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Equations of Mathematical Diffraction Theory focuses on the
comparative analysis and development of efficient analytical
methods for solving equations of mathematical diffraction theory.
Following an overview of some general properties of integral and
differential operators in the context of the linear theory of
diffraction processes, the authors provide estimates of the
operator norms for various ranges of the wave number variation, and
then examine the spectral properties of these operators. They also
present a new analytical method for constructing asymptotic
solutions of boundary integral equations in mathematical
diffraction theory for the high-frequency case. Clearly
demonstrating the close connection between heuristic and rigorous
methods in mathematical diffraction theory, this valuable book
provides you with the differential and integral equations that can
easily be used in practical applications.
This book addresses theoretical and experimental methods for
exploring microstructured metamaterials, with a special focus on
wave dynamics, mechanics, and related physical properties. The
authors use various mathematical and physical approaches to examine
the mechanical properties inherent to particular types of
metamaterials. These include: * Boundary value problems in reduced
strain gradient elasticity for composite fiber-reinforced
metamaterials * Self-organization of molecules in ferroelectric
thin films * Combined models for surface layers of nanostructures *
Computer simulation at the micro- and nanoscale * Surface effects
with anisotropic properties and imperfect temperature contacts *
Inhomogeneous anisotropic metamaterials with uncoupled and coupled
surfaces or interfaces * Special interface finite elements and
other numerical and analytical methods for composite structures
This volume deals with topical problems concerning technology and
design in construction of modern metamaterials. The authors
construct the models of mechanical, electromechanical and
acoustical behavior of the metamaterials, which are founded upon
mechanisms existing on micro-level in interaction of elementary
structures of the material. The empiric observations on the
phenomenological level are used to test the created models. The
book provides solutions, based on fundamental methods and models
using the theory of wave propagation, nonlinear theories and
composite mechanics for media with micro- and nanostructure. They
include the models containing arrays of cracks, defects, with
presence of micro- and nanosize piezoelectric elements and coupled
physical-mechanical fields of different nature. The investigations
show that the analytical, numerical and experimental methods permit
evaluation of the qualitative and quantitative properties of the
materials of this sort, with diagnosis of their effective
characteristics, frequency intervals of effective energetic cutting
and passing, as well as effective regimes of damage evaluation by
the acoustic methods.
This volume deals with topical problems concerning technology and
design in construction of modern metamaterials. The authors
construct the models of mechanical, electromechanical and
acoustical behavior of the metamaterials, which are founded upon
mechanisms existing on micro-level in interaction of elementary
structures of the material. The empiric observations on the
phenomenological level are used to test the created models. The
book provides solutions, based on fundamental methods and models
using the theory of wave propagation, nonlinear theories and
composite mechanics for media with micro- and nanostructure. They
include the models containing arrays of cracks, defects, with
presence of micro- and nanosize piezoelectric elements and coupled
physical-mechanical fields of different nature. The investigations
show that the analytical, numerical and experimental methods permit
evaluation of the qualitative and quantitative properties of the
materials of this sort, with diagnosis of their effective
characteristics, frequency intervals of effective energetic cutting
and passing, as well as effective regimes of damage evaluation by
the acoustic methods.
This book addresses theoretical and experimental methods for
exploring microstructured metamaterials, with a special focus on
wave dynamics, mechanics, and related physical properties. The
authors use various mathematical and physical approaches to examine
the mechanical properties inherent to particular types of
metamaterials. These include: * Boundary value problems in reduced
strain gradient elasticity for composite fiber-reinforced
metamaterials * Self-organization of molecules in ferroelectric
thin films * Combined models for surface layers of nanostructures *
Computer simulation at the micro- and nanoscale * Surface effects
with anisotropic properties and imperfect temperature contacts *
Inhomogeneous anisotropic metamaterials with uncoupled and coupled
surfaces or interfaces * Special interface finite elements and
other numerical and analytical methods for composite structures
Equations of Mathematical Diffraction Theory focuses on the
comparative analysis and development of efficient analytical
methods for solving equations of mathematical diffraction theory.
Following an overview of some general properties of integral and
differential operators in the context of the linear theory of
diffraction processes, the authors provide estimates of the
operator norms for various ranges of the wave number variation, and
then examine the spectral properties of these operators. They also
present a new analytical method for constructing asymptotic
solutions of boundary integral equations in mathematical
diffraction theory for the high-frequency case.
Clearly demonstrating the close connection between heuristic and
rigorous methods in mathematical diffraction theory, this valuable
book provides you with the differential and integral equations that
can easily be used in practical applications.
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