Thermodynamics of hot dense H-plasmas: Path integral Monte Carlo simulations and analytical approximations

This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between $10^{-1}$ and $10^2$ Mbar. In particular we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. Calculations were performed in a broad region of the nonideality parameter $\Gamma \lesssim 3$ and degeneracy parameter $n_e \Lambda^3 \lesssim 10$. We give a comparison with a few available results from other path integral calculations (restricted PIMC) and with analytical calculations based on Pade approximations for strongly ionized plasmas. Good agreement between the results obtained from the three independent methods is found.Comment: RevTex file, 21 pages, 5 ps-figures include

Excitation of solitons in hexagonal lattices and ways of controlling electron transport

This is a post-peer-review, pre-copyedit version of an article published in Philosophical Transactions A: Mathematical, Physical and Engineering Sciences. The final authenticated version is available online at: http://dx.doi.org/10.1007/s40435-017-0383-x.We construct metastable long-living hexagonal lattices with appropriately modified Morse interactions and show that highly-energetic solitons may be excited moving along crystallographic axes. Studying the propagation, their dynamic changes and the relaxation processes it appears that lump solitons create in the lattice running local compressions. Based on the tight-binding model we investigate the possibility that electrons are trapped and guided by the electric polarization field of the compression field of one soliton or two solitons with crossing pathways. We show that electrons may jump from a bound state with the first soliton to a bound state with a second soliton and changing accordingly the direction of their path. We discuss the possibility to control by this method the path of an excess electron from a source at a boundary to a selected drain at another chosen boundary by following straight pathways on crystallographic axes.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Doctor of Philosophy

dissertationThis dissertation studies detection-based methods to increase the estimation precision of single point-source emitters in the field of localization microscopy. Localization microscopy is a novel method allowing for the localization of optical point-source emitters below the Abbe diffraction limit of optical microscopy. This is accomplished by optically controlling the active, or bright, state of individual molecules within a sample. The use of time-multiplexing of the active state allows for the temporal and spatial isolation of single point-source emitters. Isolating individual sources within a sample allows for statistical analysis on their emission point-spread function profile, and the spatial coordinates of the point-source may be discerned below the optical response of the microscope system. Localization microscopy enables the identification of individual point-source emitter locations approximately an order of magnitude below standard, diffraction-limited optical techniques. The precision of localization microscopy methods is limited by the statistical uncertainty in which the location of these sources may be estimated. By utilizing a detection- based interferometer, an interference pattern may be super-imposed over the emission signal. Theoretical analysis and Monte-Carlo simulations by means of Fisher information theory demonstrate that the incorporation of a modulation structure over the emission signal allow for a more precise estimation when compared to conventional localization methods for the same number of recorded photons. These theoretical calculation and simulations are demonstrated through the use of two proof-of-concept experiments utilizing a modified Mach-Zehnder interferometer. The first methodology improves the localization precision of a single nanoparticle over the theoretical limit for an Airy-disk point-spread function by using self-interference to spatially modulate the recorded point-spread function. Experimental analysis demonstrates an improvement factor of ~3 to 5 over conventional localization methods. A related method employs the phase induced onto the Fourier domain signal due to path length differences in the Mach-Zehnder interferometer to improve localization precision. The localization capability of a modified Fourier domain signal generated by self-interference is utilized to yield a two-fold improvement in the localization precision for a given number of photons compared to a standard Gaussian intensity distribution of the corresponding point-spread function

Revealing the magnetic field in a distant galaxy cluster: discovery of the complex radio emission from MACS J0717.5 +3745

Aims. To study at multiple frequencies the radio emission arising from the massive galaxy cluster MACS J0717.5+3745 (z=0.55). Known to be an extremely complex cluster merger, the system is uniquely suited for an investigation of the phenomena at work in the intra-cluster medium (ICM) during cluster collisions. Methods. We use multi-frequency and multi-resolution data obtained with the Very Large Array radio telescope, and X-ray features revealed by Chandra, to probe the non-thermal and thermal components of the ICM, their relations and interactions. Results. The cluster shows highly complex radio emission. A bright, giant radio halo is detected at frequencies as high as 4.8 GHz. MACS J0717.5+3745 is the most distant cluster currently known to host a radio halo. This radio halo is also the most powerful ever observed, and the second case for which polarized radio emission has been detected, indicating that the magnetic field is ordered on large scales.Comment: 14 pages, 13 figures, Astronomy and Astrophysics, accepte

Deformable self-propelled particles

A theory of self-propelled particles is developed in two dimensions assuming that the particles can be deformed from a circular shape when the propagating velocity is increased. A coupled set of equations in terms of the velocity and a tensor variable to represent the deformation is introduced to show that there is a bifurcation from a straight motion to a circular motion of a single particle. Dynamics of assembly of the particles is studied numerically where there is a global interaction such that the particles tend to cause an orientational order.Comment: 4pages, 4figure

On anomalous diffusion in a plasma in velocity space

The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in momentum space. The generalized Fokker-Planck equation for description of diffusion (in momentum space) of particles (ions, grains etc.) in a stochastic system of light particles (electrons, or electrons and ions, respectively) is applied to the evolution of the momentum particle distribution in a plasma. In a plasma the developed approach is also applicable to the diffusion of particles with an arbitrary mass relation, due to the small characteristic momentum transfer. The cases of an exponentially decreasing in momentum space (including the Boltzmann-like) kernel in the PT-function, as well as the more general kernels, which create the anomalous diffusion in velocity space due to the long tail in the PT-function, are considered. Effective friction and diffusion coefficients for plasma-like systems are found.Comment: 18 pages, no figure

Calibration of the Mass-Temperature Relation for Clusters of Galaxies Using Weak Gravitational Lensing

The main uncertainty in current determinations of the power spectrum normalization, sigma_8, from abundances of X-ray luminous galaxy clusters arises from the calibration of the mass-temperature relation. We use our weak lensing mass determinations of 30 clusters from the hitherto largest sample of clusters with lensing masses, combined with X-ray temperature data from the literature, to calibrate the normalization of this relation at a temperature of 8 keV, M_{500c,8 keV}=(8.7 +/- 1.6) h^{-1} 10^{14} M_sun. This normalization is consistent with previous lensing-based results based on smaller cluster samples, and with some predictions from numerical simulations, but higher than most normalizations based on X-ray derived cluster masses. Assuming the theoretically expected slope alpha=3/2 of the mass-temperature relation, we derive sigma_8 = 0.88 +/-0.09 for a spatially-flat LambdaCDM universe with Omega_m = 0.3. The main systematic errors on the lensing masses result from extrapolating the cluster masses beyond the field-of-view used for the gravitational lensing measurements, and from the separation of cluster/background galaxies, contributing each with a scatter of 20%. Taking this into account, there is still significant intrinsic scatter in the mass-temperature relation indicating that this relation may not be very tight, at least at the high mass end. Furthermore, we find that dynamically relaxed clusters are 75 +/-40% hotter than non-relaxed clusters.Comment: 8 pages, 4 figures, revised version submitted to Ap