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Institute
- Institut für Physik und Astronomie (187) (remove)
Corvino, Corvino and Schoen, Chruściel and Delay have shown the existence of a large class of asymptotically flat vacuum initial data for Einstein's field equations which are static or stationary in a neighborhood of space-like infinity, yet quite general in the interior. The proof relies on some abstract, non-constructive arguments which makes it difficult to calculate such data numerically by using similar arguments. A quasilinear elliptic system of equations is presented of which we expect that it can be used to construct vacuum initial data which are asymptotically flat, time-reflection symmetric, and asymptotic to static data up to a prescribed order at space-like infinity. A perturbation argument is used to show the existence of solutions. It is valid when the order at which the solutions approach staticity is restricted to a certain range. Difficulties appear when trying to improve this result to show the existence of solutions that are asymptotically static at higher order. The problems arise from the lack of surjectivity of a certain operator. Some tensor decompositions in asymptotically flat manifolds exhibit some of the difficulties encountered above. The Helmholtz decomposition, which plays a role in the preparation of initial data for the Maxwell equations, is discussed as a model problem. A method to circumvent the difficulties that arise when fast decay rates are required is discussed. This is done in a way that opens the possibility to perform numerical computations. The insights from the analysis of the Helmholtz decomposition are applied to the York decomposition, which is related to that part of the quasilinear system which gives rise to the difficulties. For this decomposition analogous results are obtained. It turns out, however, that in this case the presence of symmetries of the underlying metric leads to certain complications. The question, whether the results obtained so far can be used again to show by a perturbation argument the existence of vacuum initial data which approach static solutions at infinity at any given order, thus remains open. The answer requires further analysis and perhaps new methods.
The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.
The Great Nebula in Carina provides an exceptional view into the violent massive star formation and feedback that typifies giant H II regions and starburst galaxies. We have mapped the Carina star-forming complex in X-rays, using archival Chandra data and a mosaic of 20 new 60 ks pointings using the Chandra X-ray Observatory's Advanced CCD Imaging Spectrometer, as a testbed for understanding recent and ongoing star formation and to probe Carina's regions of bright diffuse X-ray emission. This study has yielded a catalog of properties of > 14,000 X-ray point sources;> 9800 of them have multiwavelength counterparts. Using Chandra's unsurpassed X-ray spatial resolution, we have separated these point sources from the extensive, spatially-complex diffuse emission that pervades the region; X-ray properties of this diffuse emission suggest that it traces feedback from Carina's massive stars. In this introductory paper, we motivate the survey design, describe the Chandra observations, and present some simple results, providing a foundation for the 15 papers that follow in this special issue and that present detailed catalogs, methods, and science results.
Analysis of the operating characteristics of a dielectric elastomer actuator (DEA) submount for the high-precision positioning of optical components in one dimension is presented. Precise alignment of a single-mode fiber is demonstrated and variation of the sensitivity of the submount motion by changing the bias voltage is confirmed. A comparison of the performance of the DEA submount with a piezoelectric alignment stage is made, which demonstrates that DEAs could present a very attractive, low-cost alternative to currently used manual technologies in overcoming the hurdle of expensive packaging of single-mode optical components.
This Thesis puts its focus on the physics of neutron stars and its description with methods of numerical relativity. In the first step, a new numerical framework the Whisky2D code will be developed, which solves the relativistic equations of hydrodynamics in axisymmetry. Therefore we consider an improved formulation of the conserved form of these equations. The second part will use the new code to investigate the critical behaviour of two colliding neutron stars. Considering the analogy to phase transitions in statistical physics, we will investigate the evolution of the entropy of the neutron stars during the whole process. A better understanding of the evolution of thermodynamical quantities, like the entropy in critical process, should provide deeper understanding of thermodynamics in relativity. More specifically, we have written the Whisky2D code, which solves the general-relativistic hydrodynamics equations in a flux-conservative form and in cylindrical coordinates. This of course brings in 1/r singular terms, where r is the radial cylindrical coordinate, which must be dealt with appropriately. In the above-referenced works, the flux operator is expanded and the 1/r terms, not containing derivatives, are moved to the right-hand-side of the equation (the source term), so that the left hand side assumes a form identical to the one of the three-dimensional (3D) Cartesian formulation. We call this the standard formulation. Another possibility is not to split the flux operator and to redefine the conserved variables, via a multiplication by r. We call this the new formulation. The new equations are solved with the same methods as in the Cartesian case. From a mathematical point of view, one would not expect differences between the two ways of writing the differential operator, but, of course, a difference is present at the numerical level. Our tests show that the new formulation yields results with a global truncation error which is one or more orders of magnitude smaller than those of alternative and commonly used formulations. The second part of the Thesis uses the new code for investigations of critical phenomena in general relativity. In particular, we consider the head-on-collision of two neutron stars in a region of the parameter space where two final states a new stable neutron star or a black hole, lay close to each other. In 1993, Choptuik considered one-parameter families of solutions, S[P], of the Einstein-Klein-Gordon equations for a massless scalar field in spherical symmetry, such that for every P > P⋆, S[P] contains a black hole and for every P < P⋆, S[P] is a solution not containing singularities. He studied numerically the behavior of S[P] as P → P⋆ and found that the critical solution, S[P⋆], is universal, in the sense that it is approached by all nearly-critical solutions regardless of the particular family of initial data considered. All these phenomena have the common property that, as P approaches P⋆, S[P] approaches a universal solution S[P⋆] and that all the physical quantities of S[P] depend only on |P − P⋆|. The first study of critical phenomena concerning the head-on collision of NSs was carried out by Jin and Suen in 2007. In particular, they considered a series of families of equal-mass NSs, modeled with an ideal-gas EOS, boosted towards each other and varied the mass of the stars, their separation, velocity and the polytropic index in the EOS. In this way they could observe a critical phenomenon of type I near the threshold of black-hole formation, with the putative solution being a nonlinearly oscillating star. In a successive work, they performed similar simulations but considering the head-on collision of Gaussian distributions of matter. Also in this case they found the appearance of type-I critical behaviour, but also performed a perturbative analysis of the initial distributions of matter and of the merged object. Because of the considerable difference found in the eigenfrequencies in the two cases, they concluded that the critical solution does not represent a system near equilibrium and in particular not a perturbed Tolmann-Oppenheimer-Volkoff (TOV) solution. In this Thesis we study the dynamics of the head-on collision of two equal-mass NSs using a setup which is as similar as possible to the one considered above. While we confirm that the merged object exhibits a type-I critical behaviour, we also argue against the conclusion that the critical solution cannot be described in terms of equilibrium solution. Indeed, we show that, in analogy with what is found in, the critical solution is effectively a perturbed unstable solution of the TOV equations. Our analysis also considers fine-structure of the scaling relation of type-I critical phenomena and we show that it exhibits oscillations in a similar way to the one studied in the context of scalar-field critical collapse.
