The volume of social interactions like migration and commuting between two locations depends significantly on the distance between them. In the paper, we analysed the shape and parameters of several distance-decay functions for commuting and for migration flows, respectively. The analysis was performed for inter-municipal interactions in Slovenia in 2010–2011. The functions considered were powe...

Going beyond the analysis, a more sensitive measure of exponential decay is -&I/€ = d[ln &(x)]/dx. This is 1 times the x-dependent slope (in dB/cm) of &(x) when graphed in dB. Thus, -&I/€ is the local exponential decay rate of &. For the pulses of Figs. 1 and 2, the computed -&I/& varies from 1185-1257/m (51-55 dB/cm) for the first 60 dB of energy attenuation. This is in the range [ 2 y , 2 y ]...

Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario, the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice, several authors have found that the no-slip boundary condition at the walls of a vessel can slow down mixing considerably, turning an exponential decay into ...

In this work, we consider a class of linear dissipative evolution equations. We show that the solution of this class has a polynomial rate of decay as time tends to infinity, but does not have exponential decay. c © 2004 Elsevier Science Ltd. All rights reserved. Keywords—Dissipative systems, Decay rate, Semigroups.

We carry out a numerical study of the asymptotic dynamics of breathers in finite Fermi-Pasta-Ulam chains at zero and nonzero temperatures. While at zero temperature such breathers remain essentially stationary and decay extremely slowly over wide parameter ranges, thermal fluctuations tend to lead to breather motion and more rapid decay. In both cases the decay is essentially exponential over l...