Discrete Adjoint Method for Variational Integration of Constrained ODEs and its application to Optimal Control of Geometrically Exact Beam Dynamics

Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal solution. While the benefits of structure preserving or geometric methods have been known for decades, their exploration in the context of optimal control problems is a relatively recent field of research. In this work, the discrete adjoint method is derived for variational integrators yielding structure preserving approximations of the dynamics firstly in the ODE case and secondly for the case in which the dynamics is subject to holonomic constraints. The convergence rates are illustrated by numerical examples. Thirdly, the discrete adjoint method is applied to geometrically exact beam dynamics, represented by a holonomically constrained PDE.Comment: Funding: H2020 Marie-Sk\l{}odowska-Curie 86012

Immunogenicity of chimeric haemagglutinin-based, universal influenza virus vaccine candidates: interim results of a randomised, placebo-controlled, phase 1 clinical trial.

BackgroundInfluenza viruses cause substantial annual morbidity and mortality globally. Current vaccines protect against influenza only when well matched to the circulating strains. However, antigenic drift can cause considerable mismatches between vaccine and circulating strains, substantially reducing vaccine effectiveness. Moreover, current seasonal vaccines are ineffective against pandemic influenza, and production of a vaccine matched to a newly emerging virus strain takes months. Therefore, there is an unmet medical need for a broadly protective influenza virus vaccine. We aimed to test the ability of chimeric H1 haemagglutinin-based universal influenza virus vaccine candidates to induce broadly cross-reactive antibodies targeting the stalk domain of group 1 haemagglutinin-expressing influenza viruses.MethodsWe did a randomised, observer-blinded, phase 1 study in healthy adults in two centres in the USA. Participants were randomly assigned to one of three prime-boost, chimeric haemagglutinin-based vaccine regimens or one of two placebo groups. The vaccine regimens included a chimeric H8/1, intranasal, live-attenuated vaccine on day 1 followed by a non-adjuvanted, chimeric H5/1, intramuscular, inactivated vaccine on day 85; the same regimen but with the inactivated vaccine being adjuvanted with AS03; and an AS03-adjuvanted, chimeric H8/1, intramuscular, inactivated vaccine followed by an AS03-adjuvanted, chimeric H5/1, intramuscular, inactivated vaccine. In this planned interim analysis, the primary endpoints of reactogenicity and safety were assessed by blinded study group. We also assessed anti-H1 haemagglutinin stalk, anti-H2, anti-H9, and anti-H18 IgG antibody titres and plasmablast and memory B-cell responses in peripheral blood. This trial is registered with ClinicalTrials.gov, number NCT03300050.FindingsBetween Oct 10, 2017, and Nov 27, 2017, 65 participants were enrolled and randomly assigned. The adjuvanted inactivated vaccine, but not the live-attenuated vaccine, induced a substantial serum IgG antibody response after the prime immunisation, with a seven times increase in anti-H1 stalk antibody titres on day 29. After boost immunisation, all vaccine regimens induced detectable anti-H1 stalk antibody (2·2-5·6 times induction over baseline), cross-reactive serum IgG antibody, and peripheral blood plasmablast responses. An unsolicited adverse event was reported for 29 (48%) of 61 participants. Solicited local adverse events were reported in 12 (48%) of 25 participants following prime vaccination with intramuscular study product or placebo, in 12 (33%) of 36 after prime immunisation with intranasal study product or placebo, and in 18 (32%) of 56 following booster doses of study product or placebo. Solicited systemic adverse events were reported in 14 (56%) of 25 after prime immunisation with intramuscular study product or placebo, in 22 (61%) of 36 after immunisation with intranasal study product or placebo, and in 21 (38%) of 56 after booster doses of study product or placebo. Disaggregated safety data were not available at the time of this interim analysis.InterpretationThe tested chimeric haemagglutinin-based, universal influenza virus vaccine regimens elicited cross-reactive serum IgG antibodies that targeted the conserved haemagglutinin stalk domain. This is the first proof-of-principle study to show that high anti-stalk titres can be induced by a rationally designed vaccine in humans and opens up avenues for further development of universal influenza virus vaccines. On the basis of the blinded study group, the vaccine regimens were tolerable and no safety concerns were observed.FundingBill & Melinda Gates Foundation

Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples,”

For the modeling of large deformations in multibody dynamics problems, the absolute nodal coordinate formulation (ANCF) is advantageous since in general, the ANCF leads to a constant mass matrix. The proposed ANCF beam finite elements in this approach use the transverse slope vectors for the parameterization of the orientation of the cross section and do not employ an axial nodal slope vector. The geometric description, the degrees of freedom, and a continuum-mechanics-based and a structural-mechanics-based formulation for the elastic forces of the beam finite elements, as well as their usage in several static problems, have been presented in a previous work. A comparison to results provided in the literature to analytical solution and to the solution found by commercial finite element software shows accuracy and high order convergence in statics. The main subject of the present paper is to show the usability of the beam finite elements in dynamic and buckling applications

Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Buckling and Nonlinear Dynamic Examples

In the present paper, a three-dimensional shear deformable beam finite element is presented, which is based on the absolute nodal coordinate formulation (ANCF). The orientation of the beam's cross section is parameterized by means of slope vectors. Both a structural mechanics based formulation of the elastic forces based on Reissner's nonlinear rod theory, as well as a continuum mechanics based formulation for a St. Venant Kirchhoff material are presented in this paper. The performance of the proposed finite beam element is investigated by the analysis of several static and linearized dynamic problems. A comparison to results provided in the literature, to analytical solutions, and to the solution found by commercial finite element software shows high accuracy and high order of convergence, and therefore the present element has high potential for geometrically nonlinear problems