The disjoining pressure of charged parallel interfaces confining an electrolyte solution is to a large extent determined by the screening clouds of the surface charges. We evaluate the pressure in terms of the number density $\sigma$ of discrete charges and film thickness $d$ and find, at $\sigma d^2 \sim 1$, a crossover from the well-known law $P \sim \sigma^2$ to a linear behavior $P \sim \sigma$. For the latter case, each surface charge results in strongly inhomogeneous pressure profiles at both interfaces.
We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick (SK) model the asymptotic dynamics has for large times and large waiting times the same formal structure. In the limit of large waiting times we find in both models an intermediate time scale, scaling as a power of the waiting time with an exponent smaller than one, and thus separating the time-translation-invariant short-time dynamics from the aging regime. It is this time scale on which the fluctuation-dissipation theorem is violated. Aging in these models is similar to that observed in spin glasses at the level of correlation functions, but different at the level of response functions, and thus different at the level of experimentally accessible quantities like thermoremanent magnetization.
We investigate the problem of resource allocation in heterogeneous networks of computational resources. We provide an explicit analytical solution for a situation where the computational environment can be described by M/M/1 queueing theory. We illustrate the quality of our solution by comparing results with those obtained via a simple ad hoc resource allocation in large heterogeneous networks consisting of $N=10^4$ nodes with computational resources distributed either uniformly in a given interval, or exponentially in $\Real^+$.
A new approach to combinatorial optimization based on systematic move class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy driven. It is tested on two problems known to be NP hard, namely the problem of finding ground states of the SK spin glass and of the 3-D �J spin glass. The algorithm is sensitive to properties of phase spaces of complex systems other than those explored by simulated annealing, and it may therefore also be used as a diagnostic instrument. Moreover, dynamic freezing transitions, which are well known to hamper the performance of simulated annealing in the large system limit are not encountered by the present setup.
The present contribution deals with the central role that large numbers have played in the process of developing theories about macroscopic systems. We begin by analysing the empirical foundations of this observation, the emergence of stability and regularity through averaging in large systems, and describe their formalisation via limit theorems of mathematical statistics. We choose to adopt a formalisation which emphasises properties of descriptions on scales which are much larger than the atomic or molecular scale at which, according to current understanding, the phenomena being described have their origin. By going on to consider the consequences that the empirical foundation of our observation has for our neural information processing apparatus, we are forced to conclude that large numbers play a crucial role already in allowing stable perception and representation of external and internal reality, and thus appear to be constitutive for all theorising about the world.