578 research outputs found
On critical State Transitions between different levels in Neural Systems
The framework of Modern Theory of Critical State Transitions considers the
relation between different levels of organization in complex systems in terms
of Critical State Transitions. A State Transition between levels entails
changes of scale of observables and, concurrently, new formats of description
at reduced dimensionality. It is here suggested that this principle can be
applied to the hierarchic structure of the Nervous system, whereby the
relations between different levels of its functional organization can be viewed
as successions of State Transitions. Upon State Transition, the lower level
presents to the higher level an abstraction of itself, at reduced
dimensionality and at a coarser scale. The re-scaling in the State Transitions
is associated with new objects of description, displays new properties and
obeys new laws, commensurate to the new scale. To illustrate this process, some
aspects of the neural events thought to be associated with Cognition and
Consciousness are discussed. However, the intent is here also more general in
that State Transitions between all levels of organization are proposed as the
mechanisms by which successively higher levels of organization emerge from
lower levels.Comment: 1
Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
Here, we review the basic concepts and applications of the
phase-field-crystal (PFC) method, which is one of the latest simulation
methodologies in materials science for problems, where atomic- and microscales
are tightly coupled. The PFC method operates on atomic length and diffusive
time scales, and thus constitutes a computationally efficient alternative to
molecular simulation methods. Its intense development in materials science
started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88
(2002), p. 245701]. Since these initial studies, dynamical density functional
theory and thermodynamic concepts have been linked to the PFC approach to serve
as further theoretical fundaments for the latter. In this review, we summarize
these methodological development steps as well as the most important
applications of the PFC method with a special focus on the interaction of
development steps taken in hard and soft matter physics, respectively. Doing
so, we hope to present today's state of the art in PFC modelling as well as the
potential, which might still arise from this method in physics and materials
science in the nearby future.Comment: 95 pages, 48 figure
Thermal decomposition of RDX from reactive molecular dynamics
We use the recently developed reactive force field ReaxFF with molecular dynamics to study thermal induced chemistry in RDX [cyclic-[CH2N(NO2)]3] at various temperatures and densities. We find that the time evolution of the potential energy can be described reasonably well with a single exponential function from which we obtain an overall characteristic time of decomposition that increases with decreasing density and shows an Arrhenius temperature dependence. These characteristic timescales are in reasonable quantitative agreement with experimental measurements in a similar energetic material, HMX [cyclic-[CH2N(NO2)]4]. Our simulations show that the equilibrium population of CO and CO2 (as well as their time evolution) depend strongly of density: at low density almost all carbon atoms form CO molecules; as the density increases larger aggregates of carbon appear leading to a C deficient gas phase and the appearance of CO2 molecules. The equilibrium populations of N2 and H2O are more insensitive with respect to density and form in the early stages of the decomposition process with similar timescales
Metastability, Criticality and Phase Transitions in brain and its Models
This essay extends the previously deposited paper "Oscillations, Metastability and Phase Transitions" to incorporate the theory of Self-organizing Criticality. The twin concepts of Scaling and Universality of the theory of nonequilibrium phase transitions is applied to the role of reentrant activity in neural circuits of cerebral cortex and subcortical neural structures
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
Green function techniques in the treatment of quantum transport at the molecular scale
The theoretical investigation of charge (and spin) transport at nanometer
length scales requires the use of advanced and powerful techniques able to deal
with the dynamical properties of the relevant physical systems, to explicitly
include out-of-equilibrium situations typical for electrical/heat transport as
well as to take into account interaction effects in a systematic way.
Equilibrium Green function techniques and their extension to non-equilibrium
situations via the Keldysh formalism build one of the pillars of current
state-of-the-art approaches to quantum transport which have been implemented in
both model Hamiltonian formulations and first-principle methodologies. We offer
a tutorial overview of the applications of Green functions to deal with some
fundamental aspects of charge transport at the nanoscale, mainly focusing on
applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references,
submitted to Springer series "Lecture Notes in Physics
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