Critical phenomena in exponential random graphs

The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence between particle states in a grand canonical ensemble of statistical physics. By adjusting the specific values of these subgraph densities, one can analyze the influence of various local features on the global structure of the network. Loosely put, a phase transition occurs when a singularity arises in the limiting free energy density, as it is the generating function for the limiting expectations of all thermodynamic observables. We derive the full phase diagram for a large family of 3-parameter exponential random graph models with attraction and show that they all consist of a first order surface phase transition bordered by a second order critical curve.Comment: 14 pages, 8 figure

Absolute rate coefficients for photorecombination and electron-impact ionization of magnesium-like iron ions from measurements at a heavy-ion storage ring

Rate coefficients for photorecombination (PR) and cross sections for electron-impact ionization (EII) of Fe$^{14+}$ forming Fe$^{13+}$ and Fe$^{15+}$, respectively, have been measured by employing the electron-ion merged-beams technique at a heavy-ion storage ring. Rate coefficients for PR and EII of Fe$^{14+}$ ions in a plasma are derived from the experimental measurements. Simple parametrizations of the experimentally derived plasma rate coefficients are provided for use in the modeling of photoionized and collisionally ionized plasmas. In the temperature ranges where Fe$^{14+}$ is expected to form in such plasmas the latest theoretical rate coefficients of Altun et al. [Astron. Astrophys. 474, 1051 (2007)] for PR and of Dere [Astron. Astrophys. 466, 771 (2007)] for EII agree with the experimental results to within the experimental uncertainties. Common features in the PR and EII resonance structures are identified and discussed.Comment: 12 pages, 6 figures, 3 tables, submitted for publication to Physical Review

Electronic Raman scattering in YBCO and other superconducting cuprates

Superconductivity induced structures in the electronic Raman spectra of high-Tc superconductors are computed using the results of ab initio LDA-LMTO three-dimensional band structure calculations via numerical integrations of the mass fluctuations, either in the whole 3D Brillouin zone or limiting the integrations to the Fermi surface. The results of both calculations are rather similar, the Brillouin zone integration yielding additional weak structures related to the extended van Hove singularities. Similar calculations have been performed for the normal state of these high-Tc cuprates. Polarization configurations have been investigated and the results have been compared to experimental spectra. The assumption of a simple d_(x^2-y^2)-like gap function allows us to explain a number of experimental features but is hard to reconcile with the relative positions of the A1g and B1g peaks.Comment: 14 pages, LaTeX (RevTeX), 5 PostScript figures, uses multicol.sty, submitted to PR

Absolute rate coefficients for photorecombination of berylliumlike and boronlike silicon ions

We report measured rate coefficients for electron-ion recombination for Si10+ forming Si9+ and for Si9+ forming Si8+, respectively. The measurements were performed using the electron-ion merged-beams technique at a heavy-ion storage ring. Electron-ion collision energies ranged from 0 to 50 eV for Si9+ and from 0 to 2000 eV for Si10+, thus, extending previous measurements for Si10+ [Orban et al. 2010, Astrophys. J. 721, 1603] to much higher energies. Experimentally derived rate coefficients for the recombination of Si9+ and Si10+ ions in a plasma are presented along with simple parameterizations. These rate coefficients are useful for the modeling of the charge balance of silicon in photoionized plasmas (Si9+ and Si10+) and in collisionally ionized plasmas (Si10+ only). In the corresponding temperature ranges, the experimentally derived rate coefficients agree with the latest corresponding theoretical results within the experimental uncertainties.Comment: 17 pages, 7 figures, 3 tables, 66 references, submitted to the J. Phys. B special issue on atomic and molecular data for astrophysicist

Energy-sensitive imaging detector applied to the dissociative recombination of D2H+

We report on an energy-sensitive imaging detector for studying the fragmentation of polyatomic molecules in the dissociative recombination of fast molecular ions with electrons. The system is based on a large area (10 cm x 10 cm) position-sensitive, double-sided Si-strip detector with 128 horizontal and 128 vertical strips, whose pulse height information is read out individually. The setup allows to uniquely identify fragment masses and is thus capable of measuring branching ratios between different fragmentation channels, kinetic energy releases, as well as breakup geometries, as a function of the relative ion-electron energy. The properties of the detection system, which has been installed at the TSR storage ring facility of the Max-Planck Institute for Nuclear Physics in Heidelberg, is illustrated by an investigation of the dissociative recombination of the deuterated triatomic hydrogen cation D2H+. A huge isotope effect is observed when comparing the relative branching ratio between the D2+H and the HD+D channel; the ratio 2B(D2+H)/B(HD+D), which is measured to be 1.27 +/- 0.05 at relative electron-ion energies around 0 eV, is found to increase to 3.7 +/- 0.5 at ~5 eV.Comment: 11 pages, 12 figures, submitted to Physical Review

