Iterative solution applied to the Helmholtz equation: Complex deflation on unstructured grids

Extensions of deflation techniques developed for the Poisson and Navier equations (Aubry et al., 2008; Mut et al., 2010; Löhner et al., 2011; Aubry et al., 2011) [1], [2], [3], [4] are presented for the Helmholtz equation. Numerous difficulties arise compared to the previous case. After discretization, the matrix is now indefinite without Sommerfeld boundary conditions, or complex with them. It is generally symmetric complex but not Hermitian, discarding optimal short recurrences from an iterative solver viewpoint (Saad, 2003) [5]. Furthermore, the kernel of the operator in an infinite space typically does not belong to the discrete space. The choice of the deflation space is discussed, as well as the relationship between dispersion error and solver convergence. Similarly to the symmetric definite positive (SPD) case, subdomain deflation accelerates convergence if the low frequency eigenmodes are well described. However, the analytic eigenvectors are well represented only if the dispersion error is low. CPU savings are therefore restricted to a low to mid frequency regime compared to the mesh size, which could be still relevant from an application viewpoint, given the ease of implementation

Roadmap for optical tweezers

Optical tweezers are tools made of light that enable contactless pushing, trapping, and manipulation of objects, ranging from atoms to space light sails. Since the pioneering work by Arthur Ashkin in the 1970s, optical tweezers have evolved into sophisticated instruments and have been employed in a broad range of applications in the life sciences, physics, and engineering. These include accurate force and torque measurement at the femtonewton level, microrheology of complex fluids, single micro- and nano-particle spectroscopy, single-cell analysis, and statistical-physics experiments. This roadmap provides insights into current investigations involving optical forces and optical tweezers from their theoretical foundations to designs and setups. It also offers perspectives for applications to a wide range of research fields, from biophysics to space exploration.journal articl

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Holistic improvement of image acquisition and reconstruction in fluorescence microscopy

Recent developments in microscopic imaging led to a better understanding of intra- and intercellular metabolic processes and, for example, to visualize structural properties of viral pathogens. In this thesis, the imaging process of widefield and confocal scanning microscopy techniques is treated holistically to highlight general strategies and maximise their information content. Poisson or shot noise is assumed to be the fundamental noise process for the given measurements. A stable focus position is a basic condition for e.g. long-term measurements in order to provide reliable information about potential changes inside the Field-of-view. While newer microscopy systems can be equipped with hardware autofocus, this is not yet the widespread standard. For image-based focus analysis, different metrics for ideal, noisy and aberrated, in case of spherical aberration and astigmatism, measurements are presented. A stable focus position is also relevant in the example of 2-photon confocal imaging and at the same time the situation is aggravated in the given example, the measurement of the retina in the living mouse. In addition to the natural drift of the focal position, which can be evaluated by means of previously introduced metrics, rhythmic heartbeat, respiration, unrhythmic muscle twitching and movement of the mouse kept in artificial sleep are added. A dejittering algorithm is presented for the measurement data obtained under these circumstances. Using the additional information about the sample distribution in ISM, a method for reconstructing 3D from 2D image data is presented in the form of thick slice unmixing. This method can further be used for suppression of light generated outside the focal layer of 3D data stacks and is compared to selective layer multi-view deconvolution. To reduce phototoxicity and save valuable measurement time for a 3D stack, the method of zLEAP is presented, by which omitted Z-planes are subsequently calculated and inserted