The emergence of coordination in public good games

In physical models it is well understood that the aggregate behaviour of a system is not in one to one correspondence with the behaviour of the average individual element of that system. Yet, in many economic models the behaviour of aggregates is thought of as corresponding to that of an individual. A typical example is that of public goods experiments. A systematic feature of such experiments is that, with repetition, people contribute less to public goods. A typical explanation is that people “learn to play Nash” or something approaching it. To justify such an explanation, an individual learning model is tested on average or aggregate data. In this paper we will examine this idea by analysing average and individual behaviour in a series of public goods experiments. We analyse data from a series of games of contributions to public goods and as is usual, we test a learning model on the average data. We then look at individual data, examine the changes that this produces and see if some general model such as the EWA (Expected Weighted Attraction) with varying parameters can account for individual behaviour. We find that once we disaggregate data such models have poor explanatory power. Groups do not learn as supposed, their behaviour differs markedly from one group to another, and the behaviour of the individuals who make up the groups also varies within groups. The decline in aggregate contributions cannot be explained by resorting to a uniform model of individual behaviour. However, the Nash equilibrium of such a game is a total payment for all the individuals and there is some convergence of the group in this respect. Yet the individual contributions do not converge. How the individuals “self-organsise” to coordinate, even in this limited way remains to be explained.     

QED Derived from the Two-Body Interaction

We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour.⁽¹⁾ In Part I of this paper, we show that QED with the same transformational behaviour also holds in an alternative space we call M-space. We use the four-vector behaviour to model the two-body interaction in M and show that this has similar physical properties to the usual model in L which it predicts. In Part II of this paper we use M-space to show that QED can be reduced to two simple rules for a two-body interaction.     

Solutions to the nonlinear Schrödinger equation with sequences of initial data converging to a Dirac mass

We study the nonlinear Schrödinger equation with sequences of initial data that converge to a Dirac mass, and study the asymptotic behaviour of solutions. In doing so we find a connection to previously known long time asymptotics. We demonstrate a type of universality in the behaviour of solutions for real initial data, and we also show how this universality breaks down for examples of initial data that are not purely real.     

Renormalized tricritical behaviour for wetting transitions

In this paper we study tricritical wetting behaviour in three dimensions. In particular we concentrate on systems with short-ranged forces and apply linear functional renormalization group techniques to elucidate the effect of fluctuations upon tricriticality. In comparison with studies of critical wetting we identify an additional fluctuation regime which is relevant for values of the capillary parameter between 2/9 and 1/2. We demonstrate that this regime essentially provides a crossover from mean-field like behaviour, in which tricritical exponents are always distinct from their critical counterparts, from intermediate- and strong-fluctuation behaviour where the critical exponents for tricritical and critical wetting are found to always coincide. We conclude by discussing briefly the possible relevance of these results for experimental studies of wetting. Received 4 January 2001 and Received in final form 11 May 2001     

Superdiffusive Behaviour of a Passive Ornstein–Uhlenbeck Tracer in a Turbulent Shear Flow

In this paper, we are interested in the study of the diffusion of a passive particle with positive mass by a divergence free velocity field. We consider here the very simple turbulent shear flow case, in which we will prove the superdiffusive behaviour of the motion for large enough values of the energy spectrum of the velocity field. For small values, the proof of the diffusive behaviour of the model is also new, and it is shown that this diffusion is strictly greater than the one obtained with a non-massive particle. One interesting point to insist on is that we are able to obtain explicit hydrodynamic equations without even having the stationary measure of the studied processes     

Chaotic behaviour of nonlinear coupled reaction–diffusion system in four-dimensional space

In recent years, nonlinear coupled reaction–diffusion (CRD) system has been widely investigated by coupled map lattice method. Previously, nonlinear behaviour was observed dynamically when one or two of the three variables in the discrete system change. In this paper, we consider the chaotic behaviour when three variables change, which is called as four-dimensional chaos. When two parameters in the discrete system are unknown, we first give the existing condition of the chaos in four-dimensional space by the generalized definitions of spatial periodic orbits and spatial chaos. In addition, the chaotic behaviour will vary with the parameters. Then we propose a generalized Lyapunov exponent in four-dimensional space to characterize the different effects of parameters on the chaotic behaviour, which has not been studied in detail. In order to verify the chaotic behaviour of the system and the different effects clearly, we simulate the dynamical behaviour in two- and three-dimensional spaces.     

