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Applied Wave Mathematics II

Part of the Mathematics of Planet Earth Book Series (volume 6)

Editors: Berezovski, Arkadi; Soomere, Tarmo

DOI: 10.1007/978-3-030-29951-4

ISBN: 978-3-030-29950-7

Publisher: Springer International Publishing - Springer Journals

Nov 16, 2019

1 - 10 of 16 Chapters

LitStream

An Approximate Theory of Linear Waves in an Elastic Layer and Its Relation to Microstructured Solids

Braun, Manfred; Randrüüt, Merle

Pages: 3 –27

[For the dynamics of an infinite elastic layerElastic layer or plateElastic plate, an approximate model is introduced. The governing equations are obtained by Lagrange’s methodLagrange method with suitable restrictions imposed to the transverse deformation of the layer. It turns out that the...
LitStream

Antiplane Surface Wave Propagation Within the Stress Gradient Surface Elasticity

Eremeyev, Victor A.

Pages: 29 –37

[We discuss a new class of antiplane surface wavesAnti-plane surface wave in an elastic half space with surface stresses. Here we consider a surface elasticity within stress gradient modelStress-gradient model, that is when the surface stresses relate to surface strains through an integral...
LitStream

Dispersive and Nondispersive Nonlinear Long Wave Transformations: Numerical and Experimental Results

Torsvik, Tomas; Abdalazeez, Ahmed; Dutykh, Denys; Denissenko, Petr; Didenkulova, Ira

Pages: 41 –60

[The description of gravity wavesSurface gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long wavesLong waves in shallow waterShallow water. This provides...
LitStream

Nonlinear Models of Finite Amplitude Interfacial Waves in Shallow Two-Layer Fluid

Kurkina, Oxana; Kurkin, Andrey; Pelinovsky, Efim; Stepanyants, Yury; Talipova, Tatiana

Pages: 61 –87

[We present an example of systematic use of asymptotic methods for the description of long wavesLong waves at the interface between two fluids of different densities. The governing equations for weakly nonlinear long interfacial waves are consistently derived for a general case of nonpotential...
LitStream

Emergence of Solitonic Structures in Hierarchical Korteweg–de Vries Systems

Salupere, Andrus; Lints, Martin; Ilison, Lauri

Pages: 89 –124

[We explore numerically different types of solutions of a hierarchical Korteweg–de Vries equationKorteweg–de Vries (KdV) equationhierarchical (Giovine and Oliveri, Meccanica 30(4), 341–357 (1995)) that describes inter alia wave propagation in microstructuredMicrostructured material (dilatant...
LitStream

Nonlinear Longitudinal Bulk Strain Waves in Layered Elastic Waveguides

Khusnutdinova, Karima R.; Tranter, Matthew R.

Pages: 125 –150

[We consider long longitudinal bulk strain wavesStrain wave in layered waveguidesLayered waveguide using Boussinesq-type equationsBoussinesq(-type) equation. The equations are developed using lattice modelsLattice model, and this is viewed as an extension of the Fermi–Pasta–Ulam...
LitStream

On Two-Dimensional Longitudinal Nonlinear Waves in Graphene Lattice

Porubov, Alexey V.; Osokina, Alena E.

Pages: 151 –166

[A two-dimensional graphene lattice modelLattice modelgraphene with translational and angular interactions between the elements of two sublattices is considered. The nonlinearity is introduced via nonlinearly elastic translational forces between the masses in the lattice. The nonlinear strain...
LitStream

Shock Waves in Hyperbolic Systems of Nonequilibrium Thermodynamics

Ruggeri, Tommaso; Taniguchi, Shigeru

Pages: 167 –186

[We present the state of the art of the mathematical theory of shock wavesShock wave for hyperbolic systems. We start with a brief review of ideal shock wavesShock wave discussing, in particular, the Riemann problemRiemann problem and the phase transition induced by shock wavesShock wave in real...
LitStream

Linear and Nonlinear Theories for Thermoacoustic Waves in a Gas Filled Tube Subject to a Temperature Gradient

Sugimoto, Nobumasa; Shimizu, Dai

Pages: 187 –204

[This article reviews briefly the linear and nonlinear theories of thermoacoustic wavesThermoacoustic wave in a gas filled tube subject to a temperature gradient. In the framework of fluid dynamics, asymptotic theories are developed by two parameters on the basis of a narrow tube approximation....
LitStream

Mathematics of Nerve Signals

Peets, Tanel; Tamm, Kert

Pages: 207 –238

[Since the classical works of Hodgkin and Huxley (J. Physiol. 117(4), 500–544 (1952)), it has become evident that the nerve function is a richer phenomenon than a set of electrical action potentialsAction potential (APAction potential) alone. The propagation of an APAction potential is...

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