Analytical approximation to the multidimensional Fokker--Planck equation with steady state

The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein--Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are `far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered.Comment: Updated version as publishe

Resonances from meson-meson scattering in U(3) CHPT

In this work, the complete one loop calculation of meson-meson scattering amplitudes within U(3)\otimes U(3) chiral perturbation theory with explicit resonance states is carried out for the first time. Partial waves are unitarized from the perturbative calculation employing a non-perturbative approach based on the N/D method. Once experimental data are reproduced in a satisfactory way we then study the resonance properties, such as the pole positions, corresponding residues and their N_C behaviors. The resulting N_C dependence is the first one in the literature that takes into account the fact that the \eta_1 becomes the ninth Goldstone boson in the chiral limit for large N_C. Within this scheme the vector resonances studied, \rho(770), K^*(892) and \phi(1020), follow an N_C trajectory in agreement with their standard \bar{q}q interpretation. The scalars f_0(1370), a_0(1450) and K^*(1430) also have for large N_C a \bar{q}q pole position trajectory and all of them tend to a bare octet of scalar resonances around 1.4 GeV. The f_0(980) tends asymptotically to the bare pole position of a singlet scalar resonance around 1 GeV. The \sigma, \kappa and a_0(980) scalar resonances have a very different N_C behavior. The case of the \sigma resonance is analyzed with special detail.Comment: 50 pages, 15 figures, 1 table. Enlarged version with more detail comparisons with previous results in the literature. To match with accepted version for publicatio

Orbiter/launch system

The system includes reusable turbojet propelled booster vehicles releasably connected to a reusable rocket powered orbit vehicle. The coupled orbiter-booster combination takes off horizontally and ascends to staging altitude and speed under booster power with both orbiter and booster wings providing lift. After staging, the booster vehicles fly back to Earth for horizontal landing and the orbiter vehicle continues ascending to orbit

List decoding of noisy Reed-Muller-like codes

First- and second-order Reed-Muller (RM(1) and RM(2), respectively) codes are two fundamental error-correcting codes which arise in communication as well as in probabilistically-checkable proofs and learning. In this paper, we take the first steps toward extending the quick randomized decoding tools of RM(1) into the realm of quadratic binary and, equivalently, Z_4 codes. Our main algorithmic result is an extension of the RM(1) techniques from Goldreich-Levin and Kushilevitz-Mansour algorithms to the Hankel code, a code between RM(1) and RM(2). That is, given signal s of length N, we find a list that is a superset of all Hankel codewords phi with dot product to s at least (1/sqrt(k)) times the norm of s, in time polynomial in k and log(N). We also give a new and simple formulation of a known Kerdock code as a subcode of the Hankel code. As a corollary, we can list-decode Kerdock, too. Also, we get a quick algorithm for finding a sparse Kerdock approximation. That is, for k small compared with 1/sqrt{N} and for epsilon > 0, we find, in time polynomial in (k log(N)/epsilon), a k-Kerdock-term approximation s~ to s with Euclidean error at most the factor (1+epsilon+O(k^2/sqrt{N})) times that of the best such approximation

The largest oxigen bearing organic molecule repository

We present the first detection of complex aldehydes and isomers in three typical molecular clouds located within 200pc of the center of our Galaxy. We find very large abundances of these complex organic molecules (COMs) in the central molecular zone (CMZ), which we attribute to the ejection of COMs from grain mantles by shocks. The relative abundances of the different COMs with respect to that of CH3OH are strikingly similar for the three sources, located in very different environments in the CMZ. The similar relative abundances point toward a unique grain mantle composition in the CMZ. Studying the Galactic center clouds and objects in the Galactic disk having large abundances of COMs, we find that more saturated molecules are more abundant than the non-saturated ones. We also find differences between the relative abundance between COMs in the CMZ and the Galactic disk, suggesting different chemical histories of the grain mantles between the two regions in the Galaxy for the complex aldehydes. Different possibilities for the grain chemistry on the icy mantles in the GC clouds are briefly discussed. Cosmic rays can play an important role in the grain chemistry. With these new detections, the molecular clouds in the Galactic center appear to be one of the best laboratories for studying the formation of COMs in the Galaxy.Comment: 20 pages, 4 figures, accepted in Ap

On the properties of the transition matrix in bouncing cosmologies

We elaborate further on the evolution properties of cosmological fluctuations through a bounce. We show this evolution to be describable either by ``transmission'' and ``reflection'' coefficients or by an effective unitary S-matrix. We also show that they behave in a time reversal invariant way. Therefore, earlier results are now interpreted in a different perspective and put on a firmer basis.Comment: 4 pages, 1 figure, to appear in PR