Uniqueness of the thermodynamic limit for driven disordered elastic interfaces

We study the finite size fluctuations at the depinning transition for a one-dimensional elastic interface of size $L$ displacing in a disordered medium of transverse size $M=k L^\zeta$ with periodic boundary conditions, where $\zeta$ is the depinning roughness exponent and $k$ is a finite aspect ratio parameter. We focus on the crossover from the infinitely narrow ($k\to 0$) to the infinitely wide ($k\to \infty$) medium. We find that at the thermodynamic limit both the value of the critical force and the precise behavior of the velocity-force characteristics are {\it unique} and $k$-independent. We also show that the finite size fluctuations of the critical force (bias and variance) as well as the global width of the interface cross over from a power-law to a logarithm as a function of $k$. Our results are relevant for understanding anisotropic size-effects in force-driven and velocity-driven interfaces.Comment: 10 pages, 12 figure

Diffusion in periodic, correlated random forcing landscapes

We study the dynamics of a Brownian particle in a strongly correlated quenched random potential defined as a periodically-extended (with period $L$) finite trajectory of a fractional Brownian motion with arbitrary Hurst exponent $H \in (0,1)$. While the periodicity ensures that the ultimate long-time behavior is diffusive, the generalised Sinai potential considered here leads to a strong logarithmic confinement of particle trajectories at intermediate times. These two competing trends lead to dynamical frustration and result in a rich statistical behavior of the diffusion coefficient $D_L$: Although one has the typical value $D^{\rm typ}_L \sim \exp(-\beta L^H)$, we show via an exact analytical approach that the positive moments ($k>0$) scale like $\langle D^k_L \rangle \sim \exp{[-c' (k \beta L^{H})^{1/(1+H)}]}$, and the negative ones as $\langle D^{-k}_L \rangle \sim \exp(a' (k \beta L^{H})^2)$, $c'$ and $a'$ being numerical constants and $\beta$ the inverse temperature. These results demonstrate that $D_L$ is strongly non-self-averaging. We further show that the probability distribution of $D_L$ has a log-normal left tail and a highly singular, one-sided log-stable right tail reminiscent of a Lifshitz singularity.Comment: 5 pages (main text) + 2 pages (supplemental material); v2: 9 pages, 3 figures, published versio

Universal Statistics of the Critical Depinning Force of Elastic Systems in Random Media

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.Comment: 4 pages, 4 figure

Impactos do pisoteio humano na fauna de um costão rochoso do litoral de São Paulo, no sudeste brasileiro

Increased tourist activity in coastal regions demands management strategies to reduce impacts on rocky shores. The highly populated coastal areas in southeastern Brazil are an example of degradation caused by development of industry and tourism. Among different shore impacts, trampling has been intensively studied, and may represent a significant source of stress for intertidal fauna. A randomised blocks design was applied to experimentally study the effects of two different trampling intensities on richness, diversity, density and biomass of the rocky shore fauna of Obuseiro beach, Guarujá, southeastern Brazil. Blocks were distributed in two portions of the intertidal zone, dominated respectively by Chthamalus bisinuatus (Cirripedia) and Isognomon bicolor (Bivalvia). Blocks were trampled over three months, simulating the vacation period in Brazil and were monitored for the following nine months. Results indicate that Chthamalus bisinuatus is vulnerable to trampling impacts. Richness, diversity and turn-over index tended to be higher in trampled plots four months after trampling ceased. In general, results agree with previous trampling studies, suggesting that even low intensities of trampling may cause some impact on intertidal communities. Management strategies should include isolation of sensitive areas, construction of boardwalks, visitor education and monitoring programmes. In Brazil, additional data obtained from experimental studies are necessary in order to achieve a better understanding of trampling impacts on rocky shore communities.O aumento da atividade turística em áreas costeiras nas últimas décadas faz necessária a adoção de estratégias de manejo para reduzir os impactos gerados às comunidades de costões rochosos. A região costeira do sudeste brasileiro possui bons exemplos de degradação causada pelo turismo e desenvolvimento industrial. Dentre os diferentes distúrbios causados pela visitação, o pisoteio têm sido estudado de forma intensa e pode representar uma fonte significativa de impactos para as comunidades da zona entre-marés. Neste projeto, foi aplicado um desenho de blocos randômicos para se avaliar experimentalmente os efeitos de duas intensidades de pisoteio na riqueza, diversidade, densidade, recobrimento e biomassa da fauna de um costão situado na praia do Obuseiro, no município do Guarujá, São Paulo, Brasil. Os blocos foram alocados em dois povoamentos diferentes, dominados respectivamente por Chthamalus bisinuatus (Cirripedia) e Isognomon bicolor (Bivalvia). O pisoteio foi aplicado durante três meses, simulando a temporada de férias no Brasil, e os blocos foram monitorados nos nove meses seguintes. Os resultados indicaram que Chthamalus bisinuatus é vulnerável aos impactos do pisoteio. Os índices de riqueza, diversidade e turnover apresentaram uma tendência ao aumento nas áreas pisoteadas quatro meses após o término do pisoteio. No geral, os resultados concordam com estudos anteriores e sugerem que mesmo baixas intensidades do distúrbio podem causar impacto às comunidades bentônicas. Estratégias de manejo devem envolver o isolamento de áreas sensíveis, a construção de passarelas, a educação dos visitantes e o monitoramento das comunidades impactadas. No Brasil, a realização de maior quantidade de estudos experimentais é necessária para a melhor compreensão dos impactos do pisoteio nas comunidades de costões rochosos

