Fracture surfaces of heterogeneous materials: a 2D solvable model

Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model ensures the stability of straight cracks and allows for the study of the roughening of fracture surfaces. When neglecting the effect of the non singular stress, the problem becomes exactly solvable and yields analytic predictions for the power spectrum of the paths. This result suggests an alternative to the conventional power law analysis often used in the analysis of experimental data.Comment: 4 pages, 4 figure

Complex temperatures zeroes of partition function in spin-glass models

An approximate method is proposed for investigating complex-temperature properties of real-dimensional spin-glass models. The method uses the complex-temperature data of the ferromagnetic model on the same lattice. The universality line in the complex-temperature space is obtained.Comment: latex, corrected some misprint

Entropy of Open Lattice Systems

We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in contact with particle reservoirs at different densities. In the hydrodynamic scaling limit, L to infinity, the leading order (O(L)) behavior of this entropy has been shown by Bahadoran to be that of a product measure corresponding to strict local equilibrium; we compute the first correction, which is O(1). The computation uses a formal expansion of the entropy in terms of truncated correlation functions; for this system the k-th such correlation is shown to be O(L^{-k+1}). This entropy correction depends only on the scaled truncated pair correlation, which describes the covariance of the density field. It coincides, in the large L limit, with the corresponding correction obtained from a Gaussian measure with the same covariance.Comment: Latex, 28 pages, 4 figures as eps file

The political import of deconstruction—Derrida’s limits?: a forum on Jacques Derrida’s specters of Marx after 25 Years, part I

Jacques Derrida delivered the basis of The Specters of Marx: The State of the Debt, the Work of Mourning, & the New International as a plenary address at the conference ‘Whither Marxism?’ hosted by the University of California, Riverside, in 1993. The longer book version was published in French the same year and appeared in English and Portuguese the following year. In the decade after the publication of Specters, Derrida’s analyses provoked a large critical literature and invited both consternation and celebration by figures such as Antonio Negri, Wendy Brown and Frederic Jameson. This forum seeks to stimulate new reflections on Derrida, deconstruction and Specters of Marx by considering how the futures past announced by the book have fared after an eventful quarter century. Maja Zehfuss, Antonio Vázquez-Arroyo and Dan Bulley and Bal Sokhi-Bulley offer sharp, occasionally exasperated, meditations on the political import of deconstruction and the limits of Derrida’s diagnoses in Specters of Marx but also identify possible paths forward for a global politics taking inspiration in Derrida’s work of the 1990s

Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase

We consider the low-temperature $T<T_c$ disorder-dominated phase of the directed polymer in a random potentiel in dimension 1+1 (where $T_c=\infty$) and 1+3 (where $T_c<\infty$). To characterize the localization properties of the polymer of length $L$, we analyse the statistics of the weights $w_L(\vec r)$ of the last monomer as follows. We numerically compute the probability distributions $P_1(w)$ of the maximal weight $w_L^{max}= max_{\vec r} [w_L(\vec r)]$, the probability distribution $\Pi(Y_2)$ of the parameter $Y_2(L)= \sum_{\vec r} w_L^2(\vec r)$ as well as the average values of the higher order moments $Y_k(L)= \sum_{\vec r} w_L^k(\vec r)$. We find that there exists a temperature $T_{gap}<T_c$ such that (i) for $T<T_{gap}$, the distributions $P_1(w)$ and $\Pi(Y_2)$ present the characteristic Derrida-Flyvbjerg singularities at $w=1/n$ and $Y_2=1/n$ for $n=1,2..$. In particular, there exists a temperature-dependent exponent $\mu(T)$ that governs the main singularities $P_1(w) \sim (1-w)^{\mu(T)-1}$ and $\Pi(Y_2) \sim (1-Y_2)^{\mu(T)-1}$ as well as the power-law decay of the moments $\bar{Y_k(i)} \sim 1/k^{\mu(T)}$. The exponent $\mu(T)$ grows from the value $\mu(T=0)=0$ up to $\mu(T_{gap}) \sim 2$. (ii) for $T_{gap}<T<T_c$, the distribution $P_1(w)$ vanishes at some value $w_0(T)<1$, and accordingly the moments $\bar{Y_k(i)}$ decay exponentially as $(w_0(T))^k$ in $k$. The histograms of spatial correlations also display Derrida-Flyvbjerg singularities for $T<T_{gap}$. Both below and above $T_{gap}$, the study of typical and averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure

Spectral Degeneracies in the Totally Asymmetric Exclusion Process

We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY filling. Although the system does not possess obvious symmetries except translation invariance, the spectrum presents many multiplets with degeneracies of high order. This behaviour is explained by a hidden symmetry property of the Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the corresponding number of multiplets are derived and compared with numerical results obtained from exact diagonalisation of small size systems. This unexpected structure of the TASEP spectrum suggests the existence of an underlying large invariance group. Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.Comment: 19 pages, 1 figur

Linguistic incompetence: giving an account of researching multilingually

This paper considers the place of linguistic competence and incompetence in the context of researching multilingually. It offers a critique of the concept of competence and explores the performative dimensions of multilingual research and its narration, through the philosophy of Judith Butler, and in particular her study Giving an account of oneself. It explores aspects of risk, justice, narrative limit and a morality of multilingualism in emergent multilingual research frameworks. These theoretical dimensions are explored through consideration of ‘linguistically incompetent’ ethnographic work with refugees and asylum seekers, in contexts of hospitality and in life long learning research in the Gaza Strip, and of early attempts to learn new languages. The paper offers a prospect of a relational approach to researching multilingually and affirms the vulnerability at the heart of linguistic hospitality

Gaussian field theories, random Cantor sets and multifractality

The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian field theories in terms of random Cantor sets and show how universal multifractal scaling exponents can be calculated. We use this approach to characterize the multifractal critical wave function of Dirac fermions interacting with a random vector potential in two spatial dimensions. We show that the multifractal scaling exponents are self-averaging.Comment: Extensive modifications of previous version; exact results replace numerical calculation