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  • 1
    Electronic Resource
    Electronic Resource
    Coupled nonlinear Schrödinger equations arising in the study of monomode step-index optical fibers (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 930-936 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper it is shown that nonlinear propagation in a step-index, "monomode'' optical fiber is not generally governed by the nonlinear Schrödinger equation, even when the fiber is axially symmetric. It is governed by a coupled pair of nonlinear partial differential equations that includes the nonlinear Schrödinger equations only as a special case. Three simple types of solution to the coupled system are analyzed and the corresponding field patterns are interpreted. One case shows that, for uniform wavetrains, nonlinearity not only alters the phase speed but also causes the field pattern in an "elliptically polarized'' mode to rotate gradually about the fiber axis. The other two cases each allow the system to be reduced to a single nonlinear Schrödinger equation, so showing two distinct situations in which solutions have soliton properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528360
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  • 2
    Electronic Resource
    Electronic Resource
    On the derivation of nonlinear rod theories from three-dimensional elasticity (1984)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 35 (1984), S. 833-847 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Sommario A partire dell'elasticità tridimensionale, si dedottono le leggi costituive non-lineare elastiche per verghe sottile, utilizzando un metodo asintotico in coordinate materiau delle scale opportune. Benchè la deformazione sia piccolò, i dislocamenti e le rotazioni possono essere grandi ed il comportamento elastico è non-lineare. Nella teoria delle verghe del ordine molto basso, la coppiarisultanta ed il carico tensile si esprimono come derivate di una energia trasversale. Le equazioni di questa teoria sono analoghe di quelle nella teoria direttiva di Green & Laws. Un procedimento iterativo è delineato per la generazione delle teorie delle verghe di ordini superiori.
    Notes: Summary Nonlinear elastic constitutive laws for slender rods are derived from three-dimensional elasticity, using an asymptotic analysis in appropriate scaled material coordinates. Although the strain is everywhere small, displacements and rotations may be large and the elastic behaviour is nonlinear. In the lowest-order rod theory, the couple-resultant and tensile load are expressed as derivatives of a cross-sectional energy. The equations of this theory are similar to those in a director theory of Green and Laws. An iterative procedure for the generation of higher order rod theories is outlined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945447
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  • 3
    Electronic Resource
    Electronic Resource
    Finite amplitude one-dimensional pulses in an inhomogeneous granular material (1980)
    Springer
    Archive for rational mechanics and analysis 72 (1980), S. 265-284 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00281592
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  • 4
    Electronic Resource
    Electronic Resource
    Locally ‘simple’ unsteady deformations (1977)
    Springer
    Rheologica acta 16 (1977), S. 134-145 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Es werden verschiedene Verfahren beschrieben, mit denen exakte Lösungen nichtlinearer Gleichungen als lokale Approximationen allgemeinerer Deformationen benutzt werden können. Die Theorie der modulierten einfachen Wellen und die Whitham-Luke-Beschreibung von Modulationen in periodischen Wellenzügen werden verglichen. Die Rolle von Idealisierungen im Materialgesetz wird ebenfalls diskutiert. Die durch Inkompressibilität und Unausdehnbarkeit von Fasern eingeführten kinematischen Zwangsbedingungen führen zu einfach beschreibbaren Deformationen. Diese sind lokale Approximationen zu Deformationen in fast inkompressiblen und nahezu unausdehnbaren Körpern.
    Notes: Summary Various procedures by which exact solutions of nonlinear equations may be used as local approximations to more general deformations are described. The theory of modulated simple waves and the Whitham/Luke description of modulations in periodic wavetrains are compared. The role of material idealisations is also discussed. Incompressibility and fibre inextensibility introduce kinematic constraints which lead to simply described deformations. These are local approximations to nearly incompressible and almost inextensible deformations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01527910
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  • 5
    Electronic Resource
    Electronic Resource
    The spreading of nonlinear elastic surface waves (1990)
    Springer
    Journal of elasticity 24 (1990), S. 79-103 
    Details
    ISSN: 1573-2681
    Keywords: 73C50 ; 73D20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A theory for the lateral spreading of a beam of nonlinear surface acoustic waves across the surface of an arbitrary, homogeneous, elastic half-space is developed. The resulting evolution equation generalizes that obtained for uni-directional waves by replacing an ordinary derivative by a diffusion operator of Schrödinger type. The coefficients arising in the evolution equation are related to partial derivatives of the dispersion relation for linearized surface waves on the half space. Details are given for isotropic materials and for two special cases of beams travelling along axes of high elastic symmetry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00115554
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  • 6
    Electronic Resource
    Electronic Resource
    Dynamic flexural deformations in an ideal fibre-reinforced slab (1980)
    Springer