Cryogenic micro-calorimeters for mass spectrometric identification of neutral molecules and molecular fragments

We have systematically investigated the energy resolution of a magnetic micro-calorimeter (MMC) for atomic and molecular projectiles at impact energies ranging from $E\approx13$ to 150 keV. For atoms we obtained absolute energy resolutions down to $\Delta E \approx 120$ eV and relative energy resolutions down to $\Delta E/E\approx10^{-3}$. We also studied in detail the MMC energy-response function to molecular projectiles of up to mass 56 u. We have demonstrated the capability of identifying neutral fragmentation products of these molecules by calorimetric mass spectrometry. We have modeled the MMC energy-response function for molecular projectiles and conclude that backscattering is the dominant source of the energy spread at the impact energies investigated. We have successfully demonstrated the use of a detector absorber coating to suppress such spreads. We briefly outline the use of MMC detectors in experiments on gas-phase collision reactions with neutral products. Our findings are of general interest for mass spectrometric techniques, particularly for those desiring to make neutral-particle mass measurements

Dissociative recombination measurements of HCl+ using an ion storage ring

We have measured dissociative recombination of HCl+ with electrons using a merged beams configuration at the heavy-ion storage ring TSR located at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany. We present the measured absolute merged beams recombination rate coefficient for collision energies from 0 to 4.5 eV. We have also developed a new method for deriving the cross section from the measurements. Our approach does not suffer from approximations made by previously used methods. The cross section was transformed to a plasma rate coefficient for the electron temperature range from T=10 to 5000 K. We show that the previously used HCl+ DR data underestimate the plasma rate coefficient by a factor of 1.5 at T=10 K and overestimate it by a factor of 3.0 at T=300 K. We also find that the new data may partly explain existing discrepancies between observed abundances of chlorine-bearing molecules and their astrochemical models.Comment: Accepted for publication in ApJ (July 7, 2013

A yeast cell cycle model integrating stress, signaling, and physiology

The cell division cycle in eukaryotic cells is a series of highly coordinated molecular interactions that ensure that cell growth, duplication of genetic material, and actual cell division are precisely orchestrated to give rise to two viable progeny cells. Moreover, the cell cycle machinery is responsible for incorporating information about external cues or internal processes that the cell must keep track of to ensure a coordinated, timely progression of all related processes. This is most pronounced in multicellular organisms, but also a cardinal feature in model organisms such as baker's yeast. The complex and integrative behavior is difficult to grasp and requires mathematical modeling to fully understand the quantitative interplay of the single components within the entire system. Here, we present a self-oscillating mathematical model of the yeast cell cycle that comprises all major cyclins and their main regulators. Furthermore, it accounts for the regulation of the cell cycle machinery by a series of external stimuli such as mating pheromones and changes in osmotic pressure or nutrient quality. We demonstrate how the external perturbations modify the dynamics of cell cycle components and how the cell cycle resumes after adaptation to or relief from stress.Peer Reviewe

3D integrated superconducting qubits

As the field of superconducting quantum computing advances from the few-qubit stage to larger-scale processors, qubit addressability and extensibility will necessitate the use of 3D integration and packaging. While 3D integration is well-developed for commercial electronics, relatively little work has been performed to determine its compatibility with high-coherence solid-state qubits. Of particular concern, qubit coherence times can be suppressed by the requisite processing steps and close proximity of another chip. In this work, we use a flip-chip process to bond a chip with superconducting flux qubits to another chip containing structures for qubit readout and control. We demonstrate that high qubit coherence ($T_1$, $T_{2,\rm{echo}} > 20\,\mu$s) is maintained in a flip-chip geometry in the presence of galvanic, capacitive, and inductive coupling between the chips

A rigorous treatment of the perturbation theory for many-electron systems

Four point correlation functions for many electrons at finite temperature in periodic lattice are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite dimensional Grassmann integrals. A lower bound on the radius of convergence and an upper bound on the perturbation series are obtained. The perturbation series up to second order is numerically implemented along with the volume-independent upper bounds on the sum of the higher order terms in 2 dimensional case.Comment: 61 page