On the long time behavior of free stochastic Schrödinger evolutions

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.

Reversible thermal transition of polydiacetylene based on KTTKS collagen sequence

Here we explore the physico-chemical properties of a peptide amphiphile obtained by chemical conjugation of the collagenstimulating peptide KTTKS with 10,12-pentacosadiynoic acid which photopolymerizes as a stable and extended polydiacetylene. We investigate the self-assembly of this new polymer and rationalize its peculiar behavior in terms of a thermal conformational transition. Surprisingly, this polymer shows a thermal transition associated with a non-cooperative increase in b-sheet content at high temperature.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Fair trade and European public procurement: legal principles and governance dynamics

Purpose The article examines principles of Fair Trade in public procurement in Europe, focusing on legal dimensions related to the European Public Procurement Directives. Design/methodology/approach The article situates public procurement of Fair Trade products in relation to the rise of non-state regulatory initiatives, highlighting how they have entered into new governance dynamics in the public sector and play a part in changing practices in sustainable procurement. A review of legal position on Fair Trade in procurement law is informed by academic research and campaigning experience from the Fair Trade Advocacy Office. Findings Key findings are that the introduction of Fair Trade products into European public procurement has been marked by legal ambiguity, having developed outside comprehensive policy or legal guidelines. Following a 2012 ruling by the Court of Justice of the European Union, it is suggested that the legal position for Fair Trade in procurement has become clearer, and that forthcoming change to the Public Procurement Directives may facilitate the uptake of fair trade products by public authorities. However potential for future expansion of the public sector ‘market’ for Fair Trade is approached with caution: purchasing Fair Trade products as a marker of sustainability, which started to be embedded within procurement practice in the 2000s, is challenged by current European public austerity measures. Research limitations/implications Suggestions for future research include the need for systematic cross-institutional and multi-country comparison of the legal and governance dimensions of procurement practice with regard to Fair Trade. Practical implications A clarification of current state-of-play with regard to legal aspects of fair trade in public procurement of utility for policy and advocacy discussion. Originality/value The article provides needed elaboration on an under researched topic area of value to academia and policy makers.

Adaptation-induced collective dynamics of a single-cell protozoan

We investigate the behavior of a single-cell protozoan in a narrow tubular ring. This environment forces them to swim under a one-dimensional periodic boundary condition. Above a critical density, single-cell protozoa aggregate spontaneously without external stimulation. The high-density zone of swimming cells exhibits a characteristic collective dynamics including translation and boundary fluctuation. We analyzed the velocity distribution and turn rate of swimming cells and found that the regulation of the turing rate leads to a stable aggregation and that acceleration of velocity triggers instability of aggregation. These two opposing effects may help to explain the spontaneous dynamics of collective behavior. We also propose a stochastic model for the mechanism underlying the collective behavior of swimming cells.

The dynamics of commodity prices

In this paper we study the stochastic behavior of the prices and volatilities of a sample of six of the most important commodity markets and we compare these properties with those of the equity market. we observe a substantial degree of heterogeneity in the behavior of the series. Our findings show that it is inappropriate to treat different kinds of commodities as a single asset class as is frequently the case in the academic literature and in the industry. We demonstrate that commodities can be a useful diversifier of equity volatility as well as equity returns. Options pricing and hedging applications exemplify the economic impacts of the differences across commodities and between model specifications.

Motion planning of autonomous vehicles in a non-autonomous vehicle environment without speed lanes

Planning is one of the key problems for autonomous vehicles operating in road scenarios. Present planning algorithms operate with the assumption that traffic is organised in predefined speed lanes, which makes it impossible to allow autonomous vehicles in countries with unorganised traffic. Unorganised traffic is though capable of higher traffic bandwidths when constituting vehicles vary in their speed capabilities and sizes. Diverse vehicles in an unorganised exhibit unique driving behaviours which are analysed in this paper by a simulation study. The aim of the work reported here is to create a planning algorithm for mixed traffic consisting of both autonomous and non-autonomous vehicles without any inter-vehicle communication. The awareness (e.g. vision) of every vehicle is restricted to nearby vehicles only and a straight infinite road is assumed for decision making regarding navigation in the presence of multiple vehicles. Exhibited behaviours include obstacle avoidance, overtaking, giving way for vehicles to overtake from behind, vehicle following, adjusting the lateral lane position and so on. A conflict of plans is a major issue which will almost certainly arise in the absence of inter-vehicle communication. Hence each vehicle needs to continuously track other vehicles and rectify plans whenever a collision seems likely. Further it is observed here that driver aggression plays a vital role in overall traffic dynamics, hence this has also been factored in accordingly. This work is hence a step forward towards achieving autonomous vehicles in unorganised traffic, while similar effort would be required for planning problems such as intersections, mergers, diversions and other modules like localisation.

Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

Averaging, slaving and balance dynamics in a simple atmospheric model

We report numerical results from a study of balance dynamics using a simple model of atmospheric motion that is designed to help address the question of why balance dynamics is so stable. The non-autonomous Hamiltonian model has a chaotic slow degree of freedom (representing vortical modes) coupled to one or two linear fast oscillators (representing inertia-gravity waves). The system is said to be balanced when the fast and slow degrees of freedom are separated. We find adiabatic invariants that drift slowly in time. This drift is consistent with a random-walk behaviour at a speed which qualitatively scales, even for modest time scale separations, as the upper bound given by Neishtadt’s and Nekhoroshev’s theorems. Moreover, a similar type of scaling is observed for solutions obtained using a singular perturbation (‘slaving’) technique in resonant cases where Nekhoroshev’s theorem does not apply. We present evidence that the smaller Lyapunov exponents of the system scale exponentially as well. The results suggest that the observed stability of nearly-slow motion is a consequence of the approximate adiabatic invariance of the fast motion.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

The significance of occupancy steadiness in residential consumer response to Time of Use pricing: Evidence from a stochastic adjustment model

The recent roll-out of smart metering technologies in several developed countries has intensified research on the impacts of Time-of-Use (TOU) pricing on consumption. This paper analyses a TOU dataset from the Province of Trento in Northern Italy using a stochastic adjustment model. Findings highlight the non-steadiness of the relationship between consumption and TOU price. Weather and active occupancy can partly explain future consumption in relation to price.

Forecasting US output growth with non-linear models in the presence of data uncertainty

We consider the impact of data revisions on the forecast performance of a SETAR regime-switching model of U.S. output growth. The impact of data uncertainty in real-time forecasting will affect a model's forecast performance via the effect on the model parameter estimates as well as via the forecast being conditioned on data measured with error. We find that benchmark revisions do affect the performance of the non-linear model of the growth rate, and that the performance relative to a linear comparator deteriorates in real-time compared to a pseudo out-of-sample forecasting exercise.

Housing or property? The dynamics of housing policy and property principles in the right to buy

This paper examines the interplay and tension between housing law and policy and property law, in the specific context of the right to buy (RTB). It focuses on funding arrangements between the RTB tenant and another party. It first examines how courts determine the parties' respective entitlements in the home, highlighting the difficulty of categorising, under traditional property law principles, a contribution in the form of the statutory discount conferred on the RTB tenant. Secondly, it considers possible exploitation of the RTB scheme, both at the macro level of exploitation of the policy underpinning the legislation and, at the micro level, of exploitation of the tenant. The measures contained in the Housing Act 2004 intended to curb exploitation of the RTB are analysed to determine what can be considered to be legitimate and illegitimate uses of the scheme. It is argued that, despite the government's implicit approval, certain funding arrangements by non-resident relatives fail to give effect to the spirit of the scheme.