Symmetry properties of vibrational modes in graphene nanoribbons

We present symmetry properties of the lattice vibrations of graphene nanoribbons with pure armchair (AGNR) and zigzag edges (ZGNR). In non-symmorphic nanoribbons the phonon modes at the edge of the Brillouin zone are twofold degenerate, whereas the phonon modes in symmorphic nanoribbons are non-degenerate. We identified the Raman-active and infrared-active modes. We predict 3N and 3(N+1) Raman-active modes for N-ZGNRs and N-AGNRs, respectively (N is the number of dimers per unit cell). These modes can be used for the experimental characterization of graphene nanoribbons. Calculations based on density functional theory suggest that the frequency splitting of the LO and TO in AGNRs (corresponding to the E2g mode in graphene) exhibits characteristic width and family dependence. Further, all graphene nanoribbons have a Raman-active breathing-like mode, the frequency of which is inversely proportional to the nanoribbon width and thus might be used for experimental determination of the width of graphene nanoribbons.Comment: 10 pages, 5 figure

Mathematical modelling of plasma cell dynamics in multiple myeloma

Plasma cell dyscrasias are characterised by accumulation of malignant plasma cells in the bone marrow. Asymptomatic multiple myeloma (AMM) evolves from monoclonal gammopathy of unknown significance (MGUS) and progresses to symptomatic myeloma involving end organ damage. Three main questions are addressed by mathematical modelling. Firstly, how is growth of malignant plasma cells characterised? Secondly, how fast does progression from early asymptomatic stages (MGUS, AMM) to symptomatic myeloma happen? Thirdly, how many malignant plasma cells initially arrive at the bone marrow? New mathematical models consisting of piecewise-smooth ordinary differential equations are formulated describing the dynamics of healthy and malignant plasma cells in the bone marrow and its niche. Model analysis refers to existence and uniqueness of solutions, characterisation of solutions within invariant sets, and existence and stability properties of equilibria. Partial equilibria are identified extending the classical notion of equilibria. The models are validated using clinical data consisting of serum and urine samples (n = 8398) of patients with AMM and MGUS (n = 322 and n = 196, respectively). Model analysis and parameter estimation imply that accumulation of malignant plasma cells can be quantified by the doubling time. A faster doubling time relates to a higher probability of progression to symptomatic myeloma and correlates with a small initial number of malignant plasma cells. Instead of one single initial malignant plasma cell, initiation of myeloma can rather be explained by a „malignant wave“ comprised of a population of malignant plasma cells arriving at the bone marrow and perturbing healthy homoeostasis. This thesis is the result of an interdisciplinary doctorate and the joint work with Prof. Dr. Anna Marciniak-Czochra (Institute of Applied Mathematics, Heidelberg University) as well as with PD Dr. Dr. Dirk Hose and Dr. Anja Seckinger (Multiple Myeloma Research Laboratory, Heidelberg University Hospital)

First-principles calculations of the vibrational properties of bulk CdSe and CdSe nanowires

We present first-principles calculations on bulk CdSe and CdSe nanowires with diameters of up to 22 \AA. Density functional linear combination of atomic orbitals and plane wave calculations of the electronic and structural properties are presented and discussed. We use an iterative, symmetry-based method to relax the structures into the ground state. We find that the band gap depends on surface termination. Vibrational properties in the whole Brillouin zone of bulk CdSe and the zone-center vibrations of nanowires are calculated and analyzed. We find strongly size-dependent and nearly constant modes, depending on the displacement directions. A comparison with available experimental Raman data is be given