The mid-infrared spectrum of the transiting exoplanet HD 209458b

We report the spectroscopic detection of mid-infrared emission from the transiting exoplanet HD 209458b. Using archive data taken with the Spitzer/IRS instrument, we have determined the spectrum of HD 209458b between 7.46 and 15.25 microns. We have used two independent methods to determine the planet spectrum, one differential in wavelength and one absolute, and find the results are in good agreement. Over much of this spectral range, the planet spectrum is consistent with featureless thermal emission. Between 7.5 and 8.5 microns, we find evidence for an unidentified spectral feature. If this spectral modulation is due to absorption, it implies that the dayside vertical temperature profile of the planetary atmosphere is not entirely isothermal. Using the IRS data, we have determined the broad-band eclipse depth to be 0.00315 +/- 0.000315, implying significant redistribution of heat from the dayside to the nightside. This work required development of improved methods for Spitzer/IRS data calibration that increase the achievable absolute calibration precision and dynamic range for observations of bright point sources.Comment: 35 pages, 12 figures, revised version accepted by the Astrophysical Journa

Stationarity of SLE

A new method to study a stopped hull of SLE(kappa,rho) is presented. In this approach, the law of the conformal map associated to the hull is invariant under a SLE induced flow. The full trace of a chordal SLE(kappa) can be studied using this approach. Some example calculations are presented.Comment: 14 pages with 1 figur

The dimension of loop-erased random walk in 3D

We measure the fractal dimension of loop-erased random walk (LERW) in 3 dimensions, and estimate that it is 1.62400 +- 0.00005. LERW is closely related to the uniform spanning tree and the abelian sandpile model. We simulated LERW on both the cubic and face-centered cubic lattices; the corrections to scaling are slightly smaller for the face-centered cubic lattice.Comment: 4 pages, 4 figures. v2 has more data, minor additional change

Quantitative estimates of discrete harmonic measures

A theorem of Bourgain states that the harmonic measure for a domain in $\R^d$ is supported on a set of Hausdorff dimension strictly less than $d$ \cite{Bourgain}. We apply Bourgain's method to the discrete case, i.e., to the distribution of the first entrance point of a random walk into a subset of $\Z ^d$, $d\geq 2$. By refining the argument, we prove that for all \b>0 there exists \rho (d,\b)N(d,\b), any $x \in \Z^d$, and any $A\subset \{1,..., n\}^d$ | \{y\in\Z^d\colon \nu_{A,x}(y) \geq n^{-\b} \}| \leq n^{\rho(d,\b)}, where $\nu_{A,x} (y)$ denotes the probability that $y$ is the first entrance point of the simple random walk starting at $x$ into $A$. Furthermore, $\rho$ must converge to $d$ as \b \to \infty.Comment: 16 pages, 2 figures. Part (B) of the theorem is ne

Lifetimes, transition probabilities, and level energies in Fe I

We use time-resolved laser-induced fluorescence to measure the lifetime of 186 Fe levels with energies between 25 900 and 60 758 cm . Measured emission branching fractions for these levels yield transition probabilities for 1174 transitions in the range 225-2666 nm. We find another 640 Fe transition probabilities by interpolating level populations in the inductively coupled plasma spectral source. We demonstrate the reliability of the interpolation method by comparing our transition probabilities with absorption oscillator strengths measured by the Oxford group [Blackwell et al., Mon. Not. R. Astron. Soc. 201, 595-602 (1982)]. We derive precise Fe level energies to support the automated method that is used to identify transitions in our spectra

Limiting shapes for deterministic centrally seeded growth models

We study the rotor router model and two deterministic sandpile models. For the rotor router model in $\mathbb{Z}^d$, Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds in dimension 2 are known. A unified approach for these models with a new parameter $h$ (the initial number of particles at each site), allows to prove a number of new limiting shape results in any dimension $d \geq 1$. For the rotor router model, the limiting shape is a sphere for all values of $h$. For one of the sandpile models, and $h=2d-2$ (the maximal value), the limiting shape is a cube. For both sandpile models, the limiting shape is a sphere in the limit $h \to -\infty$. Finally, we prove that the rotor router shape contains a diamond.Comment: 18 pages, 3 figures, some errors corrected and more explanation added, to appear in Journal of Statistical Physic

Field theory conjecture for loop-erased random walks

We give evidence that the functional renormalization group (FRG), developed to study disordered systems, may provide a field theoretic description for the loop-erased random walk (LERW), allowing to compute its fractal dimension in a systematic expansion in epsilon=4-d. Up to two loop, the FRG agrees with rigorous bounds, correctly reproduces the leading logarithmic corrections at the upper critical dimension d=4, and compares well with numerical studies. We obtain the universal subleading logarithmic correction in d=4, which can be used as a further test of the conjecture.Comment: 5 page

Derivatives of spin dynamics simulations

We report analytical equations for the derivatives of spin dynamics simulations with respect to pulse sequence and spin system parameters. The methods described are significantly faster, more accurate and more reliable than the finite difference approximations typically employed. The resulting derivatives may be used in fitting, optimization, performance evaluation and stability analysis of spin dynamics simulations and experiments. Keywords: NMR, EPR, simulation, analytical derivatives, optimal control, spin chemistry, radical pair.Comment: Accepted by The Journal of Chemical Physic

Probability distribution of the sizes of largest erased-loops in loop-erased random walks

We have studied the probability distribution of the perimeter and the area of the k-th largest erased-loop in loop-erased random walks in two-dimensions for k = 1 to 3. For a random walk of N steps, for large N, the average value of the k-th largest perimeter and area scales as N^{5/8} and N respectively. The behavior of the scaled distribution functions is determined for very large and very small arguments. We have used exact enumeration for N <= 20 to determine the probability that no loop of size greater than l (ell) is erased. We show that correlations between loops have to be taken into account to describe the average size of the k-th largest erased-loops. We propose a one-dimensional Levy walk model which takes care of these correlations. The simulations of this simpler model compare very well with the simulations of the original problem.Comment: 11 pages, 1 table, 10 included figures, revte