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This book describes fundamental physical principles, together with
their mathematical formulations, for modelling the propagation of
signals in nerve fibres. Above all, it focuses on the complex
electro-mechano-thermal process that produces an ensemble of waves
composed of several components, besides the action potential. These
components include mechanical waves in the biomembrane and
axoplasm, together with the temperature change. Pursuing a
step-by-step approach, the content moves from physics and
mathematics, to describing the physiological effects, and finally
to modelling the coupling effects. The assumptions and hypotheses
used for modelling, as well as selected helpful concepts from
continuum mechanics, are systematically explained, and the
modelling is illustrated using the outcomes of numerical
simulation. The book is chiefly intended for researchers and
graduate students, providing them with a detailed description of
how to model the complex physiological processes in nerve fibres.
This book describes fundamental physical principles, together with
their mathematical formulations, for modelling the propagation of
signals in nerve fibres. Above all, it focuses on the complex
electro-mechano-thermal process that produces an ensemble of waves
composed of several components, besides the action potential. These
components include mechanical waves in the biomembrane and
axoplasm, together with the temperature change. Pursuing a
step-by-step approach, the content moves from physics and
mathematics, to describing the physiological effects, and finally
to modelling the coupling effects. The assumptions and hypotheses
used for modelling, as well as selected helpful concepts from
continuum mechanics, are systematically explained, and the
modelling is illustrated using the outcomes of numerical
simulation. The book is chiefly intended for researchers and
graduate students, providing them with a detailed description of
how to model the complex physiological processes in nerve fibres.
This book addresses the modelling of mechanical waves by asking the
right questions about them and trying to find suitable answers. The
questions follow the analytical sequence from elementary
understandings to complicated cases, following a step-by-step path
towards increased knowledge. The focus is on waves in elastic
solids, although some examples also concern non-conservative cases
for the sake of completeness. Special attention is paid to the
understanding of the influence of microstructure, nonlinearity and
internal variables in continua. With the help of many mathematical
models for describing waves, physical phenomena concerning wave
dispersion, nonlinear effects, emergence of solitary waves, scales
and hierarchies of waves as well as the governing physical
parameters are analysed. Also, the energy balance in waves and
non-conservative models with energy influx are discussed. Finally,
all answers are interwoven into the canvas of complexity.
Complex, microstructured materials are widely used in industry and
technology and include alloys, ceramics and composites. Focusing on
non-destructive evaluation (NDE), this book explores in detail the
mathematical modeling and inverse problems encountered when using
ultrasound to investigate heterogeneous microstructured materials.
The outstanding features of the text are firstly, a clear
description of both linear and nonlinear mathematical models
derived for modelling the propagation of ultrasonic deformation
waves, and secondly, the provision of solutions to the
corresponding inverse problems that determine the physical
parameters of the models. The data are related to nonlinearities at
both a macro- and micro- level, as well as to dispersion. The
authors' goal has been to construct algorithms that allow us to
determine the parameters within which we are required to
characterize microstructure. To achieve this, the authors not only
use conventional harmonic waves, but also propose a novel
methodology based on using solitary waves in NDE. The book analyzes
the uniqueness and stability of the solutions, in addition to
providing numerical examples.
Complex, microstructured materials are widely used in industry and
technology and include alloys, ceramics and composites. Focusing on
non-destructive evaluation (NDE), this book explores in detail the
mathematical modeling and inverse problems encountered when using
ultrasound to investigate heterogeneous microstructured materials.
The outstanding features of the text are firstly, a clear
description of both linear and nonlinear mathematical models
derived for modelling the propagation of ultrasonic deformation
waves, and secondly, the provision of solutions to the
corresponding inverse problems that determine the physical
parameters of the models. The data are related to nonlinearities at
both a macro- and micro- level, as well as to dispersion. The
authors' goal has been to construct algorithms that allow us to
determine the parameters within which we are required to
characterize microstructure. To achieve this, the authors not only
use conventional harmonic waves, but also propose a novel
methodology based on using solitary waves in NDE. The book analyzes
the uniqueness and stability of the solutions, in addition to
providing numerical examples.
