Quarterly Journal of Mechanics and Applied Mathematics最新文献

{"title":"Elastic waves inside and on the surface of a half-space","authors":"B. Apostol","doi":"10.1093/QJMAM/HBX009","DOIUrl":"https://doi.org/10.1093/QJMAM/HBX009","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"70 1","pages":"289-308"},"PeriodicalIF":0.9,"publicationDate":"2017-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBX009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47929506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Compensatory axon sprouting for very slow axonal die-back in a transgenic model of spinal muscular atrophy type III.","authors":"Esther Udina, Charles T Putman, Luke R Harris, Neil Tyreman, Victoria E Cook, Tessa Gordon","doi":"10.1113/JP273404","DOIUrl":"10.1113/JP273404","url":null,"abstract":"<p><strong>Key points: </strong>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.</p><p><strong>Abstract: </strong>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.</p>","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"3 1","pages":"1815-1829"},"PeriodicalIF":0.0,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5330916/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83255219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Embedding formulae for scattering in a waveguide containing polygonal obstacles","authors":"N. Biggs","doi":"10.1093/QJMAM/HBW012","DOIUrl":"https://doi.org/10.1093/QJMAM/HBW012","url":null,"abstract":"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 \u0000coefficients 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 \u0000boundaries 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.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"409-429"},"PeriodicalIF":0.9,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBW012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61240945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A sphere in a second degree polynomial creeping flow parallel to a plane, impermeable and slipping wall","authors":"N. Ghalia, F. Feuillebois, A. Sellier","doi":"10.1093/QJMAM/HBW010","DOIUrl":"https://doi.org/10.1093/QJMAM/HBW010","url":null,"abstract":"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.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"46 1","pages":"353-390"},"PeriodicalIF":0.9,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBW010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61240859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Statics of an air-inflated, heavy membrane tube section: membrane extensibility","authors":"Yoon-Rak Choi","doi":"10.1093/QJMAM/HBW011","DOIUrl":"https://doi.org/10.1093/QJMAM/HBW011","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"391-408"},"PeriodicalIF":0.9,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBW011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61240869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A dynamic contact model for viscoelastic plates","authors":"M. Sofonea, K. Bartosz","doi":"10.1093/QJMAM/HBW013","DOIUrl":"https://doi.org/10.1093/QJMAM/HBW013","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"70 1","pages":"1-19"},"PeriodicalIF":0.9,"publicationDate":"2016-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBW013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61240997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solutions of some boundary value problems for a class of constitutive relations for non-linear elastic bodies that is not Green elastic","authors":"R. Bustamante","doi":"10.1093/QJMAM/HBW007","DOIUrl":"https://doi.org/10.1093/QJMAM/HBW007","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"257-279"},"PeriodicalIF":0.9,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBW007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61241307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spectral study of the Laplace–Beltrami operator arising in the problem of acoustic wave scattering by a quarter-plane","authors":"R. Assier, C. Poon, N. Peake","doi":"10.1093/QJMAM/HBW008","DOIUrl":"https://doi.org/10.1093/QJMAM/HBW008","url":null,"abstract":"© 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.","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"281-317"},"PeriodicalIF":0.9,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBW008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61241316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The large-time development of the solution to an initial-value problem for the generalised burgers’ equation","authors":"J. Leach","doi":"10.1093/QJMAM/HBW006","DOIUrl":"https://doi.org/10.1093/QJMAM/HBW006","url":null,"abstract":"","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"231-256"},"PeriodicalIF":0.9,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBW006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61241276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of surface effect of the edge of a half-plane on the stress concentration around a nearby nanosized hole of arbitrary shape","authors":"M. Dai, P. Schiavone, C. Gao","doi":"10.1093/QJMAM/HBW005","DOIUrl":"https://doi.org/10.1093/QJMAM/HBW005","url":null,"abstract":"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)","PeriodicalId":56087,"journal":{"name":"Quarterly Journal of Mechanics and Applied Mathematics","volume":"69 1","pages":"215-229"},"PeriodicalIF":0.9,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/QJMAM/HBW005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61241260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}