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In economics, comparative analysis plays the same role as experimental research in physics. In this paper, we closely examine several methodological problems related to comparative analysis by investigating the specific example of grain markets in China and France respectively. This enables us to answer a question in economic history which has so far remained pending, namely whether or not market integration progressed in the 18th century. In economics as in physics, before any new result being accepted, it has to be checked and re-checked by different researchers. This is what we call the replication and comparison procedures. We show how these procedures should (and can) be implemented.

This paper describes three models arising from the theory of excitable media, whose primary visual feature are expanding rings of excitation. Rigorous mathematical results and experimental/computational issues are both addressed. We start with the much-studied Greenberg–Hastings model (GHM) in which the rings are very short-lived, but they do have a transient percolation property. By contrast, in the model we call annihilating nested rings (ANR), excitation centers only gradually lose strength, i.e., each time they become inactive (and then stay so forever) with a fixed probability; we show how the long-term global connectivity properties of the set of excited sites undergo a phase transition. Second part of the paper is devoted to digital boiling (DB) in which new rings spontaneously appear at rested sites with a positive probability. We focus on such (related) issues as convergence to equilibrium, equilibrium excitation level and success of the basic coupling.

Based on energy conservation in a Friedmann–Lemaître–Robertson–Walker (FLRW) Universe, on the Legendre transformation between energy density and pressure, and on nonperturbative asymptotic freedom at high temperatures, we derive the coefficient ${\nu }_{\mathrm{\text{CMB}}}$ in the high-temperature $(T)$ — redshift $(z)$ relation, $T/T_0={\nu }_{\mathrm{\text{CMB}}}(z+1)$, of the Cosmic Microwave Background (CMB). Theoretically, our calculation relies on a deconfining SU(2) rather than a U(1) photon gas. We prove that ${\nu }_{\mathrm{\text{CMB}}}={(1/4)}^{1/3}=0.629960(5)$, representing a topological invariant. Interestingly, the relative deviation of ${\nu }_{\mathrm{\text{CMB}}}$ from the critical exponent associated with the correlation length $l$ of the 3D Ising model, ${\nu }_{\mathrm{\text{Ising}}}=0.629971(4)$, is less than $2\times 10^{-5}$. We are not in a position to establish a direct theoretical link between ${\nu }_{\mathrm{\text{CMB}}}$ and ${\nu }_{\mathrm{\text{Ising}}}$ as suggested by the topological nature of ${\nu }_{\mathrm{\text{CMB}}}$ and the fact that both theories are members of the same universality class. We do, however, spell out a somewhat speculative, strictly monotonic map from the physical Ising temperature $𝜃$ to a fictitious SU(2) Yang–Mills temperature $T$, the latter continuing the asymptotic dependence of the scale factor $a$ on $T/T_0$ for $T/T_0\gg 1$ down to $T=0$, and we identify an exponential map from $a$ to $l$ to reproduce critical Ising behavior.

We report on theoretical investigation of interactions of different mechanisms and their influence onto DNA cooperativity of helix–coil transition (melting). Using the modified version of microscopic Potts-like one-dimensional model we showed that increased stacking results in decreased correlation length. The decrease in cooperativity is explained as a result of combined hydrogen bonding and stacking.

A dependence of phonon interaction on the interelectronic distance is found for a translation-invariant (TI) strong-coupling bipolaron. It is shown that the charge induced by the electrons in a TI-bipolaron state is always greater than that in a bipolaron with spontaneously broken symmetry.

The task of providing leading indicators of catastrophic regime shifts in ecosystems is fundamental in order to design management protocols for those systems. Here we address the problem of lake eutrophication (that is, nutrient enrichment leading to algal blooms) using a simple spatial lake model. We discuss and compare different spatial and temporal early warning signals announcing the catastrophic transition of an oligotrophic lake to eutrophic conditions. In particular, we consider the spatial variance and its associated patchiness of eutrophic water regions. We found that spatial variance increases as the lake approaches the point of transition to a eutrophic state. We also analyze the spatial and temporal early warnings in terms of the amount of information required by each and their respective forewarning times. From the consideration of different remedial procedures that can be followed after these early signals we conclude that some of these indicators are not early enough to avert the undesired impending shift.

Gravity-induced condensation takes the form of momentum alignment in an ensemble of identical particles. Use is made of a one-dimensional Ising model to calculate the alignment per particle and the correlation length as a function of the temperature. These parameters indicate that momentum alignment is possible in the proximity of some astrophysical objects and in Earth, or near Earth laboratories. Momenta oscillations behave as known spin oscillations and obey identical dispersion relations.

Growth behavior of interfaces is usually described by a power-law of the growth in time of the interface width. This general scaling picture is an average behavior description, which may not be valid when only a finite number of interfaces is considered. In this work we study theoretically and experimentally the growth behavior of single interfaces and show that the growth of the interface width always exhibits a non-monotonic, fluctuating behavior. We study numerically the Quenched-noise Kardar-Parisi-Zhang (QKPZ) equation, using different noise distributions, and show that this behavior results from competing mechanisms of normal growth and surface tension forces in this equation. We define a new measure of the interface width fluctuations and present a way to extract the correlation length of the interface from these fluctuations.

Dust-free semidilute and concentrated polystyrene (PS) solutions in different solvents were prepared by slow evaporation and in situ anionic polymerization, which removes the effects of troublesome artifacts such as dust contamination and concentration gradient. The dynamics was reexamined by a combination of static and dynamic laser light scattering. In benzene and toluene (good solvents for PS), only one fast diffusive mode of polymer chains can be observed when the concentration (c) is up to 20%, which is attributed to thermally agitated fluctuation of "blobs" or chain segments. Static and dynamic correlation lengths (ξ_S and ξ_D) are scaled with c as ξ_S (or ξ_D) ~ c^{-0.72 ± 0.02}. In cyclohexane, whose quality decreases with temperature in the range 32–50°C, an additional slow mode of polymer chains can be observed. Such a slow mode is viewed more obviously at a large scattering angle even in a concentrated solution with high chain entanglement. The present study indicates that the slow mode is due to the solvent quality.

The effect of ionic exchange treatment on the self-affine properties of the fracture surfaces of soda-lime-silica glass is explored. The atomic force microscopy (AFM) was used to record the topometric data from the fracture surfaces. The roughness exponent (ζ) and the correlation length (ξ) were calculated by the variable bandwidth method. The analysis for both glasses (strengthened and non-treated) for the roughness exponent shows a value ζ∼0.8, which agrees well with that reported in literature for high speed of crack propagation in different kind of materials. The correlation length shows different values for each condition. Our results suggest that the self-affine correlation length is influenced by the complex interactions of the stress field at the crack tip with that resulting from the collective behavior of the point defects introduced on glass by the ionic exchange treatment.