Equilibrium Configurations of Homogeneous Fluids in General Relativity

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core-ring and two-ring solutions. Combining our knowledge of the first four classes with post-Newtonian results and the Newtonian portion of the first ten classes, we present the qualitative behaviour of the entire relativistic solution space. The Newtonian disc limit can only be reached by going through infinitely many of the aforementioned classes. Only once this limiting process has been consummated, can one proceed again into the relativistic regime and arrive at the analytically known relativistic disc of dust.Comment: 8 pages, colour figures, v3: minor additions including one reference, accepted by MNRA

Data-driven discovery of cardiolipin-selective small molecules by computational active learning

Subtle variations in the lipid composition of mitochondrial membranes can have a profound impact on mitochondrial function. The inner mitochondrial membrane contains the phospholipid cardiolipin, which has been demonstrated to act as a biomarker for a number of diverse pathologies. Small molecule dyes capable of selectively partitioning into cardiolipin membranes enable visualization and quantification of the cardiolipin content. Here we present a data-driven approach that combines a deep learning-enabled active learning workflow with coarse-grained molecular dynamics simulations and alchemical free energy calculations to discover small organic compounds able to selectively permeate cardiolipin-containing membranes. By employing transferable coarse-grained models we efficiently navigate the all-atom design space corresponding to small organic molecules with molecular weight less than ≈500 Da. After direct simulation of only 0.42% of our coarse-grained search space we identify molecules with considerably increased levels of cardiolipin selectivity compared to a widely used cardiolipin probe 10-N-nonyl acridine orange. Our accumulated simulation data enables us to derive interpretable design rules linking coarse-grained structure to cardiolipin selectivity. The findings are corroborated by fluorescence anisotropy measurements of two compounds conforming to our defined design rules. Our findings highlight the potential of coarse-grained representations and multiscale modelling for materials discovery and design

Differentially rotating disks of dust

We present a three-parameter family of solutions to the stationary axisymmetric Einstein equations that describe differentially rotating disks of dust. They have been constructed by generalizing the Neugebauer-Meinel solution of the problem of a rigidly rotating disk of dust. The solutions correspond to disks with angular velocities depending monotonically on the radial coordinate; both decreasing and increasing behaviour is exhibited. In general, the solutions are related mathematically to Jacobi's inversion problem and can be expressed in terms of Riemann theta functions. A particularly interesting two-parameter subfamily represents Baecklund transformations to appropriate seed solutions of the Weyl class.Comment: 14 pages, 3 figures. To appear in "General Relativity and Gravitation". Second version with minor correction

Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths

A phenomenological schematic model of multipole giant resonances (GR) is considered which treats the external interaction via common decay channels on the same footing as the coherent part of the internal residual interaction. The damping due to the coupling to the sea of complicated states is neglected. As a result, the formation of GR is governed by the interplay and competition of two kinds of collectivity, the internal and the external one. The mixing of the doorway components of a GR due to the external interaction influences significantly their multipole strengths, widths and positions in energy. In particular, a narrow resonance state with an appreciable multipole strength is formed when the doorway components strongly overlap.Comment: 20 pages, LaTeX, 3 ps-figures, to appear in PRC (July 1997

Differentially rotating disks of dust: Arbitrary rotation law

In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to seed solutions of the Weyl class. It turns out that this class of solutions contains the general relativistic gravitational field of an arbitrary differentially rotating disk of dust, for which a continuous transition to some Newtonian disk exists. It will be shown how for given boundary conditions (i. e. proper surface mass density or angular velocity of the disk) the gravitational field can be approximated in terms of the above solutions. Furthermore, particular examples will be discussed, including disks with a realistic profile for the angular velocity and more exotic disks possessing two spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and Gravitation

Phase transitions in open quantum systems

We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $\alpha_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.Comment: 28 pages, 22 Postscript figure

Dirichlet Boundary Value Problems of the Ernst Equation

We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization procedure is valid is given, which also proves conjectures about earlier representations of the gravitational field corresponding to rotating disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in equation (4

Resonance trapping and saturation of decay widths

Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of different time scales appears. We investigate it under the influence of additional weakly coupled channels as well as by taking into account the real part of the coupling term between system and continuum. We observe a saturation of the mean width of the trapped states. Also the decay rates saturate as a function of the coupling strength. The mechanism of the saturation is studied in detail. In any case, the critical region of reorganization is enlarged. When the transmission coefficients for the different channels are different, the width distribution is broadened as compared to a chi_K^2 distribution where K is the number of channels. Resonance trapping takes place before the broad state overlaps regions beyond the extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.