘用户的信号质量。在考虑用户服务质量(Quality of Service,QoS)与基站发射功率限制的条件下,建立了最大化小区边缘用户可达速率的优化问题。由于该问题是非凸的,很难直接求解,将此问题分解为两个子优化问题,采用交替优化算法进行求解。具体地,采用二分法解决功率分配系数优化问题;采用均方误差(Mean-Square Error,MSE)方法将优化问题转化为等效形式,再通过最大最小化(Majorization-Minimization,MM)算法进一步解决相移优化问题。仿真结果显示,所提出的解决方案使得边缘用户可达速率明显高于其他基准方案。 展开更多
关键词 智能反射面 非正交多址接入 协同多点传输 最大最小化算法
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MATHEMATICAL MODEL FOR 2-D TIDAL FLOW AND WATER QUALITY WITH ORTHOGONAL CURVILINEAR COORDINATES 被引量:6
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作者 LiuYu-ling WeiWen-li ShenYong-ming 《Journal of Hydrodynamics》 SCIE EI CSCD 2003年第5期103-108,共6页
This paper presents a numerical method for simulating the 2-D tidal flow andwater quality with the orthogonal curvilinear coordinates. In order to overcome the computationaldifficulties in natural rivers, such as the ... This paper presents a numerical method for simulating the 2-D tidal flow andwater quality with the orthogonal curvilinear coordinates. In order to overcome the computationaldifficulties in natural rivers, such as the complicated boundary figures, the great disparitybetween length and width of computational domain, etc. , orthogonal boundary-filled grid was used.The irregular domain in physical plane was transformed into a rectangular domain in a transformedplane, and the depth-averaged momentum equations and mass equation were given and discretized basedon the alternating direction implicit finite difference scheme in curvilinear coordinates. Theapplication of the presented method was illustrated by an example of analyzing the Yangtze River inthe vicinity of Nanjing city. A fair agreement between the measured data and computed resultsdemonstrates the validity of the developed method. 展开更多
关键词 orthogonal curvilinear coordinate boundary-fitted grid numerical simulationflow water quality tidal river
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The Coordinate-Free Prediction in Finite Populations with Correlated Observations
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作者 Silvia N. Elian 《Open Journal of Statistics》 2017年第2期182-193,共12页
In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier... In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier work considering models with a known diagonal covariance matrix. We extended this result assuming any known covariance matrix. It is shown that in the particular case of the coordinatized models, this general predictor coincides with the optimal predictor of the total population under a regression super population model with correlated observations. 展开更多
关键词 coordinate-Free Models Best Linear UNBIASED PREDICTOR COVARIANCE Matrix orthogonal PROJECTION
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电磁隐形衣材料参数的简单推导方法
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作者 梅中磊 王辉 《微波学报》 CSCD 北大核心 2023年第2期1-5,共5页
在应用光学变换理论的过程中,往往牵涉到正交坐标系下的张量转换问题,计算比较繁杂。文中利用大学课程“电磁场与电磁波”中正交坐标系的理论,推导得到了电磁隐形衣的材料电磁参数。该方法采用变量替换,并将虚拟空间坐标系下的变量用物... 在应用光学变换理论的过程中,往往牵涉到正交坐标系下的张量转换问题,计算比较繁杂。文中利用大学课程“电磁场与电磁波”中正交坐标系的理论,推导得到了电磁隐形衣的材料电磁参数。该方法采用变量替换,并将虚拟空间坐标系下的变量用物理空间的变量表示出来;分析得到虚拟空间中新的坐标系为正交坐标系,并给出相应基矢和拉梅系数;然后将新坐标系下电场(磁场)的旋度方程与物理空间中标准坐标系下的旋度方程对比变形,便可以得到物理空间材料的电磁参数。 展开更多
关键词 球形隐形衣 坐标变换 正交坐标系 电磁参数
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基于高分辨率ECOMAC的桥梁结构损伤识别 被引量:1
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作者 聂振华 蔡文 +1 位作者 夏子立 马宏伟 《振动.测试与诊断》 EI CSCD 北大核心 2023年第1期179-187,205,共10页
为了达到精确定位损伤的目的,提出了利用少量传感器信息进行桥梁高分辨率全模态振型识别,获得高分辨率的全桥协调模态置信因子(enhanced coordinate modal assurance criteria,简称ECOMAC)这一动力指纹参数的方法。利用特征正交分解直... 为了达到精确定位损伤的目的,提出了利用少量传感器信息进行桥梁高分辨率全模态振型识别,获得高分辨率的全桥协调模态置信因子(enhanced coordinate modal assurance criteria,简称ECOMAC)这一动力指纹参数的方法。利用特征正交分解直接分析移动车辆荷载作用下桥梁上的少量传感器所测位移响应,获得主成分矩阵,将主成分矩阵通过低通滤波即可获得高分辨率的模态振型。利用高分辨率模态振型获得高分辨率的协调模态置信因子,并作为损伤指标进行损伤定位。为了验证该方法的有效性,对一梁桥进行数值仿真和实验。数值模拟和实验结果均表明,基于少量传感器下利用高分辨率的协调模态置信因子能够精确识别损伤。 展开更多
关键词 少量传感器 高分辨率振型 特征正交分解 协调模态置信因子
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A NON-UNIFORM SEDIMENT TRANSPORT MODEL WITH THE BOUNDARY-FITTING ORTHOGONAL COORDINATE SYSTEM 被引量:10