Thermal Effects in the dynamics of disordered elastic systems

Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW, vortices,..) can be described as generic disordered elastic systems. Understanding their static and dynamics thus poses challenging problems both from the point of view of fundamental physics and of practical applications. Despite important progress many questions remain open. In particular the temperature has drastic effects on the way these systems respond to an external force. We address here the important question of the thermal effect close to depinning, and whether these effects can be understood in the analogy with standard critical phenomena, analogy so useful to understand the zero temperature case. We show that close to the depinning force temperature leads to a rounding of the depinning transition and compute the corresponding exponent. In addition, using a novel algorithm it is possible to study precisely the behavior close to depinning, and to show that the commonly accepted analogy of the depinning with a critical phenomenon does not fully hold, since no divergent lengthscale exists in the steady state properties of the line below the depinning threshold.Comment: Proceedings of the International Workshop on Electronic Crystals, Cargese(2008

Characterization of Vehicle Behavior with Information Theory

This work proposes the use of Information Theory for the characterization of vehicles behavior through their velocities. Three public data sets were used: i.Mobile Century data set collected on Highway I-880, near Union City, California; ii.Borl\"ange GPS data set collected in the Swedish city of Borl\"ange; and iii.Beijing taxicabs data set collected in Beijing, China, where each vehicle speed is stored as a time series. The Bandt-Pompe methodology combined with the Complexity-Entropy plane were used to identify different regimes and behaviors. The global velocity is compatible with a correlated noise with f^{-k} Power Spectrum with k >= 0. With this we identify traffic behaviors as, for instance, random velocities (k aprox. 0) when there is congestion, and more correlated velocities (k aprox. 3) in the presence of free traffic flow

Roughness at the depinning threshold for a long-range elastic string

In this paper, we compute the roughness exponent zeta of a long-range elastic string, at the depinning threshold, in a random medium with high precision, using a numerical method which exploits the analytic structure of the problem (`no-passing' theorem), but avoids direct simulation of the evolution equations. This roughness exponent has recently been studied by simulations, functional renormalization group calculations, and by experiments (fracture of solids, liquid meniscus in 4He). Our result zeta = 0.390 +/- 0.002 is significantly larger than what was stated in previous simulations, which were consistent with a one-loop renormalization group calculation. The data are furthermore incompatible with the experimental results for crack propagation in solids and for a 4He contact line on a rough substrate. This implies that the experiments cannot be described by pure harmonic long-range elasticity in the quasi-static limit.Comment: 4 pages, 3 figure

Width distribution of contact lines on a disordered substrate

We have studied the roughness of a contact line of a liquid meniscus on a disordered substrate by measuring its width distribution. The comparison between the measured width distribution and the width distribution calculated in previous works, extended here to the case of open boundary conditions, confirms that the Joanny-de Gennes model is not sufficient to describe the dynamics of contact lines at the depinning threshold. This conclusion is in agreement with recent measurements which determine the roughness exponent by extrapolation to large system sizes.Comment: 4 pages, 3 figure