Miracle-dz/UniFAR-FTUs huggingface dataset:
SiO line emission from interstellar jets and outflows: silicon-containing mantles and non-stationary shock waves

Context. We study the production and emission of SiO and H\(_2\) in the gas phase of molecular outflows, extending previous work in which we considered steady-state C-type shock waves and assumed the silicon to be present only in the cores of silicate grains. Aims. We place constraints on the physical parameters of the pre-shock region, using recent observations of SiO and observations of molecular hydrogen. We show the effects of introducing SiO-containing mantles and of varying the age of the shock wave. We consider simultaneously the emission of SiO and H\(_2\) from the young L1157 outflow. Methods. The molecular outflows are studied by means of a code that can generate stationary C- and J-type shock models and approximate non-stationary solutions, which combine these two types of shock wave. The emission of molecular hydrogen is computed by this code, whereas the SiO emission is computed by means of a separate LVG model, which uses the calculated physical and chemical profiles. A grid of models has been computed, with shock speeds in the range 10 $\leq v_{\rm s}~\leq$ 35 km s -1 and pre-shock gas densities 10 4 $\leq n_{\rm H}~\leq$ 10 6 cm -3 . A wide range of magnetic field strengths has been investigated, from 45 μ G to about 600 μ G. Results. We illustrate our results by means of observational data obtained on the blue lobe of the L1157 outflow. Given the combinations of pre-shock densities and shock velocities necessary to fit the H\(_2\) observations, we find that the erosion only of the silicate material in the grains cores cannot account for the observed SiO line intensities. We investigate the possiblity that a fraction of the SiO is present initially in the grain mantles, and we succeed in constraining this fraction. Introducing even a few percent of the silicon (as SiO) into the mantles is sufficient to increase the SiO line widths and fluxes by an order of magnitude. With this assumption, it is possible to find a non-stationary shock model that provides a reasonable fit of the observations of both H\(_2\) and SiO. Conclusions. With a few percent of the silicon present initially in the grain mantles, good agreement is obtained with recent observations of SiO line integrated line intensities for a pre-shock density n H = 10 4 cm -3 and a shock speed v s = 20 km s -1 . The magnetic field strength and the shock age are not well constrained by the observations of either H\(_2\) or SiO. We show that CO observations (in particular, with the Herschel satellite) could provide further discrimination between the models.
On the Theory of Type 1,1-Operators

This dissertation concerns the pseudo-differential operators of type 1,1. These have been known especially since around 1980, when it was shown that they play an important role in the treatment of fully non-linear partial differential equations. First an account of the historical development in the area is given, including fundamental contributions due to G. Bourdaud and L. H\"ormander in 1988-89, with concise remarks on the authors contributions. Secondly a detailed exposition is given of the systematic theory of type 1,1-operators, based on the general definition of such operators proposed by the author in 2008. This includes an account of how the previous extensions are generalised hereby. Moreover, the conjecture from 1978 by C. Parenti and L. Rodino that type 1,1-operators are pseudo-local is proved in this framework. It is also analysed how such operators can change the support and the spectrum of the functions they act on. Furthermore, the question of which temperate distributions such operators have in their domains have been extensively treated, and departing from H\"ormander's analysis of the operators fulfilling the twisted diagonal condition or, more generally, belong to the self-adjoint subclass, such operators are shown to be everywhere defined. Finally the paradifferential splittings and the resulting boundedness in Lp Sobolev spaces, and the more general Besov and Lizorkin--Triebel spaces, are amply discussed.
Extracting the geometry of an obstacle and a zeroth-order coefficient of a boundary condition via the enclosure method using a single reflected wave over a finite time interval

This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of an acoustic wave over a finite time interval. It is assumed that the wave satisfies a Robin-type boundary condition with an unknown variable coefficient. The wave is generated from the initial data localized outside the obstacle and observed over a finite time interval at the same place as the support of the initial data. It is already known that, using the enclosure method, one can extract the maximum sphere whose exterior encloses the obstacle, from the data. In this paper, it is shown that the enclosure method enables us to extract also: (i) a quantity which indicates the deviation of the geometry between the maximum sphere and the boundary of the obstacle at the first-reflection points of the wave; (ii) the value of the coefficient of the boundary condition at an arbitrary first-reflection point of the wave provided, for example, that the surface of the obstacle is known in a neighbourhood of the point. Further new knowledge is obtained as follows: the enclosure method can cover the case where the data are taken over a sphere whose centre coincides with that of the support of an initial datum, and yields results corresponding to (i) and (ii).
Vacuum Energy of Eleven-dimensional Supergravity

