Bargmann-Wigner method and (6S + 1)-component wave equations

A modified Bargmann-Wigner method is used to derive (6s + 1)-component wave equations. The relation between different forms of these equations is shown.

Heavy rainfall equations for Santa Catarina, Brazil

Knowledge of intensity-duration-frequency (IDF) relationships of rainfall events is extremely important to determine the dimensions of surface drainage structures and soil erosion control. The purpose of this study was to obtain IDF equations of 13 rain gauge stations in the state of Santa Catarina in Brazil: Chapecó, Urussanga, Campos Novos, Florianópolis, Lages, Caçador, Itajaí, Itá, Ponte Serrada, Porto União, Videira, Laguna and São Joaquim. The daily rainfall data charts of each station were digitized and then the annual maximum rainfall series were determined for durations ranging from 5 to 1440 min. Based on these, with the Gumbel-Chow distribution, the maximum rainfall was estimated for durations ranging from 5 min to 24 h, considering return periods of 2, 5, 10, 20, 25, 50, and 100 years,. Data agreement with the Gumbel-Chow model was verified by the Kolmogorov-Smirnov test, at 5 % significance level. For each rain gauge station, two IDF equations of rainfall events were adjusted, one for durations from 5 to 120 min and the other from 120 to 1440 min. The results show a high variability in maximum intensity of rainfall events among the studied stations. Highest values of coefficients of variation in the annual maximum series of rainfall were observed for durations of over 600 min at the stations of the coastal region of Santa Catarina.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Uncertainties in the prediction of spatial variability of soil CO2 emissions and related properties

The soil CO2 emission has high spatial variability because it depends strongly on soil properties. The purpose of this study was to (i) characterize the spatial variability of soil respiration and related properties, (ii) evaluate the accuracy of results of the ordinary kriging method and sequential Gaussian simulation, and (iii) evaluate the uncertainty in predicting the spatial variability of soil CO2 emission and other properties using sequential Gaussian simulations. The study was conducted in a sugarcane area, using a regular sampling grid with 141 points, where soil CO2 emission, soil temperature, air-filled pore space, soil organic matter and soil bulk density were evaluated. All variables showed spatial dependence structure. The soil CO2 emission was positively correlated with organic matter (r = 0.25, p < 0.05) and air-filled pore space (r = 0.27, p < 0.01) and negatively with soil bulk density (r = -0.41, p < 0.01). However, when the estimated spatial values were considered, the air-filled pore space was the variable mainly responsible for the spatial characteristics of soil respiration, with a correlation of 0.26 (p < 0.01). For all variables, individual simulations represented the cumulative distribution functions and variograms better than ordinary kriging and E-type estimates. The greatest uncertainties in predicting soil CO2 emission were associated with areas with the highest estimated values, which produced estimates from 0.18 to 1.85 t CO2 ha-1, according to the different scenarios considered. The knowledge of the uncertainties generated by the different scenarios can be used in inventories of greenhouse gases, to provide conservative estimates of the potential emission of these gases.

Fluid dynamical prediction of changed v1 flow at energies available at the CERN Large Hadron Collider

Substantial collective flow is observed in collisions between lead nuclei at Large Hadron Collider (LHC) as evidenced by the azimuthal correlations in the transverse momentum distributions of the produced particles. Our calculations indicate that the global v1-flow, which at RHIC peaked at negative rapidities (named third flow component or antiflow), now at LHC is going to turn toward forward rapidities (to the same side and direction as the projectile residue). Potentially this can provide a sensitive barometer to estimate the pressure and transport properties of the quark-gluon plasma. Our calculations also take into account the initial state center-of-mass rapidity fluctuations, and demonstrate that these are crucial for v1 simulations. In order to better study the transverse momentum flow dependence we suggest a new "symmetrized" v1S(pt) function, and we also propose a new method to disentangle global v1 flow from the contribution generated by the random fluctuations in the initial state. This will enhance the possibilities of studying the collective Global v1 flow both at the STAR Beam Energy Scan program and at LHC.

Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Poincar wave equations as Fourier transformations of Galilei wave equations

The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.

Prediction of Infant Drug Exposure Through Breastfeeding: Population PK Modeling and Simulation of Fluoxetine Exposure.

