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Time reversibility, computer simulation, algorithms, chaos
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Description
Rating
Title
Time
reversibility
,
computer
simulation
,
algorithms
,
chaos
Creator
Hoover, William G. (William Graham), 1936
Contributors
Hoover, Carol Griswold.
World Scientific (Firm)
DescriptionAbstract
A
small
army
of
physicists
,
chemists
,
mathematicians
, and
engineers
has
joined
forces
to
attack
a
classic
problem
, the "
reversibility
paradox
", with
modern
tools
. This
book
describes
their
work
from the
perspective
of
computer
simulation
,
emphasizing
the
authors
'
approach
to the
problem
of
understanding
the
compatibility
, and
even
inevitability
, of the
irreversible
second
law
of
thermodynamics
with an
underlying
timereversible
mechanics
.
Computer
simulation
has
made
it
possible
to
probe
reversibility
from a
variety
of
directions
and "
chaos
theory
" or "
nonlinear
dynamics
" has
supplied
a
useful
vocabulary
and a
set
of
concepts
,
which
allow
a
fuller
explanation
of
irreversibility
than that
available
to
Boltzmann
or to
Green
,
Kubo
and
Onsager
.
Clear
illustration
of
concepts
is
emphasized
throughout
, and
reinforced
with a
glossary
of
technical
terms
from the
specialized
fields
which
have been
combined
here to
focus
on a
common
theme
. The
book
begins
with a
discussion
,
contrasting
the
idealized
reversibility
of
basic
physics
against
the
pragmatic
irreversibility
of
real
life
.
Computer
models
, and
simulation
, are
next
discussed
and
illustrated
.
Simulations
provide
the
means
to
assimilate
concepts
through
workedout
examples
.
Stateoftheart
analyses
, from the
point
of
view
of
dynamical
systems
, are
applied
to
manybody
examples
from
nonequilibrium
molecular
dynamics
and to
chaotic
irreversible
flows
from
finitedifference
,
finiteelement
, and
particlebased
continuum
simulations
.
Two
necessary
concepts
from
dynamicalsystems
theory

fractals
and
Lyapunov
instability

are
fundamental
to the
approach
.
Undergraduatelevel
physics
,
calculus
, and
ordinary
differential
equations
are
sufficient
background
for a
full
appreciation
of this
book
,
which
is
intended
for
advanced
undergraduates
,
graduates
, and
research
workers
. The
generous
assortment
of
examples
worked
out
in the
text
will
stimulate
readers
to
explore
the
rich
and
fruitful
field
of
study
which
links
fundamental
reversible
laws
of
physics
to the
irreversibility
surrounding
us
all
. This
expanded
edition
stresses
and
illustrates
computer
algorithms
with
many
new
workedout
examples
, and
includes
considerable
new
material
on
shockwaves
,
Lyapunov
instability
and
fluctuations
.
DescriptionTable Of Contents
1
.
Time
reversibility
,
computer
simulation
,
algorithms
,
chaos
.
1.1
.
Microscopic
reversibility
;
macroscopic
irreversibility
.
1.2
.
Time
reversibility
of
irreversible
processes
.
1.3
.
Classical
microscopic
and
macroscopic
simulation
.
1.4
.
Continuity
,
information
, and
bit
reversibility
.
1.5
.
Instability
and
chaos
.
1.6
.
Simple
explanations
of
complex
phenomena
.
1.7
. The
paradox
:
irreversibility
from
reversible
dynamics
.
1.8
.
Algorithm
:
fourthorder
RungeKutta
integrator
.
1.9
.
Example
problems
.
1.10
.
Summary
and
notes

2
.
Timereversibility
in
physics
and
computation
.
2.1
.
Introduction
.
2.2
.
Time
reversibility
.
2.3
.
Levesque
and
Verlet's
bitreversible
algorithm
.
2.4
.
Lagrangian
and
Hamiltonian
mechanics
.
2.5
.
Liouville's
incompressible
theorem
.
2.6
. What
is
macroscopic
thermodynamics
?
2.7
.
First
and
second
laws
of
thermodynamics
.
2.8
.
Temperature
,
Zeroth
law
,
reservoirs
,
thermostats
.
2.9
.
Irreversibility
from
stochastic
irreversible
equations
.
2.10
.
Irreversibility
from
timereversible
equations
?
2.11
. An
algorithm
implementing
bitreversible
dynamics
.
2.12
.
Example
problems
.
2.13
.
Summary

