Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations

In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to these equations. The proofs of our results are based on the adaptation to two dimensions of the techniques we previously used to study analogous problems on $S^1$, and on $\mathbb{R}$.Comment: 38 page

Well-posedness and stability results for the Gardner equation

In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy space H^1(R) where global well-posedness follows from the conservation laws of the system. Moreover, we construct solitons of the Gardner equation explicitly and prove that, under certain conditions, this family is orbitally stable in the energy space.Comment: 1 figure. Accepted for publication in Nonlin.Diff Eq.and App

On the 2d Zakharov system with L^2 Schr\"odinger data

We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L^2 x H^{-1/2} x H^{-3/2}. This is the space of optimal regularity in the sense that the data-to-solution map fails to be smooth at the origin for any rougher pair of spaces in the L^2-based Sobolev scale. Moreover, it is a natural space for the Cauchy problem in view of the subsonic limit equation, namely the focusing cubic nonlinear Schroedinger equation. The existence time we obtain depends only upon the corresponding norms of the initial data - a result which is false for the cubic nonlinear Schroedinger equation in dimension two - and it is optimal because Glangetas-Merle's solutions blow up at that time.Comment: 30 pages, 2 figures. Minor revision. Title has been change

Simple nonlinearity evaluation and modeling of low-noise amplifiers with application to radio astronomy receivers

This paper describes a comparative nonlinear analysis of low-noise amplifiers (LNAs) under different stimuli for use in astronomical applications. Wide-band Gaussian-noise input signals, together with the high values of gain required, make that figures of merit, such as the 1 dB compression (1 dBc) point of amplifiers, become crucial in the design process of radiometric receivers in order to guarantee the linearity in their nominal operation. The typical method to obtain the 1 dBc point is by using single-tone excitation signals to get the nonlinear amplitude to amplitude (AM-AM) characteristic but, as will be shown in the paper, in radiometers, the nature of the wide-band Gaussian-noise excitation signals makes the amplifiers present higher nonlinearity than when using single tone excitation signals. Therefore, in order to analyze the suitability of the LNA’s nominal operation, the 1 dBc point has to be obtained, but using realistic excitation signals. In this work, an analytical study of compression effects in amplifiers due to excitation signals composed of several tones is reported. Moreover, LNA nonlinear characteristics, as AM-AM, total distortion, and power to distortion ratio, have been obtained by simulation and measurement with wide-band Gaussian-noise excitation signals. This kind of signal can be considered as a limit case of a multitone signal, when the number of tones is very high. The work is illustrated by means of the extraction of realistic nonlinear characteristics, through simulation and measurement, of a 31 GHz back-end module LNA used in the radiometer of the QUIJOTE (Q U I JOint TEnerife) CMB experimen

Strain Rate Effects on Fracture Behavior of Austempered Ductile Irons

In this work, the mechanical behavior of the austempered ductile iron (ADI) JS/1050-6 was investigated, with particular attention to the strain rate effects on the material ductility. Tensile tests at different strain rates (up to 103 s(-1)) and temperatures (ranging from 213 to 343 K) were performed. Samples with different geometries, smooth and round notched bars, were used to evaluate the effect of the stress triaxiality level on the strain at fracture. For each configuration, the evolution paths of stress and strain were extracted in the point where failure is expected performing numerical analyses at the continuum scale. Stress histories were used as input in a micromechanics analysis aimed to analyze the heterogeneous state of stress, determined by the presence of the graphite nuclei, under the different loading conditions obtained in the experiments. The main result is that, under dynamic conditions, the stress field redistribution, due to the adiabatic condition, postpones the failure occurrence, regardless temperature and strain rate effects on the matrix ductility

Vacation posts on Facebook:A model for incidental vicarious travel consumption

Vicarious consumption of travel is ubiquitous. However little is known about the psychological processes this initiates or the potential for resultant behaviors beyond direct steps toward patronage. We address this gap through developing and testing the incidental vicarious travel consumption model (IVTCM), which draws from well-established knowledge of the self-concept and compensatory consumption. In the context of vicariously consuming idyllic vacation posts on Facebook, the model identifies the following: individuals’ travel-related self-discrepancies may become active, leading to feelings of dejection, initiating five possible compensatory consumption behaviors (Direct, Symbolic, Dissociation, Escapism, Fluid). A sequential mixed-method design (total n=860) provides support for the IVTCM. The primary contributions of the paper are as follows: first the IVTCM can be used to understand different forms of vicarious travel consumption. Second, specific understanding on the impact of idyllic vacation posts is contributed, furthering knowledge on the role of social media within touris

Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation

The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.Comment: 39 pages, 36 figures (high resolution figures at http://www.mis.mpg.de/preprints/index.html

Development and Validation of The SMAP Enhanced Passive Soil Moisture Product

Since the beginning of its routine science operation in March 2015, the NASA SMAP observatory has been returning interference-mitigated brightness temperature observations at L-band (1.41 GHz) frequency from space. The resulting data enable frequent global mapping of soil moisture with a retrieval uncertainty below 0.040 cu m/cu m at a 36 km spatial scale. This paper describes the development and validation of an enhanced version of the current standard soil moisture product. Compared with the standard product that is posted on a 36 km grid, the new enhanced product is posted on a 9 km grid. Derived from the same time-ordered brightness temperature observations that feed the current standard passive soil moisture product, the enhanced passive soil moisture product leverages on the Backus-Gilbert optimal interpolation technique that more fully utilizes the additional information from the original radiometer observations to achieve global mapping of soil moisture with enhanced clarity. The resulting enhanced soil moisture product was assessed using long-term in situ soil moisture observations from core validation sites located in diverse biomes and was found to exhibit an average retrieval uncertainty below 0.040 cu m/cu m. As of December 2016, the enhanced soil moisture product has been made available to the public from the NASA Distributed Active Archive Center at the National Snow and Ice Data Center

Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation

We consider the cubic defocusing nonlinear Schrödinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to higher Fourier modes. This behavior is quantified by the growth of higher Sobolev norms: given any δ[much less-than]1,K [much greater-than] 1, s > 1, we construct smooth initial data u 0 with ||u0||Hs , so that the corresponding time evolution u satisfies u(T)Hs[greater than]K at some time T. This growth occurs despite the Hamiltonian’s bound on ||u(t)||H1 and despite the conservation of the quantity ||u(t)||L2. The proof contains two arguments which may be of interest beyond the particular result described above. The first is a construction of the solution’s frequency support that simplifies the system of ODE’s describing each Fourier mode’s evolution. The second is a construction of solutions to these simpler systems of ODE’s which begin near one invariant manifold and ricochet from arbitrarily small neighborhoods of an arbitrarily large number of other invariant manifolds. The techniques used here are related to but are distinct from those traditionally used to prove Arnold Diffusion in perturbations of Hamiltonian systems

Towards a new crown indicator: an empirical analysis

We present an empirical comparison between two normalization mechanisms for citation-based indicators of research performance. These mechanisms aim to normalize citation counts for the field and the year in which a publication was published. One mechanism is applied in the current so-called crown indicator of our institute. The other mechanism is applied in the new crown indicator that our institute is currently exploring. We find that at high aggregation levels, such as at the level of large research institutions or at the level of countries, the differences between the two mechanisms are very small. At lower aggregation levels, such as at the level of research groups or at the level of journals, the differences between the two mechanisms are somewhat larger. We pay special attention to the way in which recent publications are handled. These publications typically have very low citation counts and should therefore be handled with special care