Some Location and Price Equilibria in Facility Investment with Uncertain Demand

This paper describes the spatial distribution of customer demand, supply of customer services, and facility investment as the outcome of a three-level game-like interaction between customers (e.g., shoppers), suppliers (e.g., retailers) and developers (e.g., landlords). Suppliers in each center are assumed to compete with suppliers in all other centers. Similarly, the developers of each center compete with developers of all other centers. With this specification, multi-center equilibria of the Nash type are examined for suppliers on the one hand, and for developers on the other. Suppliers in a center decide about utilized floorspace and price level in the center. Developers of a center decide about available floorspace and rent level. The uncertain customer demand is specified in probabilistic terms, representing the suppliers' and developers' perception of customer behavior. An approach to estimate customer response patterns is presented and discussed

On Planning and Forecasting the Location of Retail and Service Activity

In countries with mixed economies, planning authorities cannot usually enforce micro location and travel decisions of urban activities, but are confined to forming macro location and transport policy, within which agents can operate according to the market. An attempt is made here to describe such multilevel behavior of the planning authority, landlords, firms and customers, and to obtain non-cooperative equilibria in terms of controls exerted by each group. The behaviour of the market groups is described via entropy maximization, while alternative modes of behaviour are ascribed to the authority. In addition, a Pareto-type solution is examine

Symmetrized models of last passage percolation and non-intersecting lattice paths

It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups $U(l)$, $Sp(2l)$ and $O(l)$. We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relating to two further symmetrizations are also given.Comment: 21 pages, 5 figure

Decoherence dynamics of a qubit coupled to a quantum two-level system

We study the decoherence dynamics of a qubit coupled to a quantum two-level system (TLS) in addition to its weak coupling to a background environment. We analyze the different regimes of behaviour that arise as the values of the different parameters are varied. We classify those regimes as two weak-coupling regimes, which differ by the relation between the qubit and TLS decoherence times, and a strong-coupling one. We also find analytic expressions describing the decoherence rates in the weak-coupling regimes, and we verify numerically that those expressions have a rather wide range of validity. Along with obtaining the above-mentioned results, we address the questions of qubit-TLS entanglement and the additivity of multiple TLS contributions. We also discuss the transition from weak to strong coupling as the parameters are varied, and we numerically determine the location of the boundary between the two regimes.Comment: 9 pages (two-column), 3 figure

Fluctuation properties of the TASEP with periodic initial configuration

We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process. We then consider certain periodic initial conditions and determine the kernel in the scaling limit. This result has been announced first in a letter by one of us and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.Comment: 33 pages, 4 figure, LaTeX; We added several references to the general framework and techniques use

QuTiP: An open-source Python framework for the dynamics of open quantum systems

We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of master equation or Monte-Carlo solvers. We give an overview of the basic structure for the framework before detailing the numerical simulation of open system dynamics. Several examples are given to illustrate the build up to a complete calculation. Finally, we measure the performance of our library against that of current implementations. The framework described here is particularly well-suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction.Comment: 16 pages, 12 figure

Energy Primer

The paper introduces basic concepts and terms of energy that deal with adaptation to and mitigation of climate change. Descriptions are also provided of the more commonly used energy units and measurements. The global energy system is described, and energy consumption patterns and CO2 emissions data are presented. The concept of energy efficiency improvement potential is introduced. A historical perspective of energy consumption and CO2 emissions for the world is made, with a comparison of current energy consumption and estimates of fossil and nuclear energy reserves and resources, and the potential of renewable energy sources

Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions

We study effects of Kac-Baker long-range dispersive interaction (LRI) between particles on kink properties in the discrete sine-Gordon model. We show that the kink width increases indefinitely as the range of LRI grows only in the case of strong interparticle coupling. On the contrary, the kink becomes intrinsically localized if the coupling is under some critical value. Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI increases for supercritical values of the coupling but remains finite for subcritical values. We demonstrate that LRI essentially transforms the internal dynamics of the kinks, specifically creating their internal localized and quasilocalized modes. We also show that moving kinks radiate plane waves due to break of the Lorentz invariance by LRI.Comment: 11 pages (LaTeX) and 14 figures (Postscript); submitted to Phys. Rev.

Meson Exchange Currents in (e,e'p) recoil polarization observables

A study of the effects of meson-exchange currents and isobar configurations in $A(\vec{e},e'\vec{p})B$ reactions is presented. We use a distorted wave impulse approximation (DWIA) model where final-state interactions are treated through a phenomenological optical potential. The model includes relativistic corrections in the kinematics and in the electromagnetic one- and two-body currents. The full set of polarized response functions is analyzed, as well as the transferred polarization asymmetry. Results are presented for proton knock-out from closed-shell nuclei, for moderate to high momentum transfer.Comment: 44 pages, 18 figures. Added physical arguments explaining the dominance of OB over MEC, and a summary of differences with previous MEC calculations. To be published in PR

SIBELIUS-DARK: a galaxy catalogue of the local volume from a constrained realization simulation

Large scale structure and cosmologyGalaxie