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Nonlinear tunnelling of 3D partially nonlocal nonautonomous nondegenerate vector solitons in a linear external potential
Nondegenerate solitons were reported in the localized case, and yet partially nonlocal nonautonomous nondegenerate vector solitons are hardly...
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Nonlocal Effects in Micromechanics of Locally Elastic CMs
For either a statistically inhomogeneous medium or inhomogeneous remote boundary conditions, the eventual abandonment of the hypothesis of...
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Excitation manipulation of three-dimensional completely localized rogue waves in a partially nonlocal and inhomogeneous nonlinear medium
We study a (2 + 1)-dimensional variable-coefficient-coupled partially nonlocal nonlinear Schrödinger equation with nonlinearities localized in x and y ...
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Understanding the first-order inhomogeneous linear elasticity through local gauge transformations
It is well known that classical linear elasticity equations are not form-invariant under local transformations. This is intrinsically related to the...
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Nonlinear Problems in Micromechanics of CMs
For linearizing nonlinear functions (such as the yield or strength criterion, dissipative function) in this chapter, physically consistent...
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Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review
Recently, the mechanical performance of various mechanical, electrical, and civil structures, including static and dynamic analysis, has been widely...
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Subsequent Generalizations of Theory and Related Problems
In this chapter we obtain a unified operator form of the GIE for the general cases of local and nonlocal problems, static, and wave motion phenomena...
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Surface Energy Effect on Free Vibration Characteristics of Nano-plate Submerged in Viscous Fluid
PurposeThe free vibration problem of a thin nanoplate with surface energy immersed in a viscous fluid medium is investigated in this article to...
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Multiparticle Effective Field and Related Methods in Micromechanics of Random Structure Composites
Among the numerous methods in micromechanics mentioned in Chap. 1 (see Willis, J Appl Mech, 50:1202–1209, 1983),...
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Peridynamics Implementation of a Gauge Theory for Brittle Damage in Solids and Applications
We propose a brittle damage model based on linearized kinematic measures derived using a gauge theory. First, we obtain the fully nonlinear kinematic...
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Effect of Carbon Nanotubes and Porosity on Vibrational Behavior of Nanocomposite Structures: A Review
This paper aims to present a comprehensive review of the effect of embedding porosity and enhancing with carbon nanotube (CNT) on the vibrational...
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Trends, directions for further research, and some open problems of fractional calculus
The area of fractional calculus (FC) has been fast develo** and is presently being applied in all scientific fields. Therefore, it is of key...
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Elastic and viscoelastic foundations: a review on linear and nonlinear vibration modeling and applications
This paper presents a comprehensive review on different theoretical elastic and viscoelastic foundation models in oscillatory systems. The review...
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Gradient Extension of Classical Material Models: From Nuclear & Condensed Matter Scales to Earth & Cosmological Scales
The various mathematical models developed in the past to interpret the behavior of natural and manmade materials were based on observations and...
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A Partial Report on the Controversies About the Principle of VirtualWork: From Archytas of Tarentum to Lagrange, Piola, Mindlin and Toupin
In this chapter, we present a historical survey on the Principle of Virtual Work as the guiding principle for constructing mathematical models to...
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Oscillons, walking droplets, and skip** stones (an overview)
This article considers additional phenomena that complement the earlier topics addressed by Ibrahim [(Liquid Sloshing Dynamics: Theory and...
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Generation of ring-shaped optical vortices in dissipative media by inhomogeneous effective diffusion
By means of systematic simulations, we demonstrate generation of a variety of ring-shaped optical vortices (OVs) from a two-dimensional input with...
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Computational Analysis of Smart Magneto-Electro-Elastic Materials and Structures: Review and Classification
Magneto-electro-elastic (MEE) materials have been receiving a special attention from the research community owing to their specialized performance...
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Methodology: Meso-Scale Simulation Approach
Concrete can be regarded as a composite material consisting of aggregate particles, mortar matrix, and ITZ between them at the meso-scale level...
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Continuation for Thin Film Hydrodynamics and Related Scalar Problems
This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the...