Symmetry and structure of carbon-nitrogen complexes in gallium arsenide from infrared spectroscopy and first-principles calculations

Molecular-like carbon-nitrogen complexes in GaAs are investigated both experimentally and theoretically. Two characteristic high-frequency stretching modes at \num{1973} and \SI{2060}{cm^{-1}}, detected by Fourier transform infrared absorption (FTIR) spectroscopy, appear in carbon- and nitrogen-implanted and annealed layers. From isotopic substitution it is deduced that the chemical composition of the underlying complexes is CN$_2$ and C$_2$N, respectively. Piezospectroscopic FTIR measurements reveal that both centers have tetragonal symmetry. For density functional theory (DFT) calculations linear entities are substituted for the As anion, with the axis oriented along the \hkl direction, in accordance with the experimentally ascertained symmetry. The DFT calculations support the stability of linear N-C-N and C-C-N complexes in the GaAs host crystal in the charge states ranging from $+3$ to $-3$. The valence bonds of the complexes are analyzed using molecular-like orbitals from DFT. It turns out that internal bonds and bonds to the lattice are essentially independent of the charge state. The calculated vibrational mode frequencies are close to the experimental values and reproduce precisely the isotopic mass splitting from FTIR experiments. Finally, the formation energies show that under thermodynamic equilibrium CN$_2$ is more stable than C$_2$N

A free boundary problem involving a cusp : breakthrough of salt water

In this paper we study a two-phase free boundary problem describing the stationary flow of fresh and salt water in a porous medium, when both fluids are drawn into a well. For given discharges at the well ($Q_f$ for fresh water and $Q_s$ for salt water) we formulate the problem in terms of the stream function in an axial symmetric flow domain in {Bbb R^n(n = 2,3). We prove existence of a continuous free boundary which ends up in the well, located on the central axis. Moreover we show that the free boundary has a tangent at the well and approaches it in a $C^1$ sense. Using the method of separation of variables we also give a result about the asymptotic behaviour of the free boundary at the well. For given total discharge ($Q := Q_f + Q_s$) we consider the vanishing $Q_s$ limit. We show that a free boundary arises with a cusp at the central axis, having a positive distance from the well. This work is a continuation of [AD2,3]

A free boundary problem involving a cusp

We consider a stationary free boundary problem describing the stationary flow of fresh and salt water in a porous medium. The salt water is supposed to be stagnant, while the fresh water on top of it is drawn into wells. In a previous work it has been shown, that for pumping rates Q < Q_{cr a solution with smooth interface exists. In this part we study the case Q=Q_{cr in two dimensions. We show that the interface has isolated singularities. At each singularity the free boundary develops a cusp or becomes vertical. By means of local analysis techniques we obtain the asymptotic behaviour of the free boundary at these singularities

Status of business model and electronic market research:An interview with Paul Timmers

This interview with Paul Timmers reflects on how the domain of business models has emerged since the publication of the first business model article in Electronic Markets in 1998. The interview provides insights in how his seminal article on business models for electronic markets originated and on the role of government bodies, in particular the European Commission. Among the opinions shared are that electronic markets should be conceived as a broad concept and that interdisciplinary views are key for shaping future developments, especially in the area of ubiquitous data in many industries

Diaphragmatic Injuries among Severely Injured Patients (ISS ≥ 16)—An Indicator of Injury Pattern and Severity of Abdominal Trauma

Background and Objectives: Abdominal trauma among severely injured patients with an injury severity score (ISS) of 16 and above can lead to potentially life-threatening injuries that might need immediate surgical intervention. Traumatic injuries to the diaphragm (TID) are a challenging condition often accompanied by other injuries in the thoracoabdominal region. Materials and Methods: We retrospectively analyzed the occurrence and clinical course of TID among severely injured patients treated at our center between 2008 and 2019 and compared them to other groups of severely injured patients without TID. Results: Thirty-five patients with TID and a median ISS of 41 were treated in the period mentioned above. They were predominantly middle-aged men and mostly victims of blunt trauma as a consequence of motor vehicle accidents. A total of 70.6% had left-sided TID, and in 69.6%, the size of defect was larger than 10 cm. The diagnosis was made with computed tomography (CT) in 68.6% of the cases, while in 25.8%, it was made intraoperatively or delayed by a false-negative initial CT scan, and in 5.7%, an intraoperative diagnosis was made without preoperative CT imaging. Surgical repair was mostly conducted via laparotomy, performing a direct closure with continuous suture. A comparison to 191 patients that required laparotomy for abdominal injuries other than TID revealed significantly higher rates of concomitant injuries to several abdominal organs among patients suffering from TID. Compared to all other severely injured patients treated in the same period (n = 1377), patients suffering from TID had a significantly higher median ISS and a longer mean duration of hospital stay. Conclusions: Our findings show that TID can be seen as an indicator of particularly severe thoracoabdominal trauma that requires increased attention from the treatment team so as not to miss relevant concomitant injuries that require immediate intervention