Data-driven model of the solar corona above an active region

We aim to reproduce the structure of the corona above a solar active region as seen in the extreme ultraviolet (EUV) using a three-dimensional magnetohydrodynamic (3D MHD) model. The 3D MHD data-driven model solves the induction equation and the mass, momentum, and energy balance. To drive the system, we feed the observed evolution of the magnetic field in the photosphere of the active region AR 12139 into the bottom boundary. This creates a hot corona above the cool photosphere in a self-consistent way. We synthesize the coronal EUV emission from the densities and temperatures in the model and compare this to the actual coronal observations. We are able to reproduce the overall appearance and key features of the corona in this active region on a qualitative level. The model shows long loops, fan loops, compact loops, and diffuse emission forming at the same locations and at similar times as in the observation. Furthermore, the low-intensity contrast of the model loops in EUV matches the observations. In our model the energy input into the corona is similar as in the scenarios of fieldline-braiding or flux-tube tectonics, that is, energy is transported to the corona through the driving of the vertical magnetic field by horizontal photospheric motions. The success of our model shows the central role that this process plays for the structure, dynamics, and heating of the corona.Comment: 5 pages, 3 Figures, published in A&A letter

Thermodynamic laws in isolated systems

The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying microcanonical thermostatistics. Here, we provide a detailed comparison of the most commonly considered microcanonical entropy definitions, focussing specifically on whether they satisfy or violate the zeroth, first and second law of thermodynamics. Our analysis shows that, for a broad class of systems that includes all standard classical Hamiltonian systems, only the Gibbs volume entropy fulfills all three laws simultaneously. To avoid ambiguities, the discussion is restricted to exact results and analytically tractable examples.Comment: footnotes 19, 26 and outlook section adde

Time parameters and Lorentz transformations of relativistic stochastic processes

Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized process approaches the relativistic Juttner-Maxwell distribution, the associated proper-time parameterized process converges to a modified momentum distribution, differing by a factor proportional to the inverse energy.Comment: 5 pages, 1 figur

Meaning of temperature in different thermostatistical ensembles

Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the notion of thermodynamic temperature in different statistical ensembles, focusing in particular on subtleties that arise when ensembles become non-equivalent. The 'mother' of all ensembles, the microcanonical ensemble, uses entropy and internal energy (the most fundamental, dynamically conserved quantity) to derive temperature as a secondary thermodynamic variable. Over the past century, some confusion has been caused by the fact that several competing microcanonical entropy definitions are used in the literature, most commonly the volume and surface entropies introduced by Gibbs. It can be proved, however, that only the volume entropy satisfies exactly the traditional form of the laws of thermodynamics for a broad class of physical systems, including all standard classical Hamiltonian systems, regardless of their size. This mathematically rigorous fact implies that negative 'absolute' temperatures and Carnot efficiencies $>1$ are not achievable within a standard thermodynamical framework. As an important offspring of microcanonical thermostatistics, we shall briefly consider the canonical ensemble and comment on the validity of the Boltzmann weight factor. We conclude by addressing open mathematical problems that arise for systems with discrete energy spectrum.Comment: 11 pages, 1 figur

Current systems of coronal loops in 3D MHD simulations

We study the magnetic field and current structure associated with a coronal loop. Through this we investigate to what extent the assumptions of a force-free magnetic field break down and where they might be justified. We analyse a 3D MHD model of the solar corona in an emerging active region with the focus on the structure of the forming coronal loops. The lower boundary of this simulation is taken from a model of an emerging active region. As a consequence of the emerging magnetic flux and the horizontal motions at the surface a coronal loop forms self-consistently. We investigate the current density along magnetic field inside (and outside) this loop and study the magnetic and plasma properties in and around it. We find that the total current along the loop changes its sign from being antiparallel to parallel to the magnetic field. This is caused by the inclination of the loop together with the footpoint motion. Around the loop the currents form a complex non-force-free helical structure. This is directly related to a bipolar current structure at the loop footpoints at the base of the corona and a local reduction of the background magnetic field (i.e. outside the loop) caused by the plasma flow into and along the loop. The locally reduced magnetic pressure in the loop allows the loop to sustain a higher density, which is crucial for the emission in extreme UV. The acting of the flow on the magnetic field hosting the loop turns out to be also responsible for the observed squashing of the loop. The complex magnetic field and current system surrounding it can be modeled only in 3D MHD models where the magnetic field has to balance the plasma pressure. A 1D coronal loop model or a force-free extrapolation can not capture the current system and the complex interaction of the plasma and the magnetic field in the coronal loop, despite the fact that the loop is under low-$\beta$ conditions.Comment: 10 pages, 11 figures, published in A&

Earthquake recurrence as a record breaking process

Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record breaking events with edges between nodes in a graph generates a complex dynamical network isolated from any length, time or magnitude scales set by the observer. For Southern California, the network of recurrences reveals new statistical features of seismicity with robust scaling laws. The rupture length and its scaling with magnitude emerges as a generic measure for distance between recurrent events. Further, the relative separations for subsequent records in space (or time) form a hierarchy with unexpected scaling properties

RLFC: Random Access Light Field Compression using Key Views and Bounded Integer Encoding

We present a new hierarchical compression scheme for encoding light field images (LFI) that is suitable for interactive rendering. Our method (RLFC) exploits redundancies in the light field images by constructing a tree structure. The top level (root) of the tree captures the common high-level details across the LFI, and other levels (children) of the tree capture specific low-level details of the LFI. Our decompressing algorithm corresponds to tree traversal operations and gathers the values stored at different levels of the tree. Furthermore, we use bounded integer sequence encoding which provides random access and fast hardware decoding for compressing the blocks of children of the tree. We have evaluated our method for 4D two-plane parameterized light fields. The compression rates vary from 0.08 - 2.5 bits per pixel (bpp), resulting in compression ratios of around 200:1 to 20:1 for a PSNR quality of 40 to 50 dB. The decompression times for decoding the blocks of LFI are 1 - 3 microseconds per channel on an NVIDIA GTX-960 and we can render new views with a resolution of 512X512 at 200 fps. Our overall scheme is simple to implement and involves only bit manipulations and integer arithmetic operations.Comment: Accepted for publication at Symposium on Interactive 3D Graphics and Games (I3D '19