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Elastic waves inside and on the surface of a half-space 半空间内部和表面的弹性波
IF 0.9 4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2017-08-01 DOI: 10.1093/QJMAM/HBX009
B. Apostol
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引用次数: 11
Compensatory axon sprouting for very slow axonal die-back in a transgenic model of spinal muscular atrophy type III. 脊髓性肌肉萎缩症 III 型转基因模型中极慢轴突回缩的补偿性轴突萌发。
4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2017-03-01 Epub Date: 2017-01-25 DOI: 10.1113/JP273404
Esther Udina, Charles T Putman, Luke R Harris, Neil Tyreman, Victoria E Cook, Tessa Gordon

Key points: Smn+/- transgenic mouse is a model of the mildest form of spinal muscular atrophy. Although there is a loss of spinal motoneurons in 11-month-old animals, muscular force is maintained. This maintained muscular force is mediated by reinnervation of the denervated fibres by surviving motoneurons. The spinal motoneurons in these animals do not show an increased susceptibility to death after nerve injury and they retain their regenerative capacity. We conclude that the hypothesized immaturity of the neuromuscular system in this model cannot explain the loss of motoneurons by systematic die-back.

Abstract: Spinal muscular atrophy (SMA) is a common autosomal recessive disorder in humans and is the leading genetic cause of infantile death. Patients lack the SMN1 gene with the severity of the disease depending on the number of copies of the highly homologous SMN2 gene. Although motoneuron death in the Smn+/- transgenic mouse model of the mildest form of SMA, SMA type III, has been reported, we have used retrograde tracing of sciatic and femoral motoneurons in the hindlimb with recording of muscle and motor unit isometric forces to count the number of motoneurons with intact neuromuscular connections. Thereby, we investigated whether incomplete maturation of the neuromuscular system induced by survival motoneuron protein (SMN) defects is responsible for die-back of axons relative to survival of motoneurons. First, a reduction of ∼30% of backlabelled motoneurons began relatively late, at 11 months of age, with a significant loss of 19% at 7 months. Motor axon die-back was affirmed by motor unit number estimation. Loss of functional motor units was fully compensated by axonal sprouting to retain normal contractile force in four hindlimb muscles (three fast-twitch and one slow-twitch) innervated by branches of the sciatic nerve. Second, our evaluation of whether axotomy of motoneurons in the adult Smn+/- transgenic mouse increases their susceptibility to cell death demonstrated that all the motoneurons survived and they sustained their capacity to regenerate their nerve fibres. It is concluded the systematic die-back of motoneurons that innervate both fast- and slow-twitch muscle fibres is not related to immaturity of the neuromuscular system in SMA.

要点Smn+/- 转基因小鼠是脊髓性肌萎缩症最轻型的模型。虽然 11 个月大的小鼠会丧失脊髓运动神经元,但肌肉力量仍能保持。这种肌肉力量的维持是通过存活的运动神经元对失去神经支配的纤维进行再神经支配来实现的。这些动物的脊髓运动神经元在神经损伤后并没有表现出更高的易死性,而且它们仍具有再生能力。摘要:脊髓性肌萎缩症(SMA)是人类常见的常染色体隐性遗传疾病,也是婴儿死亡的主要遗传原因。患者缺乏 SMN1 基因,疾病的严重程度取决于高度同源的 SMN2 基因的拷贝数。虽然有报道称最轻型 SMA(SMA III 型)的 Smn+/- 转基因小鼠模型中存在运动神经元死亡,但我们利用逆行追踪后肢坐骨神经和股运动神经元并记录肌肉和运动单元等长力的方法来计算具有完整神经肌肉连接的运动神经元数量。因此,我们研究了存活运动神经元蛋白(SMN)缺陷引起的神经肌肉系统不完全成熟是否是轴突回缩而非运动神经元存活的原因。首先,背标运动神经元减少的时间相对较晚,在11个月大时减少了30%,在7个月大时显著减少了19%。运动神经元数量的估计证实了运动轴突的死亡。在坐骨神经分支支配的四块后肢肌肉(三块快肌腱肌肉和一块慢肌腱肌肉)中,功能性运动单位的缺失被轴突萌发完全补偿,从而保持了正常的收缩力。其次,我们对成年 Smn+/- 转基因小鼠运动神经元的轴突切除是否会增加它们对细胞死亡的易感性进行了评估,结果表明所有的运动神经元都存活了下来,而且它们保持了再生神经纤维的能力。结论是,支配快慢肌纤维的运动神经元的系统性死亡与 SMA 神经肌肉系统的不成熟无关。
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引用次数: 0
Embedding formulae for scattering in a waveguide containing polygonal obstacles 包含多边形障碍物的波导中散射的嵌入公式
IF 0.9 4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2016-11-01 DOI: 10.1093/QJMAM/HBW012
N. Biggs
For certain wave scattering problems embedding formulae can be derived, which express the solution, or far-field behaviour of the solution, for arbitrary plane wave incident angle in terms of the corresponding quantities for a finite number of other related problems. Their scope has so far been limited to scattering in R^2, and to a lesser extent R^3; in this paper we derive embedding formulae for wave scattering in a class of two-dimensional waveguide. The waveguide is straight and of uniform width outside a finite length region within which the boundaries are piecewise-linear and the waveguide can contain polygonal obstacles, a restriction being that all boundaries of the waveguide and obstacles must be inclined at a rational angle to the axis of the waveguide. Once solutions are determined for a finite set of incident propagating modes, the embedding formulae provide expressions for reflection and transmission coefficients for all remaining incident propagating modes. The precise number of solutions required is a function of the number and nature of the corners of the boundaries and obstacles. The formulae are illustrated for a particular waveguide geometry for which the problem can be formulated as an integral equation and approximate numerical solutions determined using the Galerkin method.
