The ergodicity solution of the cooperation puzzle.

When two entities cooperate by sharing resources, one relinquishes something of value to the other. This apparent altruism is frequently observed in nature. Why? Classical treatments assume circumstances where combining resources creates an immediate benefit, e.g. through complementarity or thresholds. Here we ask whether cooperation is predictable without such circumstances. We study a model in which resources self-multiply with fluctuations, a null model of a range of phenomena from viral spread to financial investment. Two fundamental growth rates exist: the ensemble-average growth rate, achieved by the average resources of a large population; and the time-average growth rate, achieved by individual resources over a long time. As a consequence of non-ergodicity, the latter is lower than the former by a term which depends on fluctuation size. Repeated pooling and sharing of resources reduces the effective size of fluctuations and increases the time-average growth rate, which approaches the ensemble-average growth rate in the many-cooperator limit. Therefore, cooperation is advantageous in our model for the simple reason that those who do it grow faster than those who do not. We offer this as a candidate explanation for observed cooperation in rudimentary environments, and as a behavioural baseline for cooperation more generally. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

THz-TDS Reflection Measurement of Coating Thicknesses at Non-Perpendicular Incidence: Experiment and Simulation.

Time-domain spectroscopy (TDS) in the terahertz (THz) frequency range is gaining in importance in nondestructive testing of dielectric materials. One application is the layer thickness measurement of a coating layer. To determine the thickness from the measurement data, the refractive index of the coating layer must be known in the surveyed frequency range. For perpendicular incidence of the radiation, methods exist to extract the refractive index from the measurement data themselves without prior knowledge. This paper extends these methods for non-perpendicular incidence, where the polarization of the radiation becomes important. Furthermore, modifications considering effects of surface roughness of the coating are introduced. The new methods are verified using measurement data of a sample of Inconel steel coated with yttria-stabilized zirconia (YSZ) and with COMSOL simulations of the measurement setup. To validate the thickness measurements, scanning electron microscopy (SEM) images of the layer structure are used. The results show good agreement with an average error of 1% for the simulation data and under 4% for the experimental data compared to reference measurements.

Spectrum to space transformed fast terahertz imaging.

We present an imaging technique in which the broadband frequency information of terahertz (THz) pulses is transformed into spatial resolution. Efficient blazed diffractive gratings spread the individual frequency components over a wide and defined spatial range and f-theta optics are employed to focus the individual components onto a one-dimensional image-line. Measuring the time domain waveform of the THz waves allows therefore for a direct reconstruction of spatial sample characteristics as the spatial domain information is encoded in the terahertz spectrum. We will demonstrate terahertz imaging on selected samples with an improvement in acquisition speed up to two orders of magnitude.

Polarization sensitive terahertz imaging: detection of birefringence and optical axis.

We present a practicable way to take advantage of the spectral information contained in a broadband terahertz pulse for the determination of birefringence and orientation of the optical axis in a glass fiber reinforced polymer with a single measurement. Our setup employs circularly polarized terahertz waves and a polarization-sensitive detector to measure both components of the electromagnetic field simultaneously. The anisotropic optical parameters are obtained from an analysis of the phase and frequency resolved components of the terahertz field. This method shows a high tolerance against the skew of the detection axes and is also independent of a reference measurement.

Terahertz imaging: applications and perspectives.

Terahertz (THz) spectroscopy, and especially THz imaging, holds large potential in the field of nondestructive, contact-free testing. The ongoing advances in the development of THz systems, as well as the appearance of the first related commercial products, indicate that large-scale market introduction of THz systems is rapidly approaching. We review selected industrial applications for THz systems, comprising inline monitoring of compounding processes, plastic weld joint inspection, birefringence analysis of fiber-reinforced components, water distribution monitoring in polymers and plants, as well as quality inspection of food products employing both continuous wave and pulsed THz systems.

Self-organized criticality and absorbing states: lessons from the Ising model.

We investigate a suggested path to self-organized criticality. Originally, this path was devised to "generate criticality" in systems displaying an absorbing-state phase transition, but nothing in its definition forbids the mechanism to be used in any other continuous phase transition. We used the Ising model as well as the Manna model to demonstrate how the finite-size scaling exponents depend on the tuning of driving and dissipation rates with system size. Our findings limit the explanatory power of the mechanism as it is to nonuniversal critical behavior, suggesting that the explanation of self-organized criticality in terms of absorbing-state phase transitions is incomplete.

Rain: relaxations in the sky.

We demonstrate how, from the point of view of energy flow through an open system, rain is analogous to many other relaxational processes in nature such as earthquakes. By identifying rain events as the basic entities of the phenomenon, we show that the number density of rain events per year is inversely proportional to the released water column raised to the power of 1.4. This is the rain equivalent of the Gutenberg-Richter law for earthquakes. The event durations and the waiting times between events are also characterized by scaling regions, where no typical time scale exists. The Hurst exponent of the rain intensity signal H=0.76>0.5. It is valid in the temporal range from minutes up to the full duration of the signal of half a year. All of our findings are consistent with the concept of self-organized criticality, which refers to the tendency of slowly driven nonequilibrium systems towards a state of scale-free behavior.

Avalanche behavior in an absorbing state Oslo model.

Self-organized criticality can be translated into the language of absorbing state phase transitions. Most models for which this analogy is established have been investigated for their absorbing state characteristics. In this paper, we transform the self-organized critical Oslo model into an absorbing state Oslo model and analyze the avalanche behavior. We find that the resulting gap exponent D is consistent with its value in the self-organized critical model. For the avalanche size exponent tau an analysis of the effect of the external drive and the boundary conditions is required.

The time resolution of the St Petersburg paradox.

A resolution of the St Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.

Rethinking convective quasi-equilibrium: observational constraints for stochastic convective schemes in climate models.

Convective quasi-equilibrium (QE) has for several decades stood as a key postulate for parametrization of the impacts of moist convection at small scales upon the large-scale flow. Departures from QE have motivated stochastic convective parametrization, which in its early stages may be viewed as a sensitivity study. Introducing plausible stochastic terms to modify the existing convective parametrizations can have substantial impact, but, as for so many aspects of convective parametrization, the results are sensitive to details of the assumed processes. We present observational results aimed at helping to constrain convection schemes, with implications for each of conventional, stochastic or 'superparametrization' schemes. The original vision of QE due to Arakawa fares well as a leading approximation, but with a number of updates. Some, like the imperfect connection between the boundary layer and the free troposphere, and the importance of free-tropospheric moisture to buoyancy, are quantitatively important but lie within the framework of ensemble-average convection slaved to the large scale. Observations of critical phenomena associated with a continuous phase transition for precipitation as a function of water vapour and temperature suggest a more substantial revision. While the system's attraction to the critical point is predicted by QE, several fundamental properties of the transition, including high precipitation variance in the critical region, need to be added to the theory. Long-range correlations imply that this variance does not reduce quickly under spatial averaging; scaling associated with this spatial averaging has potential implications for superparametrization. Long tails of the distribution of water vapour create relatively frequent excursions above criticality with associated strong precipitation events.

A complexity view of rainfall.

We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus size and number of droughts versus duration. In addition, the accumulated water column displays scale-less fluctuations. These statistical properties are the fingerprints of a self-organized critical process and may serve as a benchmark for models of precipitation and atmospheric processes.