Since 1972 the Schools on Nonlinear Physics in Gorky have been a
meeting place for Soviet Scientists working in this field. Since
1989 the proceedings appear in English. They present a good cross
section of nonlinear physics in the USSR. This "third volume"
emerged from material presented at the 1989 School. It contains
sections dealing with nonlinear problems in physics and
astrophysics, quantum and solid state physics, dynamical chaos and
self-organization.
TIlis volume contains the contributions to the Euromech Colloquium
No. 241 on Nonlinear Waves in Active Media at the Institute of
Cybernetics of the Estonian Academy of Sciences, Tallinn, Estonia,
USSR, September 27-30, 1988. The Co-chairmen of the Euromech
Colloquium felt that it would be a good service to the community to
publish these proceedings. First, the topic itself dealing with
various wave processes with energy influx is extremely interesting
and attracted a much larger number of participants than usual - a
clear sign of its importance to the scientific community. Second,
Euromech No. 241 was actually the first Euromech Colloquium held in
the Soviet Union and could thus be viewed as a milestone in the
extending scientific contacts between East and West. At the
colloquium 50 researchers working in very different branches of sci
ence met to lecture on their results and to discuss problems of
common interest. An introductory paper by I. Engelbrecht presents
the common motivation and background of the topics covered.
Altogether 36 speakers presented their lectures, of which 30 are
gathered here. The remaining six papers which will appear elsewhere
are listed on page X. In addition, three contributions by authors
who could not attend the colloquium are included. The two lectures
given by A.S. Mikhailov, V.S. Davydov and V.S. Zykov are here
published as one long paper.
Since 1972 the Schools on Nonlinear Physics in Gorky have been a
meeting place for Soviet scientists working in this field. Instead
of producing for the first time English proceedings it has been
decided to present a good cross section of nonlinear physics in the
USSR. Thus the participants at the last School were invited to
provide English reviews and research papers for these two volumes
(which in the years to come will be followed by the proceedings of
forthcoming schools). "The first volume" starts with a historical
overview of nonlinear dynamics from Poincare to the present day and
touches topics like attractors, nonlinear oscillators and waves,
turbulence, pattern formation, and dynamics of structures in
nonequilibrium dissipative media. It then deals with structures,
bistabilities, instabilities, chaos, dynamics of defects in 1d
systems, self-organizations, solitons, spatio-temporal structures
and wave collapse in optical systems, lasers, plasmas,
reaction-diffusion systems and solids."
Since 1972 the Schools on Nonlinear Physics in Gorky have been a
meeting place for Soviet scientists working in this field. Instead
of producing for the first time English proceedings it has been
decided to present a good cross section of nonlinear physics in the
USSR. Thus the participants at the last School were invited to
provide English reviews and research papers for these two volumes
(which in the years to come will be followed by the proceedings of
forthcoming schools). "The second volume" deals with dynamical
chaos in classical and quantum systems, with evolution in chemical
systems and self-organisation in biology, and with applications of
nonlinear dynamics to condensed matter, sea waves, and
astrophysics.
This book addresses the modelling of mechanical waves by asking the
right questions about them and trying to find suitable answers. The
questions follow the analytical sequence from elementary
understandings to complicated cases, following a step-by-step path
towards increased knowledge. The focus is on waves in elastic
solids, although some examples also concern non-conservative cases
for the sake of completeness. Special attention is paid to the
understanding of the influence of microstructure, nonlinearity and
internal variables in continua. With the help of many mathematical
models for describing waves, physical phenomena concerning wave
dispersion, nonlinear effects, emergence of solitary waves, scales
and hierarchies of waves as well as the governing physical
parameters are analysed. Also, the energy balance in waves and
non-conservative models with energy influx are discussed. Finally,
all answers are interwoven into the canvas of complexity.
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