Branching Interfaces with Infinitely Strong Couplings

A hierarchical froth model of the interface of a random $q$-state Potts ferromagnet in $2D$ is studied by recursive methods. A fraction $p$ of the nearest neighbour bonds is made inaccessible to domain walls by infinitely strong ferromagnetic couplings. Energetic and geometric scaling properties of the interface are controlled by zero temperature fixed distributions. For $p<p_c$, the directed percolation threshold, the interface behaves as for $p=0$, and scaling supports random Ising ($q=2$) critical behavior for all $q$'s. At $p=p_c$ three regimes are obtained for different ratios of ferro vs. antiferromagnetic couplings. With rates above a threshold value the interface is linear ( fractal dimension $d_f=1$) and its energy fluctuations, $\Delta E$ scale with length as $\Delta E\propto L^{\omega}$, with $\omega\simeq 0.48$. When the threshold is reached the interface branches at all scales and is fractal ($d_f\simeq 1.046$) with $\omega_c \simeq 0.51$. Thus, at $p_c$, dilution modifies both low temperature interfacial properties and critical scaling. Below threshold the interface becomes a probe of the backbone geometry (\df\simeq{\bar d}\simeq 1.305; $\bar d$ = backbone fractal dimension ), which even controls energy fluctuations ($\omega\simeq d_f\simeq\bar d$). Numerical determinations of directed percolation exponents on diamond hierarchical lattice are also presented.Comment: 16 pages, 3 Postscript figure

Scaling and efficiency determine the irreversible evolution of a market

In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable basis for simulating such series. Based on constraints imposed by market efficiency and on an inhomogeneous-time generalization of standard simple scaling, we propose an analytical model which accounts simultaneously for empirical results like the linear decorrelation of successive returns, the power law dependence on time of the volatility autocorrelation function, and the multiscaling associated to this dependence. In addition, our approach gives a justification and a quantitative assessment of the irreversible character of the index dynamics. This irreversibility enters as a key ingredient in a novel simulation strategy of index evolution which demonstrates the predictive potential of the model.Comment: 5 pages, 4 figure

Export dynamics as an optimal growth problem in the network of global economy

We analyze export data aggregated at world global level of 219 classes of products over a period of 39 years. Our main goal is to set up a dynamical model to identify and quantify plausible mechanisms by which the evolutions of the various exports affect each other. This is pursued through a stochastic differential description, partly inspired by approaches used in population dynamics or directed polymers in random media. We outline a complex network of transfer rates which describes how resources are shifted between different product classes, and determines how casual favorable conditions for one export can spread to the other ones. A calibration procedure allows to fit four free model-parameters such that the dynamical evolution becomes consistent with the average growth, the fluctuations, and the ranking of the export values observed in real data. Growth crucially depends on the balance between maintaining and shifting resources to different exports, like in an explore-exploit problem. Remarkably, the calibrated parameters warrant a close-to-maximum growth rate under the transient conditions realized in the period covered by data, implying an optimal self organization of the global export. According to the model, major structural changes in the global economy take tens of years

`In aliquibus locis est consuetudo': French Lawyers and the Lombard Customs of Fiefs in the Mid-Thirteenth Century

Jean de Blanot, the enigmatic Iacobus Aurelianus, and Jean Blanc de Marseille are the first known French lawyers trained in Italy to have shown interest in one of the most famous custumals in medieval Europe, the Lombard book of fiefs known by the name of Libri Feudorum. Considering that this compilation was increasingly gaining authority in the Italian law schools, this chapter shows how these three lawyers re-elaborated these teachings and compared (or opposed) them to local bodies of norms. By observing how they developed different notions of custom and argued about the validity of the Libri Feudorum outside Lombardy, the chapter unveils the problematic dialectics between Civil law, local custom, and practice, and provides some insights into the making of the ius commune, its practical and historical roots, its geographical dimensions