The likelihood of significant exposure to drugs in infants through breast milk is poorly defined, given the difficulties of conducting pharmacokinetics (PK) studies. Using fluoxetine (FX) as an example, we conducted a proof-of-principle study applying population PK (popPK) modeling and simulation to estimate drug exposure in infants through breast milk. We simulated data for 1,000 mother-infant pairs, assuming conservatively that the FX clearance in an infant is 20% of the allometrically adjusted value in adults. The model-generated estimate of the milk-to-plasma ratio for FX (mean: 0.59) was consistent with those reported in other studies. The median infant-to-mother ratio of FX steady-state plasma concentrations predicted by the simulation was 8.5%. Although the disposition of the active metabolite, norfluoxetine, could not be modeled, popPK-informed simulation may be valid for other drugs, particularly those without active metabolites, thereby providing a practical alternative to conventional PK studies for exposure risk assessment in this population.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Validation of a clinical prediction score for ruling out coronary heart disease in primary care patients with chest pain.

Background: A patient's chest pain raises concern for the possibility of coronary heart disease (CHD). An easy to use clinical prediction rule has been derived from the TOPIC study in Lausanne. Our objective is to validate this clinical score for ruling out CHD in primary care patients with chest pain. Methods: This secondary analysis used data collected from a oneyear follow-up cohort study attending 76 GPs in Germany. Patients attending their GP with chest pain were questioned on their age, gender, duration of chest pain (1-60 min), sternal pain location, pain increases with exertion, absence of tenderness point at palpation, cardiovascular risks factors, and personal history of cardiovascular disease. Area under the curve (ROC), sensitivity and specificity of the Lausanne CHD score were calculated for patients with full data. Results: 1190 patients were included. Full data was available for 509 patients (42.8%). Missing data was not related to having CHD (p = 0.397) or having a cardiovascular risk factor (p = 0.275). 76 (14.9%) were diagnosed with a CHD. Prevalence of CHD were respectively of 68/344 (19.8%), 2/62 (3.2%), 6/103 (5.8%) in the high, intermediate and low risk category. ROC was of 72.9 (CI95% 66.8; 78.9). Ruling out patients with low risk has a sensitivity of 92.1% (CI95% 83.0; 96.7) and a specificity of 22.4% (CI95% 18.6%; 26.7%). Conclusion: The Lausanne CHD score shows reasonably good sensitivity and can be used to rule out coronary events in patients with chest pain. Patients at risk of CHD for other rarer reasons should nevertheless also be investigated.

Ruling out coronary artery disease in primary care: development and validation of a simple prediction rule.

BACKGROUND: Chest pain can be caused by various conditions, with life-threatening cardiac disease being of greatest concern. Prediction scores to rule out coronary artery disease have been developed for use in emergency settings. We developed and validated a simple prediction rule for use in primary care. METHODS: We conducted a cross-sectional diagnostic study in 74 primary care practices in Germany. Primary care physicians recruited all consecutive patients who presented with chest pain (n = 1249) and recorded symptoms and findings for each patient (derivation cohort). An independent expert panel reviewed follow-up data obtained at six weeks and six months on symptoms, investigations, hospital admissions and medications to determine the presence or absence of coronary artery disease. Adjusted odds ratios of relevant variables were used to develop a prediction rule. We calculated measures of diagnostic accuracy for different cut-off values for the prediction scores using data derived from another prospective primary care study (validation cohort). RESULTS: The prediction rule contained five determinants (age/sex, known vascular disease, patient assumes pain is of cardiac origin, pain is worse during exercise, and pain is not reproducible by palpation), with the score ranging from 0 to 5 points. The area under the curve (receiver operating characteristic curve) was 0.87 (95% confidence interval [CI] 0.83-0.91) for the derivation cohort and 0.90 (95% CI 0.87-0.93) for the validation cohort. The best overall discrimination was with a cut-off value of 3 (positive result 3-5 points; negative result <or= 2 points), which had a sensitivity of 87.1% (95% CI 79.9%-94.2%) and a specificity of 80.8% (77.6%-83.9%). INTERPRETATION: The prediction rule for coronary artery disease in primary care proved to be robust in the validation cohort. It can help to rule out coronary artery disease in patients presenting with chest pain in primary care.

Stochastic semiclassical equations for weakly inhomogeneous cosmologies

Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.