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作者 Lu Yong-jun (River and Harbor Department, Nanjing Hydraulic Research Institute , Nanjing 210024, China) Chen Guo-xiang (College Water Resources and Environment, Hohai University, Nanjing 210024, China) 《Journal of Hydrodynamics》 SCIE EI CSCD 2002年第1期64-68,共5页
A 2-D non-uniform sediment mat hmatical model in the boundary-fitting orthogonal coordinate system was develop ed in this paper. The governing equations, the numerical scheme, the boundary con ditions, the movable bou... A 2-D non-uniform sediment mat hmatical model in the boundary-fitting orthogonal coordinate system was develop ed in this paper. The governing equations, the numerical scheme, the boundary con ditions, the movable boundary technique and the numerical solutions were present ed. The model was verified by the data of the reach 25km upstream the Jialingjia ng estuary and the 44km long main stream of the Chongqing reach of the Yangtze r iver. The calculated results show that, the water elevation, the velocity distri bution and the river bed deformation are in agreement with the measured data. 展开更多
关键词 mathematical model non-uniform sus pended load non-uniform bedload boundary-fitting orthogonal coordinate system
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智能反射面辅助的非正交多址系统高能效传输方案研究 被引量:4
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作者 张诚 王鸿 《重庆邮电大学学报(自然科学版)》 CSCD 北大核心 2023年第1期16-22,共7页
针对基站(base station, BS)功率分配和智能反射面(intelligent reflecting surface, IRS)相移相互耦合的非凸优化问题,提出一种新的交替优化方案,即交替运用最优能量效率(energy efficiency, EE)功率分配算法和块坐标上升(block coordi... 针对基站(base station, BS)功率分配和智能反射面(intelligent reflecting surface, IRS)相移相互耦合的非凸优化问题,提出一种新的交替优化方案,即交替运用最优能量效率(energy efficiency, EE)功率分配算法和块坐标上升(block coordinate ascent, BCA)技术求解功率分配与相位偏移问题,直至优化的目标值收敛。仿真结果表明,与IRS辅助的正交多址接入(orthogonal multiple access, OMA)、随机相移的IRS辅助非正交多址接入(non-orthogonal multiple access, NOMA)、无IRS辅助的纯NOMA接入技术相比,提出的IRS-NOMA传输方案能够显著提升系统的EE性能。 展开更多
关键词 智能反射面 非正交多址接入 能量效率 相移优化 块坐标上升
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A New Strategy for Dynamic Channel Allocation in CR-WMN Based on RCA
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作者 Kaleem Arshid Jianbiao Zhang +3 位作者 Muhammad Yaqub Mohammad Daud Awan Habiba Ijaz Imran Shabir Chuhan 《Computers, Materials & Continua》 SCIE EI 2023年第9期2631-2647,共17页
Channel assignment has emerged as an essential study subject in Cognitive Radio-basedWireless Mesh Networks(CR-WMN).In an era of alarming increase in Multi-Radio Multi-Channel(MRMC)network expansion interference is de... Channel assignment has emerged as an essential study subject in Cognitive Radio-basedWireless Mesh Networks(CR-WMN).In an era of alarming increase in Multi-Radio Multi-Channel(MRMC)network expansion interference is decreased and network throughput is significantly increased when non-overlapping or partially overlapping channels are correctly integrated.Because of its ad hoc behavior,dynamic channel assignment outperforms static channel assignment.Interference reduces network throughput in the CR-WMN.As a result,there is an extensive research gap for an algorithm that dynamically distributes channels while accounting for all types of interference.This work presents a method for dynamic channel allocations using unsupervisedMachine Learning(ML)that considers both coordinated and uncoordinated interference.Unsupervised machine learning uses coordinated and non-coordinated interference for dynamic channel allocation.To determine the applicability of the proposed strategy in reducing channel interference while increasingWMNthroughput,a comparison analysis was performed.When the simulation results of our proposed algorithm are compared to those of the Routing Channel Assignment(RCA)algorithm,the throughput of our proposed algorithm has increased by 34%compared to both coordinated and non-coordinated interferences. 展开更多
关键词 Carrier sensing interference coordination overlapping channels orthogonal channels
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