Interdisciplinary (retail) research: The business of geography and the geography of business

NoAt the 2005 British Academy of Management conference several well-known economic geographers, including Neil Wrigley, Gordon Clark, and Susan Christopherson, called for management researchers to engage with economic geographers on interrelated geographical and managerial issues in the study of (retail) firms. In this commentary we reflect upon the present geography -management interface.We begin by considering the term `interdisciplinary research' and its relationship to any management - geography interface. This is followed by a context-specific discussion of international retailing and the role of research on the retail transnational corporation (TNC) in developing an interdisciplinary agenda. This commentary represents an initial more business and management focused response to the call from geography academics for more/better interdisciplinary research at the geography - management interface

The development of structural adhesives systems suitable for use with liquid oxygen Annual summary report, 1 Jul. 1963 - 30 Jun. 1964

Fluorinated, chlorinated, and halogenated polymer adhesives prepared and tested for compatibility with liquid oxyge

Stretched Exponential Relaxation in the Biased Random Voter Model

We study the relaxation properties of the voter model with i.i.d. random bias. We prove under mild condions that the disorder-averaged relaxation of this biased random voter model is faster than a stretched exponential with exponent $d/(d+\alpha)$, where $0<\alpha\le 2$ depends on the transition rates of the non-biased voter model. Under an additional assumption, we show that the above upper bound is optimal. The main ingredient of our proof is a result of Donsker and Varadhan (1979).Comment: 14 pages, AMS-LaTe

Kinetics of diffusion-limited catalytically-activated reactions: An extension of the Wilemski-Fixman approach

We study kinetics of diffusion-limited catalytically-activated $A + B \to B$ reactions taking place in three dimensional systems, in which an annihilation of diffusive $A$ particles by diffusive traps $B$ may happen only if the encounter of an $A$ with any of the $B$s happens within a special catalytic subvolumen, these subvolumens being immobile and uniformly distributed within the reaction bath. Suitably extending the classical approach of Wilemski and Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. \textbf{58}:4009, 1973) to such three-molecular diffusion-limited reactions, we calculate analytically an effective reaction constant and show that it comprises several terms associated with the residence and joint residence times of Brownian paths in finite domains. The effective reaction constant exhibits a non-trivial dependence on the reaction radii, the mean density of catalytic subvolumens and particles' diffusion coefficients. Finally, we discuss the fluctuation-induced kinetic behavior in such systems.Comment: To appear in J. Chem. Phy

Survival probability of a particle in a sea of mobile traps: A tale of tails

We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move sub-diffusively, such that the mean square displacement of each trap grows as $t^{\gamma}$ with $0\leq \gamma \leq 1$. Starting from a continuous time random walk (CTRW) description of the motion of the particle and of the traps, we derive lower and upper bounds for $P(t)$ and show that for $\gamma \leq 2/(d+2)$ these bounds coincide asymptotically, thus determining asymptotically exact results. The asymptotic decay law in this regime is exactly that obtained for immobile traps. This means that for sufficiently subdiffusive traps, the moving $A$ particle sees the traps as essentially immobile, and Lifshitz or trapping tails remain unchanged. For $\gamma > 2/(d+2)$ and $d\leq 2$ the upper and lower bounds again coincide, leading to a decay law equal to that of a stationary particle. Thus, in this regime the moving traps see the particle as essentially immobile. For $d>2$, however, the upper and lower bounds in this $\gamma$ regime no longer coincide and the decay law for the survival probability of the $A$ particle remains ambiguous

Simulations for trapping reactions with subdiffusive traps and subdiffusive particles

While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square displacement $\sim t^\gamma$ with $0<\gamma<1$. Recently we calculated the asymptotic survival probability $P(t)$ of a (sub)diffusive particle ($\gamma^\prime$) surrounded by (sub)diffusive traps ($\gamma$) in one dimension. These are among the few known results for reactions involving species characterized by different anomalous exponents. Our results were obtained by bounding, above and below, the exact survival probability by two other probabilities that are asymptotically identical (except when $\gamma^\prime=1$ and $0<\gamma<2/3$). Using this approach, we were not able to estimate the time of validity of the asymptotic result, nor the way in which the survival probability approaches this regime. Toward this goal, here we present a detailed comparison of the asymptotic results with numerical simulations. In some parameter ranges the asymptotic theory describes the simulation results very well even for relatively short times. However, in other regimes more time is required for the simulation results to approach asymptotic behavior, and we arrive at situations where we are not able to reach asymptotia within our computational means. This is regrettably the case for $\gamma^\prime=1$ and $0<\gamma<2/3$, where we are therefore not able to prove or disprove even conjectures about the asymptotic survival probability of the particle.Comment: 15 pages, 10 figures, submitted to Journal of Physics: Condensed Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations, Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin and M.Tachiy

Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents

A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in ordinary diffusion is replaced by t^gamma. However, very few results are known for reactions involving different species characterized by different anomalous diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive particle surrounded by a sea of (sub)diffusive traps in one dimension. We find rigorous results for the asymptotic survival probability of the particle in most cases, with the exception of the case of a particle that diffuses normally while the anomalous diffusion exponent of the traps is smaller than 2/3.Comment: To appear in Phys. Rev.

7T functional MRI finds no evidence for distinct functional subregions in the subthalamic nucleus during a speeded decision-making task

The subthalamic nucleus (STN) is a small, subcortical brain structure. It is a target for deep brain stimulation, an invasive treatment that reduces motor symptoms of Parkinson’s disease. Side effects of DBS are commonly explained using the tripartite model of STN organization, which proposes three functionally distinct subregions in the STN specialized in cognitive, limbic, and motor processing. However, evidence for the tripartite model exclusively comes from anatomical studies and functional studies using clinical patients. Here, we provide the first experimental tests of the tripartite model in healthy volunteers using ultra-high field 7 Tesla (T) functional magnetic resonance imaging (fMRI). Thirty-four participants performed a random-dot motion decision-making task with a difficulty manipulation and a choice payoff manipulation aimed to differentially affect cognitive and limbic networks. Moreover, participants responded with their left and right index finger, differentially affecting motor networks. We analysed BOLD signal in three subregions of the STN along the dorsolateral-ventromedial axis, identified using manually delineated high resolution anatomical images and based on a previously published atlas. Using these paradigms, all segments responded equally to the experimental manipulations, and the tasks did not provide evidence for the tripartite model

Trapping in complex networks

We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $\rho(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show using theory and simulations that in ER networks, while for short times $\rho(t) \propto \exp(-Act)$, for longer times $\rho(t)$ exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the trap's location: $\rho(t)$ is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we find \rho(t)\propto\exp\left[-At/N^\frac{\gamma-2}{\gamma-1}\av{k}\right] for all $\gamma>2$, where $\gamma$ is the exponent of the degree distribution $P(k)\propto k^{-\gamma}$.Comment: Appendix adde