The authors calculate the effective potential for the bosonic sector of eleven-dimensional supergravity on the background (Minkowski)*(sphere). They find no tachyons and show that the antisymmetric tensor field does not threaten graviton dominance when the Freund-Rubin parameter (m) vanishes. The general cases (m not=0) seems intractable in the present formalism.
Domains for Dirac–Coulomb min-max levels

We consider a Dirac operator in three space dimensions, with an electrostatic (i.e. real-valued) potential $V(x)$, having a strong Coulomb-type singularity at the origin. This operator is not always essentially self-adjoint but admits a distinguished self-adjoint extension $D\_V$. In a first part we obtain new results on the domain of this extension, complementing previous works of Esteban and Loss. Then we prove the validity of min-max formulas for the eigenvalues in the spectral gap of $D\_V$, in a range of simple function spaces independent of $V$. Our results include the critical case $\liminf\_{x \to 0} |x| V(x)= -1$, with units such that $\hbar=mc^2=1$, and they are the first ones in this situation. We also give the corresponding results in two dimensions.
New wind input term consistent with experimental, theoretical and numerical considerations

We offer a new method for determining the wind source term for energy and momentum fluxes transfer from the atmosphere to the wind-driven sea. This new source-term formulation is based on extensive analysis of experimental data collected at different sites around the world. It is shown that this new wind source term to be consistent both with numerical solution of exact equation for resonant four-wave interactions and available experimental data.
Combinatorial tangle Floer homology

In this paper we extend the idea of bordered Floer homology to knots and links in $S^3$: Using a specific Heegaard diagram, we construct gluable combinatorial invariants of tangles in $S^3$, $D^3$ and $I\times S^2$. The special case of $S^3$ gives back a stabilized version of knot Floer homology.
MULTIFRACTAL ANALYSIS OF FUNCTIONS ON HEISENBERG AND CARNOT GROUPS

In this article, we investigate the pointwise behaviors of functions on the Heisenberg group. We find wavelet characterizations for the global and local Hölder exponents. Then we prove some a priori upper bounds for the multifractal spectrum of all functions in a given Hölder, Sobolev, or Besov space. These upper bounds turn out to be optimal, since in all cases they are reached by typical functions in the corresponding functional spaces. We also explain how to adapt our proof to extend our results to Carnot groups.
Linkage Extensions

Given two equidimensional Cohen-Macaulay local rings of the same dimension, one shows that a simultaneous extension of each of them by a dualizing module of the other is Gorenstein. This generalizes a theorem of Fossum. The geometrical analogue is also considered. The pairs of double lines in the projective space which are algebraically linked are classified.
Classical Dimers on Penrose Tilings

We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified with those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (defect-free dimer coverings). Instead, their maximum matchings have a monomer density of $81-50\varphi\approx 0.098$ in the thermodynamic limit, with $\varphi=\left(1+\sqrt{5}\right)/2$ the golden ratio. Maximum matchings divide the tiling into a fractal of nested closed regions bounded by loops that cannot be crossed by monomers. These loops connect second-nearest neighbour even-valence vertices, each of which lies on such a loop. Assigning a charge to each monomer with a sign fixed by its bipartite sublattice, we find that each bounded region has an excess of one charge, and a corresponding set of monomers, with adjacent regions having opposite net charge. The infinite tiling is charge neutral. We devise a simple algorithm for generating maximum matchings, and demonstrate that maximum matchings form a connected manifold under local monomer-dimer rearrangements. We show that dart-kite Penrose tilings feature an imbalance of charge between bipartite sub-lattices, leading to a minimum monomer density of $\left(7-4\varphi\right)/5\approx 0.106$ all of one charge.
Wonderful compactification of an arrangement of subvarieties

We define the wonderful compactification of an arrangement of subvarieties. Given a complex nonsingular algebraic variety $Y$ and certain collection $\mathcal{G}$ of subvarieties of $Y$, the wonderful compactification $Y_\mathcal{G}$ can be constructed by a sequence of blow-ups of $Y$ along the subvarieties of the arrangement. This generalizes the Fulton-MacPherson configuration spaces and the wonderful models given by De Concini and Procesi. We give a condition on the order of blow-ups in the construction of $Y_\mathcal{G}$ such that each blow-up is along a nonsingular center.
Lagrangian torus fibration models of Fano threefolds

Inspired by the work of Gross on topological Mirror Symmetry we construct candidate Lagrangian torus fibration models for the 105 families of smooth Fano threefolds. We prove, in the case the second Betti number is one, that the total space of each fibration is homeomorphic to the expected Fano threefold, and show that the numerical invariants coincide for all 105. Our construction relies on a notion of toric degeneration for affine manifolds with singularities, and the correspondence we obtain between polytopes and Fano manifolds is compatible with that appearing in the work of Coates-Corti-Kasprzyk et al. on Mirror Symmetry for Fano manifolds.
A One-Pass Extended Depth of Field Algorithm Based on the Over-Complete Discrete Wavelet Transform

