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Foreword

Both

of the authors of

this

book

are

disciples

and

collaborators of the

Brussels school of thermodynamics. Their

particular

domain

of competence

the

application of numerical

methods

the

many

highly nonlinear problems

which

have

arisen in the context of recent developments in the thermodynamics

irreversi-

ble

processes:

stability

states

far

from

equilibrium, search for marginal

critical

states,

bifwrcation

phenomena,

multiple stationnary

states,

dissipative

structures,

etc.

These

problems cannot in general

handled using only the

clas-

sical

and

mathematically rigorous

methods

the theory of

differential,

partial

differential,

and

int~grodifferential

equations.

The

present authors demonstrate

how

approximate methods, re

lyi

usually

powerful computers, lead

significant

progress

these

areas,

one

prepa-

red to accept a

certain

lack of

rigor,

such

as,

for

example, the lack of proof for

the convergence of the

series

used in the context of problems

which

are not

self

adjoint,

nor

even

linear.

The

results

thus obtained

must

consequently

submit-

ted

exacting confrontation with experimental observations.

Even

though, the

imited information obtained concerning

the,

often unsuspec-

ted,

mechanisms

underlying the observed

phenomena

both precious

and

frequently

sufficient.

This information

results

from

the properties of the

trial

functions

best

suited

the

constraints

of the

problem

such

the

initial,

boundary,

and

"feedback" conditions,

and

the analysis of

their

behavior in the course of the

evolution of the system.

One

can

understand,

therefore,

the appeal

such

a subject presents

the au-

thors

whose

training

encompasses comfortably both theory

and

experiment.

this

connection

will

noticed

that

most

of the subjects

treated

this

volume

have

been

thoroughly investigated

from

both points of

view

these selfsame au-

thors.

has

been

their

experience

that

these problems

necessitate

long calcula-

tions

and

almost invariably

imply

intensive

use

of the computer.

Nevertheless, in

spite

their

large

size,

the

calculations

are generally

sJmple,

least

for the reader

familiar

with the rules of usual algebra

and

clas-

sical

analysis. Certainly the authors

have

aimed

larger

public,

less

fami-

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