Adaptive transient solution of nonuniform multiconductor transmission lines using wavelets

Abstract—This paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations. The discretization of the governing equations is obtained through a weak formula-tion using biorthogonal wavelet bases as trial and test functions. It is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes. A simple yet effective time–space adaptive al-gorithm capable of selecting the minimal number of unknowns at each time iteration is described. Numerical results show the high degree of adaptivity of the proposed scheme. Index Terms—Electromagnetic (EM) transient analysis, multi-conductor transmission lines (TLs), wavelet transforms. I

Traffic flow on realistic road networks with adaptive traffic lights

We present a model of traffic flow on generic urban road networks based on cellular automata. We apply this model to an existing road network in the Australian city of Melbourne, using empirical data as input. For comparison, we also apply this model to a square-grid network using hypothetical input data. On both networks we compare the effects of non-adaptive vs adaptive traffic lights, in which instantaneous traffic state information feeds back into the traffic signal schedule. We observe that not only do adaptive traffic lights result in better averages of network observables, they also lead to significantly smaller fluctuations in these observables. We furthermore compare two different systems of adaptive traffic signals, one which is informed by the traffic state on both upstream and downstream links, and one which is informed by upstream links only. We find that, in general, both the mean and the fluctuation of the travel time are smallest when using the joint upstream-downstream control strategy.Comment: 41 pages, pdflate

Improving the chromatic dispersion tolerance in long-haul fibre links using the coherent optical orthogonal frequency division multiplexing

Numerical simulations of the coherent optical orthogonal frequency division multiplexing modems are undertaken to investigate the effect of the adaptive modulation, the number of sub-carriers, the cyclic prefix (CP) length, the clipping ratio, quantisation bit resolution and the sampling speed of analogue-to-digital converters (ADCs) on the chromatic dispersion (CD) of a single mode fibre (SMF) at data rates up to 80 Gbps. The use of a large number of sub-carriers is more effective in combating fibre dispersion than employing a long CP; moreover, the optimum number of sub-carriers in the presence of both SMF non-linearities and CD has been identified. The authors show that using a high bit resolution ADC with a high clipping ratio, the transmission distance can be increased at specific data rates. Furthermore, it is shown that ADCs with a low sampling speed also improve the system tolerance to the fibre CD. In addition, simulation results show that the use of adaptive modulation schemes improves spectrum usage efficiency, thus resulting in higher tolerance to the CD when compared with the case in which identical modulation formats are adopted across all sub-carriers

Robust oscillations in SIS epidemics on adaptive networks: Coarse-graining by automated moment closure

We investigate the dynamics of an epidemiological susceptible-infected-susceptible (SIS) model on an adaptive network. This model combines epidemic spreading (dynamics on the network) with rewiring of network connections (topological evolution of the network). We propose and implement a computational approach that enables us to study the dynamics of the network directly on an emergent, coarse-grained level. The approach sidesteps the derivation of closed low-dimensional approximations. Our investigations reveal that global coupling, which enters through the awareness of the population to the disease, can result in robust large-amplitude oscillations of the state and topology of the network.Comment: revised version 6 pages, 4 figure

Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects

Abstract—This paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index Terms—Finite difference methods, time-domain analysis, transmission lines, wavelet transforms. I

Social Diffusion and Global Drift on Networks

We study a mathematical model of social diffusion on a symmetric weighted network where individual nodes' states gradually assimilate to local social norms made by their neighbors' average states. Unlike physical diffusion, this process is not state conservational and thus the global state of the network (i.e., sum of node states) will drift. The asymptotic average node state will be the average of initial node states weighted by their strengths. Here we show that, while the global state is not conserved in this process, the inner product of strength and state vectors is conserved instead, and perfect positive correlation between node states and local averages of their self/neighbor strength ratios always results in upward (or at least neutral) global drift. We also show that the strength assortativity negatively affects the speed of homogenization. Based on these findings, we propose an adaptive link weight adjustment method to achieve the highest upward global drift by increasing the strength-state correlation. The effectiveness of the method was confirmed through numerical simulations and implications for real-world social applications are discussed.Comment: 7 pages, 3 figures; to appear in Phys. Rev.