Mnemonic Poem for memorising the structure of the second section of the Decretum Gratiani, as found in Berlin, SBPK 462, transcr. Attilio Stella

The transcript concerns a mnemonic poem in hexameters, as found in Berlin, SBPK 462, fol. 184r, created to facilitate the memorization of the number of causae and quaestiones contained in the second section of the Decretum Gratiani

Bringing the feudal law back home : social practice and the law of fiefs in Italy and Provence (1100-1250)

This work was supported by the H2020 European Research Council programme under the ERC Advanced Grant CLCLCL (no. 740611) and the EU’s Seventh Framework Programme under the Marie Skłodowska-Curie ITN PIMIC (no. 316732).The Libri feudorum is a composite law book containing the customary laws of fiefs held in Lombardy which were codified in 1100–1250. Its function in shaping a late medieval ‘feudal vocabulary’ and, ultimately, modern models of feudalism was highlighted by Susan Reynolds and lies at the core of her anti-feudalism paradigm. This paper questions the disjuncture between social practice and learned law that underlies the paradigm, by analysing the context and making of the Libri feudorum and of legal writings associated with it – by Pillius de Medicina, Iacobus de Ardizone and Jean Blanc. By showing how practice could shape legal tools used by learned lawyers to frame fiefs and by reassessing the influence of the Libri feudorum on practice, the paper challenges the idea that fiefs were the outcome of professional or academic law and unveils aspects of the practical nature and intellectual dimension of lawyerly writing.Publisher PDFPeer reviewe

The entropic cost to tie a knot

We estimate by Monte Carlo simulations the configurational entropy of $N$-steps polygons in the cubic lattice with fixed knot type. By collecting a rich statistics of configurations with very large values of $N$ we are able to analyse the asymptotic behaviour of the partition function of the problem for different knot types. Our results confirm that, in the large $N$ limit, each prime knot is localized in a small region of the polygon, regardless of the possible presence of other knots. Each prime knot component may slide along the unknotted region contributing to the overall configurational entropy with a term proportional to $\ln N$. Furthermore, we discover that the mere existence of a knot requires a well defined entropic cost that scales exponentially with its minimal length. In the case of polygons with composite knots it turns out that the partition function can be simply factorized in terms that depend only on prime components with an additional combinatorial factor that takes into account the statistical property that by interchanging two identical prime knot components in the polygon the corresponding set of overall configuration remains unaltered. Finally, the above results allow to conjecture a sequence of inequalities for the connective constants of polygons whose topology varies within a given family of composite knot types

Finite-size scaling in unbiased translocation dynamics

Finite-size scaling arguments naturally lead us to introduce a coordinate-dependent diffusion coefficient in a Fokker-Planck description of the late stage dynamics of unbiased polymer translocation through a membrane pore. The solution for the probability density function of the chemical coordinate matches the initial-stage subdiffusive regime and takes into account the equilibrium entropic drive. Precise scaling relations connect the subdiffusion exponent to the divergence with the polymer length of the translocation time, and also to the singularity of the probability density function at the absorbing boundaries. Quantitative comparisons with numerical simulation data in $d=2$ strongly support the validity of the model and of the predicted scalings.Comment: Text revision. Supplemental Material adde

Zipping and collapse of diblock copolymers

Using exact enumeration methods and Monte Carlo simulations we study the phase diagram relative to the conformational transitions of a two dimensional diblock copolymer. The polymer is made of two homogeneous strands of monomers of different species which are joined to each other at one end. We find that depending on the values of the energy parameters in the model, there is either a first order collapse from a swollen to a compact phase of spiral type, or a continuous transition to an intermediate zipped phase followed by a first order collapse at lower temperatures. Critical exponents of the zipping transition are computed and their exact values are conjectured on the basis of a mapping onto percolation geometry, thanks to recent results on path-crossing probabilities.Comment: 12 pages, RevTeX and 14 PostScript figures include