Non-perturbative Approach to Critical Dynamics

This paper is devoted to a non-perturbative renormalization group (NPRG) analysis of Model A, which stands as a paradigm for the study of critical dynamics. The NPRG formalism has appeared as a valuable theoretical tool to investigate non-equilibrium critical phenomena, yet the simplest -- and nontrivial -- models for critical dynamics have never been studied using NPRG techniques. In this paper we focus on Model A taking this opportunity to provide a pedagological introduction to NPRG methods for dynamical problems in statistical physics. The dynamical exponent $z$ is computed in $d=3$ and $d=2$ and is found in close agreement with results from other methods.Comment: 13 page

Single-site approximation for reaction-diffusion processes

We consider the branching and annihilating random walk $A\to 2A$ and $2A\to 0$ with reaction rates $\sigma$ and $\lambda$, respectively, and hopping rate $D$, and study the phase diagram in the $(\lambda/D,\sigma/D)$ plane. According to standard mean-field theory, this system is in an active state for all $\sigma/D>0$, and perturbative renormalization suggests that this mean-field result is valid for $d >2$; however, nonperturbative renormalization predicts that for all $d$ there is a phase transition line to an absorbing state in the $(\lambda/D,\sigma/D)$ plane. We show here that a simple single-site approximation reproduces with minimal effort the nonperturbative phase diagram both qualitatively and quantitatively for all dimensions $d>2$. We expect the approach to be useful for other reaction-diffusion processes involving absorbing state transitions.Comment: 15 pages, 2 figures, published versio

Mid-term report for the CORE Organic II funded project. “Innovative cropping Practices to increase soil health of organic fruit tree orchards” BIO-INCROP

Activities performed in the first part of BIO-INCROP project concern five of the eight main objectives fixed in the project proposal. They are: Evaluation of soil borne pest and pathogens involved in replant disease Role of rhizospheric bacterial and fungal communities in plant health Selection of naturally available resources to increase microbial diversity and biomass Compost and organic amendments Evaluation of biologically active formulates The document reports main research results and shows main items of dissemination activity performed in the first part of the project

Optimization of field-dependent nonperturbative renormalization group flows

We investigate the influence of the momentum cutoff function on the field-dependent nonperturbative renormalization group flows for the three-dimensional Ising model, up to the second order of the derivative expansion. We show that, even when dealing with the full functional dependence of the renormalization functions, the accuracy of the critical exponents can be simply optimized, through the principle of minimal sensitivity, which yields $\nu = 0.628$ and $\eta = 0.044$.Comment: 4 pages, 3 figure

Non Perturbative Renormalization Group, momentum dependence of nn-point functions and the transition temperature of the weakly interacting Bose gas

We propose a new approximation scheme to solve the Non Perturbative Renormalization Group equations and obtain the full momentum dependence of $n$-point functions. This scheme involves an iteration procedure built on an extension of the Local Potential Approximation commonly used within the Non Perturbative Renormalization Group. Perturbative and scaling regimes are accurately reproduced. The method is applied to the calculation of the shift $\Delta T_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is very sensitive to all momenta intermediate between these two regions. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%. The next-to-leading order differs by about 10% from the best accepted result

A viscoplastic constitutive model with strain rate variables for asphalt mixtures—numerical simulation

The study and development of recycling techniques for pavements is an increasing activity in engineering nowadays. This research line demands a more realistic characterization of the material properties with the aim of simulate the asphalt mixture’s response placed into a multilayered system over granular bases, under dynamic loads, considering also temperature variation or strength reduction for cyclic loads. In order to improve the current formulations, a new viscoplastic model has been developed assuming the strain rate dependency of the material’s response observed in the experimental tests. The strain rate variable affects in a significant way the Young modulus and the viscosity parameter of the model. According to this hypothesis a constitutive equations have been formulated. The mechanical variables involved have been calibrated according to experimental results, developing new expressions for the strain rate dependent parameters. The new viscoplastic model permits us to characterize the material’s response with a few mechanical values, easily obtained from standard laboratory tests. The results obtained show a good approximation to experimental laboratory curves for different rates of loading and temperatures. The model has been applied to simulate the response of a real flexible pavement structure conformed by two asphalt layers over two granular bases, that’s materials with different constitutive behaviors. Experimental tests in the recycled track have been made obtaining the horizontal strain evolution under dynamic load. Different loading rates and temperatures, as well as cracked and continuum pavement responses have been considered in the study. Strains were measured in the interface between the two asphalt layers and simulated using the here proposed model offering a fairly good approximation of the real response observed in the track, although the degree of variation even in the experimental curves is quite high. The results of this study represent a proper base for further developments in structural analysis of pavement layers, considering more complex phenomena, determinant in the long term material’s response, to develop a numerical tool for pavements’ design and lifetime prediction

A new nascent spreading centre at the Wagner Basin in the northern Gulf of California: a possible geothermal resource?

The probable geothermal reserves of Mexico sum up to only 1400 MW; however, they have been estimated on the basis of the high temperature systems and do not include the unconventional geothermal sources. Submarine hydrothermal systems may become in the near future a feasible energy source, especially those that occur at shallow depths. Recently discovered hydrothermal activity in the Wagner Basin may be harnessed to produce electricity using an environmentally friendly system

Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion

With a view to study the convergence properties of the derivative expansion of the exact renormalization group (RG) equation, I explicitly study the leading and next-to-leading orders of this expansion applied to the Wilson-Polchinski equation in the case of the $N$-vector model with the symmetry $\mathrm{O}(N)$. As a test, the critical exponents $$ and $\nu$ as well as the subcritical exponent $\omega$ (and higher ones) are estimated in three dimensions for values of $N$ ranging from 1 to 20. I compare the results with the corresponding estimates obtained in preceding studies or treatments of other $\mathrm{O}(N)$ exact RG equations at second order. The possibility of varying $N$ allows to size up the derivative expansion method. The values obtained from the resummation of high orders of perturbative field theory are used as standards to illustrate the eventual convergence in each case. A peculiar attention is drawn on the preservation (or not) of the reparametrisation invariance.Comment: Dedicated to Lothar Sch\"afer on the occasion of his 60th birthday. Final versio

Exchange bias effect in the phase separated Nd_{1-x}Sr_{x}CoO_3 at the spontaneous ferromagnetic/ferrimagnetic interface

We report the new results of exchange bias effect in Nd_{1-x}Sr_{x}CoO_3 for x = 0.20 and 0.40, where the exchange bias phenomenon is involved with the ferrimagnetic (FI) state in a spontaneously phase separated system. The zero-field cooled magnetization exhibits the FI (T_{FI}) and ferromagnetic (T_C) transitions at ~ 23 and \sim 70 K, respectively for x = 0.20. The negative horizontal and positive vertical shifts of the magnetic hysteresis loops are observed when the system is cooled through T_{FI} in presence of a positive static magnetic field. Training effect is observed for x = 0.20, which could be interpreted by a spin configurational relaxation model. The unidirectional shifts of the hysteresis loops as a function of temperature exhibit the absence of exchange bias above T_{FI} for x = 0.20. The analysis of the cooling field dependence of exchange bias field and magnetization indicates that the ferromagnetic (FM) clusters consist of single magnetic domain with average size around \sim 20 and ~ 40 \AA ~ for x = 0.20 and 0.40, respectively. The sizes of the FM clusters are close to the percolation threshold for x = 0.20, which grow and coalesce to form the bigger size for x = 0.40 resulting in a weak exchange bias effect.Comment: 9 pages, 9 figure