对于某些波散射问题,可以导出嵌入公式,用有限个其他相关问题的相应量表示任意平面波入射角的解或解的远场行为。到目前为止,它们的范围仅限于R^2的散射,以及较小程度的R^3;本文导出了一类二维波导中波散射的嵌入公式。波导在有限长度区域外是直的,宽度均匀,在有限长度区域内的边界是分段线性的,波导可以包含多边形障碍物,限制是波导和障碍物的所有边界必须与波导的轴线以合理的角度倾斜。一旦确定了一组有限的入射传播模式的解,嵌入公式提供了所有剩余的入射传播模式的反射和透射系数的表达式。所需解决方案的精确数量是边界和障碍的角的数量和性质的函数。公式说明了一个特定的波导几何形状的问题,可以表述为一个积分方程和近似数值解确定使用伽辽金方法。
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引用次数: 1
A sphere in a second degree polynomial creeping flow parallel to a plane, impermeable and slipping wall 一种与平面、不透水和滑动壁面平行的二阶多项式蠕变流球体
IF 0.9 4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2016-11-01 DOI: 10.1093/QJMAM/HBW010
N. Ghalia, F. Feuillebois, A. Sellier
The motion of a solid and no-slip spherical body immersed in a Newtonian liquid near a motionless, plane and impermeable slip wall is investigated, in the creeping flow approximation, using on the wall the Navier slip boundary condition. The considered cases are as follows (i) a sphere either translating or rotating parallel to the wall in a quiescent liquid; (ii) a sphere either held fixed or freely-suspended in a modulated, linear or quadratic ambient shear flow. For each case, the velocity and pressure fields about the sphere together with the associated physical quantities whenever relevant (the force, torque, non-zero stresslet component on the sphere and its translational and angular velocities) are expressed in bipolar coordinates as infinite series, the coefficients of which are governed by an infinite linear system. This system is solved numerically by first truncating at an order depending on the relevant quantity and on the sphere location and wall slip length and then applying either a Gaussian elimination or a Thomas’ algorithm for inverting a large tridiagonal matrix. Handy formulae for all key quantities are also derived as asymptotic expansions for a sphere-wall gap that is large compared with the sphere radius. The sensitivity of the computed associated normalized friction factors (force, torque, stresslet) and mobilities (translational and angular velocities) to both the sphere location and the wall slip length are then discussed.
