Development of higher-order modal methods for transient thermal and structural analysis

A force-derivative method which produces higher-order modal solutions to transient problems is evaluated. These higher-order solutions converge to an accurate response using fewer degrees-of-freedom (eigenmodes) than lower-order methods such as the mode-displacement or mode-acceleration methods. Results are presented for non-proportionally damped structural problems as well as thermal problems modeled by finite elements

Optimization by nonhierarchical asynchronous decomposition

Large scale optimization problems are tractable only if they are somehow decomposed. Hierarchical decompositions are inappropriate for some types of problems and do not parallelize well. Sobieszczanski-Sobieski has proposed a nonhierarchical decomposition strategy for nonlinear constrained optimization that is naturally parallel. Despite some successes on engineering problems, the algorithm as originally proposed fails on simple two dimensional quadratic programs. The algorithm is carefully analyzed for quadratic programs, and a number of modifications are suggested to improve its robustness

An evaluation of higher-order model methods for calculating transient structural response

A higher-order modal method proposed by Leung for transient structural analysis entitled the force-derivative method is evaluated. This method repeatedly integrates by parts with respect to time the convolution-integral form of the structural response to produce successively better approximations to the contribution of the higher modes which are neglected in the modal summation. Comparisons are made of the force-derivative, the mode-displacement, and the mode-acceleration methods for several numerical example problems for various times, levels of damping, and forcing functions. The example problems include a tip-loaded cantilevered beam and a simply-supported multispan beam. The force-derivative method is shown to converge to an accurate solution in fewer modes than either the mode-displacement or the mode-acceleration methods. In addition, for problems in which there are a large number of closely-spaced frequencies whose mode shapes have a negligible contribution to the response, the force-derivative method is very effective in representing the effect of the important, but otherwise neglected, higher modes

Sensitivity-based scaling for correlating structural response from different analytical models

A sensitivity-based linearly varying scale factor is described used to reconcile results from refined models for analysis of the same structure. The improved accuracy of the linear scale factor compared to a constant scale factor as well as the commonly used tangent approximation is demonstrated. A wing box structure is used as an example, with displacements, stresses, and frequencies correlated. The linear scale factor could permit the use of a simplified model in an optimization procedure during preliminary design to approximate the response given by a refined model over a considerable range of design changes

Isonitrile-responsive and bioorthogonally removable tetrazine protecting groups.

In vivo compatible reactions have a broad range of possible applications in chemical biology and the pharmaceutical sciences. Here we report tetrazines that can be removed by exposure to isonitriles under very mild conditions. Tetrazylmethyl derivatives are easily accessible protecting groups for amines and phenols. The isonitrile-induced removal is rapid and near-quantitative. Intriguingly, the deprotection is especially effective with (trimethylsilyl)methyl isocyanide, and serum albumin can catalyze the elimination under physiological conditions. NMR and computational studies revealed that an imine-tautomerization step is often rate limiting, and the unexpected cleavage of the Si-C bond accelerates this step in the case with (trimethylsilyl)methyl isocyanide. Tetrazylmethyl-removal is compatible with use on biomacromolecules, in cellular environments, and in living organisms as demonstrated by cytotoxicity experiments and fluorophore-release studies on proteins and in zebrafish embryos. By combining tetrazylmethyl derivatives with previously reported tetrazine-responsive 3-isocyanopropyl groups, it was possible to liberate two fluorophores in vertebrates from a single bioorthogonal reaction. This chemistry will open new opportunities towards applications involving multiplexed release schemes and is a valuable asset to the growing toolbox of bioorthogonal dissociative reactions

Coherent transient exciton transport in disordered polaritonic wires

Excitation energy transport can be significantly enhanced by strong light-matter interactions. In the present work, we explore intriguing features of coherent transient exciton wave packet dynamics on a lossless disordered polaritonic wire. Our main results can be understood in terms of the effective exciton group velocity, a new quantity we obtain from the polariton dispersion. Under weak and moderate disorder, we find that the early wave packet spread velocity is controlled by the overlap of the initial exciton momentum distribution and its effective group velocity. Conversely, when disorder is stronger, the initial state is nearly irrelevant, and red-shifted cavities support excitons with greater mobility. Our findings provide guiding principles for optimizing ultrafast coherent exciton transport based on the magnitude of disorder and the polariton dispersion. The presented perspectives may be valuable for understanding and designing new polaritonic platforms for enhanced exciton energy transport

Stresses in isostatic granular systems and emergence of force chains

Progress is reported on several questions that bedevil understanding of granular systems: (i) are the stress equations elliptic, parabolic or hyperbolic? (ii) how can the often-observed force chains be predicted from a first-principles continuous theory? (iii) How to relate insight from isostatic systems to general packings? Explicit equations are derived for the stress components in two dimensions including the dependence on the local structure. The equations are shown to be hyperbolic and their general solutions, as well as the Green function, are found. It is shown that the solutions give rise to force chains and the explicit dependence of the force chains trajectories and magnitudes on the local geometry is predicted. Direct experimental tests of the predictions are proposed. Finally, a framework is proposed to relate the analysis to non-isostatic and more realistic granular assemblies.Comment: 4 pages, 2 figures, Corrected typos and clkearer text, submitted to Phys. Rev. Let