Random walks often provide the underlying mesoscopic mechanism for transport phenomena in physics, chemistry and biology. In particular, anomalous transport in branched structures has attracted considerable attention. Combs are simple caricatures of various types of natural branched structures that belong to the category of loopless graphs. The comb model was introduced to understand anomalous transport in percolation clusters. Comb-like models have been widely adopted to describe kinetic processes in various experimental applications in medical physics and biophysics, chemistry of polymers, semiconductors, and many other interdisciplinary applications.The authors present a random walk description of the transport in specific comb geometries, ranging from simple random walks on comb structures, which provide a geometrical explanation of anomalous diffusion, to more complex types of random walks, such as non-Markovian continuous-time random walks. The simplicity of comb models allows to perform a rigorous analysis and to obtain exact analytical results for various types of random walks and reaction-transport processes.
This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simply classical diffusion (Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties. Topics addressed include transport with inertia, described by persistent random walks and hyperbolic reaction-transport equations and transport by anomalous diffusion, in particular subdiffusion, where the mean square displacement grows sublinearly with time. In particular reaction-diffusion systems are studied where the medium is in turn either spatially inhomogeneous, compositionally heterogeneous or spatially discrete. Applications span a vast range of interdisciplinary fields and the systems considered can be as different as human or animal groups migrating under external influences, population ecology and evolution, complex chemical reactions, or networks of biological cells. Several chapters treat these applications in detail.
This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simply classical diffusion (Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties. Topics addressed include transport with inertia, described by persistent random walks and hyperbolic reaction-transport equations and transport by anomalous diffusion, in particular subdiffusion, where the mean square displacement grows sublinearly with time. In particular reaction-diffusion systems are studied where the medium is in turn either spatially inhomogeneous, compositionally heterogeneous or spatially discrete. Applications span a vast range of interdisciplinary fields and the systems considered can be as different as human or animal groups migrating under external influences, population ecology and evolution, complex chemical reactions, or networks of biological cells. Several chapters treat these applications in detail.
Random walks often provide the underlying mesoscopic mechanism for transport phenomena in physics, chemistry and biology. In particular, anomalous transport in branched structures has attracted considerable attention. Combs are simple caricatures of various types of natural branched structures that belong to the category of loopless graphs. The comb model was introduced to understand anomalous transport in percolation clusters. Comb-like models have been widely adopted to describe kinetic processes in various experimental applications in medical physics and biophysics, chemistry of polymers, semiconductors, and many other interdisciplinary applications.The authors present a random walk description of the transport in specific comb geometries, ranging from simple random walks on comb structures, which provide a geometrical explanation of anomalous diffusion, to more complex types of random walks, such as non-Markovian continuous-time random walks. The simplicity of comb models allows to perform a rigorous analysis and to obtain exact analytical results for various types of random walks and reaction-transport processes.
Although the manifestation of what is taken to be indigenous knowledge could presumably be traced back roughly to the origins of humankind, the idea of indigenous knowledge is a fairly recent phenomenon. It has arguably gained conceptual and discursive currency only over the past half century, with a veritable slew of conferences, workshops, special journal editions, and anthologies devoted to the topic. Yet, there has been no treatise that offers a comprehensive, critical examination of this notion. Accounts of indigenous knowledge usually focus on explanations of “indigenous,” “local,” “traditional,” “African” and the like – but to date not a single defense of indigenous knowledge has bothered to explain the particular understanding of “knowledge” the authors are working with. Indigenous Knowledge: Philosophical and Educational Considerations’s critique of the idea of indigenous knowledge should in no way be understood as an endorsement of the evils of colonial conquest and (ongoing) exploitation, oppression, and subjugation. Nor should it be taken as an indication of a failure on the part of the Kai Horsthemke to sympathize with the struggle of indigenous peoples the world over for a dignified and sustainable way of life, for personal and communal space, and for self-determination. The aim of the book is to provide especially “indigenous” educators with theoretical tools for critical reflection and interrogation of their own and others’ preconceptions, assumptions, and epistemic practices and customs.
The study of phase transitions is among the most fascinating fields in physics. Originally limited to transition phenomena in equilibrium systems, this field has outgrown its classical confines during the last two decades. The behavior of far from equilibrium systems has received more and more attention and has been an extremely active and productive subject of research for physicists, chemists and biologists. Their studies have brought about a more unified vision of the laws which govern self-organization processes of physico-chemical and biological sys tems. A major achievement has been the extension of the notion of phase transi tion to instabilities which occur only in open nonlinear systems. The notion of phase transition has been proven fruitful in apphcation to nonequilibrium ins- bihties known for about eight decades, like certain hydrodynamic instabilities, as well as in the case of the more recently discovered instabilities in quantum optical systems such as the laser, in chemical systems such as the Belousov-Zhabotinskii reaction and in biological systems. Even outside the realm of natural sciences, this notion is now used in economics and sociology. In this monograph we show that the notion of phase transition can be extend ed even further. It apphes also to a new class of transition phenomena which occur only in nonequilibrium systems subjected to a randomly fluctuating en vironment.
If death is the cessation of life, then, as a concept, it draws its meaning from the preceding life. While death and dying are inextricably connected, dying is still a part of life—unlike death. The Meaning of Death: A Philosophical Investigation analyzes death and dying, the biotechnical quest for immortality, the afterlife, and the rationality of self-chosen death. Assuming eternal life will one day become possible, Kai Horsthemke argues that immortality is not obviously desirable, and that. even if the right to life in principle includes the right to eternal life, it must also include the right to self-determined dying and death. Although there is no creationist basis for existence and the finality of death remains a universal, inevitable prospect, this need not undermine confidence in the personal and transpersonal value of human activities. Life is valuable not only because of its uniqueness and unrepeatability, but also because it is finite. The meaning of death is essentially that it gives meaning to life.
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