Stress field around arbitrarily shaped cracks in two-dimensional elastic materials

The calculation of the stress field around an arbitrarily shaped crack in an infinite two-dimensional elastic medium is a mathematically daunting problem. With the exception of few exactly soluble crack shapes the available results are based on either perturbative approaches or on combinations of analytic and numerical techniques. We present here a general solution of this problem for any arbitrary crack. Along the way we develop a method to compute the conformal map from the exterior of a circle to the exterior of a line of arbitrary shape, offering it as a superior alternative to the classical Schwartz-Cristoffel transformation. Our calculation results in an accurate estimate of the full stress field and in particular of the stress intensity factors K_I and K_{II} and the T-stress which are essential in the theory of fracture.Comment: 7 pages, 4 figures, submitted for PR

Analogue neural networks on correlated random graphs

We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as the thermodynamic properties of the model. We find that, by properly tuning the dilution in the pattern entries, the network can recover different topological regimes characterized by peculiar scalings of the average coordination number with respect to the system size. The structure is also shown to exhibit a large degree of cliquishness, even when very sparse. Moreover, we obtain explicitly the replica symmetric free energy and the self-consistency equations for the overlaps (order parameters of the theory), which turn out to be classical weighted sums of 'sub-overlaps' defined on all possible sub-graphs. Finally, a study of criticality is performed through a small-overlap expansion of the self-consistencies and through a whole fluctuation theory developed for their rescaled correlations: Both approaches show that the net effect of dilution in pattern entries is to rescale the critical noise level at which ergodicity breaks down.Comment: 34 pages, 3 figure

Equilibrium statistical mechanics on correlated random graphs

Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists and/or, typically, such interactions are essentially (weighted) imitative. Despite such aspects are widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a-priori assumptions and in most cases still implement constant intensities for links. Here we propose a simple shift in the definition of patterns in an Hopfield model to convert frustration into dilution: By varying the bias of the pattern distribution, the network topology -which is generated by the reciprocal affinities among agents - crosses various well known regimes (fully connected, linearly diverging connectivity, extreme dilution scenario, no network), coupled with small world properties, which, in this context, are emergent and no longer imposed a-priori. The model is investigated at first focusing on these topological properties of the emergent network, then its thermodynamics is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. At least at equilibrium, dilution simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations and a naive picture is that within our approach replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible sub-graphs belonging to the main one investigated: As a consequence, for these objects a closure for a self-consistent relation is achieved.Comment: 30 pages, 4 figure

Maternal Nicotine Exposure Leads to Augmented Expression of the Antioxidant Adipose Tissue Triglyceride Lipase Long-Term in the White Adipose of Female Rat Offspring.

Globally, approximately 10-25% of women smoke during pregnancy. Since nicotine is highly addictive, women may use nicotine containing products like nicotine replacement therapies for smoking cessation, but the long-term consequences of early life exposure to nicotine remain poorly defined. Our laboratory has previously demonstrated that maternal nicotine exposed (MNE) rat offspring exhibit hypertriglyceridemia due to increased hepatic de novo lipogenesis. Hypertriglyceridemia may also be attributed to impaired white adipose tissue (WAT) lipid storage; however, the effects of MNE on WAT are not completely understood. We hypothesize that nicotine-induced alterations in adipose function (e.g. lipid storage) underlie dyslipidemia in MNE adults. Female 6 month old rats exposed to nicotine during gestation and lactation exhibited significantly decreased visceral adipocyte cell area by 40%, attributed, in part, to a 3-fold increase in adipose triglyceride lipase (ATGL) protein expression compared to vehicle. Given ATGL has antioxidant properties and in utero nicotine exposure promotes oxidative stress in various tissues, we next investigated if there was evidence of increased oxidative stress in MNE WAT. At both 3 weeks and 6 months, MNE offspring expressed 37-48% higher protein levels of SOD1 and SOD2 in WAT. Since oxidative stress can induce inflammation, we examined the inflammatory profile of WAT and found increased expression of cytokines (IL-1β, TNFα, and IL-6) by 44-61% at 6 months. Collectively, this suggests that the expression of WAT ATGL may be induced to counter MNE-induced oxidative stress and inflammation. However, higher levels of ATGL would further promote lipolysis in WAT, culminating in impaired lipid storage and long-term dyslipidemia

Iterated Conformal Dynamics and Laplacian Growth

The method of iterated conformal maps for the study of Diffusion Limited Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and related processes. We emphasize the fundamental difference between these processes: DLA is grown serially with constant size particles, while Laplacian patterns are grown by advancing each boundary point in parallel, proportionally to the gradient of the Laplacian field. We introduce a 2-parameter family of growth patterns that interpolates between DLA and a discrete version of Laplacian growth. The ultraviolet putative finite-time singularities are regularized here by a minimal tip size, equivalently for all the models in this family. With this we stress that the difference between DLA and Laplacian growth is NOT in the manner of ultraviolet regularization, but rather in their deeply different growth rules. The fractal dimensions of the asymptotic patterns depend continuously on the two parameters of the family, giving rise to a "phase diagram" in which DLA and discretized Laplacian growth are at the extreme ends. In particular we show that the fractal dimension of Laplacian growth patterns is much higher than the fractal dimension of DLA, with the possibility of dimension 2 for the former not excluded.Comment: 13 pages, 12 figures, submitted to Phys. Rev.