In this paper we describe an algorithm for extended depth of field (EDF) imaging based on the over-complete discrete wavelet transform (OCDWT). We extend previous approaches by describing a, potentially real-time, algorithm that produces the EDF image after a single pass through the "stack" of focal plane images. In addition, we specifically study the effect of over-sampling on EDF reconstruction accuracy and show that a small degree of over-sampling considerably improves the quality of the EDF image.
Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems

This paper considers a nonconvex optimization problem that evolves over time, and addresses the synthesis and analysis of regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized primal-dual gradient methods are implemented in a running fashion, in the sense that the underlying optimization problem changes during the iterations of the algorithms. For a problem with twice continuously differentiable cost and constraints, and under a generalization of the Mangasarian-Fromovitz constraint qualification, sufficient conditions are derived for the running algorithm to track a KKT trajectory. Further, asymptotic bounds for the tracking error (as a function of the time-variability of a KKT trajectory) are obtained. A continuous-time version of the algorithm, framed as a system of differential inclusions, is also considered and analytical convergence results are derived. For the continuous-time setting, a set of sufficient conditions for the KKT trajectories not to bifurcate or merge is proposed. Illustrative numerical results inspired by a real-world application are provided.
Local limits of Markov Branching trees and their volume growth

We are interested in the local limits of families of random trees that satisfy the Markov branching property, which is fulfilled by a wide range of models. Loosely, this property entails that given the sizes of the sub-trees above the root, these sub-trees are independent and their distributions only depend upon their respective sizes. The laws of the elements of a Markov branching family are characterised by a sequence of probability distributions on the sets of integer partitions which describes how the sizes of the sub-trees above the root are distributed. We prove that under some natural assumption on this sequence of probabilities, when their sizes go to infinity, the trees converge in distribution to an infinite tree which also satisfies the Markov branching property. Furthermore, when this infinite tree has a single path from the root to infinity, we give conditions to ensure its convergence in distribution under appropriate rescaling of its distance and counting measure to a self-similar fragmentation tree with immigration. In particular, this allows us to determine how, in this infinite tree, the "volume" of the ball of radius $R$ centred at the root asymptotically grows with $R$. Our unified approach will allow us to develop various new applications, in particular to different models of growing trees and cut-trees, and to recover known results. An illustrative example lies in the study of Galton-Watson trees: the distribution of a critical Galton-Watson tree conditioned on its size converges to that of Kesten's tree when the size grows to infinity. If furthermore, the offspring distribution has finite variance, under adequate rescaling, Kesten's tree converges to Aldous' self-similar CRT and the total size of the $R$ first generations asymptotically behaves like $R^2$.
A new look at Halley's life table

Summary. Edmond Halley published his Breslau life table in 1693, which was arguably the first in the world based on population data. By putting Halley's work into the scientific context of his day and through simple plots and calculations, new insights into Halley's work are made. In particular, Halley tended to round his numbers and to massage his data for easier presentation and calculation. Rather than highlighting outliers as would be done in a modern analysis, Halley instead smoothed them out. Halley's method of life table construction for early ages is examined. His lifetime distribution at higher ages, which is missing in his paper, is reconstructed and a reason is suggested for why Halley neglected to include these ages in his table.
On the generalized Chen's conjecture on biharmonic submanifolds

The generalized Chen's conjecture on biharmonic submanifolds asserts that any biharmonic submanifold of a non-positively curved manifold is minimal (see e.g., [CMO1], [MO], [BMO1], [BMO2], [BMO3], [Ba1], [Ba2], [Ou1], [Ou2], [IIU]). In this paper, we prove that this conjecture is false by constructing foliations of proper biharmonic hyperplanes in a 5-dimensional conformally flat space with negative sectional curvature. Many examples of proper biharmonic submanifolds of non-positively curved spaces are also given.
Surface emissivity and hydrometeors derived from microwave satellite observations and model reanalyses

