Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Relaxation time of processes driven by multiplicative noise

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

Le vélo électrique: un outil pour la santé ou un gadget "écolo" [Electrically assisted bicycles: health enhancement or "green" gadget?].

Electrically assisted bicycles (EAB) are flourishing in cities throughout the world and capitalize on ecological and practical advantages, helping in the fight against pollution, CO2 emissions and traffic jam. Human power is necessary to activate the electrical support, so that it equals to a moderate intensity physical activity (> 3 MET), or a vigorous one on hilly courses (>6 MET). The ecological benefits are obvious and transportation departments tend to support citizens who purchase one. EAB offer increased mobility at speeds of 15 to 25 km/h depending on hills and fitness of the rider, but could cause more accidents. EAB is linked to a real physical activity beneficial for health, but potentially more dangerous than a traditional bicycle.

Recovery of soil physical properties by green manure, liming, gypsum and pasture and spontaneous native species¹

Inadequate usage can degrade natural resources, particularly soils. More attention has been paid to practices aiming at the recovery of degraded soils in the last years, e.g, the use of organic fertilizers, liming and introduction of species adapted to adverse conditions. The purpose of this study was therefore to investigate the recovery of physical properties of a Red Latosol (Oxisol) degraded by the construction of a hydroelectric power station. In the study area, a soil layer about 8m thick had been withdrawn by heavy machines leading not only to soil compaction, but resulting in high-degree degradation. The experiment was arranged in a completely randomized design with nine treatments and four replications. The treatments consisted of: 1- soil mobilization by tilling (to ensure the effect of mechanical mobilization in all treatments) without planting, but growth of spontaneous vegetation; 2- Black velvet bean (Stizolobium aterrimum Piper & Tracy); 3- Pigeonpea (Cajanus cajan (L.) DC); 4- Liming + black velvet bean; 5-Liming + pigeonpea until 1994, when replaced by jack bean (Canavalia ensiformis); 6- Liming + gypsum + black velvet bean; 7- Liming + gypsum + pigeonpea until 1994, when replaced by jack bean; and two controls as reference: 8- Native Cerrado vegetation and 9- bare soil (no tilling and no planting), left under natural conditions and in this situation, without spontaneous vegetation. In treatments 1 through 7, the soil was tilled. Treatments were installed in 1992 and left unmanaged for seven years, until brachiaria (Brachiaria decumbens) was planted in all plots in 1999. Seventeen years after implantation, the properties soil macroporosity, microporosity, total porosity, bulk density and aggregate stability were assessed in the previously described treatments in the soil layers 0.00-0.10; 0.10-0.20 and 0.20-0.40 m, and soil Penetration Resistance and soil moisture in 0.00-0.15 and 0.15-0.30 m. The plants were evaluated for: brachiaria dry matter and spontaneous growth of native tree species in the plots as of 2006. Results were analyzed by variance analysis and Tukey´s test at 5 % for mean comparison. In all treatments, except for the bare soil (no recovery measures), ongoing recovery of the degraded soil physical properties was observed. Macroporosity, soil bulk density and total porosity were good soil quality indicators. The occurrence of spontaneous native species indicated the soil recovery process. The best adapted species was Machaerium acutifolium Vogel, with the largest number of plants and most advanced development; the dry matter production of B. decumbens in recovering soil was similar to normal conditions, evidencing soil recovery.

Binding energy and momentum distribution of nuclear matter using Green's functions methods

The influence of hole-hole (h-h) propagation in addition to the conventional particle-particle (p-p) propagation, on the energy per particle and the momentum distribution is investigated for the v2 central interaction which is derived from Reid¿s soft-core potential. The results are compared to Brueckner-Hartree-Fock calculations with a continuous choice for the single-particle (SP) spectrum. Calculation of the energy from a self-consistently determined SP spectrum leads to a lower saturation density. This result is not corroborated by calculating the energy from the hole spectral function, which is, however, not self-consistent. A generalization of previous calculations of the momentum distribution, based on a Goldstone diagram expansion, is introduced that allows the inclusion of h-h contributions to all orders. From this result an alternative calculation of the kinetic energy is obtained. In addition, a direct calculation of the potential energy is presented which is obtained from a solution of the ladder equation containing p-p and h-h propagation to all orders. These results can be considered as the contributions of selected Goldstone diagrams (including p-p and h-h terms on the same footing) to the kinetic and potential energy in which the SP energy is given by the quasiparticle energy. The results for the summation of Goldstone diagrams leads to a different momentum distribution than the one obtained from integrating the hole spectral function which in general gives less depletion of the Fermi sea. Various arguments, based partly on the results that are obtained, are put forward that a self-consistent determination of the spectral functions including the p-p and h-h ladder contributions (using a realistic interaction) will shed light on the question of nuclear saturation at a nonrelativistic level that is consistent with the observed depletion of SP orbitals in finite nuclei.