Prior probabilities and thermal characteristics of heat engines

The thermal characteristics of a heat cycle are studied from a Bayesian approach. In this approach, we assign a certain prior probability distribution to an uncertain parameter of the system. Based on that prior, we study the expected behaviour of the system and it has been found that even in the absence of complete information, we obtain thermodynamic-like behaviour of the system. Two models of heat cycles, the quantum Otto cycle and the classical Otto cycle are studied from this perspective. Various expressions for thermal efficiences can be obtained with a generalised prior of the form Π(x) ∝ 1/x ^b . The predicted thermodynamic behaviour suggests a connection between prior information about the system and thermodynamic features of the system.     

Interacting Spin 0 Fields with Torsion via Duffin-Kemmer-Petiau Theory

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KG field, a result that breaks the usual equivalence between the DKP and the KG fields.Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenböck manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed.On leave from     

Measuring time dependent volatility and cross-sectional correlation in Australian equity returns

In this study we examine the time-dependent nature of volatility and cross-correlation of Australian equity returns data. Volatility and correlation estimates are calculated using methods that allow for non-stationary behaviour. By averaging the estimates across the entire data set we show that the correlation in ASX stock returns displays evidence of significant time-dependent behaviour. We also find that the volatility estimates do not display similar non-stationary patterns.     

Dynamical behaviour of birefringent Fabry–Perot cavities

In this paper we present a theoretical and experimental study of the dynamical behaviour of birefringent cavities. Our experimental data show that usual hypothesis which provides that a Fabry–Perot cavity is a first-order low-pass filter cannot explain the behaviour of a birefringent cavity. We explain this phenomenon and give the theoretical expression of the equivalent cavity filter which corresponds to a second-order low-pass filter.     

Synchronization in multicell systems exhibiting dynamic plasticity

Collective behaviour in multicell systems arises from exchange of chemicals/ signals between cells and may be different from their intrinsic behaviour. These chemicals are products of regulated networks of biochemical pathways that underlie cellular functions, and can exhibit a variety of dynamics arising from the non-linearity of the reaction processes. We have addressed the emergent synchronization properties of a ring of cells, diffusively coupled by the end product of an intracellular model biochemical pathway exhibiting non-robust birhythmic behaviour. The aim is to examine the role of intercellular interaction in stabilizing the non-robust dynamics in the emergent collective behaviour in the ring of cells. We show that, irrespective of the inherent frequencies of individual cells, depending on the coupling strength, the collective behaviour does synchronize to only one type of oscillations above a threshold number of cells. Using two perturbation analyses, we also show that this emergent synchronized dynamical state is fairly robust under external perturbations. Thus, the inherent plasticity in the oscillatory phenotypes in these model cells may get suppressed to exhibit collective dynamics of a single type in a multicell system, but environmental influences can sometimes expose this underlying plasticity in its collective dynamics.      

Wave fronts in inhomogeneous neural field models

In this work we investigate the influence of inhomogeneities on wave front propagation in an excitatory neural field model describing synaptic activity in the absence of delays. This allows the derivation of the spatial (and hence temporal) behaviour of the front velocity under the assumption that the front is approximatively homogeneous in a very small time window. With this assumption we can also derive the spatiotemporal behaviour of the membrane potential analytically in the vicinity of the wave front. In addition to this we investigate stationary solutions such as standing wave fronts and localised activity (so-called bumps) to determine the existence condition of travelling and standing fronts. Numerical results are included to point out the accordance of theory and simulation.     

Letter: Parametrization of the Kerr-NUT Solution

The dragging of the Kerr-NUT solution does not tend to zero at infinity. To modify this solution in order to produce a good asymptotic behaviour we transform it by introducing two further parameters with the aid of a SU(1,1) transformation followed by a unitary transformation. By imposing a certain relation between these parameters we obtain a new solution with a good asymptotic behaviour for any value of l, the NUT parameter. The new solution corresponds to a parametrized Kerr solution and we show that l is linked to the form of its ergosphere.     