在蠕变流动近似下,利用Navier滑移边界条件,研究了固体无滑移球体在靠近不动的、平面的、不透水的滑移壁上浸入牛顿液体中的运动。所考虑的情况如下:(i)一个球体在静止的液体中平行于壁面平移或旋转;(ii)在调制的、线性的或二次的环境剪切流中固定或自由悬浮的球体。对于每种情况,球体的速度和压力场以及相关的物理量(力,扭矩,球体上的非零应力分量及其平动和角速度)在双极坐标中表示为无穷级数,其系数由无限线性系统控制。该系统通过首先根据相关数量和球体位置和壁滑移长度按顺序截断,然后应用高斯消去法或托马斯算法对大型三对角矩阵进行反演来进行数值求解。对于与球半径相比较大的球壁间隙,还可以推导出所有关键量的简便公式。然后讨论了计算出的相关归一化摩擦系数(力、扭矩、应力)和可动性(平动速度和角速度)对球体位置和壁面滑移长度的敏感性。
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引用次数: 4
Statics of an air-inflated, heavy membrane tube section: membrane extensibility 充气、重膜管截面的静力学:膜的延伸性
IF 0.9 4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2016-11-01 DOI: 10.1093/QJMAM/HBW011
Yoon-Rak Choi
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引用次数: 0
A dynamic contact model for viscoelastic plates 粘弹性板的动态接触模型
IF 0.9 4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2016-09-15 DOI: 10.1093/QJMAM/HBW013
M. Sofonea, K. Bartosz
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引用次数: 4
Solutions of some boundary value problems for a class of constitutive relations for non-linear elastic bodies that is not Green elastic 非格林弹性非线性弹性体的一类本构关系边值问题的解
IF 0.9 4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2016-08-01 DOI: 10.1093/QJMAM/HBW007
R. Bustamante
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引用次数: 6
Spectral study of the Laplace–Beltrami operator arising in the problem of acoustic wave scattering by a quarter-plane 声波经四分之一平面散射问题中拉普拉斯-贝尔特拉米算子的频谱研究
IF 0.9 4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2016-08-01 DOI: 10.1093/QJMAM/HBW008
R. Assier, C. Poon, N. Peake
© 2016 Published by Oxford University Press 2016. The Laplace-Beltrami operator (LBO) on a sphere with a cut arises when considering the problem of wave scattering by a quarter-plane. Recent methods developed for sound-soft (Dirichlet) and sound-hard (Neumann) quarter-planes rely on an a priori knowledge of the spectrum of the LBO. In this article we consider this spectral problem for more general boundary conditions, including Dirichlet, Neumann, real and complex impedance, where the value of the impedance varies like α/r, r being the distance from the vertex of the quarter-plane and α being constant, and any combination of these. We analyse the corresponding eigenvalues of the LBO, both theoretically and numerically. We show in particular that when the operator stops being self-adjoint, its eigenvalues are complex and are contained within a sector of the complex plane, for which we provide analytical bounds. Moreover, for impedance of small enough modulus |α|, the complex eigenvalues approach the real eigenvalues of the Neumann case.
©2016牛津大学出版社2016年出版。当考虑波在四分之一平面上的散射问题时,产生了带切口球面上的拉普拉斯-贝尔特拉米算子。最近开发的声软(狄利克雷)和声硬(诺伊曼)四分之一平面的方法依赖于LBO频谱的先验知识。在本文中,我们考虑更一般的边界条件下的谱问题,包括狄利克雷,诺伊曼,实阻抗和复阻抗,其中阻抗的值像α/r一样变化,r是到四分之一平面顶点的距离,α是常数,以及这些的任何组合。本文从理论和数值两方面分析了杠杆收购的相应特征值。我们特别证明了当算子停止自伴随时,它的特征值是复的,并且包含在复平面的一个扇形内,对此我们提供了解析界。此外,对于模量|α|足够小的阻抗,复特征值接近于Neumann情况下的实特征值。
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引用次数: 12
The large-time development of the solution to an initial-value problem for the generalised burgers’ equation 广义汉堡方程初值问题解的大时间发展
IF 0.9 4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2016-08-01 DOI: 10.1093/QJMAM/HBW006
J. Leach
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引用次数: 0
Influence of surface effect of the edge of a half-plane on the stress concentration around a nearby nanosized hole of arbitrary shape 半平面边缘表面效应对任意形状纳米孔附近应力集中的影响
IF 0.9 4区 工程技术 Q3 MATHEMATICS, APPLIED Pub Date : 2016-08-01 DOI: 10.1093/QJMAM/HBW005
M. Dai, P. Schiavone, C. Gao
QJMAM: The Quarterly Journal of Mechanics & Applied Mathematics Page: 215 215–230 INFLUENCE OF SURFACE EFFECT OF THE EDGE OF A HALF-PLANE ON THE STRESS CONCENTRATION AROUND A NEARBY NANOSIZED HOLE OF ARBITRARY SHAPE by MING DAI† (State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China and Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 1H9) PETER SCHIAVONE‡ (Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 1H9)
QJMAM:力学与应用数学季刊戴明(南京航空航天大学力学与机械结构控制国家重点实验室,南京210016;加拿大阿尔伯塔大学机械工程系,加拿大埃德蒙顿T6G 1H9) PETER SCHIAVONE‡(加拿大阿尔伯塔大学机械工程系,埃德蒙顿)加拿大阿尔伯塔省T6G 1H9)
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引用次数: 16
期刊
Quarterly Journal of Mechanics and Applied Mathematics
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