Lorenz-like systems and classical dynamical equations with memory forcing: a new point of view for singling out the origin of chaos

A novel view for the emergence of chaos in Lorenz-like systems is presented. For such purpose, the Lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one dimensional motion of a particle in a two-well potential, with a forcing term depending on the ``memory'' of the particle past motion. The dynamics of the original Lorenz system in the new particle phase space can then be rewritten in terms of an one-dimensional first-exit-time problem. The emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall. The whole problem is tackled analytically deriving a piecewise linearized Lorenz-like system which preserves all the essential properties of the original model.Comment: 48 pages, 25 figure

Stress tensor fluctuations in de Sitter spacetime

The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m^2/H^2. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.Comment: 35 pages, 4 figure

How to Stop (Worrying and Love) the Bubble: Boundary Changing Solutions

We discover that a class of bubbles of nothing are embedded as time dependent scaling limits of previous spacelike-brane solutions. With the right initial conditions, a near-bubble solution can relax its expansion and open the compact circle. Thermodynamics of the new class of solutions is discussed and the relationships between brane/flux transitions, tachyon condensation and imaginary D-branes are outlined. Finally, a related class of simultaneous connected S-branes are also examined.Comment: 47 pages; v2 introduction to Weyl cards added, comments added, references added, typos corrected, matches JHEP versio

D3/D7 Inflationary Model and M-theory

A proposal is made for a cosmological D3/D7 model with a constant magnetic flux along the D7 world-volume. It describes an N=2 gauge model with Fayet-Iliopoulos terms and the potential of the hybrid P-term inflation. The motion of the D3-brane towards D7 in a phase with spontaneously broken supersymmetry provides a period of slow-roll inflation in the de Sitter valley, the role of the inflaton being played by the distance between D3 and D7-branes. After tachyon condensation a supersymmetric ground state is formed: a D3/D7 bound state corresponding to an Abelian non-linear (non-commutative) instanton. In this model the existence of a non-vanishing cosmological constant is associated with the resolution of the instanton singularity. We discuss a possible embedding of this model into a compactified M-theory setup.Comment: 30 pages, 4 figures, LaTeX; v2, minor typos corrected, one reference adde

Exposure Assessment Techniques Applied to the Highly Censored Deepwater Horizon Gulf Oil Spill Personal Measurements

The GuLF Long-term Follow-up Study (GuLF STUDY) is investigating potential adverse health effects of workers involved in the Deepwater Horizon (DWH) oil spill response and cleanup (OSRC). Over 93% of the 160 000 personal air measurements taken on OSRC workers were below the limit of detection (LOD), as reported by the analytic labs. At this high level of censoring, our ability to develop exposure estimates was limited. The primary objective here was to reduce the number of measurements below the labs' reported LODs to reflect the analytic methods' true LODs, thereby facilitating the use of a relatively unbiased and precise Bayesian method to develop exposure estimates for study exposure groups (EGs). The estimates informed a job-exposure matrix to characterize exposure of study participants. A second objective was to develop descriptive statistics for relevant EGs that did not meet the Bayesian criteria of sample size ≥5 and censoring ≤80% to achieve the aforementioned level of bias and precision. One of the analytic labs recalculated the measurements using the analytic method's LOD; the second lab provided raw analytical data, allowing us to recalculate the data values that fell between the originally reported LOD and the analytical method's LOD. We developed rules for developing Bayesian estimates for EGs with >80% censoring. The remaining EGs were 100% censored. An order-based statistical method (OBSM) was developed to estimate exposures that considered the number of measurements, geometric standard deviation, and average LOD of the censored samples for N ≥ 20. For N 80% but enough non-censored measurements to apply Bayesian methods. We used the OBSM for 3% of the estimates and the simple substitution method for 11%. The methods presented here substantially reduced the degree of censoring in the dataset and increased the number of EGs meeting our Bayesian method's desired performance goal. The OBSM allowed for a systematic and consistent approach impacting only the lowest of the exposure estimates. This approach should be considered when dealing with highly censored datasets

Brane-Antibrane Inflation in Orbifold and Orientifold Models

We analyse the cosmological implications of brane-antibrane systems in string-theoretic orbifold and orientifold models. In a class of realistic models, consistency conditions require branes and antibranes to be stuck at different fixed points, and so their mutual attraction generates a potential for one of the radii of the underlying torus or the 4D string dilaton. Assuming that all other moduli have been fixed by string effects, we find that this potential leads naturally to a period of cosmic inflation with the radion or dilaton field as the inflaton. The slow-roll conditions are satisfied more generically than if the branes were free to move within the space. The appearance of tachyon fields at certain points in moduli space indicates the onset of phase transitions to different non-BPS brane systems, providing ways of ending inflation and reheating the corresponding observable brane universe. In each case we find relations between the inflationary parameters and the string scale to get the correct spectrum of density perturbations. In some examples the small numbers required as inputs are no smaller than 0.01, and are the same small quantities which are required to explain the gauge hierarchy.Comment: 30 pages, 2 figures. Substantial changes on version 1. New cosmological scenarios proposed including the dilaton as the inflaton. Main conclusions unchange