Soil, water and nutrient losses by interrill erosion from green cane cultivation

Interrill erosion occurs by the particle breakdown caused by raindrop impact, by particle transport in surface runoff, by dragging and suspension of particles disaggregated from the soil surface, thus removing organic matter and nutrients that are essential for agricultural production. Crop residues on the soil surface modify the characteristics of the runoff generated by rainfall and the consequent particle breakdown and sediment transport resulting from erosion. The objective of this study was to determine the minimum amount of mulch that must be maintained on the soil surface of a sugarcane plantation to reduce the soil, water and nutrient losses by decreasing interrill erosion. The study was conducted in Pradópolis, São Paulo State, in 0.5 x 1.0 m plots of an Oxisol, testing five treatments in four replications. The application rates were based on the crop residue production of the area of 1.4 kg m-2 (T1- no cane trash; T2-25 % of the cane trash; T3- 50 % trash; T4-75 % trash; T5-100 % sugarcane residues on the surface), and simulated rainfall was applied at an intensity of 65 mm h-1 for 60 min. Runoff samples were collected in plastic containers and soon after taken to the laboratory to quantify the losses of soil, water and nutrients. To minimize soil loss by interrill erosion, 75 % of the cane mulch must be maintained on the soil, to control water loss 50 % must be maintained and 25 % trash controls organic matter and nutrient losses. This information can contribute to optimize the use of this resource for soil conservation on the one hand and the production of clean energy in sugar and alcohol industries on the other.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Influence of age on retinochoroidal healing processes after argon photocoagulation in C57bl/6j mice.

PURPOSE: To analyze the influence of age on retinochoroidal wound healing processes and on glial growth factor and cytokine mRNA expression profiles observed after argon laser photocoagulation. METHODS: A cellular and morphometric study was performed that used 44 C57Bl/6J mice: 4-week-old mice (group I, n=8), 6-week-old mice (group II, n=8), 10-12-week-old mice (group III, n=14), and 1-year-old mice (group IV, n=14). All mice in these groups underwent a standard argon laser photocoagulation (50 microm, 400 mW, 0.05 s). Two separated lesions were created in each retina using a slit lamp delivery system. At 1, 3, 7, 14, 60 days, and 4 months after photocoagulation, mice from each of the four groups were sacrificed by carbon dioxide inhalation. Groups III and IV were also studied at 6, 7, and 8 months after photocoagulation. At each time point the enucleated eyes were either mounted in Tissue Tek (OCT), snap frozen and processed for immunohistochemistry or either flat mounted (left eyes of groups III and IV). To determine, by RT-PCR, the time course of glial fibrillary acidic protein (GFAP), vascular endothelial growth factor (VEGF), and monocyte chemotactic protein-1 (MCP-1) gene expression, we delivered ten laser burns (50 microm, 400 mW, 0.05 s) to each retina in 10-12-week-old mice (group III', n=10) and 1-year-old mice (group IV', n=10). Animals from Groups III' and IV' had the same age than those from Groups III and IV, but they received ten laser impacts in each eye and served for the molecular analysis. Mice from Groups III and IV received only two laser impacts per eye and served for the cellular and morphologic study. Retinal and choroidal tissues from these treated mice were collected at 16 h, and 1, 2, 3, and 7 days after photocoagulation. Two mice of each group did not receive photocoagulation and were used as controls. RESULTS: In the cellular and morphologic study, the resultant retinal pigment epithelium interruption expanse was significantly different between the four groups. It was more concise and smaller in the oldest group IV (112.1 microm+/-11.4 versus 219.1 microm+/-12.2 in group III) p<0.0001 between groups III and IV. By contrast, while choroidal neovascularization (CNV) was mild and not readily identifiable in group I, at all time points studied, CNV was more prominent in the (1-year-old mice) Group IV than in the other groups. For instance, up to 14 days after photocoagulation, CNV reaction was statistically larger in group IV than in group III ((p=0.0049 between groups III and IV on slide sections and p<0.0001 between the same groups on flat mounts). Moreover, four months after photocoagulation, the CNV area (on slide sections) was 1,282 microm(2)+/-90 for group III and 2,999 microm(2)+/-115 for group IV (p<0.0001 between groups III and IV). Accordingly, GFAP, VEGF, and MCP-1 mRNA expression profiles, determined by RT-PCR at 16 h, 1, 2, 3, and 7 days postphotocoagulation, were modified with aging. In 1-year-old mice (group IV), GFAP mRNA expression was already significantly higher than in the younger (10-12 week) group III before photocoagulation. After laser burns, GFAP mRNA expression peaked at 16-24 h and on day 7, decreasing thereafter. VEGF mRNA expression was markedly increased after photocoagulation in old mice eyes, reaching 2.7 times its basal level at day 3, while it was only slightly increased in young mice (1.3 times its level in untreated young mice 3 days postphotocoagulation). At all time points after photocoagulation, MCP-1 mRNA expression was elevated in old mice, reaching high levels of expression at 16 h and day 3 respectively. CONCLUSIONS: Our results were based on the study of four different age groups and included not only data from morphological observations but also from a molecular analysis of the various alterations of cytokine signaling and expression. One-year-old mice demonstrated more extensive CNV formation and a slower pace of regression after laser photocoagulation than younger mice. These were accompanied by differences in growth factors and cytokine expression profiles indicate that aging is a factor that aggravates CNV. The above results may provide some insight into possible therapeutic strategies in the future.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.