Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications

We present an analytical method, rooted in the non-perturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all its different regimes, including the strong-coupling one. We analyze the symmetries of the KPZ problem and derive an approximation scheme that satisfies the linearly realized ones. We implement this scheme at the minimal order in the response field, and show that it yields a complete, qualitatively correct phase diagram in all dimensions, with reasonable values for the critical exponents in physical dimensions. We also compute in one dimension the full (momentum and frequency dependent) correlation function, and the associated universal scaling functions. We find an excellent quantitative agreement with the exact results from Praehofer and Spohn (J. Stat. Phys. 115 (2004)). We emphasize that all these results, which can be systematically improved, are obtained with sole input the bare action and its symmetries, without further assumptions on the existence of scaling or on the form of the scaling function.Comment: 21 pages, 6 figures, revised version, including the correction of an inconsistency and accordingly updated figures 5 and 6 and table 2, as published in an Erratum (see Ref. below). The results are improve

Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation

We present a simple approximation of the non-perturbative renormalization group designed for the Kardar-Parisi-Zhang equation and show that it yields the correct phase diagram, including the strong-coupling phase with reasonable scaling exponent values in physical dimensions. We find indications of a possible qualitative change of behavior around $d=4$. We discuss how our approach can be systematically improved.Comment: 4 pages, 1 figure, references added, minor change

Articulations between commercial banks and microfinance institutions in Sub-Saharan Africa: the case of Cameroon

In this article, we evaluate, from the point of view of banks, the potential of articulations between commercial banks and microfinance institutions (MFIs) in Cameroun in terms of financing of the rural and the micro, small and medium enterprises (MSMEs). Furthermore, we seek to define the best form of partnership between the two types of institutions. The results obtained suggest that the articulations between banks and MFIs can potentially be beneficial to all stakeholders (banks, MFIs but also recipients). This study also highlights the fact that these articulations can be even more beneficial if national commercial banks, under the Cameroonian law in our case, participate rather than branches of foreign banking groups. Indeed, our research reveals that through these partnerships, from their cultural proximity and their propensity to take more risks, national commercial banks will more likely offer either directly or indirectly (through MFIs) more adapted financial products and services to both the rural and the MSMEs’ segments. The question of knowing if a better form of partnership between commercial banks and MFIs exists, results suggest that there is no better form of partnership as such; that the best form depends on the MFI’s development stage and that in any case this partnership should privilege a national commercial bank rather than a branch of a foreign bank. Even if the foreign banks’ contest might be necessary at a given stage of the process, the results make it also possible to consider a new model of interactions implying Microfinance investment vehicles and national commercial banks. This model would have the advantage to help mitigate risks that those vehicles perceive when deciding to directly invest in MFIs.Banks, Microfinance institutions, Microfinance investment vehicles, Sub-Saharan Africa, Cameroon

Finite-scale singularity in the renormalization group flow of a reaction-diffusion system

International audienceWe study the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD) by means of nonperturbative functional renormalization group techniques. We show that usual perturbation theory fails because the effective potential develops a nonanalyticity at a finite length scale: Perturbatively forbidden terms are dynamically generated and the flow can be continued once they are taken into account. Our results suggest that the critical behavior of PCPD can be either in the directed percolation or in a new (conjugated) universality class

General framework of the non-perturbative renormalization group for non-equilibrium steady states

This paper is devoted to presenting in detail the non-perturbative renormalization group (NPRG) formalism to investigate out-of-equilibrium systems and critical dynamics in statistical physics. The general NPRG framework for studying non-equilibrium steady states in stochastic models is expounded and fundamental technicalities are stressed, mainly regarding the role of causality and of Ito's discretization. We analyze the consequences of Ito's prescription in the NPRG framework and eventually provide an adequate regularization to encode them automatically. Besides, we show how to build a supersymmetric NPRG formalism with emphasis on time-reversal symmetric problems, whose supersymmetric structure allows for a particularly simple implementation of NPRG in which causality issues are transparent. We illustrate the two approaches on the example of Model A within the derivative expansion approximation at order two, and check that they yield identical results.Comment: 28 pages, 1 figure, minor corrections prior to publicatio

Defining Quantitative Targets for Topsoil Organic Carbon Stock Increase in European Croplands: Case Studies With Exogenous Organic Matter Inputs

The EU Mission Board for Soil Health and Food proposed a series of quantitative targets for European soils to become healthier. Among them, current soil organic carbon (SOC) concentration losses in croplands (0.5% yr(-1) on average at 20 cm depth) should be reversed to an increase of 0.1-0.4% yr(-1) by 2030. Quantitative targets are used by policy makers to incentivize the implementation of agricultural practices that increase SOC stocks. However, there are different approaches to calculate them. In this paper, we analyzed the effect of exogenous organic matter (EOM) inputs on the evolution of SOC stocks, with a particular focus on the new European targets and the different approaches to calculate them. First, we illustrated through two case-study experiments the different targets set when the SOC stock increase is calculated considering as reference: 1) the SOC stock level at the onset of the experiment and 2) the SOC stock trend in a baseline, i.e., a control treatment without EOM addition. Then, we used 11 long-term experiments (LTEs) with EOM addition in European croplands to estimate the amount of carbon (C) input needed to reach the 0.1 and 0.4% SOC stock increase targets proposed by the Mission Board for Soil Health and Food, calculated with two different approaches. We found that, to reach a 0.1 and 0.4% increase target relative to the onset of the experiment, 2.51 and 2.61 Mg C ha(-1) yr(-1) of additional C input were necessary, respectively. Reaching a 0.1 and 0.4% increase target relative to the baseline required 1.38 and 1.77 Mg C ha(-1) yr(-1) of additional input, respectively. Depending on the calculation method used, the estimated amounts of additional C input required to reach each quantitative target were significantly different from each other. Furthermore, the quality of C input as represented by the C retention rate of the additional organic material (EOM and crop residue), had a significant effect on the variation of SOC stocks. Our work highlights the necessity to take into consideration the additional C input required to increase SOC stocks, especially for soils with decreasing SOC stocks, when targets are set independently of the baseline

GC×GC-(HR)TOFMS in Cancer Research

Peer reviewe