Spin-Glass State in CuGa2O4\rm CuGa_2O_4

Magnetic susceptibility, magnetization, specific heat and positive muon spin relaxation (\musr) measurements have been used to characterize the magnetic ground-state of the spinel compound $\rm CuGa_2O_4$. We observe a spin-glass transition of the S=1/2 $\rm Cu^{2+}$ spins below $\rm T_f=2.5K$ characterized by a cusp in the susceptibility curve which suppressed when a magnetic field is applied. We show that the magnetization of $\rm CuGa_2O_4$ depends on the magnetic histo Well below $\rm T_f$, the muon signal resembles the dynamical Kubo-Toyabe expression reflecting that the spin freezing process in $\rm CuGa_2O_4$ results Gaussian distribution of the magnetic moments. By means of Monte-Carlo simulati we obtain the relevant exchange integrals between the $\rm Cu^{2+}$ spins in this compound.Comment: 6 pages, 16 figure

D-terms and D-strings in open string models

We study the Fayet-Iliopoulos (FI) D-terms on D-branes in type II Calabi-Yau backgrounds. We provide a simple worldsheet proof of the fact that, at tree level, these terms only couple to scalars in closed string hypermultiplets. At the one-loop level, the D-terms get corrections only if the gauge group has an anomalous spectrum, with the anomaly cancelled by a Green-Schwarz mechanism. We study the local type IIA model of D6-branes at SU(3) angles and show that, as in field theory, the one-loop correction suffers from a quadratic divergence in the open string channel. By studying the closed string channel, we show that this divergence is related to a closed string tadpole, and is cancelled when the tadpole is cancelled. Next, we study the cosmic strings that arise in the supersymmetric phases of these systems in light of recent work of Dvali et. al. In the type IIA intersecting D6-brane examples, we identify the D-term strings as D4-branes ending on the D6-branes. Finally, we use N=1 dualities to relate these results to previous work on the FI D-term of heterotic strings.Comment: 29 pages, 5 figures; v2: improved referencin

Primeval Corrections to the CMB Anisotropies

We show that deviations of the quantum state of the inflaton from the thermal vacuum of inflation may leave an imprint in the CMB anisotropies. The quantum dynamics of the inflaton in such a state produces corrections to the inflationary fluctuations, which may be observable. Because these effects originate from IR physics below the Planck scale, they will dominate over any trans-Planckian imprints in any theory which obeys decoupling. Inflation sweeps away these initial deviations and forces its quantum state closer to the thermal vacuum. We view this as the quantum version of the cosmic no-hair theorem. Such imprints in the CMB may be a useful, independent test of the duration of inflation, or of significant features in the inflaton potential about 60 e-folds before inflation ended, instead of an unlikely discovery of the signatures of quantum gravity. The absence of any such substructure would suggest that inflation lasted uninterrupted much longer than ${\cal O}(100)$ e-folds.Comment: 17 pages, latex, no figures; v3: added references and comments, final version to appear in Phys. Rev.

Modeled Air Pollution from In Situ Burning and Flaring of Oil and Gas Released Following the Deepwater Horizon Disaster

The GuLF STUDY, initiated by the National Institute of Environmental Health Sciences, is investigating the health effects among workers involved in the oil spill response and clean-up (OSRC) after the Deepwater Horizon (DWH) explosion in April 2010 in the Gulf of Mexico. Clean-up included in situ burning of oil on the water surface and flaring of gas and oil captured near the seabed and brought to the surface. We estimated emissions of PM2.5 and related pollutants resulting from these activities, as well as from engines of vessels working on the OSRC. PM2.5 emissions ranged from 30 to 1.33e6 kg per day and were generally uniform over time for the flares but highly episodic for the in situ burns. Hourly emissions from each source on every burn/flare day were used as inputs to the AERMOD model to develop average and maximum concentrations for 1-, 12-, and 24-h time periods. The highest predicted 24-h average concentrations sometimes exceeded 5000 μg m-3 in the first 500 m downwind of flaring and reached 71 μg m-3 within a kilometer of some in situ burns. Beyond 40 km from the DWH site, plumes appeared to be well mixed, and the predicted 24-h average concentrations from the flares and in situ burns were similar, usually below 10 μg m-3. Structured averaging of model output gave potential PM2.5 exposure estimates for OSRC workers located in various areas across the Gulf. Workers located nearest the wellhead (hot zone/source workers) were estimated to have a potential maximum 12-h exposure of 97 μg m-3 over the 2-month flaring period. The potential maximum 12-h exposure for workers who participated in in situ burns was estimated at 10 μg m-3 over the ~3-month burn period. The results suggest that burning of oil and gas during the DWH clean-up may have resulted in PM2.5 concentrations substantially above the U.S. National Ambient Air Quality Standard for PM2.5 (24-h average = 35 μg m-3). These results are being used to investigate possible adverse health effects in the GuLF STUDY epidemiologic analysis of PM2.5 exposures