3
.
Gibbs
'
statistical
mechanics
.
3.1
.
Scope
and
History
.
3.2
.
Formal
structure
of
Gibbs
'
statistical
mechanics
.
3.3
.
Initial
conditions
,
boundary
conditions
,
ergodicity
.
3.4
. From
Hamiltonian
dynamics
to
Gibbs
'
probability
.
3.5
. From
Gibbs
'
probability
to
thermodynamics
.
3.6
.
Pressure
and
energy
from
Gibbs
'
canonical
ensemble
.
3.7
.
Gibbs
'
entropy
versus
Boltzmann's
entropy
.
3.8
.
Numberdependence
and
thermodynamic
fluctuations
.
3.9
.
Green
and
Kubo's
linearresponse
theory
.
3.10
. An
algorithm
for
local
smoothparticle
averages
.
3.11
.
Example
problems
.
3.12
.
Summary

4
.
Irreversibility
in
real
life
.
4.1
.
Introduction
.
4.2
.
Phenomenology

the
linear
dissipative
laws
.
4.3
.
Microscopic
basis
of the
irreversible
linear
laws
.
4.4
.
Solving
the
linear
macroscopic
equations
.
4.5
.
Nonequilibrium
entropy
changes
.
4.6
.
Fluctuations
and
nonequilibrium
states
.
4.7
.
Deviations
from the
phenomenological
linear
laws
.
4.8
.
Causes
of
irreversibility
a
la
Boltzmann
and
Lyapunov
.
4.9
.
RayleighBenard
algorithm
with
atomistic
flow
.
4.10
.
RayleighBenard
algorithm
for a
continuum
.
4.11
.
Three
RayleighBenard
example
problems
.
4.12
.
Summary

5
.
Microscopic
computer
simulation
.
5.1
.
Introduction
.
5.2
.
Integrating
the
motion
equations
.
5.3
.
Interpretation
of
results
.
5.4
.
Control
of a
falling
particle
.
5.5
.
Second
law
of
thermodynamics
.
5.6
.
Simulating
shear
flow
and
heat
flow
.
5.7
.
Shockwaves
.
5.8
.
Algorithm
for
periodic
shear
flow
with
doll's
tensor
.
5.9
.
Example
problems
.
5.10
.
Summary
. ;
8
6
.
Shockwaves
revisited
.
6.1
.
Introduction
.
6.2
.
Equation
of
state
information
from
shockwaves
.
6.3
.
Shockwave
conditions
for
molecular
dynamics
.
6.4
.
Shockwave
stability
.
6.5
.
Thermodynamic
variables
.
6.6
.
Shockwave
profiles
from
continuum
mechanics
6.7
.
Comparing
model
profiles
with
molecular
dynamics
.
6.8
.
Lyapunov
instability
in
strong
shockwaves
.
6.9
.
Summary

7
.
Macroscopic
computer
simulation
.
7.1
.
Introduction
.
7.2
.
Continuity
and
coordinate
systems
.
7.3
.
Macroscopic
flow
variables
.
7.4
.
Finitedifference
methods
.
7.5
.
Finiteelement
methods
.
7.6
.
Smooth
particle
applied
mechanics
[SPAM]
.
7.7
. A
SPAM
algorithm
for
RayleighBenard
convection
.
7.8
.
Applications
of
SPAM
to
RayleighBenard
flows
.
7.9
.
Summary

8
.
Chaos
,
Lyapunov
instability
,
fractals
.
8.1
.
Introduction.{esc}{dollar}1
Publisher
World Scientific Pub. Co.
Subject
Statistical mechanics.
Time reversal  Computer simulation.
Identifier
9789814383172
(electronic
bk.)
;
9814383163
;
9789814383165
;
http://www.worldscientific.com/worldscibooks/10.1142/8344#t=toc
Language
eng
Type
Electronic books.
FormatExtent
xxiv, 401 p. : ill. (some col.)
Date
c2012
.
RelationIs Part Of
Advanced series in nonlinear dynamics
v. 13
OCLC number
874502270
CONTENTdm number
412
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