Ordering of dipolar Ising crystals

We study Ising systems of spins with dipolar interactions. We find a simple approximate relation for the interaction energy between pairs of parallel lattice columns of spins running along the Ising spin direction. This relation provides insight into the relation between lattice geometry and the nature of the ordered state. It can be used to calculate ground state energies. We have also obtained ground state energies and ordering temperatures T_0 from Monte Carlo simulations. Simple empirical relations, that give T_0 for simple and body centered tetragonal lattices in terms of lattice parameters are also established. Finally, the nature of the ordered state and T_0 are determined for Fe_8 clusters, which crystallize on a triclinic lattice.Comment: 13 pages, 4 eps figures, to be published in PRB. For related work, see http://pipe.unizar.es/~jf

Protogynous Interval in Elephantgrass (Pennisetum purpureum Schum.)

A study was carried out to examine the protogyny duration in elephantgrass inflorescences. Nine accessions were selected, divided into three groups, according to early, intermediate or late flowering. From each cultivar, 10 panicles were sampled for evaluation. The criterion for estimating the duration of protogyny was the time interval (number of days) from the first visual detection of exserted stigmas up to the first visual appearance of open anthers (±5%). Duration of protogyny averaged 7.43±1.37 d, confirming that the species is protoginous. Late flowering accessions exhibited an average of 8.97 d for the duration of protogyny, which was significantly higher than the values observed for the intermediate and early flowering accessions. Data also indicate that the duration of protogyny in elephantgrass is efficient to prevent panicle selfcrossing

Adverse effects of perinatal nicotine exposure on reproductive outcomes

Nicotine exposure during pregnancy through cigarette smoking, nicotine replacement therapies or e-cigarette use continues to be a widespread public health problem, impacting both fetal and postnatal health. Yet, at this time, there remains limited data regarding the safety and efficacy in using these nicotine products during pregnancy. Notably, reports assessing the effect of nicotine exposure on postnatal health outcomes in humans, including reproductive health, are severely lacking. Our current understanding regarding the consequences of nicotine exposure during pregnancy is limited to a few animal studies, which do not comprehensively address the underlying cellular mechanisms involved. This paper aims to critically review the current knowledge from human and animal studies regarding the direct and indirect effects (e.g. obesity) of maternal nicotine exposure, regardless of its source, on reproductive outcomes in pregnancy and postnatal life. Furthermore, this review highlights several key cellular mechanisms involved in these adverse reproductive deficits including oxidative stress, inflammation, and endoplasmic reticulum (ER) stress. By understanding the interplay of the cellular mechanisms involved, further strategies could be developed to prevent the reproductive abnormalities resulting from exposure to nicotine in utero and influence informed clinical guidelines for pregnant women

How perfect can graphene be?

Fabrication of graphene structures has triggered vast research efforts focused on the properties of two-dimensional systems with massless Dirac fermions. Nevertheless, further progress in exploring this quantum electrodynamics system in solid-state laboratories seems to be limited by insufficient electronic quality of manmade structures and the crucial question arises whether existing technologies have reached their limits or major advances are in principle possible. Here we show that graphene in a significantly purer state can be found in nature on the surface of bulk graphite, in form of flakes decoupled from the substrate material. Probing such flakes with Landau level spectroscopy in the THz range at very low magnetic fields, we demonstrate a superior electronic quality of these ultra low density layers (n~3x10^9 cm^-2) expressed by the carrier mobility in excess of 10^7 cm^2/(V.s). This finding represents an important challenge for further improvements of current graphene technologies.Comment: 5 pages, 4 figures, to appear in PR

Photon-assisted tunneling in a Fe8 Single-Molecule Magnet

The low temperature spin dynamics of a Fe8 Single-Molecule Magnet was studied under circularly polarized electromagnetic radiation allowing us to establish clearly photon-assisted tunneling. This effect, while linear at low power, becomes highly non-linear above a relatively low power threshold. This non-linearity is attributed to the nature of the coupling of the sample to the thermostat.These results are of great importance if such systems are to be used as quantum computers.Comment: 4 pages, 4 figure