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This monograph provides state-of-the-art theoretical and
computational findings from investigations on physical and chemical
dissolution front instability problems in porous media, based on
the author’s own work. Although numerical results are provided to
complement theoretical ones, the focus of this monograph is on the
theoretical aspects of the topic and those presented in this book
are applicable to a wide range of scientific and engineering
problems involving the instability of nonlinear dynamic systems. To
appeal to a wider readership, common mathematical notations are
used to derive the theoretical solutions. The book can be used
either as a useful textbook for postgraduate students or as a
valuable reference book for computational scientists,
mathematicians, engineers and geoscientists.
This monograph provides state-of-the-art theoretical and
computational findings from investigations on physical and chemical
dissolution front instability problems in porous media, based on
the author s own work. Although numerical results are provided to
complement theoretical ones, the focus of this monograph is on the
theoretical aspects of the topic and those presented in this book
are applicable to a wide range of scientific and engineering
problems involving the instability of nonlinear dynamic systems. To
appeal to a wider readership, common mathematical notations are
used to derive the theoretical solutions. The book can be used
either as a useful textbook for postgraduate students or as a
valuable reference book for computational scientists,
mathematicians, engineers and geoscientists."
Geoscience is a fundamental natural science discipline dealing with
the origin, evolutionary history and behaviour of the planet Earth.
As a result of its complicated and complex nature, the Earth system
not only provides the necessary materials and environment for
mankind to live, but also brings many types of natural disasters,
such as earthquakes, volcanic eruptions, tsunamis, ?oods and
tornadoes, to mention just a few. With the ever-increasing demand
for improving our living standards, it has been recognized that the
existing natural resources will be exhausted in the near future and
that our living environments are, in fact, deteriorating. To
maintain the sustainable development of our living standards and
the further improvement of our living environments, an inevitable
and challenging task that geoscientists are now confronting is how
accurately to predict not only the occurrences of these natural
disasters, but also the locations of large concealed natural
resources in the deep Earth. For this reason, geoscientists must
study the processes, rules and laws, by which the Earth system
operates, instead of simply describing and observing g- science
phenomena.
Effective and ef cient modelling of in nite media is important for
the production of accurate and useful solutions for many scienti c
and engineering problems invo- ing in nite domains (Bettess 1977,
1980; Chow and Smith 1981; Medina and Taylor 1983; Zhang and Zhao
1987; Zhao et al. 1989; Zhao and Valliappan 1993a, b, c, d; Astley
1996, 1998; Yang et al. 1996; Yang and Huang 2001; Yun et al. 2000,
2007; Wang et al. 2006). Some typical examples involving in nite
domains are as follows: (1) earthquake wave propagation within the
upper crust of the Earth in the elds of geophysics and seismology;
(2) dynamic structure-foundation interaction in the elds of
geotechnical, civil and dam engineering; and (3) transient pore-
uid ow, heat transfer and mass transport within the interior of the
Earth in the elds of g- science and geoenvironmental engineering.
Although the solid Earth is viewed as a bounded domain at the
terrestrial scale, it can be treated as an unbounded domain at the
human scale. For instance, in the case of predicting possible
property damages caused by an earthquake, only a limited region
around the epicentre is of interest because the earthquake wave
energy is signi cantly reduced as the distance from the epicentre
is increased.
The study of heat transfer mechanisms in hydrothermal systems is
important for understanding the basic physics behind orebody
formation and mineralization in the upper crust (Bickle and
Mckenzie 1987; Bjorlykke et al. 1988; Brady 1988; England and
Thompson 1989; Hoisch 1991; Connolly 1997). Generally, heat energy
may be transferred within the crust in the following forms:
conduction, advection (including forced convection) where the heat
is carried by a moving mass of rock during def- mation or by a
moving uid, convection (i. e. , free convection, natural
convection, buoyancy driven convection, temperature gradient driven
convection) and a com- nation of these processes. Since advective
ow is usually generated by a pore- uid pressure gradient, heat
transfer due to advective ow is largely dependent on the pore- uid
pressure gradient distribution in hydrothermal systems. A typical
ex- ple of this advective ow is the upward through ow caused by
lithostatic pore- uid pressure gradients within the lower crust.
Extensive studies (Connolly and Ko 1995; Etheridge et al. 1983;
England et al. 1987; Fyfe et al. 1978; Walther and Orville 1982;
Peacock 1989; Yardley and Bottrell 1992; Hanson 1992; Yardley and
Lloyd 1995; Norton and Knapp 1970) have shown that lithostatic
pore- uid pressure can be built up by metamorphic uids arising from
devolatilization and dehydration - actions, if the permeability is
low enough to control uid ow in the lower crust.
Geoscience is a fundamental natural science discipline dealing with
the origin, evolutionary history and behaviour of the planet Earth.
As a result of its complicated and complex nature, the Earth system
not only provides the necessary materials and environment for
mankind to live, but also brings many types of natural disasters,
such as earthquakes, volcanic eruptions, tsunamis, ?oods and
tornadoes, to mention just a few. With the ever-increasing demand
for improving our living standards, it has been recognized that the
existing natural resources will be exhausted in the near future and
that our living environments are, in fact, deteriorating. To
maintain the sustainable development of our living standards and
the further improvement of our living environments, an inevitable
and challenging task that geoscientists are now confronting is how
accurately to predict not only the occurrences of these natural
disasters, but also the locations of large concealed natural
resources in the deep Earth. For this reason, geoscientists must
study the processes, rules and laws, by which the Earth system
operates, instead of simply describing and observing g- science
phenomena.
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