578 research outputs found

    On critical State Transitions between different levels in Neural Systems

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    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

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    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

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    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

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    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

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    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

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    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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