The zero momentum limit of the vacuum polarization at finite temperature

We examine the zero momentum limit of the finite temperature vacuum polarization for a quantized scalar field coupled to a classical external field. Ordinarily, this type of Feynman diagram is plagued by nonanalytic behaviour when the external momentum tends to zero. Using imaginary-time, we show that this behaviour is not present in an exact background field solution and how the Feynman diagram calculation may be trivially modified to match the exact solution. Comparisons with recent real-time results are also made.     

The Effect of Polydispersity in Primary Particle Size on Measurement of the Fractal Dimension of Aggregates

The use of the mass fractal dimension has become a popular method of characterising the structure of aggregates of fine particles. This parameter is often inferred from scattering experiments that exhibit a power law correlation between scattered intensity and the scattering vector. In this paper we demonstrate deviations from this behaviour that occur when the particles making up the aggregate are not monodisperse, even though the aggregate maintains the same fractal structure as observed in the monodisperse case. We have performed light scattering experiments with aggregating colloidal haematite and performed DLCA computer simulations to explain the observed behaviour. The behaviour can influence the determination of the mass fractal dimension, as can other factors such as scattering effects from primary particles.     

Variables in the use and design of acoustic emission transducers

Previously,¹1 we presented a theory to explain the resonant behaviour of a couplant/multilayer acoustic emission transducer system. Here we present experiments used to verify the applicability of the theory in describing the behaviour of such a system. An acoustic emission transducer/couplant system is typically five layers; but to obtain agreement between theory and experiment, it was necessary to extend the theory to six layers and carry out six-layer measurements.Agreement between theory and experiment is quite good and we believe that this theory provides a basis for a better understanding of the effect of couplant thickness on measured acoustic emission parameters. In the longer term, this will produce greater measurement precision and more effective interpretation of data.     

Multi-bump, self-similar, blow-up solutions of the Ginzburg-Landau equation

For the Ginzburg-Landau equation (GL), we establish the existence and local uniqueness of two classes of multi-bump, self-similar, blow-up solutions for all dimensions 2<d<4 (under certain conditions on the coefficients in the equation). In numerical simulation and via asymptotic analysis, one class of solutions was already found; the second class of multi-bump solutions is new.In the analysis, we treat the GL as a small perturbation of the cubic nonlinear Schrödinger equation (NLS). The existence result given here is a major extension of results established previously for the NLS, since for the NLS the construction only holds for d close to the critical dimension d=2.The behaviour of the self-similar solutions is described by a nonlinear, non-autonomous ordinary differential equation (ODE). After linearisation, this ODE exhibits hyperbolic behaviour near the origin and elliptic behaviour asymptotically. We call the region where the type of behaviour changes the mid-range. All of the bumps of the solutions that we construct lie in the mid-range.For the construction, we track a manifold of solutions of the ODE that satisfy the condition at the origin forward, and a manifold of solutions that satisfy the asymptotic conditions backward, to a common point in the mid-range. Then, we show that these manifolds intersect transversely. We study the dynamics in the mid-range by using geometric singular perturbation theory, adiabatic Melnikov theory, and the Exchange Lemma.     

A mesoscopic approach to the “negative” viscosity effect in ferrofluids

We present a mesoscopic approach to analyse the dynamics of a single magnetic dipole under the influence of an oscillating magnetic field, based on the formulation of a Fokker–Planck equation. The dissipated power and the viscosity of a suspension of such magnetic dipoles are calculated from non-equilibrium thermodynamics of magnetized systems. By means of this method we have found a non-monotonous behaviour of the viscosity as a function of the frequency of the field which has been referred to as the “negative” viscosity effect. Moreover, we have shown that the viscosity depends on the vorticity field thus exhibiting non-Newtonian behaviour. Our analysis is complemented with numerical simulations which reproduce the behaviour of the viscosity we have found and extend the scope of our analytical approach to higher values of the magnetic field.     

Estimation of bit error rate for pseudo-linear differential phase shift keyed transmission links

From studying the statistical behaviour of return-to-zero (RZ) differential phase shift keyed (DPSK) transmission links dominated by fibre nonlinearity, we observe strictly non-Gaussian behaviour in the tails of underlying received current probability density functions. Using this analysis, we derive a new statistical estimate of bit error rate (BER) in pseudo-linear transmission regimes under the growing influence of fibre nonlinearity.