Manifolds in random media: A variational approach to the spatial probability distribution

We develop a new variational scheme to approximate the position dependent spatial probability distribution of a zero dimensional manifold in a random medium. This celebrated 'toy-model' is associated via a mapping with directed polymers in 1+1 dimension, and also describes features of the commensurate-incommensurate phase transition. It consists of a pointlike 'interface' in one dimension subject to a combination of a harmonic potential plus a random potential with long range spatial correlations. The variational approach we develop gives far better results for the tail of the spatial distribution than the hamiltonian version, developed by Mezard and Parisi, as compared with numerical simulations for a range of temperatures. This is because the variational parameters are determined as functions of position. The replica method is utilized, and solutions for the variational parameters are presented. In this paper we limit ourselves to the replica symmetric solution.Comment: 22 pages, 3 figures available on request, Revte

Alfred Müller-Armack and Ludwig Erhard: Social Market Liberalism

"Soziale Marktwirtschaft" (Social Market Economy) is the economic order that was established in Western Germany after 1945. It is not a precisely outlined theoretical system but more a cipher for a "mélange" of socio-political ideas for a free and socially just society and some general rules of economic policy. It is a decided liberal concept, based on individual freedom and the belief that well-functioning markets and competition lead to economic efficiency and by this, to economic development (or in the case of Germany, recovery) and social improvement. But in sharp distinction to the harmonious Smithian world of the "invisible hand", the "founding fathers" of the post-war economic order in Germany were convinced that the economic system must be guided by an "economic constitution" provided by the state. --

Discursive design thinking: the role of explicit knowledge in creative architectural design reasoning

The main hypothesis investigated in this paper is based upon the suggestion that the discursive reasoning in architecture supported by an explicit knowledge of spatial configurations can enhance both design productivity and the intelligibility of design solutions. The study consists of an examination of an architect’s performance while solving intuitively a well-defined problem followed by an analysis of the spatial structure of their design solutions. One group of architects will attempt to solve the design problem logically, rationalizing their design decisions by implementing their explicit knowledge of spatial configurations. The other group will use an implicit form of such knowledge arising from their architectural education to reason about their design acts. An integrated model of protocol analysis combining linkography and macroscopic coding is used to analyze the design processes. The resulting design outcomes will be evaluated quantitatively in terms of their spatial configurations. The analysis appears to show that an explicit knowledge of the rules of spatial configurations, as possessed by the first group of architects can partially enhance their function-driven judgment producing permeable and well-structured spaces. These findings are particularly significant as they imply that an explicit rather than an implicit knowledge of the fundamental rules that make a layout possible can lead to a considerable improvement in both the design process and product. This suggests that by externalizing th

Asymptotics of the allele frequency spectrum associated with the Bolthausen-Sznitman coalescent

We work in the context of the infinitely many alleles model. The allelic partition associated with a coalescent process started from n individuals is obtained by placing mutations along the skeleton of the coalescent tree; for each individual, we trace back to the most recent mutation affecting it and group together individuals whose most recent mutations are the same. The number of blocks of each of the different possible sizes in this partition is the allele frequency spectrum. The celebrated Ewens sampling formula gives precise probabilities for the allele frequency spectrum associated with Kingman's coalescent. This (and the degenerate star-shaped coalescent) are the only Lambda coalescents for which explicit probabilities are known, although they are known to satisfy a recursion due to Moehle. Recently, Berestycki, Berestycki and Schweinsberg have proved asymptotic results for the allele frequency spectra of the Beta(2-alpha,alpha) coalescents with alpha in (1,2). In this paper, we prove full asymptotics for the case of the Bolthausen-Sznitman coalescent.Comment: 26 pages, 1 figur

Quantum Monte Carlo simulations of a particle in a random potential

In this paper we carry out Quantum Monte Carlo simulations of a quantum particle in a one-dimensional random potential (plus a fixed harmonic potential) at a finite temperature. This is the simplest model of an interface in a disordered medium and may also pertain to an electron in a dirty metal. We compare with previous analytical results, and also derive an expression for the sample to sample fluctuations of the mean square displacement from the origin which is a measure of the glassiness of the system. This quantity as well as the mean square displacement of the particle are measured in the simulation. The similarity to the quantum spin glass in a transverse field is noted. The effect of quantum fluctuations on the glassy behavior is discussed.Comment: 23 pages, 7 figures included as eps files, uses RevTeX. Accepted for publication in J. of Physics A: Mathematical and Genera