Symmetries and Fixed Point Stability of Stochastic Differential Equations Modeling Self-Organized Criticality

A stochastic nonlinear partial differential equation is built for two different models exhibiting self-organized criticality, the Bak, Tang, and Wiesenfeld (BTW) sandpile model and the Zhang's model. The dynamic renormalization group (DRG) enables to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.Comment: 19 pages, RevTex, includes 6 PostScript figures, Phys. Rev. E (March 97?

Simulation study of the inhomogeneous Olami-Feder-Christensen model of earthquakes

Statistical properties of the inhomogeneous version of the Olami-Feder-Christensen (OFC) model of earthquakes is investigated by numerical simulations. The spatial inhomogeneity is assumed to be dynamical. Critical features found in the original homogeneous OFC model, e.g., the Gutenberg-Richter law and the Omori law are often weakened or suppressed in the presence of inhomogeneity, whereas the characteristic features found in the original homogeneous OFC model, e.g., the near-periodic recurrence of large events and the asperity-like phenomena persist.Comment: Shortened from the first version. To appear in European Physical Journal

Statistics of extremal intensities for Gaussian interfaces

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not coincide with the distribution of the integrated power spectrum (i.e. roughness of the surface), nor does it obey any of the known extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit distribution is, however, recovered in three cases: (i) in the non-dispersive (white noise) limit, (ii) for high dimensions, and (iii) when only short-wavelength modes are kept. In the last two cases the limit distribution emerges in novel scenarios.Comment: 15 pages, including 7 ps figure

Effect of Trends on Detrended Fluctuation Analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.Comment: 20 pages, 16 figure

Effect of nonstationarities on detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy'', heterogeneous and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts -- a ``cutting'' procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitude, and (iii) generating a signal comprised of segments with different properties -- e.g. different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities.Comment: 17 pages, 10 figures, corrected some typos, added one referenc

Optical coherence tomography-based contact indentation for diaphragm mechanics in a mouse model of transforming growth factor alpha induced lung disease

This study tested the utility of optical coherence tomography (OCT)-based indentation to assess mechanical properties of respiratory tissues in disease. Using OCT-based indentation, the elastic modulus of mouse diaphragm was measured from changes in diaphragm thickness in response to an applied force provided by an indenter. We used a transgenic mouse model of chronic lung disease induced by the overexpression of transforming growth factor-alpha (TGF-a), established by the presence of pleural and peribronchial fibrosis and impaired lung mechanics determined by the forced oscillation technique and plethysmography. Diaphragm elastic modulus assessed by OCT-based indentation was reduced by TGF-a at both left and right lateral locations (p < 0.05). Diaphragm elastic modulus at left and right lateral locations were correlated within mice (r = 0.67, p < 0.01) suggesting that measurements were representative of tissue beyond the indenter field. Co-localised images of diaphragm after TGF-a overexpression revealed a layered fibrotic appearance. Maximum diaphragm force in conventional organ bath studies was also reduced by TGF-a overexpression (p < 0.01). Results show that OCT-based indentation provided clear delineation of diseased diaphragm, and together with organ bath assessment, provides new evidence suggesting that TGF-a overexpression produces impairment in diaphragm function and, therefore, an increase in the work of breathing in chronic lung disease

Maternal high fat diet compromises survival and modulates lung development of offspring, and impairs lung function of dams (female mice)

© 2019 The Author(s). Published in Respiratory Research. Background: Epidemiological studies have identified strong relationships between maternal obesity and offspring respiratory dysfunction; however, the causal direction is not known. We tested whether maternal obesity alters respiratory function of offspring in early life. Methods: Female C57Bl/6 J mice were fed a high or low fat diet prior to and during two rounds of mating and resulting pregnancies with offspring lung function assessed at 2 weeks of age. The lung function of dams was measured at 33 weeks of age. Results: A high fat diet caused significant weight gain prior to conception with dams exhibiting elevated fasting glucose, and glucose intolerance. The number of surviving litters was significantly less for dams fed a high fat diet, and surviving offspring weighed more, were longer and had larger lung volumes than those born to dams fed a low fat diet. The larger lung volumes significantly correlated in a linear fashion with body length. Pups born from the second pregnancy had reduced tissue elastance compared to pups born from the first pregnancy, regardless of the dam's diet. As there was reduced offspring survival born to dams fed a high fat diet, the statistical power of lung function measures of offspring was limited. There were signs of increased inflammation in the bronchoalveolar lavage fluid of dams (but not offspring) fed a high fat diet, with more tumour necrosis factor-α, interleukin(IL)-5, IL-33 and leptin detected. Dams that were fed a high fat diet and became pregnant twice had reduced fasting glucose immediately prior to the second mating, and lower levels of IL-33 and leptin in bronchoalveolar lavage fluid. Conclusions: While maternal high fat diet compromised litter survival, it also promoted somatic and lung growth (increased lung volume) in the offspring. Further studies are required to examine downstream effects of this enhanced lung volume on respiratory function in disease settings