Shape Optimization for Time-dependent Domains

In this thesis, we treat shape optimization for parabolic equations on time-dependent domains. As a theoretical foundation we extend the solution theory of parabolic boundary integral equations in the canonical Sobolev spaces from the cylindrical to the time-dependent case. The results imply existence and uniqueness of solutions. This is followed by a review of shape optimization theory on time-dependent domains, where we complement a few proofs which seem to be missing in the literature. Building on these foundations we give general formulae for shape gradients of functionals. These theoretical results are complemented by two numerical examples. The first example is concerned with a time-dependent shape detection problem, reformulated as a time-dependent shape optimization problem. The second example is a time-dependent one-phase Stefan problem in multiple dimensions, also reformulated as a shape optimization problem

Spiral phases and two-particle bound states from a systematic low-energy effective theory for magnons, electrons, and holes in an antiferromagnet

We have constructed a systematic low-energy effective theory for hole- and electron-doped antiferromagnets, where holes reside in momentum space pockets centered at $(\pm\frac{\pi}{2a},\pm\frac{\pi}{2a})$ and where electrons live in pockets centered at $(\frac{\pi}{a},0)$ or $(0,\frac{\pi}{a})$. The effective theory is used to investigate the magnon-mediated binding between two holes or two electrons in an otherwise undoped system. We derive the one-magnon exchange potential from the effective theory and then solve the corresponding two-quasiparticle Schr\"odinger equation. As a result, we find bound state wave functions that resemble $d_{x^2-y^2}$-like or $d_{xy}$-like symmetry. We also study possible ground states of lightly doped antiferromagnets.Comment: 2 Pages; Proc. of SCES'07, Housto

Health Universities - Konzept, Relevanz und Best Practice : Mit regionaler Versorgung und interprofessioneller Bildung zu bedarfsgerechten Gesundheitsfachleuten

Das Konzept der Health Universities entstand als eine Antwort auf die Herausforderungen des Gesundheitswesens in den 1960er und 1970er Jahren. Es vereint bildungs- und versorgungspolitische Ansprüche, die schwierig unter einen Hut zu bringen sind. Wie hat sich dieses Konzept in Europa weiter entwickelt? Welche Bedeutung hat es für die Herausforderungen von heute? Dieser Bericht zeigt das Potential der Health Universities für eine bedarfsgerechte Ausbildung von Gesundheitsfachleuten zu Beginn des 21. Jahrhunderts, indem Konzept, Relevanz und Best Practice beschrieben werden

Emotions while awaiting lung transplantation : a comprehensive qualitative analysis

Patients awaiting lung transplantation are at risk of negative emotional and physical experiences. How do they talk about emotions? Semi-structured interviews were performed (15 patients). Categorical analysis focusing on emotion-related descriptions was organized into positive–negative–neutral descriptions: for primary and secondary emotions, evaluation processes, coping strategies, personal characteristics, emotion descriptions associated with physical states, (and) contexts were listed. Patients develop different strategies to maintain positive identity and attitude, while preserving significant others from extra emotional load. Results are discussed within various theoretical and research backgrounds, in emphasizing their importance in the definition of emotional support starting from the patient’s perspective

Magnon-mediated binding between holes in an antiferromagnet

Abstract.: The long-range forces between holes in an antiferromagnet are due to magnon exchange. The one-magnon exchange potential between two holes is proportional to cos(2 ϕ)/r 2 where r is the distance vector of the holes and ϕ is the angle between r and an axis of the square crystal lattice. One-magnon exchange leads to bound states of holes with antiparallel spins resembling d-wave symmetr

Thermodynamics of Two-Dimensional Ideal Ferromagnets - Three-Loop Analysis

Within the effective Lagrangian framework, we explicitly evaluate the partition function of two-dimensional ideal ferromagnets up to three loops at low temperatures and in the presence of a weak external magnetic field. The low-temperature series for the free energy density, energy density, heat capacity, entropy density, as well as the magnetization are given and their range of validity is critically examined in view of the Mermin-Wagner theorem. The calculation involves the renormalization and numerical evaluation of a particular three-loop graph which is discussed in detail. Interestingly, in the low-temperature series for the two-dimensional ideal ferromagnet, the spin-wave interaction manifests itself in the form of logarithmic terms. In the free energy density the leading such term is of order $T^4 \ln T$ -- remarkably, in the case of the three-dimensional ideal ferromagnet no logarithmic terms arise in the low-temperature series. While the present study demonstrates that it is straightforward to consider effects up to three-loop order in the effective field theory framework, this precision seems to be far beyond the reach of microscopic methods such as modified spin-wave theory.Comment: 31 pages, 2 figure

Homogeneous versus Spiral Phases of Hole-doped Antiferromagnets: A Systematic Effective Field Theory Investigation

Using the low-energy effective field theory for magnons and holes -- the condensed matter analog of baryon chiral perturbation theory for pions and nucleons in QCD -- we study different phases of doped antiferromagnets. We systematically investigate configurations of the staggered magnetization that provide a constant background field for doped holes. The most general configuration of this type is either constant itself or it represents a spiral in the staggered magnetization. Depending on the values of the low-energy parameters, a homogeneous phase, a spiral phase, or an inhomogeneous phase is energetically favored. The reduction of the staggered magnetization upon doping is also investigated.Comment: 35 pages, 5 figure

Systematic Low-Energy Effective Field Theory for Electron-Doped Antiferromagnets

In contrast to hole-doped systems which have hole pockets centered at $(\pm \frac{\pi}{2a},\pm \frac{\pi}{2a})$, in lightly electron-doped antiferromagnets the charged quasiparticles reside in momentum space pockets centered at $(\frac{\pi}{a},0)$ or $(0,\frac{\pi}{a})$. This has important consequences for the corresponding low-energy effective field theory of magnons and electrons which is constructed in this paper. In particular, in contrast to the hole-doped case, the magnon-mediated forces between two electrons depend on the total momentum $\vec P$ of the pair. For $\vec P = 0$ the one-magnon exchange potential between two electrons at distance $r$ is proportional to $1/r^4$, while in the hole case it has a $1/r^2$ dependence. The effective theory predicts that spiral phases are absent in electron-doped antiferromagnets.Comment: 25 pages, 7 figure

Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet

Identifying the correct low-energy effective theory for magnons and holes in an antiferromagnet has remained an open problem for a long time. In analogy to the effective theory for pions and nucleons in QCD, based on a symmetry analysis of Hubbard and t-J-type models, we construct a systematic low-energy effective field theory for magnons and holes located inside pockets centered at lattice momenta (\pm pi/2a,\pm pi/2a). The effective theory is based on a nonlinear realization of the spontaneously broken spin symmetry and makes model-independent universal predictions for the entire class of lightly doped antiferromagnetic precursors of high-temperature superconductors. The predictions of the effective theory are exact, order by order in a systematic low-energy expansion. We derive the one-magnon exchange potentials between two holes in an otherwise undoped system. Remarkably, in some cases the corresponding two-hole Schr\"odinger equations can even be solved analytically. The resulting bound states have d-wave characteristics. The ground state wave function of two holes residing in different hole pockets has a d_{x^2-y^2}-like symmetry, while for two holes in the same pocket the symmetry resembles d_{xy}.Comment: 35 pages, 11 figure