We investigate the origin and physical properties of O vi absorbers at low redshift (z = 0.25) using a subset of cosmological, hydrodynamical simulations from the OverWhelmingly Large Simulations (OWLS) project. Intervening O vi absorbers are believed to trace shock-heated gas in the warm-hot intergalactic medium (WHIM) and may thus play a key role in the search for the missing baryons in the present-day Universe. When compared to observations, the predicted distributions of the different O vi line parameters (column density, Doppler parameter, rest equivalent width W-r) from our simulations exhibit a lack of strong O vi absorbers, a discrepancy that has also been found by Oppenheimer & Dave. This suggests that physical processes on subgrid scales (e.g. turbulence) may strongly influence the observed properties of O vi systems. We find that the intervening O vi absorption arises mainly in highly metal enriched (10-1 < Z/Z(circle dot) less than or similar to 1) gas at typical overdensities of 1 < /<<>> less than or similar to 102. One-third of the O vi absorbers in our simulation are found to trace gas at temperatures T < 105 K, while the rest arises in gas at higher temperatures, most of them around T = 105.3 +/- 0.5 K. These temperatures are much higher than inferred by Oppenheimer & Dave, probably because that work did not take the suppression of metal-line cooling by the photoionizing background radiation into account. While the O vi resides in a similar region of (, T)-space as much of the shock-heated baryonic matter, the vast majority of this gas has a lower metal content and does not give rise to detectable O vi absorption. As a consequence of the patchy metal distribution, O vi absorbers in our simulations trace only a very small fraction of the cosmic baryons (< 2 per cent) and the cosmic metals. Instead, these systems presumably trace previously shock-heated, metal-rich material from galactic winds that is now mixing with the ambient gas and cooling. The common approach of comparing O vi and H i column densities to estimate the physical conditions in intervening absorbers from QSO observations may be misleading, as most of the H i (and most of the gas mass) is not physically connected with the high-metallicity patches that give rise to the O vi absorption.
We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial conditions even in certain models that are far from integrable. We show that in such situations the equilibrium states are still described by a maximum entropy or generalized Gibbs ensemble, regardless of whether a model is integrable or not, thereby contributing to a recent debate. In addition, we discuss individual aspects of the thermalization process, comment on the role of Anderson localization, and collect and compare different notions of integrability.
A soft X-ray approach to electron-phonon interactions beyond the Born-Oppenheimer approximation
(2011)
With modern soft X-ray methods, the whole field of electron-phonon interactions becomes accessible directly in the ultrafast time domain with ultrashort pulsed X-ray sources, as well as in the energy domain through modern highly resolving spectrometers. The well-known core-hole clock approach plays an intermediate role, resolving energetic and temporal features at the same time. In this perspective paper, we review several experiments to illustrate the modern advances in the selective study of electron-phonon interactions as fundamentally determining ingredients for materials properties. We present the different complementary approaches that can be taken with soft X-ray methods to conquer this field beyond the Born-Oppenheimer approximation.
The discovery of a plume of water vapour and ice particles emerging from warm fractures ('tiger stripes') in Saturn's small, icy moon Enceladus(1-6) raised the question of whether the plume emerges from a subsurface liquid source(6-8) or from the decomposition of ice(9-12). Previous compositional analyses of particles injected by the plume into Saturn's diffuse E ring have already indicated the presence of liquid water(8), but the mechanisms driving the plume emission are still debated(13). Here we report an analysis of the composition of freshly ejected particles close to the sources. Salt-rich ice particles are found to dominate the total mass flux of ejected solids (more than 99 per cent) but they are depleted in the population escaping into Saturn's E ring. Ice grains containing organic compounds are found to be more abundant in dense parts of the plume. Whereas previous Cassini observations were compatible with a variety of plume formation mechanisms, these data eliminate or severely constrain non-liquid models and strongly imply that a salt-water reservoir with a large evaporating surface(7,8) provides nearly all of the matter in the plume.