Satellite-observed Microwave Sounding Unit (MSU) channel 1 (Chl) brightness temperature, and General Circulation Model (GCM) reanalyses over the globe, as well as radiative transfer simulations, have been used to investigate microwave surface emissivity, and low-tropospheric hydrometeors, during the period from January 1981 to December 1993. The average model Ch1 temperature has been derived from three kinds of GCM reanalyses, based on the MSU weighting function. Since the Ch1 temperature constructed from GCM-reanalysis air temperature neglects effects from surface emissivity differences and hydrometeors, it is highest in the summer hemisphere. On the other hand, MSU temperature over land is much higher than it is over ocean, due to depressed surface emissivity over water. Over the high latitude ocean the MSU Ch1 temperature is enhanced because of ice/snow emissivity, while it is reduced over the high latitude land. The difference values of Chl temperature between reanalysis and MSU decrease, in the regions of the ITCZ, SPCZ and sea ice mainly because of increased MSU temperature. The values decrease by about 4-6 K in the ITCZ and SPCZ regions, due to hydrometeors. This difference is found to decrease by about 10-30 K in sea ice regions, due to change in surface emissivity. To explain these results, we have estimated the contribution of surface emissivity and hydrometeors to the MSU Ch1 temperature, utilizing radiative transfer theory. The increase of 4-6 K in the temperature over the ITCZ and SPCZ is estimated to result from hydrometeors that give a precipitation rate of 1-1.5 mm/day under the horizontal homogeneity of rain within the MSU radiometer field of view (fov, ∼110 km), and 7-11 mm/day under inhomogeneous rain distribution within the fov, consistent with TRMM observations. The increase of 10-30 K over the high latitude ocean, arises from ice emissivity of 0.6-0.9. Seasonal movements of sea ice boundary also have been discussed. This study could be valuable by providing an independent technique of computing surface emissivity and hydrometeors over the globe, and for long time periods from microwave measurements, such as MSU and AMSU.
Optimization of unsteady incompressible Navier–Stokes flows using variational level set method

This paper presents the optimization of unsteady Navier–Stokes flows using the variational level set method. The solid–liquid interface is expressed by the level set function implicitly, and the fluid velocity is constrained to be zero in the solid domain. An optimization problem, which is constrained by the Navier–Stokes equations and a fluid volume constraint, is analyzed by the Lagrangian multiplier based adjoint approach. The corresponding continuous adjoint equations and the shape sensitivity are derived. The level set function is evolved by solving the Hamilton–Jacobian equation with the upwind finite difference method. The optimization method can be used to design channels for flows with or without body forces. The numerical examples demonstrate the feasibility and robustness of this optimization method for unsteady Navier–Stokes flows.Copyright © 2012 John Wiley & Sons, Ltd.
Branching Brownian Motion, mean curvature flow and the motion of hybrid zones

We provide a probabilistic proof of a well known connection between a special case of the Allen-Cahn equation and mean curvature flow. We then prove a corresponding result for scaling limits of the spatial Λ-Fleming-Viot process with selection, in which the selection mechanism is chosen to model what are known in population genetics as hybrid zones. Our proofs will exploit a duality with a system of branching (and coalescing) random walkers which is of some interest in its own right.
A fully non-linear optimization approach to acousto-electric tomography

This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric tomography, in which the measurement setup in electrical impedance tomography is modulated by ultrasonic waves thus giving rise to a method potentially having both high contrast and high resolution. We formulate the inverse problem as a regularized non-linear optimization problem, show the existence of a minimizer, and derive optimality conditions. We propose a non-linear conjugate gradient scheme for finding a minimizer based on the optimality conditions. All our numerical experiments are done in two-dimensions. The experiments reveal new insight into the non-linear effects in the reconstruction. One of the interesting features we observe is that, depending on the choice of regularization, there is a trade-off between high resolution and high contrast in the reconstructed images. Our proposed non-linear optimization framework can be generalized to other hybrid imaging modalities.
$n$-dimension central affine curve flows

We construct a sequence of commuting central affine curve flows on $R^n\backslash 0$ invariant under the action of $SL(n,R)$ and prove the following results: (a) The central affine curvatures of a solution of the j-th central affine curve flow is a solution of the j-th flow of Gelfand-Dickey (GD$_n$) hierarchy on the space of n-th order differential operators. (b) We use the solution of the Cauchy problems of the GD$_n$ flow to solve the Cauchy problems for the central affine curve flows with periodic initial data and also with initial data whose central affine curvatures are rapidly decaying. (c) We obtain a bi-Hamiltonian structure for the central affine curve flow hierarchy and prove that it arises naturally from the Poisson structures of certain co-adjoint orbits. (d) We construct Backlund transformations, infinitely many families of explicit solutions and give a permutability formula for these curve flows.
Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrödinger equations

Small-amplitude weakly coupled oscillators of the Klein–Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the recent literature. The first method relies on a priori energy estimates and multi-scale decompositions. The second method is based on a resonant normal form theorem. We show that although the two methods are different in the implementation, they produce equivalent results as the end product. We also discuss the applications of the discrete nonlinear Schrodinger equation in the context of existence and stability of breathers of the Klein–Gordon lattice.
Some remarks on mean field games

Abstract In this article, we study three aspects of mean field games (MFG). The first one is the case when the dynamics of each player depend on the strategies of the other players. The second one concerns the modeling of “noise” in discrete space models and the formulation of the Master Equation in this case. Finally, we show how MFG reduce to agent based models when the intertemporal preference rate goes to infinity, i.e. when the anticipation of the players vanishes.