A phase field approach for multivariant martensitic transformations of stable and metastable phases

A phase field model approach for multivariant martensitic transformations of stable and metastable phases is introduced. The evolution of the microstructure is examined with respect to elastic energy minimization in which one or two martensitic orientation variants are considered. In this context, the martensitic nucleation behavior is simulated for different activation barriers. Furthermore, the influence of time-dependent external loads on the formation of the different phases is studied. The numerical implementation is performed with finite elements and an implicit time integration scheme.     

An Inexact Modified Subgradient Algorithm for Primal-Dual Problems via Augmented Lagrangians

We consider a primal optimization problem in a reflexive Banach space and a duality scheme via generalized augmented Lagrangians. For solving the dual problem (in a Hilbert space), we introduce and analyze a new parameterized Inexact Modified Subgradient (IMSg) algorithm. The IMSg generates a primal-dual sequence, and we focus on two simple new choices of the stepsize. We prove that every weak accumulation point of the primal sequence is a primal solution and the dual sequence converges weakly to a dual solution, as long as the dual optimal set is nonempty. Moreover, we establish primal convergence even when the dual optimal set is empty. Our second choice of the stepsize gives rise to a variant of IMSg which has finite termination.     

A Phase Field Approach for Martensitic Transformations and Crystal Plasticity

This work is motivated by cryogenic turning which allows end shape machining and simultaneously attaining a hardened surface due to deformation induced martensitic transformations. To study the process on the microscale, a multivariant phase field model for martensitic transformations in conjunction with a crystal plastic material model is introduced. The evolution of microstructure is assumed to follow a time-dependent Ginzburg-Landau equation. To solve the field equations the finite element method is used. Time integration is performed with Euler backward schemes, on the global level for the evolution equation of the phase field, and on the element level for the crystal plastic material law. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

A theorem on the unitarizability of loop group valued monodromyrepresentations is presented and applied to show the existenceof new families of constant mean curvature surfaces homeomorphicto a thrice-punctured sphere in the simply connected 3-dimensionalspace forms ³, ³ and ³. Additionally, the extended frame forany associated family of Delaunay surfaces is computed.     

Tail behavior of conditional sojourn times in Processor-Sharing queues

We investigate the tail behavior of the sojourn-time distribution for a request of a given length in an M/G/1 Processor-Sharing (PS) queue. An exponential asymptote is proven for general service times in two special cases: when the traffic load is sufficiently high and when the request length is sufficiently small. Furthermore, using the branching process technique we derive exact asymptotics of exponential type for the sojourn time in the M/M/1 queue. We obtain an equation for the asymptotic decay rate and an exact expression for the asymptotic constant. The decay rate is studied in detail and is compared to other service disciplines. Finally, using numerical methods, we investigate the accuracy of the exponential asymptote. AMS 2000 Subject Classifications Primary:60K25,Secondary: 60F10,68M20,90B22     

Monotonic convergent optimal control theory with strict limitations on the spectrum of optimized laser fields

We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields. A frequency constraint is introduced and derived mathematically correct, without losing monotonic convergence of the algorithm. The method guarantees a close link to learning loop control experiments and is demonstrated for the challenging control of nonresonant Raman transitions, which are used to implement a set of global quantum gates for molecular vibrational qubits.     

Laser Based Techniques for Ultra Trace Isotope Production, Spectroscopy and Detection

A variety of research activities in the field of fundamental and applied nuclear physics has evolved in the last years using resonantly tuned radiation from powerful lasers. The technique of resonance ionization spectroscopy has delivered outstanding results and found broad acceptance in the last years as a particularly efficient and highly selective method for rare and exotic radioisotope studies. It is used for production, spectroscopy and detection of these species and provides complete isobaric, high isotopic and even some isomeric selection, which altogether is needed for on-line investigation of short lived species far off stability as well as for ultra trace determination. Good overall efficiency pushes the experimental limits of detection in elemental trace analysis down to below 10⁶ atoms per sample, and additionally isotopic selectivity as high as 3 × 10¹² has been demonstrated. The widespread potential of resonance ionization techniques is discussed, focusing on the experimental arrangements for applications in selective on-line isotope production, spectroscopy of rare radioisotopes and ultra trace determination of radiotoxic isotopes like ²³⁸Pu to ²⁴⁴Pu, ^135,137Cs, ^89,90Sr or ⁴¹Ca in environmental, technical and biomedical samples.     

Multimode pumped continuous-wave solid-state Raman laser

We demonstrate the continuous-wave operation of a solid-state Raman laser containing a barium nitrate crystal as the Raman medium. The Raman laser, which has a singly resonant cavity, is pumped by multimode radiation. The Raman oscillation threshold is reached at approximately 2 W of pump power. As much as 500 kW/cm2 of Stokes power density at 60-kW/cm2 pump power density is obtained in the cavity.     

Enhancing nucleation and controlling crystal orientation by rubbing/scratching the surface of a thin polymer film

We used the tip of an atomic force microscope (AFM) in the contact mode to scratch/rub the surface of a glassy polymer thin film, i.e., isotactic polystyrene (i-PS) at room temperature. After subsequent isothermal crystallization, an extremely high nucleation density of edge-on crystals within the rubbed region or at the edge of the scratched area was observed. Furthermore, a transition from edge-on to flat-on lamellae occurred beyond a certain distance from the edge of the scratched region. Our results demonstrate that both, soft rubbing or hard scratching, allow to lower the nucleation barrier for polymer crystallization and to control the orientation of the resulting crystalline lamellae. The role of scratching/rubbing on chain deformation and its relation to nucleation and crystal orientation in polymer thin films is discussed.