Diffusion-limited reactions on a two-dimensional lattice with binary disorder

Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous desorption of particles. Hopping and desorption are taken to be thermally activated processes. The activation energies are drawn from a binary distribution of well depths, corresponding to `shallow' and `deep' sites. This is the simplest non-trivial distribution, which we use to examine and explain fundamental features of the system. We simulate the system using kinetic Monte Carlo methods and provide a thorough understanding of our findings. We show that the combination of shallow and deep sites broadens the temperature window in which the reaction is efficient, compared to either homogeneous system. We also examine the role of spatial correlations, including systems where one type of site is arranged in a cluster or a sublattice. Finally, we show that a simple rate equation model reproduces simulation results with very good accuracy.Comment: 9 pages, 5 figure

Switching between phenotypes and population extinction

Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to stress. Previous theoretical studies of such bacterial populations have focused on the \emph{fitness}: the asymptotic rate of unbounded growth of the population. Yet for an isolated population of established (and not very large) size, a more relevant measure may be the population \emph{extinction risk} due to the interplay of adverse extrinsic variations and intrinsic noise of birth, death and switching processes. Applying a WKB approximation to the pertinent master equation of such a two-population system, we quantify the extinction risk, and find the most likely path to extinction under both favorable and adverse conditions. Analytical results are obtained both in the biologically relevant regime when the switching is rare compared with the birth and death processes, and in the opposite regime of frequent switching. We show that rare switches are most beneficial in reducing the extinction risk.Comment: 11 pages, 5 figures. Additional discussion paragraph, minor language improvements; content as published in Phys. Rev.

Diffusion-limited reactions and mortal random walkers in confined geometries

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two walkers, which is evaluated in limiting cases and checked against extensive kinetic Monte Carlo simulations. We analyze the continuum limit which is approached very slowly, with corrections that vanish logarithmically with the lattice size. We then examine the influence of the shape of the lattice on the first-passage probability, where we focus on the aspect ratio dependence: Distorting the lattice always reduces the encounter probability of two walkers and can exhibit a crossover to the behavior of a genuinely one-dimensional random walk. The nature of this transition is also explained qualitatively.Comment: 18 pages, 16 figure

Ego-Splitting and the Transcendental Subject. Kant’s Original Insight and Husserl’s Reappraisal

In this paper, I contend that there are at least two essential traits that commonly define being an I: self-identity and self-consciousness. I argue that they bear quite an odd relation to each other in the sense that self-consciousness seems to jeopardize self-identity. My main concern is to elucidate this issue within the range of the transcendental philosophies of Immanuel Kant and Edmund Husserl. In the first section, I shall briefly consider Kant’s own rendition of the problem of the Egosplitting. My reading of the Kantian texts reveals that Kant himself was aware of this phenomenon but eventually deems it an unexplainable fact. The second part of the paper tackles the same problematic from the standpoint of Husserlian phenomenology. What Husserl’s extensive analyses on this topic bring to light is that the phenomenon of the Ego-splitting constitutes the bedrock not only of his thought but also of every philosophy that works within the framework of transcendental thinking

China and the changing economic geography of coffee value chains

For the past three centuries, the economic geography of the global coffee sector has been characterized by the supply of beans from tropical countries for consumption in North America and Europe, with various modes of value chain coordination enacted by lead firms to ensure reliable and affordable supply. This pattern is now fundamentally changing, with growth in coffee consumption in emerging markets, including China, exceeding that in established markets. But China is not only a growing consumer market, it is less well known that rapidly increasing agricultural production in Yunnan province of southwest China has also inserted the country as an important source region for coffee, and this has been pivotal in facilitating the emergence of Chinese lead firms in the sector. This article presents the emergence of China, and Chinese firms, at a critical juncture for the structure and governance of the global value chain for coffee. The processes through which this is occurring are outlined, and the implications for regional development prospects across Southeast Asia are discussed. We argue that the changing economic geography of coffee value chains, and their increasing driven-ness by Chinese actors, is starting to reshape the regional coffee industry in profoundly new ways

Pointer states for primordial fluctuations in inflationary cosmology

Primordial fluctuations in inflationary cosmology acquire classical properties through decoherence when their wavelengths become larger than the Hubble scale. Although decoherence is effective, it is not complete, so a significant part of primordial correlations remains up to the present moment. We address the issue of the pointer states which provide a classical basis for the fluctuations with respect to the influence by an environment (other fields). Applying methods from the quantum theory of open systems (the Lindblad equation), we show that this basis is given by narrow Gaussians that approximate eigenstates of field amplitudes. We calculate both the von Neumann and linear entropy of the fluctuations. Their ratio to the maximal entropy per field mode defines a degree of partial decoherence in the entropy sense. We also determine the time of partial decoherence making the Wigner function positive everywhere which, for super-Hubble modes during inflation, is virtually independent of coupling to the environment and is only slightly larger than the Hubble time. On the other hand, assuming a representative environment (a photon bath), the decoherence time for sub-Hubble modes is finite only if some real dissipation exists.Comment: 32 pages, 2 figures, matches published version: discussion expanded, references added, conclusions unchange

The Early Husserl on Typicality

This paper presents and evaluates the early Husserl’s account of typicality. In the Logical Investigations, Husserl holds that the meaning of ordinary language (common) names is sensitive to typicality: this meaning depends on typical examples which vary in different contexts and are more or less similar to one another. This seems to entail that meanings, which according to Husserl are concepts, are “fluctuating” (schwankend) and vague. Prima facie, such a claim contravenes his theory of ideal meanings, or concepts, which are “fixed” (fest) and sharp. However, Husserl wants to save this theory. He claims that the fluctuation and vagueness in question are not to be found in the meaning itself, or the concept, but rather derive from the act of meaning. Thus, he apparently manages to make room for typicality in ordinary language while accepting only fixed and sharp meanings. After presenting Husserl’s theory, I evaluate it and ask whether he will still be committed, despite his own claims, to accepting prototype concepts to account for typicality in ordinary language