Abstract:
The electronic structure of nanocrystalline (nc-) TiC/amorphous C nanocomposites has been investigated by soft x-ray absorption and emission spectroscopy. The measured spectra at the Ti 2p and C 1s thresholds of the nanocomposites are compared to those of Ti metal and amorphous C. The corresponding intensities of the electronic states for the valence and conduction bands in the nanocomposites are shown to strongly depend on the TiC carbide grain size. An increased charge-transfer between the Ti 3d-eg states and the C 2p states has been identified as the grain size decreases, causing an increased ionicity of the TiC nanocrystallites. It is suggested that the charge-transfer occurs at the interface between the nanocrystalline TiC and the amorphous C matrix and represents an interface bonding which may be essential for the understanding of the properties of nc-TiC/amorphous C and similar nanocomposites.

As opposed to blind patriotism, a moderate form of constructive patriotism has been depicted in previous research and empirically observed. The major distinction between blind patriotism and constructive patriotism lies in the latter’s capacity for criticism. Our research suggests, however, an additional distinction dividing constructive patriotism into two forms: one form is capable of practical judgment (hence, political constructive patriotism), and the other form is critical on grounds of ethical issues (hence moral constructive patriotism). This study then seeks to examine which sort of patriotism prevails within society during wartime; of special interest, for that matter, are the suggested variations of constructive patriotism. Two diverse cases have been chosen in order to examine the reactions within a democratic society: The American case of the 2003 invasion of Iraq and the Israeli case of the 2006 war in Lebanon. A substantive content analysis has been employed, surveying social processes through a variety of articles in an American and an Israeli daily newspaper. The findings reveal that in both cases among expressions of constructive patriotism, those of political constructive patriotism form a vast majority and only a few of them express moral constructive patriotism. It therefore seems that constructive patriots are not necessarily as moral as they might seem to be at first glance, even though they criticize state and society. The case of war in particular proves how on moral grounds criticism is important, but not enough.

Abstract:
We have performed first principles density functional theory calculations on TiC alloyed on the Ti sublattice with 3d transition metals ranging from Sc to Zn. The theory is accompanied with experimental investigations, both as regards materials synthesis as well as characterization. Our results show that by dissolving a metal with a weak ability to form carbides, the stability of the alloy is lowered and a driving force for the release of carbon from the carbide is created. During thin film growth of a metal carbide this effect will favor the formation of a nanocomposite with carbide grains in a carbon matrix. The choice of alloying elements as well as their concentrations will affect the relative amount of carbon in the carbide and in the carbon matrix. This can be used to design the structure of nanocomposites and their physical and chemical properties. One example of applications is as low-friction coatings. Of the materials studied, we suggest the late 3d transition metals as the most promising elements for this phenomenon, at least when alloying with TiC.

Abstract:
In this study we report on the film growth and characterization of thin (approximately 50 nm thick) Ti-Fe-C films deposited on amorphous quartz. The experimental studies have been complemented by first principles density functional theory (DFT) calculations. Upon annealing of as-prepared films, the composition of the metastable Ti-Fe-C film changes. An iron-rich phase is first formed close to the film surface, but with increasing annealing time this phase is gradually displaced toward the film-substrate interface where its position stabilizes. Both the magnetic ordering temperature and the saturation magnetization changes significantly upon annealing. The DFT calculations show that the critical temperature and the magnetic moment both increase with increasing Fe and C-vacancy concentration. The formation of the metastable iron-rich Ti-Fe-C compound is reflected in the strong increase of the magnetic ordering temperature. Eventually, after enough annealing time ($\geq 10$ minutes), nano-crystalline $\alpha$-Fe starts to precipitate and the amount and size of these precipitates can be controlled by the annealing procedure; after 20 minutes of annealing, the experimental results indicate a nano-crystalline iron-film embedded in a wear resistant TiC compound. This conclusion is further supported by transmission electron microscopy studies on epitaxial Ti-Fe-C films deposited on single crystalline MgO substrates where, upon annealing, an iron film embedded in TiC is formed. Our results suggest that annealing of metastable Ti-Fe-C films can be used as an efficient way of creating a wear-resistant magnetic thin film material.

Abstract:
We have analyzed ~600 ks of Rossi X-ray Timing Explorer data of the neutron star low-mass X-ray binary and Z source GX 17+2. A study was performed of the properties of the noise components and quasi-periodic oscillations (QPOs) as a function of the spectral properties, with the main goal to study the relation between the frequencies of the horizontal branch and upper kHz QPOs. It was found that when the upper kHz QPO frequency is below 1030 Hz these frequencies correlate, whereas above 1030 Hz they anti-correlate. GX 17+2 is the first source in which this is observed. We also found that the frequency difference of the high frequency QPOs was not constant and that the quality factors (Q values) of the HBO, its second harmonic, and the kHz QPOs are similar, and vary almost hand in hand by a factor of more than three. Observations of the normal branch oscillations during two type I X-ray bursts showed that their absolute amplitude decreased as the flux from the neutron star became stronger. We discuss these and other findings in terms of models that have been proposed for these phenomena. We also compare the behavior of GX 17+2 and other Z sources with that of black hole sources and consider the possibility that the mass accretion rate might not be driving force behind all spectral and variability changes.

Abstract:
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. We provide several important properties of this topology and use them to provide a simple proof of the famous HVZ theorem in the repulsive case. In a second step we recall the method of geometric localization in Fock space as proposed by Derezi\'nski and G\'erard, and we relate this tool to our weak topology. We then provide several applications. We start by studying the so-called finite-rank approximation which consists in imposing that the many-body wavefunction can be expanded using finitely many one-body functions. We thereby emphasize geometric properties of Hartree-Fock states and prove nonlinear versions of the HVZ theorem, in the spirit of works of Friesecke. In the last section we study translation-invariant many-body systems comprising a nonlinear term, which effectively describes the interactions with a second system. As an example, we prove the existence of the multi-polaron in the Pekar-Tomasevich approximation, for certain values of the coupling constant.

Abstract:
We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the polarized Dirac sea. We quickly derive this model from Quantum Electrodynamics and state the existence of solutions, imposing an ultraviolet cut-off $\Lambda$. We then discuss the limit $\Lambda\to\infty$ in detail, by resorting to charge renormalization.

Abstract:
We describe several recent results obtained in collaboration with P. Gravejat, C. Hainzl, E. S\'er\'e and J.P. Solovej, concerning a nonlinear model for the relativistic quantum vacuum in interaction with a classical electromagnetic field.

Abstract:
We review recent results about the derivation of the Gross-Pitaevskii equation and of the Bogoliubov excitation spectrum, starting from many-body quantum mechanics. We focus on the mean-field regime, where the interaction is multiplied by a coupling constant of order 1/N where N is the number of particles in the system.

Abstract:
In a recent paper published in Nonlinear Analysis: Theory, Methods & Applications, C. Argaez and M. Melgaard studied excited states for pseudo-relativistic multi-configuration methods. Their paper follows a previous work of mine in the non-relativistic case (Arch. Rat. Mech. Anal., 171, 2004). The main results of the paper of C. Argaez and M. Melgaard are correct, but the proofs are both wrong and incomplete.