Bylivsindex – fokus på de bløde trafikanter og kvalitativ data

Smart mobilitet i Plan og Miljø i Aarhus Kommune gennemførte i september 2017 projektet Bylivsindex, der sætter fokus på cyklister og fodgængeres anvendelse af og holdninger til byens rum og forbindelser. Formålet med Bylivsindex er at tage en temperaturmåling på de bløde trafikanter og med de indsamlede data og indsigter kunne bidrage til at kvalificere mobilitetsdebatten og følge op på de målsætninger, der i Aarhus er til den gode by i relation til mobilitet. Resultaterne af undersøgelsen foreligger nu og baserer sig på 1499 stop-op-interviews og 98 timers observation + tælling fordelt på 10 udvalgte lokaliteter

An Investigation Into the Significance of Dissipation in Statistical Mechanics

The dissipation function is a key quantity in nonequilibrium statistical mechanics. It was originally derived for use in the Evans-Searles Fluctuation Theorem, which quantitatively describes thermal fluctuations in nonequilibrium systems. It is now the subject of a number of other exact results, including the Dissipation Theorem, describing the evolution of a system in time, and the Relaxation Theorem, proving the ubiquitous phenomena of relaxation to equilibrium. The aim of this work is to study the significance of the dissipation function, and examine a number of exact results for which it is the argument. First, we investigate a simple system relaxing towards equilibrium, and use this as a medium to investigate the role of the dissipation function in relaxation. The initial system has a non-uniform density distribution. We demonstrate some of the existing significant exact results in nonequilibrium statistical mechanics. By modifying the initial conditions of our system we are able to observe both monotonic and non-monotonic relaxation towards equilibrium. A direct result of the Evans-Searles Fluctuation Theorem is the Nonequilibrium Partition Identity (NPI), an ensemble average involving the dissipation function. While the derivation is straightforward, calculation of this quantity is anything but. The statistics of the average are difficult to work with because its value is extremely dependent on rare events. It is often observed to converge with high accuracy to a value less than expected. We investigate the mechanism for this asymmetric bias and provide alternatives to calculating the full ensemble average that display better statistics. While the NPI is derived exactly for transient systems it is expected that it will hold in steady state systems as well. We show that this is not true, regardless of the statistics of the calculation. A new exact result involving the dissipation function, the Instantaneous Fluctuation Theorem, is derived and demonstrated computationally. This new theorem has the same form as previous fluctuation theorems, but provides information about the instantaneous value of phase functions, rather than path integrals. We extend this work by deriving an approximate form of the theorem for steady state systems, and examine the validity of the assumptions used

Dissipation in monotonic and non-monotonic relaxation to equilibrium

Using molecular dynamics simulations, we study field free relaxation from a non-uniform initial density, monitored using both density distributions and the dissipation function. When this density gradient is applied to colour labelled particles, the density distribution decays to a sine curve of fundamental wavelength, which then decays conformally towards a uniform distribution. For conformal relaxation, the dissipation function is found to decay towards equilibrium monotonically, consistent with the predictions of the relaxation theorem. When the system is initiated with a more dramatic density gradient, applied to all particles, non-conformal relaxation is seen in both the dissipation function and the Fourier components of the density distribution. At times, the system appears to be moving away from a uniform density distribution. In both cases, the dissipation function satisfies the modified second law inequality, and the dissipation theorem is demonstrated

The instantaneous fluctuation theorem

We give a derivation of a new instantaneous fluctuation relation for an arbitrary phase function which is odd under time reversal. The form of this new relation is not obvious, and involves observing the system along its transient phase space trajectory both before and after the point in time at which the fluctuations are being compared. We demonstrate this relation computationally for a number of phase functions in a shear flow system and show that this non-locality in time is an essential component of the instantaneous fluctuation theorem