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Understanding the functional dynamics of the mammalian brain is one of the central aims of modern neuroscience. Mathematical modeling and computational simulations of neural networks can help in this quest. In recent publications, a multilevel model has been presented to simulate the resting-state dynamics of the cortico-cortical connectivity of the mammalian brain. In the present work we investigate how much of the dynamical behavior of the multilevel model can be reproduced by a strongly simplified model. We find that replacing each cortical area by a single Rulkov map recreates the patterns of dynamical correlation of the multilevel model, while the outcome of other models and setups mainly depends on the local network properties, e. g. the input degree of each vertex. In general, we find that a simple simulation whose dynamics depends on the global topology of the whole network is far from trivial. A systematic analysis of different dynamical models and coupling setups is required.
Many real-world networks are characterized by adaptive changes in their topology depending on the state of their nodes. Here we study epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections. This gives rise to assortative degree correlation, oscillations, hysteresis, and first order transitions. We propose a low-dimensional model to describe the system and present a full local bifurcation analysis. Our results indicate that the interplay between dynamics and topology can have important consequences for the spreading of infectious diseases and related applications
We report a noise-memory induced phase transition in an array of oscillatory neural systems, which leads to the suppression of synchronous oscillations and restoration of excitable dynamics. This phenomenon is caused by the systematic contributions of temporally correlated parametric noise, i.e., possessing a memory, which stabilizes a deterministically unstable fixed point. Changing the noise correlation time, a reentrant phase transition to noise- induced excitability is observed in a globally coupled array. Since noise-induced excitability implies the restoration of the ability to transmit information, associated spatiotemporal patterns are observed afterwards. Furthermore, an analytic approach to predict the systematic effects of exponentially correlated noise is presented and its results are compared with the simulations
Motivated by the successful Karlsruhe dynamo experiment, a relatively low-dimensional dynamo model is proposed. It is based on a strong truncation of the magnetohydrodynamic (MHD) equations with an external forcing of the Roberts type and the requirement that the model system satisfies the symmetries of the full MHD system, so that the first symmetry-breaking bifurcations can be captured. The backbone of the Roberts dynamo is formed by the Roberts flow, a helical mean magnetic field and another part of the magnetic field coupled to these two by triadic mode interactions. A minimum truncation model (MTM) containing only these energetically dominating primary mode triads is fully equivalent to the widely used first-order smoothing approximation. However, it is shown that this approach works only in the limit of small wave numbers of the excited magnetic field or small magnetic Reynolds numbers ($Rm ll 1$). To obtain dynamo action under more general conditions, secondary mode
There is strong observational evidence of shocks and clumping in radiation-driven stellar winds from hot, luminous stars. The resulting non nous monotonic velocity law allows for radiative coupling between distant locations, which is so far not accounted for in hydrodynamic wind simulations. In the present paper, we determine the Sobolev source function and radiative line force in the presence of radiative coupling in spherically symmetric flows, extending the geometry-free formalism of Rybicki & Hummer (1978, ApJ, 219, 654) to the case of three-point coupling, which can result from, e. g., corotating interaction regions, wind shocks, or mass overloading. For a simple model of an overloaded wind, we find that, surprisingly, the flow decelerates at all radii above a certain height when nonlocal radiative coupling is accounted for. We discuss whether radiation-driven winds might in general not be able to re- accelerate after a non monotonicity has occurred in the velocity law
We present a theoretical framework for the analysis of the statistical properties of thermal fluctuations on a lossy transmission line. A quantization scheme of the electrical signals in the transmission line is formulated. We discuss two applications in detail. Noise spectra at finite temperature for voltage and current are shown to deviate significantly from the Johnson-Nyquist limit, and they depend on the position on the transmission line. We analyze the spontaneous emission, at low temperature, of a Rydberg atom and its resonant enhancement due to vacuum fluctuations in a capacitively coupled transmission line. The theory can also be applied to study the performance of microscale and nanoscale devices, including high-resolution sensors and quantum information processors
Zerstörungsfreie Tomographie von Raumladungs- und Polarisationsverteilungen mittles Wärmepulsen
(2007)
Non-destructive, three-dimensional imaging of space-charge and polarization distributions in electret materials has been implemented by means of laser-induced thermal pulses. In pyroelectric films of poled poly(vinylidene fluoride), images of up to 45 x 45 pixels with a depth resolution of less than 0.5 mu m and a lateral resolution of 40 mu m were recorded, the latter being limited by fast thermal diffusion in the absorbing metallic front electrode. Initial applications include the analysis of polarization distributions in corona-poled piezoelectric sensor cables and the detection of patterned space-charge distributions in polytetrafluoroethylene films.
We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of correlations follows for both the ground state and thermal states. Considering the converse direction, we show that an energy gap can follow from algebraic decay and always does for exponential decay. The underlying lattices are described as general graphs of not necessarily integer dimension, including translationally invariant instances of cubic lattices as special cases. Any local quadratic couplings in position and momentum coordinates are allowed for, leading to quasi-free ( Gaussian) ground states. We make use of methods of deriving bounds to matrix functions of banded matrices corresponding to local interactions on general graphs. Finally, we give an explicit entanglement-area relationship in terms of the energy gap for arbitrary, not necessarily contiguous regions on lattices characterized by general graphs
A new approach for efficient second-harmonic generation using diode lasers is presented. The experimental setup is based on a tapered amplifier operated in a ring resonator that is coupled to a miniaturized enhancement ring resonator containing a periodically poled lithium niobate crystal. Frequency locking of the diode laser emission to the resonance frequency of the enhancement cavity is realized purely optically, resulting in stable, single-frequency operation. Blue light at 488 nm with an output power of 310 mW is generated with an optical-to-optical conversion efficiency of 18%.
The parameters of the nutations are now known with a good accuracy, and the theory accounts for most of their values. Dissipative friction at the core-mantle boundary (CMB) and at the inner core boundary is an important ingredient of the theory. Up to now, viscous coupling at a smooth interface and electromagnetic coupling have been considered. In some cases they appear hardly strong enough to account for the observations. We advocate here that the CMB has a small- scale roughness and estimate the dissipation resulting from the interaction of the fluid core motion with this topography. We conclude that it might be significant