    Journal of engineering mathematics 14 (1980), S. 57-75 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary A kinematic description is derived for plane strain deformations of unrestricted amplitude in an incompressible material ideally reinforced parallel to one axis of Lagrangian coordinates. The deformation is simply related to the configuration of one reference ‘fibre’. For a slab of uniform thickness, equations of motion are derived by integration over cross-sections. They relate the motion of the central fibre to the resultant tensile and shearing loads over each cross section. The equations predict that, in many materials, flexural waves may propagate. In this paper only elastic materials are considered. The simple wave solutions are discussed, showing how wave profiles may distort until a ‘crease’ forms at one surface of the slab. These creases play a role somewhat similar to shocks in gas dynamics. Some novel differences are revealed by an analysis of the equations governing deformations on either side of a crease.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00042865
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  • 7
    Electronic Resource
    Electronic Resource
    Analysis and computation for nonlinear elastic surface waves of permanent form (1985)
    Springer
    Journal of elasticity 15 (1985), S. 389-426 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Linear elastic surface waves are nondispersive. All wavelengths travel at the Rayleigh wave speed c R. This absence of frequency dispersion means that nonlinear waves of permanent form cannot be determined as a small perturbation from a sinusoidal wavetrain. By representing the general Rayleigh wave of the linear theory in terms of a pair of conjugate harmonic functions, waves which propagate without distortion are characterized as those having surface elevation profiles which satisfy a certain nonlinear functional equation. In the small-strain limit, this reduces to a quadratic functional equation. Methods for the analysis of this equation are presented for both periodic and nonperiodic waveforms. For periodic waveforms, the infinite system of quadratic equations for the Fourier coefficients of the profile is solved numerically in the case of a certain ‘harmonic’ elastic material. Two distinct families of profiles having phase speed differing from the linearized Rayleigh wave speed are found. Additionally, two families of exceptional waveforms are found, describing profiles which travel at the Rayleigh wave speed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00042530
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  • 8
    Electronic Resource
    Electronic Resource
    An extension of Key's principle to nonlinear elasticity (2000)
    Springer
    Journal of engineering mathematics 37 (2000), S. 171-190 
    Details
    ISSN: 1573-2703
    Keywords: nonlinear elasticity ; near incompressibility ; variational formulation ; finite deformations ; finite elements.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract A variational principle for finite isothermal deformations of anisotropic compressible and nearly incompressible hyperelastic materials is presented. It is equivalent to the nonlinear elastic field (Lagrangian) equations expressed in terms of the displacement field and a scalar function associated with the hydrostatic mean stress. The formulation for incompressible materials is recovered from the compressible one simply as a limit. The principle is particularly useful in the development of finite element analysis of nearly incompressible and of incompressible materials and is general in the sense that it uses a general form of constitutive equation. It can be considered as an extension of Key's principle to nonlinear elasticity. Various numerical implementations are used to illustrate the efficiency of the proposed formulation and to show the convergence behaviour for different types of elements. These numerical tests suggest that the formulation gives results which change smoothly as the material varies from compressible to incompressible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004734311626
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  • 9
    Electronic Resource
    Electronic Resource
    Explicit solitary and periodic solutions for optical cascading (1999)
    Springer
    Journal of engineering mathematics 36 (1999), S. 149-162 
    Details
    ISSN: 1573-2703
    Keywords: optical cascading ; exact solutions ; Jacobian elliptic functions ; spatial vector solitons.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Many types of periodic solutions to the pair of nonlinear partial differential equations describing optical cascading are obtained in terms of Jacobian elliptic functions. The choice of appropriate forms for periodic solutions is based on the known solitary-wave solutions of the system. By a straightforward procedure for determining coefficients, it is possible to construct periodic analogues of some classes of solitary wave solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004502225151
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Changes in strength and cross sectional area of the elbow flexors as a result of isometric strength training (1988)
    Springer
    European journal of applied physiology 57 (1988), S. 667-670 
    Details
    ISSN: 1439-6327
    Keywords: Strength training ; Isometric force ; Muscle size
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Changes in strength and size of the elbow flexor muscles have been compared during six weeks of isometric strength training in six male and six female subjects. Isometric training of one arm resulted in a significant increase in isometric force (14.5±5.1%, mean±SD,n = 12). No differences were seen in the response of male and female subjects. The extent of the change was similar to that reported for training studies of other muscles, thus refuting the suggestion that the elbow flexors may be especially amenable to training. Biceps and brachialis cross-sectional area (CSA) was measured from mid-upper arm X-ray computerized tomography before and after training. Muscles increased in area (5.4±3.8%) but this was smaller than, and not correlated with, the increase in strength. The main change in the first six weeks of strength training was therefore an increase in the force generated per unit cross-sectional area of muscle. The arrangement of fibres in the biceps is nearly parallel to the action of the muscle and it is argued that the increase in force per unit cross-sectional area is unlikely to be due to changes in the pennation of the muscle fibres as has been suggested for other muscles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01075986
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